From 83edb601d2375a1ff2d84743a14fdba5a8fb5db0 Mon Sep 17 00:00:00 2001
From: Kamil Worek <kamil.worek@protonmail.com>
Date: Mon, 20 Sep 2021 23:49:07 +0200
Subject: [PATCH] Added DMA to DFSDM module, tested DMA function, updated CMSIS
 math.

---
 .cproject                      |     7 +
 cmsis/arm_common_tables.h      |   514 +-
 cmsis/arm_const_structs.h      |   145 +-
 cmsis/arm_math.h               | 14515 ++++++++++++++++---------------
 cmsis/libarm_cortexM4lf_math.a |   Bin 3097502 -> 5359640 bytes
 drivers/stm32l4/dfsdm.cpp      |    99 +-
 drivers/stm32l4/dfsdm.hpp      |    25 +-
 main.cpp                       |    39 +-
 system/startup-cortex-m4.S     |   167 +
 9 files changed, 8114 insertions(+), 7397 deletions(-)

diff --git a/.cproject b/.cproject
index f8f79a1..af6ca60 100644
--- a/.cproject
+++ b/.cproject
@@ -46,6 +46,7 @@
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 							<option id="ilg.gnuarmeclipse.managedbuild.cross.option.optimization.lto.1477720257" name="Link-time optimizer (-flto)" superClass="ilg.gnuarmeclipse.managedbuild.cross.option.optimization.lto" value="false" valueType="boolean"/>
+							<option id="ilg.gnuarmeclipse.managedbuild.cross.option.optimization.spconstant.1176134621" superClass="ilg.gnuarmeclipse.managedbuild.cross.option.optimization.spconstant" value="true" valueType="boolean"/>
 							<targetPlatform archList="all" binaryParser="org.eclipse.cdt.core.ELF" id="ilg.gnuarmeclipse.managedbuild.cross.targetPlatform.606965169" isAbstract="false" osList="all" superClass="ilg.gnuarmeclipse.managedbuild.cross.targetPlatform"/>
 							<builder buildPath="${workspace_loc:/spl-meter}/Debug" id="ilg.gnuarmeclipse.managedbuild.cross.builder.1896274702" keepEnvironmentInBuildfile="false" managedBuildOn="true" name="Gnu Make Builder" parallelBuildOn="true" parallelizationNumber="optimal" superClass="ilg.gnuarmeclipse.managedbuild.cross.builder"/>
 							<tool id="ilg.gnuarmeclipse.managedbuild.cross.tool.assembler.1143574246" name="GNU ARM Cross Assembler" superClass="ilg.gnuarmeclipse.managedbuild.cross.tool.assembler">
@@ -103,6 +104,12 @@
 								<option IS_BUILTIN_EMPTY="false" IS_VALUE_EMPTY="false" id="ilg.gnuarmeclipse.managedbuild.cross.option.cpp.linker.scriptfile.918967578" name="Script files (-T)" superClass="ilg.gnuarmeclipse.managedbuild.cross.option.cpp.linker.scriptfile" useByScannerDiscovery="false" valueType="stringList">
 									<listOptionValue builtIn="false" value="&quot;${workspace_loc:/${ProjName}/system/arm-cortex-m.ld}&quot;"/>
 								</option>
+								<option IS_BUILTIN_EMPTY="false" IS_VALUE_EMPTY="false" id="ilg.gnuarmeclipse.managedbuild.cross.option.cpp.linker.libs.935073743" name="Libraries (-l)" superClass="ilg.gnuarmeclipse.managedbuild.cross.option.cpp.linker.libs" useByScannerDiscovery="false" valueType="libs">
+									<listOptionValue builtIn="false" value="arm_cortexM4lf_math"/>
+								</option>
+								<option IS_BUILTIN_EMPTY="false" IS_VALUE_EMPTY="false" id="ilg.gnuarmeclipse.managedbuild.cross.option.cpp.linker.paths.244931437" name="Library search path (-L)" superClass="ilg.gnuarmeclipse.managedbuild.cross.option.cpp.linker.paths" useByScannerDiscovery="false" valueType="libPaths">
+									<listOptionValue builtIn="false" value="&quot;${workspace_loc:/${ProjName}/cmsis}&quot;"/>
+								</option>
 								<inputType id="ilg.gnuarmeclipse.managedbuild.cross.tool.cpp.linker.input.1605737169" superClass="ilg.gnuarmeclipse.managedbuild.cross.tool.cpp.linker.input">
 									<additionalInput kind="additionalinputdependency" paths="$(USER_OBJS)"/>
 									<additionalInput kind="additionalinput" paths="$(LIBS)"/>
diff --git a/cmsis/arm_common_tables.h b/cmsis/arm_common_tables.h
index d5d7241..6a4337f 100644
--- a/cmsis/arm_common_tables.h
+++ b/cmsis/arm_common_tables.h
@@ -1,136 +1,378 @@
-/* ----------------------------------------------------------------------
-* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
-*
-* $Date:        19. October 2015
-* $Revision: 	V.1.4.5 a
-*
-* Project: 	    CMSIS DSP Library
-* Title:	    arm_common_tables.h
-*
-* Description:	This file has extern declaration for common tables like Bitreverse, reciprocal etc which are used across different functions
-*
-* Target Processor: Cortex-M4/Cortex-M3
-*
-* Redistribution and use in source and binary forms, with or without
-* modification, are permitted provided that the following conditions
-* are met:
-*   - Redistributions of source code must retain the above copyright
-*     notice, this list of conditions and the following disclaimer.
-*   - Redistributions in binary form must reproduce the above copyright
-*     notice, this list of conditions and the following disclaimer in
-*     the documentation and/or other materials provided with the
-*     distribution.
-*   - Neither the name of ARM LIMITED nor the names of its contributors
-*     may be used to endorse or promote products derived from this
-*     software without specific prior written permission.
-*
-* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
-* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
-* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
-* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
-* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
-* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
-* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
-* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
-* POSSIBILITY OF SUCH DAMAGE.
-* -------------------------------------------------------------------- */
-
-#ifndef _ARM_COMMON_TABLES_H
-#define _ARM_COMMON_TABLES_H
-
-#include "arm_math.h"
-
-extern const uint16_t armBitRevTable[1024];
-extern const q15_t armRecipTableQ15[64];
-extern const q31_t armRecipTableQ31[64];
-/* extern const q31_t realCoefAQ31[1024]; */
-/* extern const q31_t realCoefBQ31[1024]; */
-extern const float32_t twiddleCoef_16[32];
-extern const float32_t twiddleCoef_32[64];
-extern const float32_t twiddleCoef_64[128];
-extern const float32_t twiddleCoef_128[256];
-extern const float32_t twiddleCoef_256[512];
-extern const float32_t twiddleCoef_512[1024];
-extern const float32_t twiddleCoef_1024[2048];
-extern const float32_t twiddleCoef_2048[4096];
-extern const float32_t twiddleCoef_4096[8192];
-#define twiddleCoef twiddleCoef_4096
-extern const q31_t twiddleCoef_16_q31[24];
-extern const q31_t twiddleCoef_32_q31[48];
-extern const q31_t twiddleCoef_64_q31[96];
-extern const q31_t twiddleCoef_128_q31[192];
-extern const q31_t twiddleCoef_256_q31[384];
-extern const q31_t twiddleCoef_512_q31[768];
-extern const q31_t twiddleCoef_1024_q31[1536];
-extern const q31_t twiddleCoef_2048_q31[3072];
-extern const q31_t twiddleCoef_4096_q31[6144];
-extern const q15_t twiddleCoef_16_q15[24];
-extern const q15_t twiddleCoef_32_q15[48];
-extern const q15_t twiddleCoef_64_q15[96];
-extern const q15_t twiddleCoef_128_q15[192];
-extern const q15_t twiddleCoef_256_q15[384];
-extern const q15_t twiddleCoef_512_q15[768];
-extern const q15_t twiddleCoef_1024_q15[1536];
-extern const q15_t twiddleCoef_2048_q15[3072];
-extern const q15_t twiddleCoef_4096_q15[6144];
-extern const float32_t twiddleCoef_rfft_32[32];
-extern const float32_t twiddleCoef_rfft_64[64];
-extern const float32_t twiddleCoef_rfft_128[128];
-extern const float32_t twiddleCoef_rfft_256[256];
-extern const float32_t twiddleCoef_rfft_512[512];
-extern const float32_t twiddleCoef_rfft_1024[1024];
-extern const float32_t twiddleCoef_rfft_2048[2048];
-extern const float32_t twiddleCoef_rfft_4096[4096];
-
-
-/* floating-point bit reversal tables */
-#define ARMBITREVINDEXTABLE__16_TABLE_LENGTH ((uint16_t)20  )
-#define ARMBITREVINDEXTABLE__32_TABLE_LENGTH ((uint16_t)48  )
-#define ARMBITREVINDEXTABLE__64_TABLE_LENGTH ((uint16_t)56  )
-#define ARMBITREVINDEXTABLE_128_TABLE_LENGTH ((uint16_t)208 )
-#define ARMBITREVINDEXTABLE_256_TABLE_LENGTH ((uint16_t)440 )
-#define ARMBITREVINDEXTABLE_512_TABLE_LENGTH ((uint16_t)448 )
-#define ARMBITREVINDEXTABLE1024_TABLE_LENGTH ((uint16_t)1800)
-#define ARMBITREVINDEXTABLE2048_TABLE_LENGTH ((uint16_t)3808)
-#define ARMBITREVINDEXTABLE4096_TABLE_LENGTH ((uint16_t)4032)
-
-extern const uint16_t armBitRevIndexTable16[ARMBITREVINDEXTABLE__16_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable32[ARMBITREVINDEXTABLE__32_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable64[ARMBITREVINDEXTABLE__64_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable128[ARMBITREVINDEXTABLE_128_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable256[ARMBITREVINDEXTABLE_256_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable512[ARMBITREVINDEXTABLE_512_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable1024[ARMBITREVINDEXTABLE1024_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable2048[ARMBITREVINDEXTABLE2048_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable4096[ARMBITREVINDEXTABLE4096_TABLE_LENGTH];
-
-/* fixed-point bit reversal tables */
-#define ARMBITREVINDEXTABLE_FIXED___16_TABLE_LENGTH ((uint16_t)12  )
-#define ARMBITREVINDEXTABLE_FIXED___32_TABLE_LENGTH ((uint16_t)24  )
-#define ARMBITREVINDEXTABLE_FIXED___64_TABLE_LENGTH ((uint16_t)56  )
-#define ARMBITREVINDEXTABLE_FIXED__128_TABLE_LENGTH ((uint16_t)112 )
-#define ARMBITREVINDEXTABLE_FIXED__256_TABLE_LENGTH ((uint16_t)240 )
-#define ARMBITREVINDEXTABLE_FIXED__512_TABLE_LENGTH ((uint16_t)480 )
-#define ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH ((uint16_t)992 )
-#define ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH ((uint16_t)1984)
-#define ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH ((uint16_t)4032)
-
-extern const uint16_t armBitRevIndexTable_fixed_16[ARMBITREVINDEXTABLE_FIXED___16_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable_fixed_32[ARMBITREVINDEXTABLE_FIXED___32_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable_fixed_64[ARMBITREVINDEXTABLE_FIXED___64_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable_fixed_128[ARMBITREVINDEXTABLE_FIXED__128_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable_fixed_256[ARMBITREVINDEXTABLE_FIXED__256_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable_fixed_512[ARMBITREVINDEXTABLE_FIXED__512_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable_fixed_1024[ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable_fixed_2048[ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH];
-extern const uint16_t armBitRevIndexTable_fixed_4096[ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH];
-
-/* Tables for Fast Math Sine and Cosine */
-extern const float32_t sinTable_f32[FAST_MATH_TABLE_SIZE + 1];
-extern const q31_t sinTable_q31[FAST_MATH_TABLE_SIZE + 1];
-extern const q15_t sinTable_q15[FAST_MATH_TABLE_SIZE + 1];
-
-#endif /*  ARM_COMMON_TABLES_H */
+/* ----------------------------------------------------------------------
+ * Project:      CMSIS DSP Library
+ * Title:        arm_common_tables.h
+ * Description:  Extern declaration for common tables
+ *
+ * $Date:        27. January 2017
+ * $Revision:    V.1.5.1
+ *
+ * Target Processor: Cortex-M cores
+ * -------------------------------------------------------------------- */
+/*
+ * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
+ *
+ * SPDX-License-Identifier: Apache-2.0
+ *
+ * Licensed under the Apache License, Version 2.0 (the License); you may
+ * not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an AS IS BASIS, WITHOUT
+ * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef _ARM_COMMON_TABLES_H
+#define _ARM_COMMON_TABLES_H
+
+#include "arm_math.h"
+
+#if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_FFT_ALLOW_TABLES) 
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREV_1024)
+    extern const uint16_t armBitRevTable[1024];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_F32_16)
+    extern const float32_t twiddleCoef_16[32];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_F32_32)
+    extern const float32_t twiddleCoef_32[64];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_F32_64)
+    extern const float32_t twiddleCoef_64[128];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_F32_128)
+    extern const float32_t twiddleCoef_128[256];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_F32_256)
+    extern const float32_t twiddleCoef_256[512];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_F32_512)
+    extern const float32_t twiddleCoef_512[1024];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_F32_1024)
+    extern const float32_t twiddleCoef_1024[2048];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_F32_2048)
+    extern const float32_t twiddleCoef_2048[4096];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_F32_4096)
+    extern const float32_t twiddleCoef_4096[8192];
+    #define twiddleCoef twiddleCoef_4096
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q31_16)
+    extern const q31_t twiddleCoef_16_q31[24];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q31_32)
+    extern const q31_t twiddleCoef_32_q31[48];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q31_64)
+    extern const q31_t twiddleCoef_64_q31[96];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q31_128)
+    extern const q31_t twiddleCoef_128_q31[192];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q31_256)
+    extern const q31_t twiddleCoef_256_q31[384];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q31_512)
+    extern const q31_t twiddleCoef_512_q31[768];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q31_1024)
+    extern const q31_t twiddleCoef_1024_q31[1536];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q31_2048)
+    extern const q31_t twiddleCoef_2048_q31[3072];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q31_4096)
+    extern const q31_t twiddleCoef_4096_q31[6144];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q15_16)
+    extern const q15_t twiddleCoef_16_q15[24];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q15_32)
+    extern const q15_t twiddleCoef_32_q15[48];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q15_64)
+    extern const q15_t twiddleCoef_64_q15[96];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q15_128)
+    extern const q15_t twiddleCoef_128_q15[192];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q15_256)
+    extern const q15_t twiddleCoef_256_q15[384];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q15_512)
+    extern const q15_t twiddleCoef_512_q15[768];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q15_1024)
+    extern const q15_t twiddleCoef_1024_q15[1536];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q15_2048)
+    extern const q15_t twiddleCoef_2048_q15[3072];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_Q15_4096)
+    extern const q15_t twiddleCoef_4096_q15[6144];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_RFFT_F32_32)
+    extern const float32_t twiddleCoef_rfft_32[32];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_RFFT_F32_64)
+    extern const float32_t twiddleCoef_rfft_64[64];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_RFFT_F32_128)
+    extern const float32_t twiddleCoef_rfft_128[128];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_RFFT_F32_256)
+    extern const float32_t twiddleCoef_rfft_256[256];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_RFFT_F32_512)
+    extern const float32_t twiddleCoef_rfft_512[512];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_RFFT_F32_1024)
+    extern const float32_t twiddleCoef_rfft_1024[1024];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_RFFT_F32_2048)
+    extern const float32_t twiddleCoef_rfft_2048[2048];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_TWIDDLECOEF_RFFT_F32_4096)
+    extern const float32_t twiddleCoef_rfft_4096[4096];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  /* floating-point bit reversal tables */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FLT_16)
+    #define ARMBITREVINDEXTABLE_16_TABLE_LENGTH ((uint16_t)20)
+    extern const uint16_t armBitRevIndexTable16[ARMBITREVINDEXTABLE_16_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FLT_32)
+    #define ARMBITREVINDEXTABLE_32_TABLE_LENGTH ((uint16_t)48)
+    extern const uint16_t armBitRevIndexTable32[ARMBITREVINDEXTABLE_32_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FLT_64)
+    #define ARMBITREVINDEXTABLE_64_TABLE_LENGTH ((uint16_t)56)
+    extern const uint16_t armBitRevIndexTable64[ARMBITREVINDEXTABLE_64_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FLT_128)
+    #define ARMBITREVINDEXTABLE_128_TABLE_LENGTH ((uint16_t)208)
+    extern const uint16_t armBitRevIndexTable128[ARMBITREVINDEXTABLE_128_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FLT_256)
+    #define ARMBITREVINDEXTABLE_256_TABLE_LENGTH ((uint16_t)440)
+    extern const uint16_t armBitRevIndexTable256[ARMBITREVINDEXTABLE_256_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FLT_512)
+    #define ARMBITREVINDEXTABLE_512_TABLE_LENGTH ((uint16_t)448)
+    extern const uint16_t armBitRevIndexTable512[ARMBITREVINDEXTABLE_512_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FLT_1024)
+    #define ARMBITREVINDEXTABLE_1024_TABLE_LENGTH ((uint16_t)1800)
+    extern const uint16_t armBitRevIndexTable1024[ARMBITREVINDEXTABLE_1024_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FLT_2048)
+    #define ARMBITREVINDEXTABLE_2048_TABLE_LENGTH ((uint16_t)3808)
+    extern const uint16_t armBitRevIndexTable2048[ARMBITREVINDEXTABLE_2048_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FLT_4096)
+    #define ARMBITREVINDEXTABLE_4096_TABLE_LENGTH ((uint16_t)4032)
+    extern const uint16_t armBitRevIndexTable4096[ARMBITREVINDEXTABLE_4096_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  
+  /* fixed-point bit reversal tables */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FXT_16)
+    #define ARMBITREVINDEXTABLE_FIXED_16_TABLE_LENGTH ((uint16_t)12)
+    extern const uint16_t armBitRevIndexTable_fixed_16[ARMBITREVINDEXTABLE_FIXED_16_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FXT_32)
+    #define ARMBITREVINDEXTABLE_FIXED_32_TABLE_LENGTH ((uint16_t)24)
+    extern const uint16_t armBitRevIndexTable_fixed_32[ARMBITREVINDEXTABLE_FIXED_32_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FXT_64)
+    #define ARMBITREVINDEXTABLE_FIXED_64_TABLE_LENGTH ((uint16_t)56)
+    extern const uint16_t armBitRevIndexTable_fixed_64[ARMBITREVINDEXTABLE_FIXED_64_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FXT_128)
+    #define ARMBITREVINDEXTABLE_FIXED_128_TABLE_LENGTH ((uint16_t)112)
+    extern const uint16_t armBitRevIndexTable_fixed_128[ARMBITREVINDEXTABLE_FIXED_128_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FXT_256)
+    #define ARMBITREVINDEXTABLE_FIXED_256_TABLE_LENGTH ((uint16_t)240)
+    extern const uint16_t armBitRevIndexTable_fixed_256[ARMBITREVINDEXTABLE_FIXED_256_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FXT_512)
+    #define ARMBITREVINDEXTABLE_FIXED_512_TABLE_LENGTH ((uint16_t)480)
+    extern const uint16_t armBitRevIndexTable_fixed_512[ARMBITREVINDEXTABLE_FIXED_512_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FXT_1024)
+    #define ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH ((uint16_t)992)
+    extern const uint16_t armBitRevIndexTable_fixed_1024[ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FXT_2048)
+    #define ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH ((uint16_t)1984)
+    extern const uint16_t armBitRevIndexTable_fixed_2048[ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_BITREVIDX_FXT_4096)
+    #define ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH ((uint16_t)4032)
+    extern const uint16_t armBitRevIndexTable_fixed_4096[ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) */
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_REALCOEF_F32)
+    extern const float32_t realCoefA[8192];
+    extern const float32_t realCoefB[8192];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_REALCOEF_Q31)
+    extern const q31_t realCoefAQ31[8192];
+    extern const q31_t realCoefBQ31[8192];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_REALCOEF_Q15)
+    extern const q15_t realCoefAQ15[8192];
+    extern const q15_t realCoefBQ15[8192];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_DCT4_F32_128)
+    extern const float32_t Weights_128[256];
+    extern const float32_t cos_factors_128[128];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_DCT4_F32_512)
+    extern const float32_t Weights_512[1024];
+    extern const float32_t cos_factors_512[512];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_DCT4_F32_2048)
+    extern const float32_t Weights_2048[4096];
+    extern const float32_t cos_factors_2048[2048];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_DCT4_F32_8192)
+    extern const float32_t Weights_8192[16384];
+    extern const float32_t cos_factors_8192[8192];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_DCT4_Q15_128)
+    extern const q15_t WeightsQ15_128[256];
+    extern const q15_t cos_factorsQ15_128[128];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_DCT4_Q15_512)
+    extern const q15_t WeightsQ15_512[1024];
+    extern const q15_t cos_factorsQ15_512[512];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_DCT4_Q15_2048)
+    extern const q15_t WeightsQ15_2048[4096];
+    extern const q15_t cos_factorsQ15_2048[2048];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_DCT4_Q15_8192)
+    extern const q15_t WeightsQ15_8192[16384];
+    extern const q15_t cos_factorsQ15_8192[8192];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_DCT4_Q31_128)  
+    extern const q31_t WeightsQ31_128[256];
+    extern const q31_t cos_factorsQ31_128[128];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_DCT4_Q31_512) 
+    extern const q31_t WeightsQ31_512[1024];
+    extern const q31_t cos_factorsQ31_512[512];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_DCT4_Q31_2048) 
+    extern const q31_t WeightsQ31_2048[4096];
+    extern const q31_t cos_factorsQ31_2048[2048];
+  #endif
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FFT_TABLES) || defined(ARM_TABLE_DCT4_Q31_8192) 
+    extern const q31_t WeightsQ31_8192[16384];
+    extern const q31_t cos_factorsQ31_8192[8192];
+  #endif
+    
+#endif /* if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_FFT_TABLES) */
+
+#if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_FAST_ALLOW_TABLES)
+
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FAST_TABLES) || defined(ARM_TABLE_RECIP_Q15)
+    extern const q15_t armRecipTableQ15[64];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) defined(ARM_ALL_FAST_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FAST_TABLES) || defined(ARM_TABLE_RECIP_Q31)
+    extern const q31_t armRecipTableQ31[64];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) defined(ARM_ALL_FAST_TABLES) */
+  
+  /* Tables for Fast Math Sine and Cosine */
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FAST_TABLES) || defined(ARM_TABLE_SIN_F32)
+    extern const float32_t sinTable_f32[FAST_MATH_TABLE_SIZE + 1];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) defined(ARM_ALL_FAST_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FAST_TABLES) || defined(ARM_TABLE_SIN_Q31)
+    extern const q31_t sinTable_q31[FAST_MATH_TABLE_SIZE + 1];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) defined(ARM_ALL_FAST_TABLES) */
+  
+  #if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_ALL_FAST_TABLES) || defined(ARM_TABLE_SIN_Q15)
+    extern const q15_t sinTable_q15[FAST_MATH_TABLE_SIZE + 1];
+  #endif /* !defined(ARM_DSP_CONFIG_TABLES) defined(ARM_ALL_FAST_TABLES) */
+
+#endif /* if !defined(ARM_DSP_CONFIG_TABLES) || defined(ARM_FAST_TABLES) */
+
+#endif /*  ARM_COMMON_TABLES_H */
diff --git a/cmsis/arm_const_structs.h b/cmsis/arm_const_structs.h
index 54595f5..80a3e8b 100644
--- a/cmsis/arm_const_structs.h
+++ b/cmsis/arm_const_structs.h
@@ -1,79 +1,66 @@
-/* ----------------------------------------------------------------------
-* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
-*
-* $Date:        19. March 2015
-* $Revision: 	V.1.4.5
-*
-* Project: 	    CMSIS DSP Library
-* Title:	    arm_const_structs.h
-*
-* Description:	This file has constant structs that are initialized for
-*              user convenience.  For example, some can be given as
-*              arguments to the arm_cfft_f32() function.
-*
-* Target Processor: Cortex-M4/Cortex-M3
-*
-* Redistribution and use in source and binary forms, with or without
-* modification, are permitted provided that the following conditions
-* are met:
-*   - Redistributions of source code must retain the above copyright
-*     notice, this list of conditions and the following disclaimer.
-*   - Redistributions in binary form must reproduce the above copyright
-*     notice, this list of conditions and the following disclaimer in
-*     the documentation and/or other materials provided with the
-*     distribution.
-*   - Neither the name of ARM LIMITED nor the names of its contributors
-*     may be used to endorse or promote products derived from this
-*     software without specific prior written permission.
-*
-* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
-* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
-* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
-* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
-* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
-* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
-* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
-* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
-* POSSIBILITY OF SUCH DAMAGE.
-* -------------------------------------------------------------------- */
-
-#ifndef _ARM_CONST_STRUCTS_H
-#define _ARM_CONST_STRUCTS_H
-
-#include "arm_math.h"
-#include "arm_common_tables.h"
-
-   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len16;
-   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len32;
-   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len64;
-   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len128;
-   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len256;
-   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len512;
-   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len1024;
-   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len2048;
-   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len4096;
-
-   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len16;
-   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len32;
-   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len64;
-   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len128;
-   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len256;
-   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len512;
-   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len1024;
-   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len2048;
-   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len4096;
-
-   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len16;
-   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len32;
-   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len64;
-   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len128;
-   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len256;
-   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len512;
-   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len1024;
-   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len2048;
-   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len4096;
-
-#endif
+/* ----------------------------------------------------------------------
+ * Project:      CMSIS DSP Library
+ * Title:        arm_const_structs.h
+ * Description:  Constant structs that are initialized for user convenience.
+ *               For example, some can be given as arguments to the arm_cfft_f32() function.
+ *
+ * $Date:        27. January 2017
+ * $Revision:    V.1.5.1
+ *
+ * Target Processor: Cortex-M cores
+ * -------------------------------------------------------------------- */
+/*
+ * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
+ *
+ * SPDX-License-Identifier: Apache-2.0
+ *
+ * Licensed under the Apache License, Version 2.0 (the License); you may
+ * not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an AS IS BASIS, WITHOUT
+ * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef _ARM_CONST_STRUCTS_H
+#define _ARM_CONST_STRUCTS_H
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len16;
+   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len32;
+   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len64;
+   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len128;
+   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len256;
+   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len512;
+   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len1024;
+   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len2048;
+   extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len4096;
+
+   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len16;
+   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len32;
+   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len64;
+   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len128;
+   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len256;
+   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len512;
+   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len1024;
+   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len2048;
+   extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len4096;
+
+   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len16;
+   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len32;
+   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len64;
+   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len128;
+   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len256;
+   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len512;
+   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len1024;
+   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len2048;
+   extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len4096;
+
+#endif
diff --git a/cmsis/arm_math.h b/cmsis/arm_math.h
index 580cbbd..eb37f82 100644
--- a/cmsis/arm_math.h
+++ b/cmsis/arm_math.h
@@ -1,7154 +1,7361 @@
-/* ----------------------------------------------------------------------
-* Copyright (C) 2010-2015 ARM Limited. All rights reserved.
-*
-* $Date:        20. October 2015
-* $Revision:    V1.4.5 b
-*
-* Project:      CMSIS DSP Library
-* Title:        arm_math.h
-*
-* Description:  Public header file for CMSIS DSP Library
-*
-* Target Processor: Cortex-M7/Cortex-M4/Cortex-M3/Cortex-M0
-*
-* Redistribution and use in source and binary forms, with or without
-* modification, are permitted provided that the following conditions
-* are met:
-*   - Redistributions of source code must retain the above copyright
-*     notice, this list of conditions and the following disclaimer.
-*   - Redistributions in binary form must reproduce the above copyright
-*     notice, this list of conditions and the following disclaimer in
-*     the documentation and/or other materials provided with the
-*     distribution.
-*   - Neither the name of ARM LIMITED nor the names of its contributors
-*     may be used to endorse or promote products derived from this
-*     software without specific prior written permission.
-*
-* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
-* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
-* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
-* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
-* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
-* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
-* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
-* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
-* POSSIBILITY OF SUCH DAMAGE.
- * -------------------------------------------------------------------- */
-
-/**
-   \mainpage CMSIS DSP Software Library
-   *
-   * Introduction
-   * ------------
-   *
-   * This user manual describes the CMSIS DSP software library,
-   * a suite of common signal processing functions for use on Cortex-M processor based devices.
-   *
-   * The library is divided into a number of functions each covering a specific category:
-   * - Basic math functions
-   * - Fast math functions
-   * - Complex math functions
-   * - Filters
-   * - Matrix functions
-   * - Transforms
-   * - Motor control functions
-   * - Statistical functions
-   * - Support functions
-   * - Interpolation functions
-   *
-   * The library has separate functions for operating on 8-bit integers, 16-bit integers,
-   * 32-bit integer and 32-bit floating-point values.
-   *
-   * Using the Library
-   * ------------
-   *
-   * The library installer contains prebuilt versions of the libraries in the <code>Lib</code> folder.
-   * - arm_cortexM7lfdp_math.lib (Little endian and Double Precision Floating Point Unit on Cortex-M7)
-   * - arm_cortexM7bfdp_math.lib (Big endian and Double Precision Floating Point Unit on Cortex-M7)
-   * - arm_cortexM7lfsp_math.lib (Little endian and Single Precision Floating Point Unit on Cortex-M7)
-   * - arm_cortexM7bfsp_math.lib (Big endian and Single Precision Floating Point Unit on Cortex-M7)
-   * - arm_cortexM7l_math.lib (Little endian on Cortex-M7)
-   * - arm_cortexM7b_math.lib (Big endian on Cortex-M7)
-   * - arm_cortexM4lf_math.lib (Little endian and Floating Point Unit on Cortex-M4)
-   * - arm_cortexM4bf_math.lib (Big endian and Floating Point Unit on Cortex-M4)
-   * - arm_cortexM4l_math.lib (Little endian on Cortex-M4)
-   * - arm_cortexM4b_math.lib (Big endian on Cortex-M4)
-   * - arm_cortexM3l_math.lib (Little endian on Cortex-M3)
-   * - arm_cortexM3b_math.lib (Big endian on Cortex-M3)
-   * - arm_cortexM0l_math.lib (Little endian on Cortex-M0 / CortexM0+)
-   * - arm_cortexM0b_math.lib (Big endian on Cortex-M0 / CortexM0+)
-   *
-   * The library functions are declared in the public file <code>arm_math.h</code> which is placed in the <code>Include</code> folder.
-   * Simply include this file and link the appropriate library in the application and begin calling the library functions. The Library supports single
-   * public header file <code> arm_math.h</code> for Cortex-M7/M4/M3/M0/M0+ with little endian and big endian. Same header file will be used for floating point unit(FPU) variants.
-   * Define the appropriate pre processor MACRO ARM_MATH_CM7 or ARM_MATH_CM4 or  ARM_MATH_CM3 or
-   * ARM_MATH_CM0 or ARM_MATH_CM0PLUS depending on the target processor in the application.
-   *
-   * Examples
-   * --------
-   *
-   * The library ships with a number of examples which demonstrate how to use the library functions.
-   *
-   * Toolchain Support
-   * ------------
-   *
-   * The library has been developed and tested with MDK-ARM version 5.14.0.0
-   * The library is being tested in GCC and IAR toolchains and updates on this activity will be made available shortly.
-   *
-   * Building the Library
-   * ------------
-   *
-   * The library installer contains a project file to re build libraries on MDK-ARM Tool chain in the <code>CMSIS\\DSP_Lib\\Source\\ARM</code> folder.
-   * - arm_cortexM_math.uvprojx
-   *
-   *
-   * The libraries can be built by opening the arm_cortexM_math.uvprojx project in MDK-ARM, selecting a specific target, and defining the optional pre processor MACROs detailed above.
-   *
-   * Pre-processor Macros
-   * ------------
-   *
-   * Each library project have differant pre-processor macros.
-   *
-   * - UNALIGNED_SUPPORT_DISABLE:
-   *
-   * Define macro UNALIGNED_SUPPORT_DISABLE, If the silicon does not support unaligned memory access
-   *
-   * - ARM_MATH_BIG_ENDIAN:
-   *
-   * Define macro ARM_MATH_BIG_ENDIAN to build the library for big endian targets. By default library builds for little endian targets.
-   *
-   * - ARM_MATH_MATRIX_CHECK:
-   *
-   * Define macro ARM_MATH_MATRIX_CHECK for checking on the input and output sizes of matrices
-   *
-   * - ARM_MATH_ROUNDING:
-   *
-   * Define macro ARM_MATH_ROUNDING for rounding on support functions
-   *
-   * - ARM_MATH_CMx:
-   *
-   * Define macro ARM_MATH_CM4 for building the library on Cortex-M4 target, ARM_MATH_CM3 for building library on Cortex-M3 target
-   * and ARM_MATH_CM0 for building library on Cortex-M0 target, ARM_MATH_CM0PLUS for building library on Cortex-M0+ target, and
-   * ARM_MATH_CM7 for building the library on cortex-M7.
-   *
-   * - __FPU_PRESENT:
-   *
-   * Initialize macro __FPU_PRESENT = 1 when building on FPU supported Targets. Enable this macro for M4bf and M4lf libraries
-   *
-   * <hr>
-   * CMSIS-DSP in ARM::CMSIS Pack
-   * -----------------------------
-   *
-   * The following files relevant to CMSIS-DSP are present in the <b>ARM::CMSIS</b> Pack directories:
-   * |File/Folder                   |Content                                                                 |
-   * |------------------------------|------------------------------------------------------------------------|
-   * |\b CMSIS\\Documentation\\DSP  | This documentation                                                     |
-   * |\b CMSIS\\DSP_Lib             | Software license agreement (license.txt)                               |
-   * |\b CMSIS\\DSP_Lib\\Examples   | Example projects demonstrating the usage of the library functions      |
-   * |\b CMSIS\\DSP_Lib\\Source     | Source files for rebuilding the library                                |
-   *
-   * <hr>
-   * Revision History of CMSIS-DSP
-   * ------------
-   * Please refer to \ref ChangeLog_pg.
-   *
-   * Copyright Notice
-   * ------------
-   *
-   * Copyright (C) 2010-2015 ARM Limited. All rights reserved.
-   */
-
-
-/**
- * @defgroup groupMath Basic Math Functions
- */
-
-/**
- * @defgroup groupFastMath Fast Math Functions
- * This set of functions provides a fast approximation to sine, cosine, and square root.
- * As compared to most of the other functions in the CMSIS math library, the fast math functions
- * operate on individual values and not arrays.
- * There are separate functions for Q15, Q31, and floating-point data.
- *
- */
-
-/**
- * @defgroup groupCmplxMath Complex Math Functions
- * This set of functions operates on complex data vectors.
- * The data in the complex arrays is stored in an interleaved fashion
- * (real, imag, real, imag, ...).
- * In the API functions, the number of samples in a complex array refers
- * to the number of complex values; the array contains twice this number of
- * real values.
- */
-
-/**
- * @defgroup groupFilters Filtering Functions
- */
-
-/**
- * @defgroup groupMatrix Matrix Functions
- *
- * This set of functions provides basic matrix math operations.
- * The functions operate on matrix data structures.  For example,
- * the type
- * definition for the floating-point matrix structure is shown
- * below:
- * <pre>
- *     typedef struct
- *     {
- *       uint16_t numRows;     // number of rows of the matrix.
- *       uint16_t numCols;     // number of columns of the matrix.
- *       float32_t *pData;     // points to the data of the matrix.
- *     } arm_matrix_instance_f32;
- * </pre>
- * There are similar definitions for Q15 and Q31 data types.
- *
- * The structure specifies the size of the matrix and then points to
- * an array of data.  The array is of size <code>numRows X numCols</code>
- * and the values are arranged in row order.  That is, the
- * matrix element (i, j) is stored at:
- * <pre>
- *     pData[i*numCols + j]
- * </pre>
- *
- * \par Init Functions
- * There is an associated initialization function for each type of matrix
- * data structure.
- * The initialization function sets the values of the internal structure fields.
- * Refer to the function <code>arm_mat_init_f32()</code>, <code>arm_mat_init_q31()</code>
- * and <code>arm_mat_init_q15()</code> for floating-point, Q31 and Q15 types,  respectively.
- *
- * \par
- * Use of the initialization function is optional. However, if initialization function is used
- * then the instance structure cannot be placed into a const data section.
- * To place the instance structure in a const data
- * section, manually initialize the data structure.  For example:
- * <pre>
- * <code>arm_matrix_instance_f32 S = {nRows, nColumns, pData};</code>
- * <code>arm_matrix_instance_q31 S = {nRows, nColumns, pData};</code>
- * <code>arm_matrix_instance_q15 S = {nRows, nColumns, pData};</code>
- * </pre>
- * where <code>nRows</code> specifies the number of rows, <code>nColumns</code>
- * specifies the number of columns, and <code>pData</code> points to the
- * data array.
- *
- * \par Size Checking
- * By default all of the matrix functions perform size checking on the input and
- * output matrices.  For example, the matrix addition function verifies that the
- * two input matrices and the output matrix all have the same number of rows and
- * columns.  If the size check fails the functions return:
- * <pre>
- *     ARM_MATH_SIZE_MISMATCH
- * </pre>
- * Otherwise the functions return
- * <pre>
- *     ARM_MATH_SUCCESS
- * </pre>
- * There is some overhead associated with this matrix size checking.
- * The matrix size checking is enabled via the \#define
- * <pre>
- *     ARM_MATH_MATRIX_CHECK
- * </pre>
- * within the library project settings.  By default this macro is defined
- * and size checking is enabled.  By changing the project settings and
- * undefining this macro size checking is eliminated and the functions
- * run a bit faster.  With size checking disabled the functions always
- * return <code>ARM_MATH_SUCCESS</code>.
- */
-
-/**
- * @defgroup groupTransforms Transform Functions
- */
-
-/**
- * @defgroup groupController Controller Functions
- */
-
-/**
- * @defgroup groupStats Statistics Functions
- */
-/**
- * @defgroup groupSupport Support Functions
- */
-
-/**
- * @defgroup groupInterpolation Interpolation Functions
- * These functions perform 1- and 2-dimensional interpolation of data.
- * Linear interpolation is used for 1-dimensional data and
- * bilinear interpolation is used for 2-dimensional data.
- */
-
-/**
- * @defgroup groupExamples Examples
- */
-#ifndef _ARM_MATH_H
-#define _ARM_MATH_H
-
-/* ignore some GCC warnings */
-#if defined ( __GNUC__ )
-#pragma GCC diagnostic push
-#pragma GCC diagnostic ignored "-Wsign-conversion"
-#pragma GCC diagnostic ignored "-Wconversion"
-#pragma GCC diagnostic ignored "-Wunused-parameter"
-#endif
-
-#define __CMSIS_GENERIC         /* disable NVIC and Systick functions */
-
-#if defined(ARM_MATH_CM7)
-  #include "core_cm7.h"
-#elif defined (ARM_MATH_CM4)
-  #include "core_cm4.h"
-#elif defined (ARM_MATH_CM3)
-  #include "core_cm3.h"
-#elif defined (ARM_MATH_CM0)
-  #include "core_cm0.h"
-  #define ARM_MATH_CM0_FAMILY
-#elif defined (ARM_MATH_CM0PLUS)
-  #include "core_cm0plus.h"
-  #define ARM_MATH_CM0_FAMILY
-#else
-  #error "Define according the used Cortex core ARM_MATH_CM7, ARM_MATH_CM4, ARM_MATH_CM3, ARM_MATH_CM0PLUS or ARM_MATH_CM0"
-#endif
-
-#undef  __CMSIS_GENERIC         /* enable NVIC and Systick functions */
-#include "string.h"
-#include "math.h"
-#ifdef   __cplusplus
-extern "C"
-{
-#endif
-
-
-  /**
-   * @brief Macros required for reciprocal calculation in Normalized LMS
-   */
-
-#define DELTA_Q31          (0x100)
-#define DELTA_Q15          0x5
-#define INDEX_MASK         0x0000003F
-#ifndef PI
-#define PI                 3.14159265358979f
-#endif
-
-  /**
-   * @brief Macros required for SINE and COSINE Fast math approximations
-   */
-
-#define FAST_MATH_TABLE_SIZE  512
-#define FAST_MATH_Q31_SHIFT   (32 - 10)
-#define FAST_MATH_Q15_SHIFT   (16 - 10)
-#define CONTROLLER_Q31_SHIFT  (32 - 9)
-#define TABLE_SIZE  256
-#define TABLE_SPACING_Q31     0x400000
-#define TABLE_SPACING_Q15     0x80
-
-  /**
-   * @brief Macros required for SINE and COSINE Controller functions
-   */
-  /* 1.31(q31) Fixed value of 2/360 */
-  /* -1 to +1 is divided into 360 values so total spacing is (2/360) */
-#define INPUT_SPACING         0xB60B61
-
-  /**
-   * @brief Macro for Unaligned Support
-   */
-#ifndef UNALIGNED_SUPPORT_DISABLE
-    #define ALIGN4
-#else
-  #if defined  (__GNUC__)
-    #define ALIGN4 __attribute__((aligned(4)))
-  #else
-    #define ALIGN4 __align(4)
-  #endif
-#endif   /* #ifndef UNALIGNED_SUPPORT_DISABLE */
-
-  /**
-   * @brief Error status returned by some functions in the library.
-   */
-
-  typedef enum
-  {
-    ARM_MATH_SUCCESS = 0,                /**< No error */
-    ARM_MATH_ARGUMENT_ERROR = -1,        /**< One or more arguments are incorrect */
-    ARM_MATH_LENGTH_ERROR = -2,          /**< Length of data buffer is incorrect */
-    ARM_MATH_SIZE_MISMATCH = -3,         /**< Size of matrices is not compatible with the operation. */
-    ARM_MATH_NANINF = -4,                /**< Not-a-number (NaN) or infinity is generated */
-    ARM_MATH_SINGULAR = -5,              /**< Generated by matrix inversion if the input matrix is singular and cannot be inverted. */
-    ARM_MATH_TEST_FAILURE = -6           /**< Test Failed  */
-  } arm_status;
-
-  /**
-   * @brief 8-bit fractional data type in 1.7 format.
-   */
-  typedef int8_t q7_t;
-
-  /**
-   * @brief 16-bit fractional data type in 1.15 format.
-   */
-  typedef int16_t q15_t;
-
-  /**
-   * @brief 32-bit fractional data type in 1.31 format.
-   */
-  typedef int32_t q31_t;
-
-  /**
-   * @brief 64-bit fractional data type in 1.63 format.
-   */
-  typedef int64_t q63_t;
-
-  /**
-   * @brief 32-bit floating-point type definition.
-   */
-  typedef float float32_t;
-
-  /**
-   * @brief 64-bit floating-point type definition.
-   */
-  typedef double float64_t;
-
-  /**
-   * @brief definition to read/write two 16 bit values.
-   */
-#if defined __CC_ARM
-  #define __SIMD32_TYPE int32_t __packed
-  #define CMSIS_UNUSED __attribute__((unused))
-
-#elif defined(__ARMCC_VERSION) && (__ARMCC_VERSION >= 6010050)
-  #define __SIMD32_TYPE int32_t
-  #define CMSIS_UNUSED __attribute__((unused))
-
-#elif defined __GNUC__
-  #define __SIMD32_TYPE int32_t
-  #define CMSIS_UNUSED __attribute__((unused))
-
-#elif defined __ICCARM__
-  #define __SIMD32_TYPE int32_t __packed
-  #define CMSIS_UNUSED
-
-#elif defined __CSMC__
-  #define __SIMD32_TYPE int32_t
-  #define CMSIS_UNUSED
-
-#elif defined __TASKING__
-  #define __SIMD32_TYPE __unaligned int32_t
-  #define CMSIS_UNUSED
-
-#else
-  #error Unknown compiler
-#endif
-
-#define __SIMD32(addr)        (*(__SIMD32_TYPE **) & (addr))
-#define __SIMD32_CONST(addr)  ((__SIMD32_TYPE *)(addr))
-#define _SIMD32_OFFSET(addr)  (*(__SIMD32_TYPE *)  (addr))
-#define __SIMD64(addr)        (*(int64_t **) & (addr))
-
-#if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY)
-  /**
-   * @brief definition to pack two 16 bit values.
-   */
-#define __PKHBT(ARG1, ARG2, ARG3)      ( (((int32_t)(ARG1) <<  0) & (int32_t)0x0000FFFF) | \
-                                         (((int32_t)(ARG2) << ARG3) & (int32_t)0xFFFF0000)  )
-#define __PKHTB(ARG1, ARG2, ARG3)      ( (((int32_t)(ARG1) <<  0) & (int32_t)0xFFFF0000) | \
-                                         (((int32_t)(ARG2) >> ARG3) & (int32_t)0x0000FFFF)  )
-
-#endif
-
-
-   /**
-   * @brief definition to pack four 8 bit values.
-   */
-#ifndef ARM_MATH_BIG_ENDIAN
-
-#define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v0) <<  0) & (int32_t)0x000000FF) | \
-                                (((int32_t)(v1) <<  8) & (int32_t)0x0000FF00) | \
-                                (((int32_t)(v2) << 16) & (int32_t)0x00FF0000) | \
-                                (((int32_t)(v3) << 24) & (int32_t)0xFF000000)  )
-#else
-
-#define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v3) <<  0) & (int32_t)0x000000FF) | \
-                                (((int32_t)(v2) <<  8) & (int32_t)0x0000FF00) | \
-                                (((int32_t)(v1) << 16) & (int32_t)0x00FF0000) | \
-                                (((int32_t)(v0) << 24) & (int32_t)0xFF000000)  )
-
-#endif
-
-
-  /**
-   * @brief Clips Q63 to Q31 values.
-   */
-  static __INLINE q31_t clip_q63_to_q31(
-  q63_t x)
-  {
-    return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
-      ((0x7FFFFFFF ^ ((q31_t) (x >> 63)))) : (q31_t) x;
-  }
-
-  /**
-   * @brief Clips Q63 to Q15 values.
-   */
-  static __INLINE q15_t clip_q63_to_q15(
-  q63_t x)
-  {
-    return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
-      ((0x7FFF ^ ((q15_t) (x >> 63)))) : (q15_t) (x >> 15);
-  }
-
-  /**
-   * @brief Clips Q31 to Q7 values.
-   */
-  static __INLINE q7_t clip_q31_to_q7(
-  q31_t x)
-  {
-    return ((q31_t) (x >> 24) != ((q31_t) x >> 23)) ?
-      ((0x7F ^ ((q7_t) (x >> 31)))) : (q7_t) x;
-  }
-
-  /**
-   * @brief Clips Q31 to Q15 values.
-   */
-  static __INLINE q15_t clip_q31_to_q15(
-  q31_t x)
-  {
-    return ((q31_t) (x >> 16) != ((q31_t) x >> 15)) ?
-      ((0x7FFF ^ ((q15_t) (x >> 31)))) : (q15_t) x;
-  }
-
-  /**
-   * @brief Multiplies 32 X 64 and returns 32 bit result in 2.30 format.
-   */
-
-  static __INLINE q63_t mult32x64(
-  q63_t x,
-  q31_t y)
-  {
-    return ((((q63_t) (x & 0x00000000FFFFFFFF) * y) >> 32) +
-            (((q63_t) (x >> 32) * y)));
-  }
-
-/*
-  #if defined (ARM_MATH_CM0_FAMILY) && defined ( __CC_ARM   )
-  #define __CLZ __clz
-  #endif
- */
-/* note: function can be removed when all toolchain support __CLZ for Cortex-M0 */
-#if defined (ARM_MATH_CM0_FAMILY) && ((defined (__ICCARM__))  )
-  static __INLINE uint32_t __CLZ(
-  q31_t data);
-
-  static __INLINE uint32_t __CLZ(
-  q31_t data)
-  {
-    uint32_t count = 0;
-    uint32_t mask = 0x80000000;
-
-    while((data & mask) == 0)
-    {
-      count += 1u;
-      mask = mask >> 1u;
-    }
-
-    return (count);
-  }
-#endif
-
-  /**
-   * @brief Function to Calculates 1/in (reciprocal) value of Q31 Data type.
-   */
-
-  static __INLINE uint32_t arm_recip_q31(
-  q31_t in,
-  q31_t * dst,
-  q31_t * pRecipTable)
-  {
-    q31_t out;
-    uint32_t tempVal;
-    uint32_t index, i;
-    uint32_t signBits;
-
-    if(in > 0)
-    {
-      signBits = ((uint32_t) (__CLZ( in) - 1));
-    }
-    else
-    {
-      signBits = ((uint32_t) (__CLZ(-in) - 1));
-    }
-
-    /* Convert input sample to 1.31 format */
-    in = (in << signBits);
-
-    /* calculation of index for initial approximated Val */
-    index = (uint32_t)(in >> 24);
-    index = (index & INDEX_MASK);
-
-    /* 1.31 with exp 1 */
-    out = pRecipTable[index];
-
-    /* calculation of reciprocal value */
-    /* running approximation for two iterations */
-    for (i = 0u; i < 2u; i++)
-    {
-      tempVal = (uint32_t) (((q63_t) in * out) >> 31);
-      tempVal = 0x7FFFFFFFu - tempVal;
-      /*      1.31 with exp 1 */
-      /* out = (q31_t) (((q63_t) out * tempVal) >> 30); */
-      out = clip_q63_to_q31(((q63_t) out * tempVal) >> 30);
-    }
-
-    /* write output */
-    *dst = out;
-
-    /* return num of signbits of out = 1/in value */
-    return (signBits + 1u);
-  }
-
-
-  /**
-   * @brief Function to Calculates 1/in (reciprocal) value of Q15 Data type.
-   */
-  static __INLINE uint32_t arm_recip_q15(
-  q15_t in,
-  q15_t * dst,
-  q15_t * pRecipTable)
-  {
-    q15_t out = 0;
-    uint32_t tempVal = 0;
-    uint32_t index = 0, i = 0;
-    uint32_t signBits = 0;
-
-    if(in > 0)
-    {
-      signBits = ((uint32_t)(__CLZ( in) - 17));
-    }
-    else
-    {
-      signBits = ((uint32_t)(__CLZ(-in) - 17));
-    }
-
-    /* Convert input sample to 1.15 format */
-    in = (in << signBits);
-
-    /* calculation of index for initial approximated Val */
-    index = (uint32_t)(in >>  8);
-    index = (index & INDEX_MASK);
-
-    /*      1.15 with exp 1  */
-    out = pRecipTable[index];
-
-    /* calculation of reciprocal value */
-    /* running approximation for two iterations */
-    for (i = 0u; i < 2u; i++)
-    {
-      tempVal = (uint32_t) (((q31_t) in * out) >> 15);
-      tempVal = 0x7FFFu - tempVal;
-      /*      1.15 with exp 1 */
-      out = (q15_t) (((q31_t) out * tempVal) >> 14);
-      /* out = clip_q31_to_q15(((q31_t) out * tempVal) >> 14); */
-    }
-
-    /* write output */
-    *dst = out;
-
-    /* return num of signbits of out = 1/in value */
-    return (signBits + 1);
-  }
-
-
-  /*
-   * @brief C custom defined intrinisic function for only M0 processors
-   */
-#if defined(ARM_MATH_CM0_FAMILY)
-  static __INLINE q31_t __SSAT(
-  q31_t x,
-  uint32_t y)
-  {
-    int32_t posMax, negMin;
-    uint32_t i;
-
-    posMax = 1;
-    for (i = 0; i < (y - 1); i++)
-    {
-      posMax = posMax * 2;
-    }
-
-    if(x > 0)
-    {
-      posMax = (posMax - 1);
-
-      if(x > posMax)
-      {
-        x = posMax;
-      }
-    }
-    else
-    {
-      negMin = -posMax;
-
-      if(x < negMin)
-      {
-        x = negMin;
-      }
-    }
-    return (x);
-  }
-#endif /* end of ARM_MATH_CM0_FAMILY */
-
-
-  /*
-   * @brief C custom defined intrinsic function for M3 and M0 processors
-   */
-#if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY)
-
-  /*
-   * @brief C custom defined QADD8 for M3 and M0 processors
-   */
-  static __INLINE uint32_t __QADD8(
-  uint32_t x,
-  uint32_t y)
-  {
-    q31_t r, s, t, u;
-
-    r = __SSAT(((((q31_t)x << 24) >> 24) + (((q31_t)y << 24) >> 24)), 8) & (int32_t)0x000000FF;
-    s = __SSAT(((((q31_t)x << 16) >> 24) + (((q31_t)y << 16) >> 24)), 8) & (int32_t)0x000000FF;
-    t = __SSAT(((((q31_t)x <<  8) >> 24) + (((q31_t)y <<  8) >> 24)), 8) & (int32_t)0x000000FF;
-    u = __SSAT(((((q31_t)x      ) >> 24) + (((q31_t)y      ) >> 24)), 8) & (int32_t)0x000000FF;
-
-    return ((uint32_t)((u << 24) | (t << 16) | (s <<  8) | (r      )));
-  }
-
-
-  /*
-   * @brief C custom defined QSUB8 for M3 and M0 processors
-   */
-  static __INLINE uint32_t __QSUB8(
-  uint32_t x,
-  uint32_t y)
-  {
-    q31_t r, s, t, u;
-
-    r = __SSAT(((((q31_t)x << 24) >> 24) - (((q31_t)y << 24) >> 24)), 8) & (int32_t)0x000000FF;
-    s = __SSAT(((((q31_t)x << 16) >> 24) - (((q31_t)y << 16) >> 24)), 8) & (int32_t)0x000000FF;
-    t = __SSAT(((((q31_t)x <<  8) >> 24) - (((q31_t)y <<  8) >> 24)), 8) & (int32_t)0x000000FF;
-    u = __SSAT(((((q31_t)x      ) >> 24) - (((q31_t)y      ) >> 24)), 8) & (int32_t)0x000000FF;
-
-    return ((uint32_t)((u << 24) | (t << 16) | (s <<  8) | (r      )));
-  }
-
-
-  /*
-   * @brief C custom defined QADD16 for M3 and M0 processors
-   */
-  static __INLINE uint32_t __QADD16(
-  uint32_t x,
-  uint32_t y)
-  {
-/*  q31_t r,     s;  without initialisation 'arm_offset_q15 test' fails  but 'intrinsic' tests pass! for armCC */
-    q31_t r = 0, s = 0;
-
-    r = __SSAT(((((q31_t)x << 16) >> 16) + (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
-    s = __SSAT(((((q31_t)x      ) >> 16) + (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
-
-    return ((uint32_t)((s << 16) | (r      )));
-  }
-
-
-  /*
-   * @brief C custom defined SHADD16 for M3 and M0 processors
-   */
-  static __INLINE uint32_t __SHADD16(
-  uint32_t x,
-  uint32_t y)
-  {
-    q31_t r, s;
-
-    r = (((((q31_t)x << 16) >> 16) + (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
-    s = (((((q31_t)x      ) >> 16) + (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
-
-    return ((uint32_t)((s << 16) | (r      )));
-  }
-
-
-  /*
-   * @brief C custom defined QSUB16 for M3 and M0 processors
-   */
-  static __INLINE uint32_t __QSUB16(
-  uint32_t x,
-  uint32_t y)
-  {
-    q31_t r, s;
-
-    r = __SSAT(((((q31_t)x << 16) >> 16) - (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
-    s = __SSAT(((((q31_t)x      ) >> 16) - (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
-
-    return ((uint32_t)((s << 16) | (r      )));
-  }
-
-
-  /*
-   * @brief C custom defined SHSUB16 for M3 and M0 processors
-   */
-  static __INLINE uint32_t __SHSUB16(
-  uint32_t x,
-  uint32_t y)
-  {
-    q31_t r, s;
-
-    r = (((((q31_t)x << 16) >> 16) - (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
-    s = (((((q31_t)x      ) >> 16) - (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
-
-    return ((uint32_t)((s << 16) | (r      )));
-  }
-
-
-  /*
-   * @brief C custom defined QASX for M3 and M0 processors
-   */
-  static __INLINE uint32_t __QASX(
-  uint32_t x,
-  uint32_t y)
-  {
-    q31_t r, s;
-
-    r = __SSAT(((((q31_t)x << 16) >> 16) - (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
-    s = __SSAT(((((q31_t)x      ) >> 16) + (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
-
-    return ((uint32_t)((s << 16) | (r      )));
-  }
-
-
-  /*
-   * @brief C custom defined SHASX for M3 and M0 processors
-   */
-  static __INLINE uint32_t __SHASX(
-  uint32_t x,
-  uint32_t y)
-  {
-    q31_t r, s;
-
-    r = (((((q31_t)x << 16) >> 16) - (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
-    s = (((((q31_t)x      ) >> 16) + (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
-
-    return ((uint32_t)((s << 16) | (r      )));
-  }
-
-
-  /*
-   * @brief C custom defined QSAX for M3 and M0 processors
-   */
-  static __INLINE uint32_t __QSAX(
-  uint32_t x,
-  uint32_t y)
-  {
-    q31_t r, s;
-
-    r = __SSAT(((((q31_t)x << 16) >> 16) + (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
-    s = __SSAT(((((q31_t)x      ) >> 16) - (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
-
-    return ((uint32_t)((s << 16) | (r      )));
-  }
-
-
-  /*
-   * @brief C custom defined SHSAX for M3 and M0 processors
-   */
-  static __INLINE uint32_t __SHSAX(
-  uint32_t x,
-  uint32_t y)
-  {
-    q31_t r, s;
-
-    r = (((((q31_t)x << 16) >> 16) + (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
-    s = (((((q31_t)x      ) >> 16) - (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
-
-    return ((uint32_t)((s << 16) | (r      )));
-  }
-
-
-  /*
-   * @brief C custom defined SMUSDX for M3 and M0 processors
-   */
-  static __INLINE uint32_t __SMUSDX(
-  uint32_t x,
-  uint32_t y)
-  {
-    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) -
-                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16))   ));
-  }
-
-  /*
-   * @brief C custom defined SMUADX for M3 and M0 processors
-   */
-  static __INLINE uint32_t __SMUADX(
-  uint32_t x,
-  uint32_t y)
-  {
-    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) +
-                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16))   ));
-  }
-
-
-  /*
-   * @brief C custom defined QADD for M3 and M0 processors
-   */
-  static __INLINE int32_t __QADD(
-  int32_t x,
-  int32_t y)
-  {
-    return ((int32_t)(clip_q63_to_q31((q63_t)x + (q31_t)y)));
-  }
-
-
-  /*
-   * @brief C custom defined QSUB for M3 and M0 processors
-   */
-  static __INLINE int32_t __QSUB(
-  int32_t x,
-  int32_t y)
-  {
-    return ((int32_t)(clip_q63_to_q31((q63_t)x - (q31_t)y)));
-  }
-
-
-  /*
-   * @brief C custom defined SMLAD for M3 and M0 processors
-   */
-  static __INLINE uint32_t __SMLAD(
-  uint32_t x,
-  uint32_t y,
-  uint32_t sum)
-  {
-    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) +
-                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16)) +
-                       ( ((q31_t)sum    )                                  )   ));
-  }
-
-
-  /*
-   * @brief C custom defined SMLADX for M3 and M0 processors
-   */
-  static __INLINE uint32_t __SMLADX(
-  uint32_t x,
-  uint32_t y,
-  uint32_t sum)
-  {
-    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) +
-                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16)) +
-                       ( ((q31_t)sum    )                                  )   ));
-  }
-
-
-  /*
-   * @brief C custom defined SMLSDX for M3 and M0 processors
-   */
-  static __INLINE uint32_t __SMLSDX(
-  uint32_t x,
-  uint32_t y,
-  uint32_t sum)
-  {
-    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) -
-                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16)) +
-                       ( ((q31_t)sum    )                                  )   ));
-  }
-
-
-  /*
-   * @brief C custom defined SMLALD for M3 and M0 processors
-   */
-  static __INLINE uint64_t __SMLALD(
-  uint32_t x,
-  uint32_t y,
-  uint64_t sum)
-  {
-/*  return (sum + ((q15_t) (x >> 16) * (q15_t) (y >> 16)) + ((q15_t) x * (q15_t) y)); */
-    return ((uint64_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) +
-                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16)) +
-                       ( ((q63_t)sum    )                                  )   ));
-  }
-
-
-  /*
-   * @brief C custom defined SMLALDX for M3 and M0 processors
-   */
-  static __INLINE uint64_t __SMLALDX(
-  uint32_t x,
-  uint32_t y,
-  uint64_t sum)
-  {
-/*  return (sum + ((q15_t) (x >> 16) * (q15_t) y)) + ((q15_t) x * (q15_t) (y >> 16)); */
-    return ((uint64_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) +
-                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16)) +
-                       ( ((q63_t)sum    )                                  )   ));
-  }
-
-
-  /*
-   * @brief C custom defined SMUAD for M3 and M0 processors
-   */
-  static __INLINE uint32_t __SMUAD(
-  uint32_t x,
-  uint32_t y)
-  {
-    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) +
-                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16))   ));
-  }
-
-
-  /*
-   * @brief C custom defined SMUSD for M3 and M0 processors
-   */
-  static __INLINE uint32_t __SMUSD(
-  uint32_t x,
-  uint32_t y)
-  {
-    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) -
-                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16))   ));
-  }
-
-
-  /*
-   * @brief C custom defined SXTB16 for M3 and M0 processors
-   */
-  static __INLINE uint32_t __SXTB16(
-  uint32_t x)
-  {
-    return ((uint32_t)(((((q31_t)x << 24) >> 24) & (q31_t)0x0000FFFF) |
-                       ((((q31_t)x <<  8) >>  8) & (q31_t)0xFFFF0000)  ));
-  }
-
-#endif /* defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY) */
-
-
-  /**
-   * @brief Instance structure for the Q7 FIR filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;        /**< number of filter coefficients in the filter. */
-    q7_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
-    q7_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
-  } arm_fir_instance_q7;
-
-  /**
-   * @brief Instance structure for the Q15 FIR filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;         /**< number of filter coefficients in the filter. */
-    q15_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
-    q15_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
-  } arm_fir_instance_q15;
-
-  /**
-   * @brief Instance structure for the Q31 FIR filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;         /**< number of filter coefficients in the filter. */
-    q31_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
-    q31_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps. */
-  } arm_fir_instance_q31;
-
-  /**
-   * @brief Instance structure for the floating-point FIR filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;     /**< number of filter coefficients in the filter. */
-    float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
-    float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
-  } arm_fir_instance_f32;
-
-
-  /**
-   * @brief Processing function for the Q7 FIR filter.
-   * @param[in]  S          points to an instance of the Q7 FIR filter structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_fir_q7(
-  const arm_fir_instance_q7 * S,
-  q7_t * pSrc,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the Q7 FIR filter.
-   * @param[in,out] S          points to an instance of the Q7 FIR structure.
-   * @param[in]     numTaps    Number of filter coefficients in the filter.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     blockSize  number of samples that are processed.
-   */
-  void arm_fir_init_q7(
-  arm_fir_instance_q7 * S,
-  uint16_t numTaps,
-  q7_t * pCoeffs,
-  q7_t * pState,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the Q15 FIR filter.
-   * @param[in]  S          points to an instance of the Q15 FIR structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_fir_q15(
-  const arm_fir_instance_q15 * S,
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the fast Q15 FIR filter for Cortex-M3 and Cortex-M4.
-   * @param[in]  S          points to an instance of the Q15 FIR filter structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_fir_fast_q15(
-  const arm_fir_instance_q15 * S,
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the Q15 FIR filter.
-   * @param[in,out] S          points to an instance of the Q15 FIR filter structure.
-   * @param[in]     numTaps    Number of filter coefficients in the filter. Must be even and greater than or equal to 4.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     blockSize  number of samples that are processed at a time.
-   * @return The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_ARGUMENT_ERROR if
-   * <code>numTaps</code> is not a supported value.
-   */
-  arm_status arm_fir_init_q15(
-  arm_fir_instance_q15 * S,
-  uint16_t numTaps,
-  q15_t * pCoeffs,
-  q15_t * pState,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the Q31 FIR filter.
-   * @param[in]  S          points to an instance of the Q31 FIR filter structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_fir_q31(
-  const arm_fir_instance_q31 * S,
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the fast Q31 FIR filter for Cortex-M3 and Cortex-M4.
-   * @param[in]  S          points to an instance of the Q31 FIR structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_fir_fast_q31(
-  const arm_fir_instance_q31 * S,
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the Q31 FIR filter.
-   * @param[in,out] S          points to an instance of the Q31 FIR structure.
-   * @param[in]     numTaps    Number of filter coefficients in the filter.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     blockSize  number of samples that are processed at a time.
-   */
-  void arm_fir_init_q31(
-  arm_fir_instance_q31 * S,
-  uint16_t numTaps,
-  q31_t * pCoeffs,
-  q31_t * pState,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the floating-point FIR filter.
-   * @param[in]  S          points to an instance of the floating-point FIR structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_fir_f32(
-  const arm_fir_instance_f32 * S,
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the floating-point FIR filter.
-   * @param[in,out] S          points to an instance of the floating-point FIR filter structure.
-   * @param[in]     numTaps    Number of filter coefficients in the filter.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     blockSize  number of samples that are processed at a time.
-   */
-  void arm_fir_init_f32(
-  arm_fir_instance_f32 * S,
-  uint16_t numTaps,
-  float32_t * pCoeffs,
-  float32_t * pState,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Instance structure for the Q15 Biquad cascade filter.
-   */
-  typedef struct
-  {
-    int8_t numStages;        /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
-    q15_t *pState;           /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
-    q15_t *pCoeffs;          /**< Points to the array of coefficients.  The array is of length 5*numStages. */
-    int8_t postShift;        /**< Additional shift, in bits, applied to each output sample. */
-  } arm_biquad_casd_df1_inst_q15;
-
-  /**
-   * @brief Instance structure for the Q31 Biquad cascade filter.
-   */
-  typedef struct
-  {
-    uint32_t numStages;      /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
-    q31_t *pState;           /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
-    q31_t *pCoeffs;          /**< Points to the array of coefficients.  The array is of length 5*numStages. */
-    uint8_t postShift;       /**< Additional shift, in bits, applied to each output sample. */
-  } arm_biquad_casd_df1_inst_q31;
-
-  /**
-   * @brief Instance structure for the floating-point Biquad cascade filter.
-   */
-  typedef struct
-  {
-    uint32_t numStages;      /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
-    float32_t *pState;       /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
-    float32_t *pCoeffs;      /**< Points to the array of coefficients.  The array is of length 5*numStages. */
-  } arm_biquad_casd_df1_inst_f32;
-
-
-  /**
-   * @brief Processing function for the Q15 Biquad cascade filter.
-   * @param[in]  S          points to an instance of the Q15 Biquad cascade structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_biquad_cascade_df1_q15(
-  const arm_biquad_casd_df1_inst_q15 * S,
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the Q15 Biquad cascade filter.
-   * @param[in,out] S          points to an instance of the Q15 Biquad cascade structure.
-   * @param[in]     numStages  number of 2nd order stages in the filter.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     postShift  Shift to be applied to the output. Varies according to the coefficients format
-   */
-  void arm_biquad_cascade_df1_init_q15(
-  arm_biquad_casd_df1_inst_q15 * S,
-  uint8_t numStages,
-  q15_t * pCoeffs,
-  q15_t * pState,
-  int8_t postShift);
-
-
-  /**
-   * @brief Fast but less precise processing function for the Q15 Biquad cascade filter for Cortex-M3 and Cortex-M4.
-   * @param[in]  S          points to an instance of the Q15 Biquad cascade structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_biquad_cascade_df1_fast_q15(
-  const arm_biquad_casd_df1_inst_q15 * S,
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the Q31 Biquad cascade filter
-   * @param[in]  S          points to an instance of the Q31 Biquad cascade structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_biquad_cascade_df1_q31(
-  const arm_biquad_casd_df1_inst_q31 * S,
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Fast but less precise processing function for the Q31 Biquad cascade filter for Cortex-M3 and Cortex-M4.
-   * @param[in]  S          points to an instance of the Q31 Biquad cascade structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_biquad_cascade_df1_fast_q31(
-  const arm_biquad_casd_df1_inst_q31 * S,
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the Q31 Biquad cascade filter.
-   * @param[in,out] S          points to an instance of the Q31 Biquad cascade structure.
-   * @param[in]     numStages  number of 2nd order stages in the filter.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     postShift  Shift to be applied to the output. Varies according to the coefficients format
-   */
-  void arm_biquad_cascade_df1_init_q31(
-  arm_biquad_casd_df1_inst_q31 * S,
-  uint8_t numStages,
-  q31_t * pCoeffs,
-  q31_t * pState,
-  int8_t postShift);
-
-
-  /**
-   * @brief Processing function for the floating-point Biquad cascade filter.
-   * @param[in]  S          points to an instance of the floating-point Biquad cascade structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_biquad_cascade_df1_f32(
-  const arm_biquad_casd_df1_inst_f32 * S,
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the floating-point Biquad cascade filter.
-   * @param[in,out] S          points to an instance of the floating-point Biquad cascade structure.
-   * @param[in]     numStages  number of 2nd order stages in the filter.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   */
-  void arm_biquad_cascade_df1_init_f32(
-  arm_biquad_casd_df1_inst_f32 * S,
-  uint8_t numStages,
-  float32_t * pCoeffs,
-  float32_t * pState);
-
-
-  /**
-   * @brief Instance structure for the floating-point matrix structure.
-   */
-  typedef struct
-  {
-    uint16_t numRows;     /**< number of rows of the matrix.     */
-    uint16_t numCols;     /**< number of columns of the matrix.  */
-    float32_t *pData;     /**< points to the data of the matrix. */
-  } arm_matrix_instance_f32;
-
-
-  /**
-   * @brief Instance structure for the floating-point matrix structure.
-   */
-  typedef struct
-  {
-    uint16_t numRows;     /**< number of rows of the matrix.     */
-    uint16_t numCols;     /**< number of columns of the matrix.  */
-    float64_t *pData;     /**< points to the data of the matrix. */
-  } arm_matrix_instance_f64;
-
-  /**
-   * @brief Instance structure for the Q15 matrix structure.
-   */
-  typedef struct
-  {
-    uint16_t numRows;     /**< number of rows of the matrix.     */
-    uint16_t numCols;     /**< number of columns of the matrix.  */
-    q15_t *pData;         /**< points to the data of the matrix. */
-  } arm_matrix_instance_q15;
-
-  /**
-   * @brief Instance structure for the Q31 matrix structure.
-   */
-  typedef struct
-  {
-    uint16_t numRows;     /**< number of rows of the matrix.     */
-    uint16_t numCols;     /**< number of columns of the matrix.  */
-    q31_t *pData;         /**< points to the data of the matrix. */
-  } arm_matrix_instance_q31;
-
-
-  /**
-   * @brief Floating-point matrix addition.
-   * @param[in]  pSrcA  points to the first input matrix structure
-   * @param[in]  pSrcB  points to the second input matrix structure
-   * @param[out] pDst   points to output matrix structure
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_add_f32(
-  const arm_matrix_instance_f32 * pSrcA,
-  const arm_matrix_instance_f32 * pSrcB,
-  arm_matrix_instance_f32 * pDst);
-
-
-  /**
-   * @brief Q15 matrix addition.
-   * @param[in]   pSrcA  points to the first input matrix structure
-   * @param[in]   pSrcB  points to the second input matrix structure
-   * @param[out]  pDst   points to output matrix structure
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_add_q15(
-  const arm_matrix_instance_q15 * pSrcA,
-  const arm_matrix_instance_q15 * pSrcB,
-  arm_matrix_instance_q15 * pDst);
-
-
-  /**
-   * @brief Q31 matrix addition.
-   * @param[in]  pSrcA  points to the first input matrix structure
-   * @param[in]  pSrcB  points to the second input matrix structure
-   * @param[out] pDst   points to output matrix structure
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_add_q31(
-  const arm_matrix_instance_q31 * pSrcA,
-  const arm_matrix_instance_q31 * pSrcB,
-  arm_matrix_instance_q31 * pDst);
-
-
-  /**
-   * @brief Floating-point, complex, matrix multiplication.
-   * @param[in]  pSrcA  points to the first input matrix structure
-   * @param[in]  pSrcB  points to the second input matrix structure
-   * @param[out] pDst   points to output matrix structure
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_cmplx_mult_f32(
-  const arm_matrix_instance_f32 * pSrcA,
-  const arm_matrix_instance_f32 * pSrcB,
-  arm_matrix_instance_f32 * pDst);
-
-
-  /**
-   * @brief Q15, complex,  matrix multiplication.
-   * @param[in]  pSrcA  points to the first input matrix structure
-   * @param[in]  pSrcB  points to the second input matrix structure
-   * @param[out] pDst   points to output matrix structure
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_cmplx_mult_q15(
-  const arm_matrix_instance_q15 * pSrcA,
-  const arm_matrix_instance_q15 * pSrcB,
-  arm_matrix_instance_q15 * pDst,
-  q15_t * pScratch);
-
-
-  /**
-   * @brief Q31, complex, matrix multiplication.
-   * @param[in]  pSrcA  points to the first input matrix structure
-   * @param[in]  pSrcB  points to the second input matrix structure
-   * @param[out] pDst   points to output matrix structure
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_cmplx_mult_q31(
-  const arm_matrix_instance_q31 * pSrcA,
-  const arm_matrix_instance_q31 * pSrcB,
-  arm_matrix_instance_q31 * pDst);
-
-
-  /**
-   * @brief Floating-point matrix transpose.
-   * @param[in]  pSrc  points to the input matrix
-   * @param[out] pDst  points to the output matrix
-   * @return    The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
-   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_trans_f32(
-  const arm_matrix_instance_f32 * pSrc,
-  arm_matrix_instance_f32 * pDst);
-
-
-  /**
-   * @brief Q15 matrix transpose.
-   * @param[in]  pSrc  points to the input matrix
-   * @param[out] pDst  points to the output matrix
-   * @return    The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
-   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_trans_q15(
-  const arm_matrix_instance_q15 * pSrc,
-  arm_matrix_instance_q15 * pDst);
-
-
-  /**
-   * @brief Q31 matrix transpose.
-   * @param[in]  pSrc  points to the input matrix
-   * @param[out] pDst  points to the output matrix
-   * @return    The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
-   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_trans_q31(
-  const arm_matrix_instance_q31 * pSrc,
-  arm_matrix_instance_q31 * pDst);
-
-
-  /**
-   * @brief Floating-point matrix multiplication
-   * @param[in]  pSrcA  points to the first input matrix structure
-   * @param[in]  pSrcB  points to the second input matrix structure
-   * @param[out] pDst   points to output matrix structure
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_mult_f32(
-  const arm_matrix_instance_f32 * pSrcA,
-  const arm_matrix_instance_f32 * pSrcB,
-  arm_matrix_instance_f32 * pDst);
-
-
-  /**
-   * @brief Q15 matrix multiplication
-   * @param[in]  pSrcA   points to the first input matrix structure
-   * @param[in]  pSrcB   points to the second input matrix structure
-   * @param[out] pDst    points to output matrix structure
-   * @param[in]  pState  points to the array for storing intermediate results
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_mult_q15(
-  const arm_matrix_instance_q15 * pSrcA,
-  const arm_matrix_instance_q15 * pSrcB,
-  arm_matrix_instance_q15 * pDst,
-  q15_t * pState);
-
-
-  /**
-   * @brief Q15 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
-   * @param[in]  pSrcA   points to the first input matrix structure
-   * @param[in]  pSrcB   points to the second input matrix structure
-   * @param[out] pDst    points to output matrix structure
-   * @param[in]  pState  points to the array for storing intermediate results
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_mult_fast_q15(
-  const arm_matrix_instance_q15 * pSrcA,
-  const arm_matrix_instance_q15 * pSrcB,
-  arm_matrix_instance_q15 * pDst,
-  q15_t * pState);
-
-
-  /**
-   * @brief Q31 matrix multiplication
-   * @param[in]  pSrcA  points to the first input matrix structure
-   * @param[in]  pSrcB  points to the second input matrix structure
-   * @param[out] pDst   points to output matrix structure
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_mult_q31(
-  const arm_matrix_instance_q31 * pSrcA,
-  const arm_matrix_instance_q31 * pSrcB,
-  arm_matrix_instance_q31 * pDst);
-
-
-  /**
-   * @brief Q31 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
-   * @param[in]  pSrcA  points to the first input matrix structure
-   * @param[in]  pSrcB  points to the second input matrix structure
-   * @param[out] pDst   points to output matrix structure
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_mult_fast_q31(
-  const arm_matrix_instance_q31 * pSrcA,
-  const arm_matrix_instance_q31 * pSrcB,
-  arm_matrix_instance_q31 * pDst);
-
-
-  /**
-   * @brief Floating-point matrix subtraction
-   * @param[in]  pSrcA  points to the first input matrix structure
-   * @param[in]  pSrcB  points to the second input matrix structure
-   * @param[out] pDst   points to output matrix structure
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_sub_f32(
-  const arm_matrix_instance_f32 * pSrcA,
-  const arm_matrix_instance_f32 * pSrcB,
-  arm_matrix_instance_f32 * pDst);
-
-
-  /**
-   * @brief Q15 matrix subtraction
-   * @param[in]  pSrcA  points to the first input matrix structure
-   * @param[in]  pSrcB  points to the second input matrix structure
-   * @param[out] pDst   points to output matrix structure
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_sub_q15(
-  const arm_matrix_instance_q15 * pSrcA,
-  const arm_matrix_instance_q15 * pSrcB,
-  arm_matrix_instance_q15 * pDst);
-
-
-  /**
-   * @brief Q31 matrix subtraction
-   * @param[in]  pSrcA  points to the first input matrix structure
-   * @param[in]  pSrcB  points to the second input matrix structure
-   * @param[out] pDst   points to output matrix structure
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_sub_q31(
-  const arm_matrix_instance_q31 * pSrcA,
-  const arm_matrix_instance_q31 * pSrcB,
-  arm_matrix_instance_q31 * pDst);
-
-
-  /**
-   * @brief Floating-point matrix scaling.
-   * @param[in]  pSrc   points to the input matrix
-   * @param[in]  scale  scale factor
-   * @param[out] pDst   points to the output matrix
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_scale_f32(
-  const arm_matrix_instance_f32 * pSrc,
-  float32_t scale,
-  arm_matrix_instance_f32 * pDst);
-
-
-  /**
-   * @brief Q15 matrix scaling.
-   * @param[in]  pSrc        points to input matrix
-   * @param[in]  scaleFract  fractional portion of the scale factor
-   * @param[in]  shift       number of bits to shift the result by
-   * @param[out] pDst        points to output matrix
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_scale_q15(
-  const arm_matrix_instance_q15 * pSrc,
-  q15_t scaleFract,
-  int32_t shift,
-  arm_matrix_instance_q15 * pDst);
-
-
-  /**
-   * @brief Q31 matrix scaling.
-   * @param[in]  pSrc        points to input matrix
-   * @param[in]  scaleFract  fractional portion of the scale factor
-   * @param[in]  shift       number of bits to shift the result by
-   * @param[out] pDst        points to output matrix structure
-   * @return     The function returns either
-   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
-   */
-  arm_status arm_mat_scale_q31(
-  const arm_matrix_instance_q31 * pSrc,
-  q31_t scaleFract,
-  int32_t shift,
-  arm_matrix_instance_q31 * pDst);
-
-
-  /**
-   * @brief  Q31 matrix initialization.
-   * @param[in,out] S         points to an instance of the floating-point matrix structure.
-   * @param[in]     nRows     number of rows in the matrix.
-   * @param[in]     nColumns  number of columns in the matrix.
-   * @param[in]     pData     points to the matrix data array.
-   */
-  void arm_mat_init_q31(
-  arm_matrix_instance_q31 * S,
-  uint16_t nRows,
-  uint16_t nColumns,
-  q31_t * pData);
-
-
-  /**
-   * @brief  Q15 matrix initialization.
-   * @param[in,out] S         points to an instance of the floating-point matrix structure.
-   * @param[in]     nRows     number of rows in the matrix.
-   * @param[in]     nColumns  number of columns in the matrix.
-   * @param[in]     pData     points to the matrix data array.
-   */
-  void arm_mat_init_q15(
-  arm_matrix_instance_q15 * S,
-  uint16_t nRows,
-  uint16_t nColumns,
-  q15_t * pData);
-
-
-  /**
-   * @brief  Floating-point matrix initialization.
-   * @param[in,out] S         points to an instance of the floating-point matrix structure.
-   * @param[in]     nRows     number of rows in the matrix.
-   * @param[in]     nColumns  number of columns in the matrix.
-   * @param[in]     pData     points to the matrix data array.
-   */
-  void arm_mat_init_f32(
-  arm_matrix_instance_f32 * S,
-  uint16_t nRows,
-  uint16_t nColumns,
-  float32_t * pData);
-
-
-
-  /**
-   * @brief Instance structure for the Q15 PID Control.
-   */
-  typedef struct
-  {
-    q15_t A0;           /**< The derived gain, A0 = Kp + Ki + Kd . */
-#ifdef ARM_MATH_CM0_FAMILY
-    q15_t A1;
-    q15_t A2;
-#else
-    q31_t A1;           /**< The derived gain A1 = -Kp - 2Kd | Kd.*/
-#endif
-    q15_t state[3];     /**< The state array of length 3. */
-    q15_t Kp;           /**< The proportional gain. */
-    q15_t Ki;           /**< The integral gain. */
-    q15_t Kd;           /**< The derivative gain. */
-  } arm_pid_instance_q15;
-
-  /**
-   * @brief Instance structure for the Q31 PID Control.
-   */
-  typedef struct
-  {
-    q31_t A0;            /**< The derived gain, A0 = Kp + Ki + Kd . */
-    q31_t A1;            /**< The derived gain, A1 = -Kp - 2Kd. */
-    q31_t A2;            /**< The derived gain, A2 = Kd . */
-    q31_t state[3];      /**< The state array of length 3. */
-    q31_t Kp;            /**< The proportional gain. */
-    q31_t Ki;            /**< The integral gain. */
-    q31_t Kd;            /**< The derivative gain. */
-  } arm_pid_instance_q31;
-
-  /**
-   * @brief Instance structure for the floating-point PID Control.
-   */
-  typedef struct
-  {
-    float32_t A0;          /**< The derived gain, A0 = Kp + Ki + Kd . */
-    float32_t A1;          /**< The derived gain, A1 = -Kp - 2Kd. */
-    float32_t A2;          /**< The derived gain, A2 = Kd . */
-    float32_t state[3];    /**< The state array of length 3. */
-    float32_t Kp;          /**< The proportional gain. */
-    float32_t Ki;          /**< The integral gain. */
-    float32_t Kd;          /**< The derivative gain. */
-  } arm_pid_instance_f32;
-
-
-
-  /**
-   * @brief  Initialization function for the floating-point PID Control.
-   * @param[in,out] S               points to an instance of the PID structure.
-   * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
-   */
-  void arm_pid_init_f32(
-  arm_pid_instance_f32 * S,
-  int32_t resetStateFlag);
-
-
-  /**
-   * @brief  Reset function for the floating-point PID Control.
-   * @param[in,out] S  is an instance of the floating-point PID Control structure
-   */
-  void arm_pid_reset_f32(
-  arm_pid_instance_f32 * S);
-
-
-  /**
-   * @brief  Initialization function for the Q31 PID Control.
-   * @param[in,out] S               points to an instance of the Q15 PID structure.
-   * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
-   */
-  void arm_pid_init_q31(
-  arm_pid_instance_q31 * S,
-  int32_t resetStateFlag);
-
-
-  /**
-   * @brief  Reset function for the Q31 PID Control.
-   * @param[in,out] S   points to an instance of the Q31 PID Control structure
-   */
-
-  void arm_pid_reset_q31(
-  arm_pid_instance_q31 * S);
-
-
-  /**
-   * @brief  Initialization function for the Q15 PID Control.
-   * @param[in,out] S               points to an instance of the Q15 PID structure.
-   * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
-   */
-  void arm_pid_init_q15(
-  arm_pid_instance_q15 * S,
-  int32_t resetStateFlag);
-
-
-  /**
-   * @brief  Reset function for the Q15 PID Control.
-   * @param[in,out] S  points to an instance of the q15 PID Control structure
-   */
-  void arm_pid_reset_q15(
-  arm_pid_instance_q15 * S);
-
-
-  /**
-   * @brief Instance structure for the floating-point Linear Interpolate function.
-   */
-  typedef struct
-  {
-    uint32_t nValues;           /**< nValues */
-    float32_t x1;               /**< x1 */
-    float32_t xSpacing;         /**< xSpacing */
-    float32_t *pYData;          /**< pointer to the table of Y values */
-  } arm_linear_interp_instance_f32;
-
-  /**
-   * @brief Instance structure for the floating-point bilinear interpolation function.
-   */
-  typedef struct
-  {
-    uint16_t numRows;   /**< number of rows in the data table. */
-    uint16_t numCols;   /**< number of columns in the data table. */
-    float32_t *pData;   /**< points to the data table. */
-  } arm_bilinear_interp_instance_f32;
-
-   /**
-   * @brief Instance structure for the Q31 bilinear interpolation function.
-   */
-  typedef struct
-  {
-    uint16_t numRows;   /**< number of rows in the data table. */
-    uint16_t numCols;   /**< number of columns in the data table. */
-    q31_t *pData;       /**< points to the data table. */
-  } arm_bilinear_interp_instance_q31;
-
-   /**
-   * @brief Instance structure for the Q15 bilinear interpolation function.
-   */
-  typedef struct
-  {
-    uint16_t numRows;   /**< number of rows in the data table. */
-    uint16_t numCols;   /**< number of columns in the data table. */
-    q15_t *pData;       /**< points to the data table. */
-  } arm_bilinear_interp_instance_q15;
-
-   /**
-   * @brief Instance structure for the Q15 bilinear interpolation function.
-   */
-  typedef struct
-  {
-    uint16_t numRows;   /**< number of rows in the data table. */
-    uint16_t numCols;   /**< number of columns in the data table. */
-    q7_t *pData;        /**< points to the data table. */
-  } arm_bilinear_interp_instance_q7;
-
-
-  /**
-   * @brief Q7 vector multiplication.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_mult_q7(
-  q7_t * pSrcA,
-  q7_t * pSrcB,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Q15 vector multiplication.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_mult_q15(
-  q15_t * pSrcA,
-  q15_t * pSrcB,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Q31 vector multiplication.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_mult_q31(
-  q31_t * pSrcA,
-  q31_t * pSrcB,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Floating-point vector multiplication.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_mult_f32(
-  float32_t * pSrcA,
-  float32_t * pSrcB,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Instance structure for the Q15 CFFT/CIFFT function.
-   */
-  typedef struct
-  {
-    uint16_t fftLen;                 /**< length of the FFT. */
-    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
-    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
-    q15_t *pTwiddle;                 /**< points to the Sin twiddle factor table. */
-    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
-    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
-    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
-  } arm_cfft_radix2_instance_q15;
-
-/* Deprecated */
-  arm_status arm_cfft_radix2_init_q15(
-  arm_cfft_radix2_instance_q15 * S,
-  uint16_t fftLen,
-  uint8_t ifftFlag,
-  uint8_t bitReverseFlag);
-
-/* Deprecated */
-  void arm_cfft_radix2_q15(
-  const arm_cfft_radix2_instance_q15 * S,
-  q15_t * pSrc);
-
-
-  /**
-   * @brief Instance structure for the Q15 CFFT/CIFFT function.
-   */
-  typedef struct
-  {
-    uint16_t fftLen;                 /**< length of the FFT. */
-    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
-    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
-    q15_t *pTwiddle;                 /**< points to the twiddle factor table. */
-    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
-    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
-    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
-  } arm_cfft_radix4_instance_q15;
-
-/* Deprecated */
-  arm_status arm_cfft_radix4_init_q15(
-  arm_cfft_radix4_instance_q15 * S,
-  uint16_t fftLen,
-  uint8_t ifftFlag,
-  uint8_t bitReverseFlag);
-
-/* Deprecated */
-  void arm_cfft_radix4_q15(
-  const arm_cfft_radix4_instance_q15 * S,
-  q15_t * pSrc);
-
-  /**
-   * @brief Instance structure for the Radix-2 Q31 CFFT/CIFFT function.
-   */
-  typedef struct
-  {
-    uint16_t fftLen;                 /**< length of the FFT. */
-    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
-    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
-    q31_t *pTwiddle;                 /**< points to the Twiddle factor table. */
-    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
-    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
-    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
-  } arm_cfft_radix2_instance_q31;
-
-/* Deprecated */
-  arm_status arm_cfft_radix2_init_q31(
-  arm_cfft_radix2_instance_q31 * S,
-  uint16_t fftLen,
-  uint8_t ifftFlag,
-  uint8_t bitReverseFlag);
-
-/* Deprecated */
-  void arm_cfft_radix2_q31(
-  const arm_cfft_radix2_instance_q31 * S,
-  q31_t * pSrc);
-
-  /**
-   * @brief Instance structure for the Q31 CFFT/CIFFT function.
-   */
-  typedef struct
-  {
-    uint16_t fftLen;                 /**< length of the FFT. */
-    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
-    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
-    q31_t *pTwiddle;                 /**< points to the twiddle factor table. */
-    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
-    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
-    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
-  } arm_cfft_radix4_instance_q31;
-
-/* Deprecated */
-  void arm_cfft_radix4_q31(
-  const arm_cfft_radix4_instance_q31 * S,
-  q31_t * pSrc);
-
-/* Deprecated */
-  arm_status arm_cfft_radix4_init_q31(
-  arm_cfft_radix4_instance_q31 * S,
-  uint16_t fftLen,
-  uint8_t ifftFlag,
-  uint8_t bitReverseFlag);
-
-  /**
-   * @brief Instance structure for the floating-point CFFT/CIFFT function.
-   */
-  typedef struct
-  {
-    uint16_t fftLen;                   /**< length of the FFT. */
-    uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
-    uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
-    float32_t *pTwiddle;               /**< points to the Twiddle factor table. */
-    uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
-    uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
-    uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
-    float32_t onebyfftLen;             /**< value of 1/fftLen. */
-  } arm_cfft_radix2_instance_f32;
-
-/* Deprecated */
-  arm_status arm_cfft_radix2_init_f32(
-  arm_cfft_radix2_instance_f32 * S,
-  uint16_t fftLen,
-  uint8_t ifftFlag,
-  uint8_t bitReverseFlag);
-
-/* Deprecated */
-  void arm_cfft_radix2_f32(
-  const arm_cfft_radix2_instance_f32 * S,
-  float32_t * pSrc);
-
-  /**
-   * @brief Instance structure for the floating-point CFFT/CIFFT function.
-   */
-  typedef struct
-  {
-    uint16_t fftLen;                   /**< length of the FFT. */
-    uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
-    uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
-    float32_t *pTwiddle;               /**< points to the Twiddle factor table. */
-    uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
-    uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
-    uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
-    float32_t onebyfftLen;             /**< value of 1/fftLen. */
-  } arm_cfft_radix4_instance_f32;
-
-/* Deprecated */
-  arm_status arm_cfft_radix4_init_f32(
-  arm_cfft_radix4_instance_f32 * S,
-  uint16_t fftLen,
-  uint8_t ifftFlag,
-  uint8_t bitReverseFlag);
-
-/* Deprecated */
-  void arm_cfft_radix4_f32(
-  const arm_cfft_radix4_instance_f32 * S,
-  float32_t * pSrc);
-
-  /**
-   * @brief Instance structure for the fixed-point CFFT/CIFFT function.
-   */
-  typedef struct
-  {
-    uint16_t fftLen;                   /**< length of the FFT. */
-    const q15_t *pTwiddle;             /**< points to the Twiddle factor table. */
-    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
-    uint16_t bitRevLength;             /**< bit reversal table length. */
-  } arm_cfft_instance_q15;
-
-void arm_cfft_q15(
-    const arm_cfft_instance_q15 * S,
-    q15_t * p1,
-    uint8_t ifftFlag,
-    uint8_t bitReverseFlag);
-
-  /**
-   * @brief Instance structure for the fixed-point CFFT/CIFFT function.
-   */
-  typedef struct
-  {
-    uint16_t fftLen;                   /**< length of the FFT. */
-    const q31_t *pTwiddle;             /**< points to the Twiddle factor table. */
-    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
-    uint16_t bitRevLength;             /**< bit reversal table length. */
-  } arm_cfft_instance_q31;
-
-void arm_cfft_q31(
-    const arm_cfft_instance_q31 * S,
-    q31_t * p1,
-    uint8_t ifftFlag,
-    uint8_t bitReverseFlag);
-
-  /**
-   * @brief Instance structure for the floating-point CFFT/CIFFT function.
-   */
-  typedef struct
-  {
-    uint16_t fftLen;                   /**< length of the FFT. */
-    const float32_t *pTwiddle;         /**< points to the Twiddle factor table. */
-    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
-    uint16_t bitRevLength;             /**< bit reversal table length. */
-  } arm_cfft_instance_f32;
-
-  void arm_cfft_f32(
-  const arm_cfft_instance_f32 * S,
-  float32_t * p1,
-  uint8_t ifftFlag,
-  uint8_t bitReverseFlag);
-
-  /**
-   * @brief Instance structure for the Q15 RFFT/RIFFT function.
-   */
-  typedef struct
-  {
-    uint32_t fftLenReal;                      /**< length of the real FFT. */
-    uint8_t ifftFlagR;                        /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
-    uint8_t bitReverseFlagR;                  /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
-    uint32_t twidCoefRModifier;               /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
-    q15_t *pTwiddleAReal;                     /**< points to the real twiddle factor table. */
-    q15_t *pTwiddleBReal;                     /**< points to the imag twiddle factor table. */
-    const arm_cfft_instance_q15 *pCfft;       /**< points to the complex FFT instance. */
-  } arm_rfft_instance_q15;
-
-  arm_status arm_rfft_init_q15(
-  arm_rfft_instance_q15 * S,
-  uint32_t fftLenReal,
-  uint32_t ifftFlagR,
-  uint32_t bitReverseFlag);
-
-  void arm_rfft_q15(
-  const arm_rfft_instance_q15 * S,
-  q15_t * pSrc,
-  q15_t * pDst);
-
-  /**
-   * @brief Instance structure for the Q31 RFFT/RIFFT function.
-   */
-  typedef struct
-  {
-    uint32_t fftLenReal;                        /**< length of the real FFT. */
-    uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
-    uint8_t bitReverseFlagR;                    /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
-    uint32_t twidCoefRModifier;                 /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
-    q31_t *pTwiddleAReal;                       /**< points to the real twiddle factor table. */
-    q31_t *pTwiddleBReal;                       /**< points to the imag twiddle factor table. */
-    const arm_cfft_instance_q31 *pCfft;         /**< points to the complex FFT instance. */
-  } arm_rfft_instance_q31;
-
-  arm_status arm_rfft_init_q31(
-  arm_rfft_instance_q31 * S,
-  uint32_t fftLenReal,
-  uint32_t ifftFlagR,
-  uint32_t bitReverseFlag);
-
-  void arm_rfft_q31(
-  const arm_rfft_instance_q31 * S,
-  q31_t * pSrc,
-  q31_t * pDst);
-
-  /**
-   * @brief Instance structure for the floating-point RFFT/RIFFT function.
-   */
-  typedef struct
-  {
-    uint32_t fftLenReal;                        /**< length of the real FFT. */
-    uint16_t fftLenBy2;                         /**< length of the complex FFT. */
-    uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
-    uint8_t bitReverseFlagR;                    /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
-    uint32_t twidCoefRModifier;                     /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
-    float32_t *pTwiddleAReal;                   /**< points to the real twiddle factor table. */
-    float32_t *pTwiddleBReal;                   /**< points to the imag twiddle factor table. */
-    arm_cfft_radix4_instance_f32 *pCfft;        /**< points to the complex FFT instance. */
-  } arm_rfft_instance_f32;
-
-  arm_status arm_rfft_init_f32(
-  arm_rfft_instance_f32 * S,
-  arm_cfft_radix4_instance_f32 * S_CFFT,
-  uint32_t fftLenReal,
-  uint32_t ifftFlagR,
-  uint32_t bitReverseFlag);
-
-  void arm_rfft_f32(
-  const arm_rfft_instance_f32 * S,
-  float32_t * pSrc,
-  float32_t * pDst);
-
-  /**
-   * @brief Instance structure for the floating-point RFFT/RIFFT function.
-   */
-typedef struct
-  {
-    arm_cfft_instance_f32 Sint;      /**< Internal CFFT structure. */
-    uint16_t fftLenRFFT;             /**< length of the real sequence */
-    float32_t * pTwiddleRFFT;        /**< Twiddle factors real stage  */
-  } arm_rfft_fast_instance_f32 ;
-
-arm_status arm_rfft_fast_init_f32 (
-   arm_rfft_fast_instance_f32 * S,
-   uint16_t fftLen);
-
-void arm_rfft_fast_f32(
-  arm_rfft_fast_instance_f32 * S,
-  float32_t * p, float32_t * pOut,
-  uint8_t ifftFlag);
-
-  /**
-   * @brief Instance structure for the floating-point DCT4/IDCT4 function.
-   */
-  typedef struct
-  {
-    uint16_t N;                          /**< length of the DCT4. */
-    uint16_t Nby2;                       /**< half of the length of the DCT4. */
-    float32_t normalize;                 /**< normalizing factor. */
-    float32_t *pTwiddle;                 /**< points to the twiddle factor table. */
-    float32_t *pCosFactor;               /**< points to the cosFactor table. */
-    arm_rfft_instance_f32 *pRfft;        /**< points to the real FFT instance. */
-    arm_cfft_radix4_instance_f32 *pCfft; /**< points to the complex FFT instance. */
-  } arm_dct4_instance_f32;
-
-
-  /**
-   * @brief  Initialization function for the floating-point DCT4/IDCT4.
-   * @param[in,out] S          points to an instance of floating-point DCT4/IDCT4 structure.
-   * @param[in]     S_RFFT     points to an instance of floating-point RFFT/RIFFT structure.
-   * @param[in]     S_CFFT     points to an instance of floating-point CFFT/CIFFT structure.
-   * @param[in]     N          length of the DCT4.
-   * @param[in]     Nby2       half of the length of the DCT4.
-   * @param[in]     normalize  normalizing factor.
-   * @return      arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported transform length.
-   */
-  arm_status arm_dct4_init_f32(
-  arm_dct4_instance_f32 * S,
-  arm_rfft_instance_f32 * S_RFFT,
-  arm_cfft_radix4_instance_f32 * S_CFFT,
-  uint16_t N,
-  uint16_t Nby2,
-  float32_t normalize);
-
-
-  /**
-   * @brief Processing function for the floating-point DCT4/IDCT4.
-   * @param[in]     S              points to an instance of the floating-point DCT4/IDCT4 structure.
-   * @param[in]     pState         points to state buffer.
-   * @param[in,out] pInlineBuffer  points to the in-place input and output buffer.
-   */
-  void arm_dct4_f32(
-  const arm_dct4_instance_f32 * S,
-  float32_t * pState,
-  float32_t * pInlineBuffer);
-
-
-  /**
-   * @brief Instance structure for the Q31 DCT4/IDCT4 function.
-   */
-  typedef struct
-  {
-    uint16_t N;                          /**< length of the DCT4. */
-    uint16_t Nby2;                       /**< half of the length of the DCT4. */
-    q31_t normalize;                     /**< normalizing factor. */
-    q31_t *pTwiddle;                     /**< points to the twiddle factor table. */
-    q31_t *pCosFactor;                   /**< points to the cosFactor table. */
-    arm_rfft_instance_q31 *pRfft;        /**< points to the real FFT instance. */
-    arm_cfft_radix4_instance_q31 *pCfft; /**< points to the complex FFT instance. */
-  } arm_dct4_instance_q31;
-
-
-  /**
-   * @brief  Initialization function for the Q31 DCT4/IDCT4.
-   * @param[in,out] S          points to an instance of Q31 DCT4/IDCT4 structure.
-   * @param[in]     S_RFFT     points to an instance of Q31 RFFT/RIFFT structure
-   * @param[in]     S_CFFT     points to an instance of Q31 CFFT/CIFFT structure
-   * @param[in]     N          length of the DCT4.
-   * @param[in]     Nby2       half of the length of the DCT4.
-   * @param[in]     normalize  normalizing factor.
-   * @return      arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
-   */
-  arm_status arm_dct4_init_q31(
-  arm_dct4_instance_q31 * S,
-  arm_rfft_instance_q31 * S_RFFT,
-  arm_cfft_radix4_instance_q31 * S_CFFT,
-  uint16_t N,
-  uint16_t Nby2,
-  q31_t normalize);
-
-
-  /**
-   * @brief Processing function for the Q31 DCT4/IDCT4.
-   * @param[in]     S              points to an instance of the Q31 DCT4 structure.
-   * @param[in]     pState         points to state buffer.
-   * @param[in,out] pInlineBuffer  points to the in-place input and output buffer.
-   */
-  void arm_dct4_q31(
-  const arm_dct4_instance_q31 * S,
-  q31_t * pState,
-  q31_t * pInlineBuffer);
-
-
-  /**
-   * @brief Instance structure for the Q15 DCT4/IDCT4 function.
-   */
-  typedef struct
-  {
-    uint16_t N;                          /**< length of the DCT4. */
-    uint16_t Nby2;                       /**< half of the length of the DCT4. */
-    q15_t normalize;                     /**< normalizing factor. */
-    q15_t *pTwiddle;                     /**< points to the twiddle factor table. */
-    q15_t *pCosFactor;                   /**< points to the cosFactor table. */
-    arm_rfft_instance_q15 *pRfft;        /**< points to the real FFT instance. */
-    arm_cfft_radix4_instance_q15 *pCfft; /**< points to the complex FFT instance. */
-  } arm_dct4_instance_q15;
-
-
-  /**
-   * @brief  Initialization function for the Q15 DCT4/IDCT4.
-   * @param[in,out] S          points to an instance of Q15 DCT4/IDCT4 structure.
-   * @param[in]     S_RFFT     points to an instance of Q15 RFFT/RIFFT structure.
-   * @param[in]     S_CFFT     points to an instance of Q15 CFFT/CIFFT structure.
-   * @param[in]     N          length of the DCT4.
-   * @param[in]     Nby2       half of the length of the DCT4.
-   * @param[in]     normalize  normalizing factor.
-   * @return      arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
-   */
-  arm_status arm_dct4_init_q15(
-  arm_dct4_instance_q15 * S,
-  arm_rfft_instance_q15 * S_RFFT,
-  arm_cfft_radix4_instance_q15 * S_CFFT,
-  uint16_t N,
-  uint16_t Nby2,
-  q15_t normalize);
-
-
-  /**
-   * @brief Processing function for the Q15 DCT4/IDCT4.
-   * @param[in]     S              points to an instance of the Q15 DCT4 structure.
-   * @param[in]     pState         points to state buffer.
-   * @param[in,out] pInlineBuffer  points to the in-place input and output buffer.
-   */
-  void arm_dct4_q15(
-  const arm_dct4_instance_q15 * S,
-  q15_t * pState,
-  q15_t * pInlineBuffer);
-
-
-  /**
-   * @brief Floating-point vector addition.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_add_f32(
-  float32_t * pSrcA,
-  float32_t * pSrcB,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Q7 vector addition.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_add_q7(
-  q7_t * pSrcA,
-  q7_t * pSrcB,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Q15 vector addition.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_add_q15(
-  q15_t * pSrcA,
-  q15_t * pSrcB,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Q31 vector addition.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_add_q31(
-  q31_t * pSrcA,
-  q31_t * pSrcB,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Floating-point vector subtraction.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_sub_f32(
-  float32_t * pSrcA,
-  float32_t * pSrcB,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Q7 vector subtraction.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_sub_q7(
-  q7_t * pSrcA,
-  q7_t * pSrcB,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Q15 vector subtraction.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_sub_q15(
-  q15_t * pSrcA,
-  q15_t * pSrcB,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Q31 vector subtraction.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_sub_q31(
-  q31_t * pSrcA,
-  q31_t * pSrcB,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Multiplies a floating-point vector by a scalar.
-   * @param[in]  pSrc       points to the input vector
-   * @param[in]  scale      scale factor to be applied
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in the vector
-   */
-  void arm_scale_f32(
-  float32_t * pSrc,
-  float32_t scale,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Multiplies a Q7 vector by a scalar.
-   * @param[in]  pSrc        points to the input vector
-   * @param[in]  scaleFract  fractional portion of the scale value
-   * @param[in]  shift       number of bits to shift the result by
-   * @param[out] pDst        points to the output vector
-   * @param[in]  blockSize   number of samples in the vector
-   */
-  void arm_scale_q7(
-  q7_t * pSrc,
-  q7_t scaleFract,
-  int8_t shift,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Multiplies a Q15 vector by a scalar.
-   * @param[in]  pSrc        points to the input vector
-   * @param[in]  scaleFract  fractional portion of the scale value
-   * @param[in]  shift       number of bits to shift the result by
-   * @param[out] pDst        points to the output vector
-   * @param[in]  blockSize   number of samples in the vector
-   */
-  void arm_scale_q15(
-  q15_t * pSrc,
-  q15_t scaleFract,
-  int8_t shift,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Multiplies a Q31 vector by a scalar.
-   * @param[in]  pSrc        points to the input vector
-   * @param[in]  scaleFract  fractional portion of the scale value
-   * @param[in]  shift       number of bits to shift the result by
-   * @param[out] pDst        points to the output vector
-   * @param[in]  blockSize   number of samples in the vector
-   */
-  void arm_scale_q31(
-  q31_t * pSrc,
-  q31_t scaleFract,
-  int8_t shift,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Q7 vector absolute value.
-   * @param[in]  pSrc       points to the input buffer
-   * @param[out] pDst       points to the output buffer
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_abs_q7(
-  q7_t * pSrc,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Floating-point vector absolute value.
-   * @param[in]  pSrc       points to the input buffer
-   * @param[out] pDst       points to the output buffer
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_abs_f32(
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Q15 vector absolute value.
-   * @param[in]  pSrc       points to the input buffer
-   * @param[out] pDst       points to the output buffer
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_abs_q15(
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Q31 vector absolute value.
-   * @param[in]  pSrc       points to the input buffer
-   * @param[out] pDst       points to the output buffer
-   * @param[in]  blockSize  number of samples in each vector
-   */
-  void arm_abs_q31(
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Dot product of floating-point vectors.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[in]  blockSize  number of samples in each vector
-   * @param[out] result     output result returned here
-   */
-  void arm_dot_prod_f32(
-  float32_t * pSrcA,
-  float32_t * pSrcB,
-  uint32_t blockSize,
-  float32_t * result);
-
-
-  /**
-   * @brief Dot product of Q7 vectors.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[in]  blockSize  number of samples in each vector
-   * @param[out] result     output result returned here
-   */
-  void arm_dot_prod_q7(
-  q7_t * pSrcA,
-  q7_t * pSrcB,
-  uint32_t blockSize,
-  q31_t * result);
-
-
-  /**
-   * @brief Dot product of Q15 vectors.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[in]  blockSize  number of samples in each vector
-   * @param[out] result     output result returned here
-   */
-  void arm_dot_prod_q15(
-  q15_t * pSrcA,
-  q15_t * pSrcB,
-  uint32_t blockSize,
-  q63_t * result);
-
-
-  /**
-   * @brief Dot product of Q31 vectors.
-   * @param[in]  pSrcA      points to the first input vector
-   * @param[in]  pSrcB      points to the second input vector
-   * @param[in]  blockSize  number of samples in each vector
-   * @param[out] result     output result returned here
-   */
-  void arm_dot_prod_q31(
-  q31_t * pSrcA,
-  q31_t * pSrcB,
-  uint32_t blockSize,
-  q63_t * result);
-
-
-  /**
-   * @brief  Shifts the elements of a Q7 vector a specified number of bits.
-   * @param[in]  pSrc       points to the input vector
-   * @param[in]  shiftBits  number of bits to shift.  A positive value shifts left; a negative value shifts right.
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in the vector
-   */
-  void arm_shift_q7(
-  q7_t * pSrc,
-  int8_t shiftBits,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Shifts the elements of a Q15 vector a specified number of bits.
-   * @param[in]  pSrc       points to the input vector
-   * @param[in]  shiftBits  number of bits to shift.  A positive value shifts left; a negative value shifts right.
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in the vector
-   */
-  void arm_shift_q15(
-  q15_t * pSrc,
-  int8_t shiftBits,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Shifts the elements of a Q31 vector a specified number of bits.
-   * @param[in]  pSrc       points to the input vector
-   * @param[in]  shiftBits  number of bits to shift.  A positive value shifts left; a negative value shifts right.
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in the vector
-   */
-  void arm_shift_q31(
-  q31_t * pSrc,
-  int8_t shiftBits,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Adds a constant offset to a floating-point vector.
-   * @param[in]  pSrc       points to the input vector
-   * @param[in]  offset     is the offset to be added
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in the vector
-   */
-  void arm_offset_f32(
-  float32_t * pSrc,
-  float32_t offset,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Adds a constant offset to a Q7 vector.
-   * @param[in]  pSrc       points to the input vector
-   * @param[in]  offset     is the offset to be added
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in the vector
-   */
-  void arm_offset_q7(
-  q7_t * pSrc,
-  q7_t offset,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Adds a constant offset to a Q15 vector.
-   * @param[in]  pSrc       points to the input vector
-   * @param[in]  offset     is the offset to be added
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in the vector
-   */
-  void arm_offset_q15(
-  q15_t * pSrc,
-  q15_t offset,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Adds a constant offset to a Q31 vector.
-   * @param[in]  pSrc       points to the input vector
-   * @param[in]  offset     is the offset to be added
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in the vector
-   */
-  void arm_offset_q31(
-  q31_t * pSrc,
-  q31_t offset,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Negates the elements of a floating-point vector.
-   * @param[in]  pSrc       points to the input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in the vector
-   */
-  void arm_negate_f32(
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Negates the elements of a Q7 vector.
-   * @param[in]  pSrc       points to the input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in the vector
-   */
-  void arm_negate_q7(
-  q7_t * pSrc,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Negates the elements of a Q15 vector.
-   * @param[in]  pSrc       points to the input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in the vector
-   */
-  void arm_negate_q15(
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Negates the elements of a Q31 vector.
-   * @param[in]  pSrc       points to the input vector
-   * @param[out] pDst       points to the output vector
-   * @param[in]  blockSize  number of samples in the vector
-   */
-  void arm_negate_q31(
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Copies the elements of a floating-point vector.
-   * @param[in]  pSrc       input pointer
-   * @param[out] pDst       output pointer
-   * @param[in]  blockSize  number of samples to process
-   */
-  void arm_copy_f32(
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Copies the elements of a Q7 vector.
-   * @param[in]  pSrc       input pointer
-   * @param[out] pDst       output pointer
-   * @param[in]  blockSize  number of samples to process
-   */
-  void arm_copy_q7(
-  q7_t * pSrc,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Copies the elements of a Q15 vector.
-   * @param[in]  pSrc       input pointer
-   * @param[out] pDst       output pointer
-   * @param[in]  blockSize  number of samples to process
-   */
-  void arm_copy_q15(
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Copies the elements of a Q31 vector.
-   * @param[in]  pSrc       input pointer
-   * @param[out] pDst       output pointer
-   * @param[in]  blockSize  number of samples to process
-   */
-  void arm_copy_q31(
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Fills a constant value into a floating-point vector.
-   * @param[in]  value      input value to be filled
-   * @param[out] pDst       output pointer
-   * @param[in]  blockSize  number of samples to process
-   */
-  void arm_fill_f32(
-  float32_t value,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Fills a constant value into a Q7 vector.
-   * @param[in]  value      input value to be filled
-   * @param[out] pDst       output pointer
-   * @param[in]  blockSize  number of samples to process
-   */
-  void arm_fill_q7(
-  q7_t value,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Fills a constant value into a Q15 vector.
-   * @param[in]  value      input value to be filled
-   * @param[out] pDst       output pointer
-   * @param[in]  blockSize  number of samples to process
-   */
-  void arm_fill_q15(
-  q15_t value,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Fills a constant value into a Q31 vector.
-   * @param[in]  value      input value to be filled
-   * @param[out] pDst       output pointer
-   * @param[in]  blockSize  number of samples to process
-   */
-  void arm_fill_q31(
-  q31_t value,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-/**
- * @brief Convolution of floating-point sequences.
- * @param[in]  pSrcA    points to the first input sequence.
- * @param[in]  srcALen  length of the first input sequence.
- * @param[in]  pSrcB    points to the second input sequence.
- * @param[in]  srcBLen  length of the second input sequence.
- * @param[out] pDst     points to the location where the output result is written.  Length srcALen+srcBLen-1.
- */
-  void arm_conv_f32(
-  float32_t * pSrcA,
-  uint32_t srcALen,
-  float32_t * pSrcB,
-  uint32_t srcBLen,
-  float32_t * pDst);
-
-
-  /**
-   * @brief Convolution of Q15 sequences.
-   * @param[in]  pSrcA      points to the first input sequence.
-   * @param[in]  srcALen    length of the first input sequence.
-   * @param[in]  pSrcB      points to the second input sequence.
-   * @param[in]  srcBLen    length of the second input sequence.
-   * @param[out] pDst       points to the block of output data  Length srcALen+srcBLen-1.
-   * @param[in]  pScratch1  points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
-   * @param[in]  pScratch2  points to scratch buffer of size min(srcALen, srcBLen).
-   */
-  void arm_conv_opt_q15(
-  q15_t * pSrcA,
-  uint32_t srcALen,
-  q15_t * pSrcB,
-  uint32_t srcBLen,
-  q15_t * pDst,
-  q15_t * pScratch1,
-  q15_t * pScratch2);
-
-
-/**
- * @brief Convolution of Q15 sequences.
- * @param[in]  pSrcA    points to the first input sequence.
- * @param[in]  srcALen  length of the first input sequence.
- * @param[in]  pSrcB    points to the second input sequence.
- * @param[in]  srcBLen  length of the second input sequence.
- * @param[out] pDst     points to the location where the output result is written.  Length srcALen+srcBLen-1.
- */
-  void arm_conv_q15(
-  q15_t * pSrcA,
-  uint32_t srcALen,
-  q15_t * pSrcB,
-  uint32_t srcBLen,
-  q15_t * pDst);
-
-
-  /**
-   * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
-   * @param[in]  pSrcA    points to the first input sequence.
-   * @param[in]  srcALen  length of the first input sequence.
-   * @param[in]  pSrcB    points to the second input sequence.
-   * @param[in]  srcBLen  length of the second input sequence.
-   * @param[out] pDst     points to the block of output data  Length srcALen+srcBLen-1.
-   */
-  void arm_conv_fast_q15(
-          q15_t * pSrcA,
-          uint32_t srcALen,
-          q15_t * pSrcB,
-          uint32_t srcBLen,
-          q15_t * pDst);
-
-
-  /**
-   * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
-   * @param[in]  pSrcA      points to the first input sequence.
-   * @param[in]  srcALen    length of the first input sequence.
-   * @param[in]  pSrcB      points to the second input sequence.
-   * @param[in]  srcBLen    length of the second input sequence.
-   * @param[out] pDst       points to the block of output data  Length srcALen+srcBLen-1.
-   * @param[in]  pScratch1  points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
-   * @param[in]  pScratch2  points to scratch buffer of size min(srcALen, srcBLen).
-   */
-  void arm_conv_fast_opt_q15(
-  q15_t * pSrcA,
-  uint32_t srcALen,
-  q15_t * pSrcB,
-  uint32_t srcBLen,
-  q15_t * pDst,
-  q15_t * pScratch1,
-  q15_t * pScratch2);
-
-
-  /**
-   * @brief Convolution of Q31 sequences.
-   * @param[in]  pSrcA    points to the first input sequence.
-   * @param[in]  srcALen  length of the first input sequence.
-   * @param[in]  pSrcB    points to the second input sequence.
-   * @param[in]  srcBLen  length of the second input sequence.
-   * @param[out] pDst     points to the block of output data  Length srcALen+srcBLen-1.
-   */
-  void arm_conv_q31(
-  q31_t * pSrcA,
-  uint32_t srcALen,
-  q31_t * pSrcB,
-  uint32_t srcBLen,
-  q31_t * pDst);
-
-
-  /**
-   * @brief Convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
-   * @param[in]  pSrcA    points to the first input sequence.
-   * @param[in]  srcALen  length of the first input sequence.
-   * @param[in]  pSrcB    points to the second input sequence.
-   * @param[in]  srcBLen  length of the second input sequence.
-   * @param[out] pDst     points to the block of output data  Length srcALen+srcBLen-1.
-   */
-  void arm_conv_fast_q31(
-  q31_t * pSrcA,
-  uint32_t srcALen,
-  q31_t * pSrcB,
-  uint32_t srcBLen,
-  q31_t * pDst);
-
-
-    /**
-   * @brief Convolution of Q7 sequences.
-   * @param[in]  pSrcA      points to the first input sequence.
-   * @param[in]  srcALen    length of the first input sequence.
-   * @param[in]  pSrcB      points to the second input sequence.
-   * @param[in]  srcBLen    length of the second input sequence.
-   * @param[out] pDst       points to the block of output data  Length srcALen+srcBLen-1.
-   * @param[in]  pScratch1  points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
-   * @param[in]  pScratch2  points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
-   */
-  void arm_conv_opt_q7(
-  q7_t * pSrcA,
-  uint32_t srcALen,
-  q7_t * pSrcB,
-  uint32_t srcBLen,
-  q7_t * pDst,
-  q15_t * pScratch1,
-  q15_t * pScratch2);
-
-
-  /**
-   * @brief Convolution of Q7 sequences.
-   * @param[in]  pSrcA    points to the first input sequence.
-   * @param[in]  srcALen  length of the first input sequence.
-   * @param[in]  pSrcB    points to the second input sequence.
-   * @param[in]  srcBLen  length of the second input sequence.
-   * @param[out] pDst     points to the block of output data  Length srcALen+srcBLen-1.
-   */
-  void arm_conv_q7(
-  q7_t * pSrcA,
-  uint32_t srcALen,
-  q7_t * pSrcB,
-  uint32_t srcBLen,
-  q7_t * pDst);
-
-
-  /**
-   * @brief Partial convolution of floating-point sequences.
-   * @param[in]  pSrcA       points to the first input sequence.
-   * @param[in]  srcALen     length of the first input sequence.
-   * @param[in]  pSrcB       points to the second input sequence.
-   * @param[in]  srcBLen     length of the second input sequence.
-   * @param[out] pDst        points to the block of output data
-   * @param[in]  firstIndex  is the first output sample to start with.
-   * @param[in]  numPoints   is the number of output points to be computed.
-   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
-   */
-  arm_status arm_conv_partial_f32(
-  float32_t * pSrcA,
-  uint32_t srcALen,
-  float32_t * pSrcB,
-  uint32_t srcBLen,
-  float32_t * pDst,
-  uint32_t firstIndex,
-  uint32_t numPoints);
-
-
-  /**
-   * @brief Partial convolution of Q15 sequences.
-   * @param[in]  pSrcA       points to the first input sequence.
-   * @param[in]  srcALen     length of the first input sequence.
-   * @param[in]  pSrcB       points to the second input sequence.
-   * @param[in]  srcBLen     length of the second input sequence.
-   * @param[out] pDst        points to the block of output data
-   * @param[in]  firstIndex  is the first output sample to start with.
-   * @param[in]  numPoints   is the number of output points to be computed.
-   * @param[in]  pScratch1   points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
-   * @param[in]  pScratch2   points to scratch buffer of size min(srcALen, srcBLen).
-   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
-   */
-  arm_status arm_conv_partial_opt_q15(
-  q15_t * pSrcA,
-  uint32_t srcALen,
-  q15_t * pSrcB,
-  uint32_t srcBLen,
-  q15_t * pDst,
-  uint32_t firstIndex,
-  uint32_t numPoints,
-  q15_t * pScratch1,
-  q15_t * pScratch2);
-
-
-  /**
-   * @brief Partial convolution of Q15 sequences.
-   * @param[in]  pSrcA       points to the first input sequence.
-   * @param[in]  srcALen     length of the first input sequence.
-   * @param[in]  pSrcB       points to the second input sequence.
-   * @param[in]  srcBLen     length of the second input sequence.
-   * @param[out] pDst        points to the block of output data
-   * @param[in]  firstIndex  is the first output sample to start with.
-   * @param[in]  numPoints   is the number of output points to be computed.
-   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
-   */
-  arm_status arm_conv_partial_q15(
-  q15_t * pSrcA,
-  uint32_t srcALen,
-  q15_t * pSrcB,
-  uint32_t srcBLen,
-  q15_t * pDst,
-  uint32_t firstIndex,
-  uint32_t numPoints);
-
-
-  /**
-   * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
-   * @param[in]  pSrcA       points to the first input sequence.
-   * @param[in]  srcALen     length of the first input sequence.
-   * @param[in]  pSrcB       points to the second input sequence.
-   * @param[in]  srcBLen     length of the second input sequence.
-   * @param[out] pDst        points to the block of output data
-   * @param[in]  firstIndex  is the first output sample to start with.
-   * @param[in]  numPoints   is the number of output points to be computed.
-   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
-   */
-  arm_status arm_conv_partial_fast_q15(
-  q15_t * pSrcA,
-  uint32_t srcALen,
-  q15_t * pSrcB,
-  uint32_t srcBLen,
-  q15_t * pDst,
-  uint32_t firstIndex,
-  uint32_t numPoints);
-
-
-  /**
-   * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
-   * @param[in]  pSrcA       points to the first input sequence.
-   * @param[in]  srcALen     length of the first input sequence.
-   * @param[in]  pSrcB       points to the second input sequence.
-   * @param[in]  srcBLen     length of the second input sequence.
-   * @param[out] pDst        points to the block of output data
-   * @param[in]  firstIndex  is the first output sample to start with.
-   * @param[in]  numPoints   is the number of output points to be computed.
-   * @param[in]  pScratch1   points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
-   * @param[in]  pScratch2   points to scratch buffer of size min(srcALen, srcBLen).
-   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
-   */
-  arm_status arm_conv_partial_fast_opt_q15(
-  q15_t * pSrcA,
-  uint32_t srcALen,
-  q15_t * pSrcB,
-  uint32_t srcBLen,
-  q15_t * pDst,
-  uint32_t firstIndex,
-  uint32_t numPoints,
-  q15_t * pScratch1,
-  q15_t * pScratch2);
-
-
-  /**
-   * @brief Partial convolution of Q31 sequences.
-   * @param[in]  pSrcA       points to the first input sequence.
-   * @param[in]  srcALen     length of the first input sequence.
-   * @param[in]  pSrcB       points to the second input sequence.
-   * @param[in]  srcBLen     length of the second input sequence.
-   * @param[out] pDst        points to the block of output data
-   * @param[in]  firstIndex  is the first output sample to start with.
-   * @param[in]  numPoints   is the number of output points to be computed.
-   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
-   */
-  arm_status arm_conv_partial_q31(
-  q31_t * pSrcA,
-  uint32_t srcALen,
-  q31_t * pSrcB,
-  uint32_t srcBLen,
-  q31_t * pDst,
-  uint32_t firstIndex,
-  uint32_t numPoints);
-
-
-  /**
-   * @brief Partial convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
-   * @param[in]  pSrcA       points to the first input sequence.
-   * @param[in]  srcALen     length of the first input sequence.
-   * @param[in]  pSrcB       points to the second input sequence.
-   * @param[in]  srcBLen     length of the second input sequence.
-   * @param[out] pDst        points to the block of output data
-   * @param[in]  firstIndex  is the first output sample to start with.
-   * @param[in]  numPoints   is the number of output points to be computed.
-   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
-   */
-  arm_status arm_conv_partial_fast_q31(
-  q31_t * pSrcA,
-  uint32_t srcALen,
-  q31_t * pSrcB,
-  uint32_t srcBLen,
-  q31_t * pDst,
-  uint32_t firstIndex,
-  uint32_t numPoints);
-
-
-  /**
-   * @brief Partial convolution of Q7 sequences
-   * @param[in]  pSrcA       points to the first input sequence.
-   * @param[in]  srcALen     length of the first input sequence.
-   * @param[in]  pSrcB       points to the second input sequence.
-   * @param[in]  srcBLen     length of the second input sequence.
-   * @param[out] pDst        points to the block of output data
-   * @param[in]  firstIndex  is the first output sample to start with.
-   * @param[in]  numPoints   is the number of output points to be computed.
-   * @param[in]  pScratch1   points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
-   * @param[in]  pScratch2   points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
-   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
-   */
-  arm_status arm_conv_partial_opt_q7(
-  q7_t * pSrcA,
-  uint32_t srcALen,
-  q7_t * pSrcB,
-  uint32_t srcBLen,
-  q7_t * pDst,
-  uint32_t firstIndex,
-  uint32_t numPoints,
-  q15_t * pScratch1,
-  q15_t * pScratch2);
-
-
-/**
-   * @brief Partial convolution of Q7 sequences.
-   * @param[in]  pSrcA       points to the first input sequence.
-   * @param[in]  srcALen     length of the first input sequence.
-   * @param[in]  pSrcB       points to the second input sequence.
-   * @param[in]  srcBLen     length of the second input sequence.
-   * @param[out] pDst        points to the block of output data
-   * @param[in]  firstIndex  is the first output sample to start with.
-   * @param[in]  numPoints   is the number of output points to be computed.
-   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
-   */
-  arm_status arm_conv_partial_q7(
-  q7_t * pSrcA,
-  uint32_t srcALen,
-  q7_t * pSrcB,
-  uint32_t srcBLen,
-  q7_t * pDst,
-  uint32_t firstIndex,
-  uint32_t numPoints);
-
-
-  /**
-   * @brief Instance structure for the Q15 FIR decimator.
-   */
-  typedef struct
-  {
-    uint8_t M;                  /**< decimation factor. */
-    uint16_t numTaps;           /**< number of coefficients in the filter. */
-    q15_t *pCoeffs;             /**< points to the coefficient array. The array is of length numTaps.*/
-    q15_t *pState;              /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
-  } arm_fir_decimate_instance_q15;
-
-  /**
-   * @brief Instance structure for the Q31 FIR decimator.
-   */
-  typedef struct
-  {
-    uint8_t M;                  /**< decimation factor. */
-    uint16_t numTaps;           /**< number of coefficients in the filter. */
-    q31_t *pCoeffs;             /**< points to the coefficient array. The array is of length numTaps.*/
-    q31_t *pState;              /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
-  } arm_fir_decimate_instance_q31;
-
-  /**
-   * @brief Instance structure for the floating-point FIR decimator.
-   */
-  typedef struct
-  {
-    uint8_t M;                  /**< decimation factor. */
-    uint16_t numTaps;           /**< number of coefficients in the filter. */
-    float32_t *pCoeffs;         /**< points to the coefficient array. The array is of length numTaps.*/
-    float32_t *pState;          /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
-  } arm_fir_decimate_instance_f32;
-
-
-  /**
-   * @brief Processing function for the floating-point FIR decimator.
-   * @param[in]  S          points to an instance of the floating-point FIR decimator structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data
-   * @param[in]  blockSize  number of input samples to process per call.
-   */
-  void arm_fir_decimate_f32(
-  const arm_fir_decimate_instance_f32 * S,
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the floating-point FIR decimator.
-   * @param[in,out] S          points to an instance of the floating-point FIR decimator structure.
-   * @param[in]     numTaps    number of coefficients in the filter.
-   * @param[in]     M          decimation factor.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     blockSize  number of input samples to process per call.
-   * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
-   * <code>blockSize</code> is not a multiple of <code>M</code>.
-   */
-  arm_status arm_fir_decimate_init_f32(
-  arm_fir_decimate_instance_f32 * S,
-  uint16_t numTaps,
-  uint8_t M,
-  float32_t * pCoeffs,
-  float32_t * pState,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the Q15 FIR decimator.
-   * @param[in]  S          points to an instance of the Q15 FIR decimator structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data
-   * @param[in]  blockSize  number of input samples to process per call.
-   */
-  void arm_fir_decimate_q15(
-  const arm_fir_decimate_instance_q15 * S,
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the Q15 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
-   * @param[in]  S          points to an instance of the Q15 FIR decimator structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data
-   * @param[in]  blockSize  number of input samples to process per call.
-   */
-  void arm_fir_decimate_fast_q15(
-  const arm_fir_decimate_instance_q15 * S,
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the Q15 FIR decimator.
-   * @param[in,out] S          points to an instance of the Q15 FIR decimator structure.
-   * @param[in]     numTaps    number of coefficients in the filter.
-   * @param[in]     M          decimation factor.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     blockSize  number of input samples to process per call.
-   * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
-   * <code>blockSize</code> is not a multiple of <code>M</code>.
-   */
-  arm_status arm_fir_decimate_init_q15(
-  arm_fir_decimate_instance_q15 * S,
-  uint16_t numTaps,
-  uint8_t M,
-  q15_t * pCoeffs,
-  q15_t * pState,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the Q31 FIR decimator.
-   * @param[in]  S     points to an instance of the Q31 FIR decimator structure.
-   * @param[in]  pSrc  points to the block of input data.
-   * @param[out] pDst  points to the block of output data
-   * @param[in] blockSize number of input samples to process per call.
-   */
-  void arm_fir_decimate_q31(
-  const arm_fir_decimate_instance_q31 * S,
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-  /**
-   * @brief Processing function for the Q31 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
-   * @param[in]  S          points to an instance of the Q31 FIR decimator structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data
-   * @param[in]  blockSize  number of input samples to process per call.
-   */
-  void arm_fir_decimate_fast_q31(
-  arm_fir_decimate_instance_q31 * S,
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the Q31 FIR decimator.
-   * @param[in,out] S          points to an instance of the Q31 FIR decimator structure.
-   * @param[in]     numTaps    number of coefficients in the filter.
-   * @param[in]     M          decimation factor.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     blockSize  number of input samples to process per call.
-   * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
-   * <code>blockSize</code> is not a multiple of <code>M</code>.
-   */
-  arm_status arm_fir_decimate_init_q31(
-  arm_fir_decimate_instance_q31 * S,
-  uint16_t numTaps,
-  uint8_t M,
-  q31_t * pCoeffs,
-  q31_t * pState,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Instance structure for the Q15 FIR interpolator.
-   */
-  typedef struct
-  {
-    uint8_t L;                      /**< upsample factor. */
-    uint16_t phaseLength;           /**< length of each polyphase filter component. */
-    q15_t *pCoeffs;                 /**< points to the coefficient array. The array is of length L*phaseLength. */
-    q15_t *pState;                  /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
-  } arm_fir_interpolate_instance_q15;
-
-  /**
-   * @brief Instance structure for the Q31 FIR interpolator.
-   */
-  typedef struct
-  {
-    uint8_t L;                      /**< upsample factor. */
-    uint16_t phaseLength;           /**< length of each polyphase filter component. */
-    q31_t *pCoeffs;                 /**< points to the coefficient array. The array is of length L*phaseLength. */
-    q31_t *pState;                  /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
-  } arm_fir_interpolate_instance_q31;
-
-  /**
-   * @brief Instance structure for the floating-point FIR interpolator.
-   */
-  typedef struct
-  {
-    uint8_t L;                     /**< upsample factor. */
-    uint16_t phaseLength;          /**< length of each polyphase filter component. */
-    float32_t *pCoeffs;            /**< points to the coefficient array. The array is of length L*phaseLength. */
-    float32_t *pState;             /**< points to the state variable array. The array is of length phaseLength+numTaps-1. */
-  } arm_fir_interpolate_instance_f32;
-
-
-  /**
-   * @brief Processing function for the Q15 FIR interpolator.
-   * @param[in]  S          points to an instance of the Q15 FIR interpolator structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of input samples to process per call.
-   */
-  void arm_fir_interpolate_q15(
-  const arm_fir_interpolate_instance_q15 * S,
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the Q15 FIR interpolator.
-   * @param[in,out] S          points to an instance of the Q15 FIR interpolator structure.
-   * @param[in]     L          upsample factor.
-   * @param[in]     numTaps    number of filter coefficients in the filter.
-   * @param[in]     pCoeffs    points to the filter coefficient buffer.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     blockSize  number of input samples to process per call.
-   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
-   * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
-   */
-  arm_status arm_fir_interpolate_init_q15(
-  arm_fir_interpolate_instance_q15 * S,
-  uint8_t L,
-  uint16_t numTaps,
-  q15_t * pCoeffs,
-  q15_t * pState,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the Q31 FIR interpolator.
-   * @param[in]  S          points to an instance of the Q15 FIR interpolator structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of input samples to process per call.
-   */
-  void arm_fir_interpolate_q31(
-  const arm_fir_interpolate_instance_q31 * S,
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the Q31 FIR interpolator.
-   * @param[in,out] S          points to an instance of the Q31 FIR interpolator structure.
-   * @param[in]     L          upsample factor.
-   * @param[in]     numTaps    number of filter coefficients in the filter.
-   * @param[in]     pCoeffs    points to the filter coefficient buffer.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     blockSize  number of input samples to process per call.
-   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
-   * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
-   */
-  arm_status arm_fir_interpolate_init_q31(
-  arm_fir_interpolate_instance_q31 * S,
-  uint8_t L,
-  uint16_t numTaps,
-  q31_t * pCoeffs,
-  q31_t * pState,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the floating-point FIR interpolator.
-   * @param[in]  S          points to an instance of the floating-point FIR interpolator structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of input samples to process per call.
-   */
-  void arm_fir_interpolate_f32(
-  const arm_fir_interpolate_instance_f32 * S,
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the floating-point FIR interpolator.
-   * @param[in,out] S          points to an instance of the floating-point FIR interpolator structure.
-   * @param[in]     L          upsample factor.
-   * @param[in]     numTaps    number of filter coefficients in the filter.
-   * @param[in]     pCoeffs    points to the filter coefficient buffer.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     blockSize  number of input samples to process per call.
-   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
-   * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
-   */
-  arm_status arm_fir_interpolate_init_f32(
-  arm_fir_interpolate_instance_f32 * S,
-  uint8_t L,
-  uint16_t numTaps,
-  float32_t * pCoeffs,
-  float32_t * pState,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Instance structure for the high precision Q31 Biquad cascade filter.
-   */
-  typedef struct
-  {
-    uint8_t numStages;       /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
-    q63_t *pState;           /**< points to the array of state coefficients.  The array is of length 4*numStages. */
-    q31_t *pCoeffs;          /**< points to the array of coefficients.  The array is of length 5*numStages. */
-    uint8_t postShift;       /**< additional shift, in bits, applied to each output sample. */
-  } arm_biquad_cas_df1_32x64_ins_q31;
-
-
-  /**
-   * @param[in]  S          points to an instance of the high precision Q31 Biquad cascade filter structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_biquad_cas_df1_32x64_q31(
-  const arm_biquad_cas_df1_32x64_ins_q31 * S,
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @param[in,out] S          points to an instance of the high precision Q31 Biquad cascade filter structure.
-   * @param[in]     numStages  number of 2nd order stages in the filter.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     postShift  shift to be applied to the output. Varies according to the coefficients format
-   */
-  void arm_biquad_cas_df1_32x64_init_q31(
-  arm_biquad_cas_df1_32x64_ins_q31 * S,
-  uint8_t numStages,
-  q31_t * pCoeffs,
-  q63_t * pState,
-  uint8_t postShift);
-
-
-  /**
-   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
-   */
-  typedef struct
-  {
-    uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
-    float32_t *pState;         /**< points to the array of state coefficients.  The array is of length 2*numStages. */
-    float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
-  } arm_biquad_cascade_df2T_instance_f32;
-
-  /**
-   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
-   */
-  typedef struct
-  {
-    uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
-    float32_t *pState;         /**< points to the array of state coefficients.  The array is of length 4*numStages. */
-    float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
-  } arm_biquad_cascade_stereo_df2T_instance_f32;
-
-  /**
-   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
-   */
-  typedef struct
-  {
-    uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
-    float64_t *pState;         /**< points to the array of state coefficients.  The array is of length 2*numStages. */
-    float64_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
-  } arm_biquad_cascade_df2T_instance_f64;
-
-
-  /**
-   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
-   * @param[in]  S          points to an instance of the filter data structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_biquad_cascade_df2T_f32(
-  const arm_biquad_cascade_df2T_instance_f32 * S,
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. 2 channels
-   * @param[in]  S          points to an instance of the filter data structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_biquad_cascade_stereo_df2T_f32(
-  const arm_biquad_cascade_stereo_df2T_instance_f32 * S,
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
-   * @param[in]  S          points to an instance of the filter data structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_biquad_cascade_df2T_f64(
-  const arm_biquad_cascade_df2T_instance_f64 * S,
-  float64_t * pSrc,
-  float64_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
-   * @param[in,out] S          points to an instance of the filter data structure.
-   * @param[in]     numStages  number of 2nd order stages in the filter.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   */
-  void arm_biquad_cascade_df2T_init_f32(
-  arm_biquad_cascade_df2T_instance_f32 * S,
-  uint8_t numStages,
-  float32_t * pCoeffs,
-  float32_t * pState);
-
-
-  /**
-   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
-   * @param[in,out] S          points to an instance of the filter data structure.
-   * @param[in]     numStages  number of 2nd order stages in the filter.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   */
-  void arm_biquad_cascade_stereo_df2T_init_f32(
-  arm_biquad_cascade_stereo_df2T_instance_f32 * S,
-  uint8_t numStages,
-  float32_t * pCoeffs,
-  float32_t * pState);
-
-
-  /**
-   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
-   * @param[in,out] S          points to an instance of the filter data structure.
-   * @param[in]     numStages  number of 2nd order stages in the filter.
-   * @param[in]     pCoeffs    points to the filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   */
-  void arm_biquad_cascade_df2T_init_f64(
-  arm_biquad_cascade_df2T_instance_f64 * S,
-  uint8_t numStages,
-  float64_t * pCoeffs,
-  float64_t * pState);
-
-
-  /**
-   * @brief Instance structure for the Q15 FIR lattice filter.
-   */
-  typedef struct
-  {
-    uint16_t numStages;                  /**< number of filter stages. */
-    q15_t *pState;                       /**< points to the state variable array. The array is of length numStages. */
-    q15_t *pCoeffs;                      /**< points to the coefficient array. The array is of length numStages. */
-  } arm_fir_lattice_instance_q15;
-
-  /**
-   * @brief Instance structure for the Q31 FIR lattice filter.
-   */
-  typedef struct
-  {
-    uint16_t numStages;                  /**< number of filter stages. */
-    q31_t *pState;                       /**< points to the state variable array. The array is of length numStages. */
-    q31_t *pCoeffs;                      /**< points to the coefficient array. The array is of length numStages. */
-  } arm_fir_lattice_instance_q31;
-
-  /**
-   * @brief Instance structure for the floating-point FIR lattice filter.
-   */
-  typedef struct
-  {
-    uint16_t numStages;                  /**< number of filter stages. */
-    float32_t *pState;                   /**< points to the state variable array. The array is of length numStages. */
-    float32_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numStages. */
-  } arm_fir_lattice_instance_f32;
-
-
-  /**
-   * @brief Initialization function for the Q15 FIR lattice filter.
-   * @param[in] S          points to an instance of the Q15 FIR lattice structure.
-   * @param[in] numStages  number of filter stages.
-   * @param[in] pCoeffs    points to the coefficient buffer.  The array is of length numStages.
-   * @param[in] pState     points to the state buffer.  The array is of length numStages.
-   */
-  void arm_fir_lattice_init_q15(
-  arm_fir_lattice_instance_q15 * S,
-  uint16_t numStages,
-  q15_t * pCoeffs,
-  q15_t * pState);
-
-
-  /**
-   * @brief Processing function for the Q15 FIR lattice filter.
-   * @param[in]  S          points to an instance of the Q15 FIR lattice structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_fir_lattice_q15(
-  const arm_fir_lattice_instance_q15 * S,
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Initialization function for the Q31 FIR lattice filter.
-   * @param[in] S          points to an instance of the Q31 FIR lattice structure.
-   * @param[in] numStages  number of filter stages.
-   * @param[in] pCoeffs    points to the coefficient buffer.  The array is of length numStages.
-   * @param[in] pState     points to the state buffer.   The array is of length numStages.
-   */
-  void arm_fir_lattice_init_q31(
-  arm_fir_lattice_instance_q31 * S,
-  uint16_t numStages,
-  q31_t * pCoeffs,
-  q31_t * pState);
-
-
-  /**
-   * @brief Processing function for the Q31 FIR lattice filter.
-   * @param[in]  S          points to an instance of the Q31 FIR lattice structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_fir_lattice_q31(
-  const arm_fir_lattice_instance_q31 * S,
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-/**
- * @brief Initialization function for the floating-point FIR lattice filter.
- * @param[in] S          points to an instance of the floating-point FIR lattice structure.
- * @param[in] numStages  number of filter stages.
- * @param[in] pCoeffs    points to the coefficient buffer.  The array is of length numStages.
- * @param[in] pState     points to the state buffer.  The array is of length numStages.
- */
-  void arm_fir_lattice_init_f32(
-  arm_fir_lattice_instance_f32 * S,
-  uint16_t numStages,
-  float32_t * pCoeffs,
-  float32_t * pState);
-
-
-  /**
-   * @brief Processing function for the floating-point FIR lattice filter.
-   * @param[in]  S          points to an instance of the floating-point FIR lattice structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_fir_lattice_f32(
-  const arm_fir_lattice_instance_f32 * S,
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Instance structure for the Q15 IIR lattice filter.
-   */
-  typedef struct
-  {
-    uint16_t numStages;                  /**< number of stages in the filter. */
-    q15_t *pState;                       /**< points to the state variable array. The array is of length numStages+blockSize. */
-    q15_t *pkCoeffs;                     /**< points to the reflection coefficient array. The array is of length numStages. */
-    q15_t *pvCoeffs;                     /**< points to the ladder coefficient array. The array is of length numStages+1. */
-  } arm_iir_lattice_instance_q15;
-
-  /**
-   * @brief Instance structure for the Q31 IIR lattice filter.
-   */
-  typedef struct
-  {
-    uint16_t numStages;                  /**< number of stages in the filter. */
-    q31_t *pState;                       /**< points to the state variable array. The array is of length numStages+blockSize. */
-    q31_t *pkCoeffs;                     /**< points to the reflection coefficient array. The array is of length numStages. */
-    q31_t *pvCoeffs;                     /**< points to the ladder coefficient array. The array is of length numStages+1. */
-  } arm_iir_lattice_instance_q31;
-
-  /**
-   * @brief Instance structure for the floating-point IIR lattice filter.
-   */
-  typedef struct
-  {
-    uint16_t numStages;                  /**< number of stages in the filter. */
-    float32_t *pState;                   /**< points to the state variable array. The array is of length numStages+blockSize. */
-    float32_t *pkCoeffs;                 /**< points to the reflection coefficient array. The array is of length numStages. */
-    float32_t *pvCoeffs;                 /**< points to the ladder coefficient array. The array is of length numStages+1. */
-  } arm_iir_lattice_instance_f32;
-
-
-  /**
-   * @brief Processing function for the floating-point IIR lattice filter.
-   * @param[in]  S          points to an instance of the floating-point IIR lattice structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_iir_lattice_f32(
-  const arm_iir_lattice_instance_f32 * S,
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Initialization function for the floating-point IIR lattice filter.
-   * @param[in] S          points to an instance of the floating-point IIR lattice structure.
-   * @param[in] numStages  number of stages in the filter.
-   * @param[in] pkCoeffs   points to the reflection coefficient buffer.  The array is of length numStages.
-   * @param[in] pvCoeffs   points to the ladder coefficient buffer.  The array is of length numStages+1.
-   * @param[in] pState     points to the state buffer.  The array is of length numStages+blockSize-1.
-   * @param[in] blockSize  number of samples to process.
-   */
-  void arm_iir_lattice_init_f32(
-  arm_iir_lattice_instance_f32 * S,
-  uint16_t numStages,
-  float32_t * pkCoeffs,
-  float32_t * pvCoeffs,
-  float32_t * pState,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the Q31 IIR lattice filter.
-   * @param[in]  S          points to an instance of the Q31 IIR lattice structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_iir_lattice_q31(
-  const arm_iir_lattice_instance_q31 * S,
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Initialization function for the Q31 IIR lattice filter.
-   * @param[in] S          points to an instance of the Q31 IIR lattice structure.
-   * @param[in] numStages  number of stages in the filter.
-   * @param[in] pkCoeffs   points to the reflection coefficient buffer.  The array is of length numStages.
-   * @param[in] pvCoeffs   points to the ladder coefficient buffer.  The array is of length numStages+1.
-   * @param[in] pState     points to the state buffer.  The array is of length numStages+blockSize.
-   * @param[in] blockSize  number of samples to process.
-   */
-  void arm_iir_lattice_init_q31(
-  arm_iir_lattice_instance_q31 * S,
-  uint16_t numStages,
-  q31_t * pkCoeffs,
-  q31_t * pvCoeffs,
-  q31_t * pState,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the Q15 IIR lattice filter.
-   * @param[in]  S          points to an instance of the Q15 IIR lattice structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[out] pDst       points to the block of output data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_iir_lattice_q15(
-  const arm_iir_lattice_instance_q15 * S,
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-/**
- * @brief Initialization function for the Q15 IIR lattice filter.
- * @param[in] S          points to an instance of the fixed-point Q15 IIR lattice structure.
- * @param[in] numStages  number of stages in the filter.
- * @param[in] pkCoeffs   points to reflection coefficient buffer.  The array is of length numStages.
- * @param[in] pvCoeffs   points to ladder coefficient buffer.  The array is of length numStages+1.
- * @param[in] pState     points to state buffer.  The array is of length numStages+blockSize.
- * @param[in] blockSize  number of samples to process per call.
- */
-  void arm_iir_lattice_init_q15(
-  arm_iir_lattice_instance_q15 * S,
-  uint16_t numStages,
-  q15_t * pkCoeffs,
-  q15_t * pvCoeffs,
-  q15_t * pState,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Instance structure for the floating-point LMS filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;    /**< number of coefficients in the filter. */
-    float32_t *pState;   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
-    float32_t *pCoeffs;  /**< points to the coefficient array. The array is of length numTaps. */
-    float32_t mu;        /**< step size that controls filter coefficient updates. */
-  } arm_lms_instance_f32;
-
-
-  /**
-   * @brief Processing function for floating-point LMS filter.
-   * @param[in]  S          points to an instance of the floating-point LMS filter structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[in]  pRef       points to the block of reference data.
-   * @param[out] pOut       points to the block of output data.
-   * @param[out] pErr       points to the block of error data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_lms_f32(
-  const arm_lms_instance_f32 * S,
-  float32_t * pSrc,
-  float32_t * pRef,
-  float32_t * pOut,
-  float32_t * pErr,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Initialization function for floating-point LMS filter.
-   * @param[in] S          points to an instance of the floating-point LMS filter structure.
-   * @param[in] numTaps    number of filter coefficients.
-   * @param[in] pCoeffs    points to the coefficient buffer.
-   * @param[in] pState     points to state buffer.
-   * @param[in] mu         step size that controls filter coefficient updates.
-   * @param[in] blockSize  number of samples to process.
-   */
-  void arm_lms_init_f32(
-  arm_lms_instance_f32 * S,
-  uint16_t numTaps,
-  float32_t * pCoeffs,
-  float32_t * pState,
-  float32_t mu,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Instance structure for the Q15 LMS filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;    /**< number of coefficients in the filter. */
-    q15_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
-    q15_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
-    q15_t mu;            /**< step size that controls filter coefficient updates. */
-    uint32_t postShift;  /**< bit shift applied to coefficients. */
-  } arm_lms_instance_q15;
-
-
-  /**
-   * @brief Initialization function for the Q15 LMS filter.
-   * @param[in] S          points to an instance of the Q15 LMS filter structure.
-   * @param[in] numTaps    number of filter coefficients.
-   * @param[in] pCoeffs    points to the coefficient buffer.
-   * @param[in] pState     points to the state buffer.
-   * @param[in] mu         step size that controls filter coefficient updates.
-   * @param[in] blockSize  number of samples to process.
-   * @param[in] postShift  bit shift applied to coefficients.
-   */
-  void arm_lms_init_q15(
-  arm_lms_instance_q15 * S,
-  uint16_t numTaps,
-  q15_t * pCoeffs,
-  q15_t * pState,
-  q15_t mu,
-  uint32_t blockSize,
-  uint32_t postShift);
-
-
-  /**
-   * @brief Processing function for Q15 LMS filter.
-   * @param[in]  S          points to an instance of the Q15 LMS filter structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[in]  pRef       points to the block of reference data.
-   * @param[out] pOut       points to the block of output data.
-   * @param[out] pErr       points to the block of error data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_lms_q15(
-  const arm_lms_instance_q15 * S,
-  q15_t * pSrc,
-  q15_t * pRef,
-  q15_t * pOut,
-  q15_t * pErr,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Instance structure for the Q31 LMS filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;    /**< number of coefficients in the filter. */
-    q31_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
-    q31_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
-    q31_t mu;            /**< step size that controls filter coefficient updates. */
-    uint32_t postShift;  /**< bit shift applied to coefficients. */
-  } arm_lms_instance_q31;
-
-
-  /**
-   * @brief Processing function for Q31 LMS filter.
-   * @param[in]  S          points to an instance of the Q15 LMS filter structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[in]  pRef       points to the block of reference data.
-   * @param[out] pOut       points to the block of output data.
-   * @param[out] pErr       points to the block of error data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_lms_q31(
-  const arm_lms_instance_q31 * S,
-  q31_t * pSrc,
-  q31_t * pRef,
-  q31_t * pOut,
-  q31_t * pErr,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Initialization function for Q31 LMS filter.
-   * @param[in] S          points to an instance of the Q31 LMS filter structure.
-   * @param[in] numTaps    number of filter coefficients.
-   * @param[in] pCoeffs    points to coefficient buffer.
-   * @param[in] pState     points to state buffer.
-   * @param[in] mu         step size that controls filter coefficient updates.
-   * @param[in] blockSize  number of samples to process.
-   * @param[in] postShift  bit shift applied to coefficients.
-   */
-  void arm_lms_init_q31(
-  arm_lms_instance_q31 * S,
-  uint16_t numTaps,
-  q31_t * pCoeffs,
-  q31_t * pState,
-  q31_t mu,
-  uint32_t blockSize,
-  uint32_t postShift);
-
-
-  /**
-   * @brief Instance structure for the floating-point normalized LMS filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;     /**< number of coefficients in the filter. */
-    float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
-    float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
-    float32_t mu;         /**< step size that control filter coefficient updates. */
-    float32_t energy;     /**< saves previous frame energy. */
-    float32_t x0;         /**< saves previous input sample. */
-  } arm_lms_norm_instance_f32;
-
-
-  /**
-   * @brief Processing function for floating-point normalized LMS filter.
-   * @param[in]  S          points to an instance of the floating-point normalized LMS filter structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[in]  pRef       points to the block of reference data.
-   * @param[out] pOut       points to the block of output data.
-   * @param[out] pErr       points to the block of error data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_lms_norm_f32(
-  arm_lms_norm_instance_f32 * S,
-  float32_t * pSrc,
-  float32_t * pRef,
-  float32_t * pOut,
-  float32_t * pErr,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Initialization function for floating-point normalized LMS filter.
-   * @param[in] S          points to an instance of the floating-point LMS filter structure.
-   * @param[in] numTaps    number of filter coefficients.
-   * @param[in] pCoeffs    points to coefficient buffer.
-   * @param[in] pState     points to state buffer.
-   * @param[in] mu         step size that controls filter coefficient updates.
-   * @param[in] blockSize  number of samples to process.
-   */
-  void arm_lms_norm_init_f32(
-  arm_lms_norm_instance_f32 * S,
-  uint16_t numTaps,
-  float32_t * pCoeffs,
-  float32_t * pState,
-  float32_t mu,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Instance structure for the Q31 normalized LMS filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;     /**< number of coefficients in the filter. */
-    q31_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
-    q31_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
-    q31_t mu;             /**< step size that controls filter coefficient updates. */
-    uint8_t postShift;    /**< bit shift applied to coefficients. */
-    q31_t *recipTable;    /**< points to the reciprocal initial value table. */
-    q31_t energy;         /**< saves previous frame energy. */
-    q31_t x0;             /**< saves previous input sample. */
-  } arm_lms_norm_instance_q31;
-
-
-  /**
-   * @brief Processing function for Q31 normalized LMS filter.
-   * @param[in]  S          points to an instance of the Q31 normalized LMS filter structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[in]  pRef       points to the block of reference data.
-   * @param[out] pOut       points to the block of output data.
-   * @param[out] pErr       points to the block of error data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_lms_norm_q31(
-  arm_lms_norm_instance_q31 * S,
-  q31_t * pSrc,
-  q31_t * pRef,
-  q31_t * pOut,
-  q31_t * pErr,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Initialization function for Q31 normalized LMS filter.
-   * @param[in] S          points to an instance of the Q31 normalized LMS filter structure.
-   * @param[in] numTaps    number of filter coefficients.
-   * @param[in] pCoeffs    points to coefficient buffer.
-   * @param[in] pState     points to state buffer.
-   * @param[in] mu         step size that controls filter coefficient updates.
-   * @param[in] blockSize  number of samples to process.
-   * @param[in] postShift  bit shift applied to coefficients.
-   */
-  void arm_lms_norm_init_q31(
-  arm_lms_norm_instance_q31 * S,
-  uint16_t numTaps,
-  q31_t * pCoeffs,
-  q31_t * pState,
-  q31_t mu,
-  uint32_t blockSize,
-  uint8_t postShift);
-
-
-  /**
-   * @brief Instance structure for the Q15 normalized LMS filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;     /**< Number of coefficients in the filter. */
-    q15_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
-    q15_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
-    q15_t mu;             /**< step size that controls filter coefficient updates. */
-    uint8_t postShift;    /**< bit shift applied to coefficients. */
-    q15_t *recipTable;    /**< Points to the reciprocal initial value table. */
-    q15_t energy;         /**< saves previous frame energy. */
-    q15_t x0;             /**< saves previous input sample. */
-  } arm_lms_norm_instance_q15;
-
-
-  /**
-   * @brief Processing function for Q15 normalized LMS filter.
-   * @param[in]  S          points to an instance of the Q15 normalized LMS filter structure.
-   * @param[in]  pSrc       points to the block of input data.
-   * @param[in]  pRef       points to the block of reference data.
-   * @param[out] pOut       points to the block of output data.
-   * @param[out] pErr       points to the block of error data.
-   * @param[in]  blockSize  number of samples to process.
-   */
-  void arm_lms_norm_q15(
-  arm_lms_norm_instance_q15 * S,
-  q15_t * pSrc,
-  q15_t * pRef,
-  q15_t * pOut,
-  q15_t * pErr,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Initialization function for Q15 normalized LMS filter.
-   * @param[in] S          points to an instance of the Q15 normalized LMS filter structure.
-   * @param[in] numTaps    number of filter coefficients.
-   * @param[in] pCoeffs    points to coefficient buffer.
-   * @param[in] pState     points to state buffer.
-   * @param[in] mu         step size that controls filter coefficient updates.
-   * @param[in] blockSize  number of samples to process.
-   * @param[in] postShift  bit shift applied to coefficients.
-   */
-  void arm_lms_norm_init_q15(
-  arm_lms_norm_instance_q15 * S,
-  uint16_t numTaps,
-  q15_t * pCoeffs,
-  q15_t * pState,
-  q15_t mu,
-  uint32_t blockSize,
-  uint8_t postShift);
-
-
-  /**
-   * @brief Correlation of floating-point sequences.
-   * @param[in]  pSrcA    points to the first input sequence.
-   * @param[in]  srcALen  length of the first input sequence.
-   * @param[in]  pSrcB    points to the second input sequence.
-   * @param[in]  srcBLen  length of the second input sequence.
-   * @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
-   */
-  void arm_correlate_f32(
-  float32_t * pSrcA,
-  uint32_t srcALen,
-  float32_t * pSrcB,
-  uint32_t srcBLen,
-  float32_t * pDst);
-
-
-   /**
-   * @brief Correlation of Q15 sequences
-   * @param[in]  pSrcA     points to the first input sequence.
-   * @param[in]  srcALen   length of the first input sequence.
-   * @param[in]  pSrcB     points to the second input sequence.
-   * @param[in]  srcBLen   length of the second input sequence.
-   * @param[out] pDst      points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
-   * @param[in]  pScratch  points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
-   */
-  void arm_correlate_opt_q15(
-  q15_t * pSrcA,
-  uint32_t srcALen,
-  q15_t * pSrcB,
-  uint32_t srcBLen,
-  q15_t * pDst,
-  q15_t * pScratch);
-
-
-  /**
-   * @brief Correlation of Q15 sequences.
-   * @param[in]  pSrcA    points to the first input sequence.
-   * @param[in]  srcALen  length of the first input sequence.
-   * @param[in]  pSrcB    points to the second input sequence.
-   * @param[in]  srcBLen  length of the second input sequence.
-   * @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
-   */
-
-  void arm_correlate_q15(
-  q15_t * pSrcA,
-  uint32_t srcALen,
-  q15_t * pSrcB,
-  uint32_t srcBLen,
-  q15_t * pDst);
-
-
-  /**
-   * @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
-   * @param[in]  pSrcA    points to the first input sequence.
-   * @param[in]  srcALen  length of the first input sequence.
-   * @param[in]  pSrcB    points to the second input sequence.
-   * @param[in]  srcBLen  length of the second input sequence.
-   * @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
-   */
-
-  void arm_correlate_fast_q15(
-  q15_t * pSrcA,
-  uint32_t srcALen,
-  q15_t * pSrcB,
-  uint32_t srcBLen,
-  q15_t * pDst);
-
-
-  /**
-   * @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
-   * @param[in]  pSrcA     points to the first input sequence.
-   * @param[in]  srcALen   length of the first input sequence.
-   * @param[in]  pSrcB     points to the second input sequence.
-   * @param[in]  srcBLen   length of the second input sequence.
-   * @param[out] pDst      points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
-   * @param[in]  pScratch  points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
-   */
-  void arm_correlate_fast_opt_q15(
-  q15_t * pSrcA,
-  uint32_t srcALen,
-  q15_t * pSrcB,
-  uint32_t srcBLen,
-  q15_t * pDst,
-  q15_t * pScratch);
-
-
-  /**
-   * @brief Correlation of Q31 sequences.
-   * @param[in]  pSrcA    points to the first input sequence.
-   * @param[in]  srcALen  length of the first input sequence.
-   * @param[in]  pSrcB    points to the second input sequence.
-   * @param[in]  srcBLen  length of the second input sequence.
-   * @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
-   */
-  void arm_correlate_q31(
-  q31_t * pSrcA,
-  uint32_t srcALen,
-  q31_t * pSrcB,
-  uint32_t srcBLen,
-  q31_t * pDst);
-
-
-  /**
-   * @brief Correlation of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
-   * @param[in]  pSrcA    points to the first input sequence.
-   * @param[in]  srcALen  length of the first input sequence.
-   * @param[in]  pSrcB    points to the second input sequence.
-   * @param[in]  srcBLen  length of the second input sequence.
-   * @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
-   */
-  void arm_correlate_fast_q31(
-  q31_t * pSrcA,
-  uint32_t srcALen,
-  q31_t * pSrcB,
-  uint32_t srcBLen,
-  q31_t * pDst);
-
-
- /**
-   * @brief Correlation of Q7 sequences.
-   * @param[in]  pSrcA      points to the first input sequence.
-   * @param[in]  srcALen    length of the first input sequence.
-   * @param[in]  pSrcB      points to the second input sequence.
-   * @param[in]  srcBLen    length of the second input sequence.
-   * @param[out] pDst       points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
-   * @param[in]  pScratch1  points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
-   * @param[in]  pScratch2  points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
-   */
-  void arm_correlate_opt_q7(
-  q7_t * pSrcA,
-  uint32_t srcALen,
-  q7_t * pSrcB,
-  uint32_t srcBLen,
-  q7_t * pDst,
-  q15_t * pScratch1,
-  q15_t * pScratch2);
-
-
-  /**
-   * @brief Correlation of Q7 sequences.
-   * @param[in]  pSrcA    points to the first input sequence.
-   * @param[in]  srcALen  length of the first input sequence.
-   * @param[in]  pSrcB    points to the second input sequence.
-   * @param[in]  srcBLen  length of the second input sequence.
-   * @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
-   */
-  void arm_correlate_q7(
-  q7_t * pSrcA,
-  uint32_t srcALen,
-  q7_t * pSrcB,
-  uint32_t srcBLen,
-  q7_t * pDst);
-
-
-  /**
-   * @brief Instance structure for the floating-point sparse FIR filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;             /**< number of coefficients in the filter. */
-    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
-    float32_t *pState;            /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
-    float32_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
-    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
-    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
-  } arm_fir_sparse_instance_f32;
-
-  /**
-   * @brief Instance structure for the Q31 sparse FIR filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;             /**< number of coefficients in the filter. */
-    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
-    q31_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
-    q31_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
-    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
-    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
-  } arm_fir_sparse_instance_q31;
-
-  /**
-   * @brief Instance structure for the Q15 sparse FIR filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;             /**< number of coefficients in the filter. */
-    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
-    q15_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
-    q15_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
-    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
-    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
-  } arm_fir_sparse_instance_q15;
-
-  /**
-   * @brief Instance structure for the Q7 sparse FIR filter.
-   */
-  typedef struct
-  {
-    uint16_t numTaps;             /**< number of coefficients in the filter. */
-    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
-    q7_t *pState;                 /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
-    q7_t *pCoeffs;                /**< points to the coefficient array. The array is of length numTaps.*/
-    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
-    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
-  } arm_fir_sparse_instance_q7;
-
-
-  /**
-   * @brief Processing function for the floating-point sparse FIR filter.
-   * @param[in]  S           points to an instance of the floating-point sparse FIR structure.
-   * @param[in]  pSrc        points to the block of input data.
-   * @param[out] pDst        points to the block of output data
-   * @param[in]  pScratchIn  points to a temporary buffer of size blockSize.
-   * @param[in]  blockSize   number of input samples to process per call.
-   */
-  void arm_fir_sparse_f32(
-  arm_fir_sparse_instance_f32 * S,
-  float32_t * pSrc,
-  float32_t * pDst,
-  float32_t * pScratchIn,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the floating-point sparse FIR filter.
-   * @param[in,out] S          points to an instance of the floating-point sparse FIR structure.
-   * @param[in]     numTaps    number of nonzero coefficients in the filter.
-   * @param[in]     pCoeffs    points to the array of filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     pTapDelay  points to the array of offset times.
-   * @param[in]     maxDelay   maximum offset time supported.
-   * @param[in]     blockSize  number of samples that will be processed per block.
-   */
-  void arm_fir_sparse_init_f32(
-  arm_fir_sparse_instance_f32 * S,
-  uint16_t numTaps,
-  float32_t * pCoeffs,
-  float32_t * pState,
-  int32_t * pTapDelay,
-  uint16_t maxDelay,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the Q31 sparse FIR filter.
-   * @param[in]  S           points to an instance of the Q31 sparse FIR structure.
-   * @param[in]  pSrc        points to the block of input data.
-   * @param[out] pDst        points to the block of output data
-   * @param[in]  pScratchIn  points to a temporary buffer of size blockSize.
-   * @param[in]  blockSize   number of input samples to process per call.
-   */
-  void arm_fir_sparse_q31(
-  arm_fir_sparse_instance_q31 * S,
-  q31_t * pSrc,
-  q31_t * pDst,
-  q31_t * pScratchIn,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the Q31 sparse FIR filter.
-   * @param[in,out] S          points to an instance of the Q31 sparse FIR structure.
-   * @param[in]     numTaps    number of nonzero coefficients in the filter.
-   * @param[in]     pCoeffs    points to the array of filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     pTapDelay  points to the array of offset times.
-   * @param[in]     maxDelay   maximum offset time supported.
-   * @param[in]     blockSize  number of samples that will be processed per block.
-   */
-  void arm_fir_sparse_init_q31(
-  arm_fir_sparse_instance_q31 * S,
-  uint16_t numTaps,
-  q31_t * pCoeffs,
-  q31_t * pState,
-  int32_t * pTapDelay,
-  uint16_t maxDelay,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the Q15 sparse FIR filter.
-   * @param[in]  S            points to an instance of the Q15 sparse FIR structure.
-   * @param[in]  pSrc         points to the block of input data.
-   * @param[out] pDst         points to the block of output data
-   * @param[in]  pScratchIn   points to a temporary buffer of size blockSize.
-   * @param[in]  pScratchOut  points to a temporary buffer of size blockSize.
-   * @param[in]  blockSize    number of input samples to process per call.
-   */
-  void arm_fir_sparse_q15(
-  arm_fir_sparse_instance_q15 * S,
-  q15_t * pSrc,
-  q15_t * pDst,
-  q15_t * pScratchIn,
-  q31_t * pScratchOut,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the Q15 sparse FIR filter.
-   * @param[in,out] S          points to an instance of the Q15 sparse FIR structure.
-   * @param[in]     numTaps    number of nonzero coefficients in the filter.
-   * @param[in]     pCoeffs    points to the array of filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     pTapDelay  points to the array of offset times.
-   * @param[in]     maxDelay   maximum offset time supported.
-   * @param[in]     blockSize  number of samples that will be processed per block.
-   */
-  void arm_fir_sparse_init_q15(
-  arm_fir_sparse_instance_q15 * S,
-  uint16_t numTaps,
-  q15_t * pCoeffs,
-  q15_t * pState,
-  int32_t * pTapDelay,
-  uint16_t maxDelay,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Processing function for the Q7 sparse FIR filter.
-   * @param[in]  S            points to an instance of the Q7 sparse FIR structure.
-   * @param[in]  pSrc         points to the block of input data.
-   * @param[out] pDst         points to the block of output data
-   * @param[in]  pScratchIn   points to a temporary buffer of size blockSize.
-   * @param[in]  pScratchOut  points to a temporary buffer of size blockSize.
-   * @param[in]  blockSize    number of input samples to process per call.
-   */
-  void arm_fir_sparse_q7(
-  arm_fir_sparse_instance_q7 * S,
-  q7_t * pSrc,
-  q7_t * pDst,
-  q7_t * pScratchIn,
-  q31_t * pScratchOut,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Initialization function for the Q7 sparse FIR filter.
-   * @param[in,out] S          points to an instance of the Q7 sparse FIR structure.
-   * @param[in]     numTaps    number of nonzero coefficients in the filter.
-   * @param[in]     pCoeffs    points to the array of filter coefficients.
-   * @param[in]     pState     points to the state buffer.
-   * @param[in]     pTapDelay  points to the array of offset times.
-   * @param[in]     maxDelay   maximum offset time supported.
-   * @param[in]     blockSize  number of samples that will be processed per block.
-   */
-  void arm_fir_sparse_init_q7(
-  arm_fir_sparse_instance_q7 * S,
-  uint16_t numTaps,
-  q7_t * pCoeffs,
-  q7_t * pState,
-  int32_t * pTapDelay,
-  uint16_t maxDelay,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Floating-point sin_cos function.
-   * @param[in]  theta   input value in degrees
-   * @param[out] pSinVal  points to the processed sine output.
-   * @param[out] pCosVal  points to the processed cos output.
-   */
-  void arm_sin_cos_f32(
-  float32_t theta,
-  float32_t * pSinVal,
-  float32_t * pCosVal);
-
-
-  /**
-   * @brief  Q31 sin_cos function.
-   * @param[in]  theta    scaled input value in degrees
-   * @param[out] pSinVal  points to the processed sine output.
-   * @param[out] pCosVal  points to the processed cosine output.
-   */
-  void arm_sin_cos_q31(
-  q31_t theta,
-  q31_t * pSinVal,
-  q31_t * pCosVal);
-
-
-  /**
-   * @brief  Floating-point complex conjugate.
-   * @param[in]  pSrc        points to the input vector
-   * @param[out] pDst        points to the output vector
-   * @param[in]  numSamples  number of complex samples in each vector
-   */
-  void arm_cmplx_conj_f32(
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t numSamples);
-
-  /**
-   * @brief  Q31 complex conjugate.
-   * @param[in]  pSrc        points to the input vector
-   * @param[out] pDst        points to the output vector
-   * @param[in]  numSamples  number of complex samples in each vector
-   */
-  void arm_cmplx_conj_q31(
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t numSamples);
-
-
-  /**
-   * @brief  Q15 complex conjugate.
-   * @param[in]  pSrc        points to the input vector
-   * @param[out] pDst        points to the output vector
-   * @param[in]  numSamples  number of complex samples in each vector
-   */
-  void arm_cmplx_conj_q15(
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t numSamples);
-
-
-  /**
-   * @brief  Floating-point complex magnitude squared
-   * @param[in]  pSrc        points to the complex input vector
-   * @param[out] pDst        points to the real output vector
-   * @param[in]  numSamples  number of complex samples in the input vector
-   */
-  void arm_cmplx_mag_squared_f32(
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t numSamples);
-
-
-  /**
-   * @brief  Q31 complex magnitude squared
-   * @param[in]  pSrc        points to the complex input vector
-   * @param[out] pDst        points to the real output vector
-   * @param[in]  numSamples  number of complex samples in the input vector
-   */
-  void arm_cmplx_mag_squared_q31(
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t numSamples);
-
-
-  /**
-   * @brief  Q15 complex magnitude squared
-   * @param[in]  pSrc        points to the complex input vector
-   * @param[out] pDst        points to the real output vector
-   * @param[in]  numSamples  number of complex samples in the input vector
-   */
-  void arm_cmplx_mag_squared_q15(
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t numSamples);
-
-
- /**
-   * @ingroup groupController
-   */
-
-  /**
-   * @defgroup PID PID Motor Control
-   *
-   * A Proportional Integral Derivative (PID) controller is a generic feedback control
-   * loop mechanism widely used in industrial control systems.
-   * A PID controller is the most commonly used type of feedback controller.
-   *
-   * This set of functions implements (PID) controllers
-   * for Q15, Q31, and floating-point data types.  The functions operate on a single sample
-   * of data and each call to the function returns a single processed value.
-   * <code>S</code> points to an instance of the PID control data structure.  <code>in</code>
-   * is the input sample value. The functions return the output value.
-   *
-   * \par Algorithm:
-   * <pre>
-   *    y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]
-   *    A0 = Kp + Ki + Kd
-   *    A1 = (-Kp ) - (2 * Kd )
-   *    A2 = Kd  </pre>
-   *
-   * \par
-   * where \c Kp is proportional constant, \c Ki is Integral constant and \c Kd is Derivative constant
-   *
-   * \par
-   * \image html PID.gif "Proportional Integral Derivative Controller"
-   *
-   * \par
-   * The PID controller calculates an "error" value as the difference between
-   * the measured output and the reference input.
-   * The controller attempts to minimize the error by adjusting the process control inputs.
-   * The proportional value determines the reaction to the current error,
-   * the integral value determines the reaction based on the sum of recent errors,
-   * and the derivative value determines the reaction based on the rate at which the error has been changing.
-   *
-   * \par Instance Structure
-   * The Gains A0, A1, A2 and state variables for a PID controller are stored together in an instance data structure.
-   * A separate instance structure must be defined for each PID Controller.
-   * There are separate instance structure declarations for each of the 3 supported data types.
-   *
-   * \par Reset Functions
-   * There is also an associated reset function for each data type which clears the state array.
-   *
-   * \par Initialization Functions
-   * There is also an associated initialization function for each data type.
-   * The initialization function performs the following operations:
-   * - Initializes the Gains A0, A1, A2 from Kp,Ki, Kd gains.
-   * - Zeros out the values in the state buffer.
-   *
-   * \par
-   * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.
-   *
-   * \par Fixed-Point Behavior
-   * Care must be taken when using the fixed-point versions of the PID Controller functions.
-   * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
-   * Refer to the function specific documentation below for usage guidelines.
-   */
-
-  /**
-   * @addtogroup PID
-   * @{
-   */
-
-  /**
-   * @brief  Process function for the floating-point PID Control.
-   * @param[in,out] S   is an instance of the floating-point PID Control structure
-   * @param[in]     in  input sample to process
-   * @return out processed output sample.
-   */
-  static __INLINE float32_t arm_pid_f32(
-  arm_pid_instance_f32 * S,
-  float32_t in)
-  {
-    float32_t out;
-
-    /* y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]  */
-    out = (S->A0 * in) +
-      (S->A1 * S->state[0]) + (S->A2 * S->state[1]) + (S->state[2]);
-
-    /* Update state */
-    S->state[1] = S->state[0];
-    S->state[0] = in;
-    S->state[2] = out;
-
-    /* return to application */
-    return (out);
-
-  }
-
-  /**
-   * @brief  Process function for the Q31 PID Control.
-   * @param[in,out] S  points to an instance of the Q31 PID Control structure
-   * @param[in]     in  input sample to process
-   * @return out processed output sample.
-   *
-   * <b>Scaling and Overflow Behavior:</b>
-   * \par
-   * The function is implemented using an internal 64-bit accumulator.
-   * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
-   * Thus, if the accumulator result overflows it wraps around rather than clip.
-   * In order to avoid overflows completely the input signal must be scaled down by 2 bits as there are four additions.
-   * After all multiply-accumulates are performed, the 2.62 accumulator is truncated to 1.32 format and then saturated to 1.31 format.
-   */
-  static __INLINE q31_t arm_pid_q31(
-  arm_pid_instance_q31 * S,
-  q31_t in)
-  {
-    q63_t acc;
-    q31_t out;
-
-    /* acc = A0 * x[n]  */
-    acc = (q63_t) S->A0 * in;
-
-    /* acc += A1 * x[n-1] */
-    acc += (q63_t) S->A1 * S->state[0];
-
-    /* acc += A2 * x[n-2]  */
-    acc += (q63_t) S->A2 * S->state[1];
-
-    /* convert output to 1.31 format to add y[n-1] */
-    out = (q31_t) (acc >> 31u);
-
-    /* out += y[n-1] */
-    out += S->state[2];
-
-    /* Update state */
-    S->state[1] = S->state[0];
-    S->state[0] = in;
-    S->state[2] = out;
-
-    /* return to application */
-    return (out);
-  }
-
-
-  /**
-   * @brief  Process function for the Q15 PID Control.
-   * @param[in,out] S   points to an instance of the Q15 PID Control structure
-   * @param[in]     in  input sample to process
-   * @return out processed output sample.
-   *
-   * <b>Scaling and Overflow Behavior:</b>
-   * \par
-   * The function is implemented using a 64-bit internal accumulator.
-   * Both Gains and state variables are represented in 1.15 format and multiplications yield a 2.30 result.
-   * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.
-   * There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.
-   * After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits.
-   * Lastly, the accumulator is saturated to yield a result in 1.15 format.
-   */
-  static __INLINE q15_t arm_pid_q15(
-  arm_pid_instance_q15 * S,
-  q15_t in)
-  {
-    q63_t acc;
-    q15_t out;
-
-#ifndef ARM_MATH_CM0_FAMILY
-    __SIMD32_TYPE *vstate;
-
-    /* Implementation of PID controller */
-
-    /* acc = A0 * x[n]  */
-    acc = (q31_t) __SMUAD((uint32_t)S->A0, (uint32_t)in);
-
-    /* acc += A1 * x[n-1] + A2 * x[n-2]  */
-    vstate = __SIMD32_CONST(S->state);
-    acc = (q63_t)__SMLALD((uint32_t)S->A1, (uint32_t)*vstate, (uint64_t)acc);
-#else
-    /* acc = A0 * x[n]  */
-    acc = ((q31_t) S->A0) * in;
-
-    /* acc += A1 * x[n-1] + A2 * x[n-2]  */
-    acc += (q31_t) S->A1 * S->state[0];
-    acc += (q31_t) S->A2 * S->state[1];
-#endif
-
-    /* acc += y[n-1] */
-    acc += (q31_t) S->state[2] << 15;
-
-    /* saturate the output */
-    out = (q15_t) (__SSAT((acc >> 15), 16));
-
-    /* Update state */
-    S->state[1] = S->state[0];
-    S->state[0] = in;
-    S->state[2] = out;
-
-    /* return to application */
-    return (out);
-  }
-
-  /**
-   * @} end of PID group
-   */
-
-
-  /**
-   * @brief Floating-point matrix inverse.
-   * @param[in]  src   points to the instance of the input floating-point matrix structure.
-   * @param[out] dst   points to the instance of the output floating-point matrix structure.
-   * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
-   * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR.
-   */
-  arm_status arm_mat_inverse_f32(
-  const arm_matrix_instance_f32 * src,
-  arm_matrix_instance_f32 * dst);
-
-
-  /**
-   * @brief Floating-point matrix inverse.
-   * @param[in]  src   points to the instance of the input floating-point matrix structure.
-   * @param[out] dst   points to the instance of the output floating-point matrix structure.
-   * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
-   * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR.
-   */
-  arm_status arm_mat_inverse_f64(
-  const arm_matrix_instance_f64 * src,
-  arm_matrix_instance_f64 * dst);
-
-
-
-  /**
-   * @ingroup groupController
-   */
-
-  /**
-   * @defgroup clarke Vector Clarke Transform
-   * Forward Clarke transform converts the instantaneous stator phases into a two-coordinate time invariant vector.
-   * Generally the Clarke transform uses three-phase currents <code>Ia, Ib and Ic</code> to calculate currents
-   * in the two-phase orthogonal stator axis <code>Ialpha</code> and <code>Ibeta</code>.
-   * When <code>Ialpha</code> is superposed with <code>Ia</code> as shown in the figure below
-   * \image html clarke.gif Stator current space vector and its components in (a,b).
-   * and <code>Ia + Ib + Ic = 0</code>, in this condition <code>Ialpha</code> and <code>Ibeta</code>
-   * can be calculated using only <code>Ia</code> and <code>Ib</code>.
-   *
-   * The function operates on a single sample of data and each call to the function returns the processed output.
-   * The library provides separate functions for Q31 and floating-point data types.
-   * \par Algorithm
-   * \image html clarkeFormula.gif
-   * where <code>Ia</code> and <code>Ib</code> are the instantaneous stator phases and
-   * <code>pIalpha</code> and <code>pIbeta</code> are the two coordinates of time invariant vector.
-   * \par Fixed-Point Behavior
-   * Care must be taken when using the Q31 version of the Clarke transform.
-   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
-   * Refer to the function specific documentation below for usage guidelines.
-   */
-
-  /**
-   * @addtogroup clarke
-   * @{
-   */
-
-  /**
-   *
-   * @brief  Floating-point Clarke transform
-   * @param[in]  Ia       input three-phase coordinate <code>a</code>
-   * @param[in]  Ib       input three-phase coordinate <code>b</code>
-   * @param[out] pIalpha  points to output two-phase orthogonal vector axis alpha
-   * @param[out] pIbeta   points to output two-phase orthogonal vector axis beta
-   */
-  static __INLINE void arm_clarke_f32(
-  float32_t Ia,
-  float32_t Ib,
-  float32_t * pIalpha,
-  float32_t * pIbeta)
-  {
-    /* Calculate pIalpha using the equation, pIalpha = Ia */
-    *pIalpha = Ia;
-
-    /* Calculate pIbeta using the equation, pIbeta = (1/sqrt(3)) * Ia + (2/sqrt(3)) * Ib */
-    *pIbeta = ((float32_t) 0.57735026919 * Ia + (float32_t) 1.15470053838 * Ib);
-  }
-
-
-  /**
-   * @brief  Clarke transform for Q31 version
-   * @param[in]  Ia       input three-phase coordinate <code>a</code>
-   * @param[in]  Ib       input three-phase coordinate <code>b</code>
-   * @param[out] pIalpha  points to output two-phase orthogonal vector axis alpha
-   * @param[out] pIbeta   points to output two-phase orthogonal vector axis beta
-   *
-   * <b>Scaling and Overflow Behavior:</b>
-   * \par
-   * The function is implemented using an internal 32-bit accumulator.
-   * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
-   * There is saturation on the addition, hence there is no risk of overflow.
-   */
-  static __INLINE void arm_clarke_q31(
-  q31_t Ia,
-  q31_t Ib,
-  q31_t * pIalpha,
-  q31_t * pIbeta)
-  {
-    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
-
-    /* Calculating pIalpha from Ia by equation pIalpha = Ia */
-    *pIalpha = Ia;
-
-    /* Intermediate product is calculated by (1/(sqrt(3)) * Ia) */
-    product1 = (q31_t) (((q63_t) Ia * 0x24F34E8B) >> 30);
-
-    /* Intermediate product is calculated by (2/sqrt(3) * Ib) */
-    product2 = (q31_t) (((q63_t) Ib * 0x49E69D16) >> 30);
-
-    /* pIbeta is calculated by adding the intermediate products */
-    *pIbeta = __QADD(product1, product2);
-  }
-
-  /**
-   * @} end of clarke group
-   */
-
-  /**
-   * @brief  Converts the elements of the Q7 vector to Q31 vector.
-   * @param[in]  pSrc       input pointer
-   * @param[out] pDst       output pointer
-   * @param[in]  blockSize  number of samples to process
-   */
-  void arm_q7_to_q31(
-  q7_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-
-  /**
-   * @ingroup groupController
-   */
-
-  /**
-   * @defgroup inv_clarke Vector Inverse Clarke Transform
-   * Inverse Clarke transform converts the two-coordinate time invariant vector into instantaneous stator phases.
-   *
-   * The function operates on a single sample of data and each call to the function returns the processed output.
-   * The library provides separate functions for Q31 and floating-point data types.
-   * \par Algorithm
-   * \image html clarkeInvFormula.gif
-   * where <code>pIa</code> and <code>pIb</code> are the instantaneous stator phases and
-   * <code>Ialpha</code> and <code>Ibeta</code> are the two coordinates of time invariant vector.
-   * \par Fixed-Point Behavior
-   * Care must be taken when using the Q31 version of the Clarke transform.
-   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
-   * Refer to the function specific documentation below for usage guidelines.
-   */
-
-  /**
-   * @addtogroup inv_clarke
-   * @{
-   */
-
-   /**
-   * @brief  Floating-point Inverse Clarke transform
-   * @param[in]  Ialpha  input two-phase orthogonal vector axis alpha
-   * @param[in]  Ibeta   input two-phase orthogonal vector axis beta
-   * @param[out] pIa     points to output three-phase coordinate <code>a</code>
-   * @param[out] pIb     points to output three-phase coordinate <code>b</code>
-   */
-  static __INLINE void arm_inv_clarke_f32(
-  float32_t Ialpha,
-  float32_t Ibeta,
-  float32_t * pIa,
-  float32_t * pIb)
-  {
-    /* Calculating pIa from Ialpha by equation pIa = Ialpha */
-    *pIa = Ialpha;
-
-    /* Calculating pIb from Ialpha and Ibeta by equation pIb = -(1/2) * Ialpha + (sqrt(3)/2) * Ibeta */
-    *pIb = -0.5f * Ialpha + 0.8660254039f * Ibeta;
-  }
-
-
-  /**
-   * @brief  Inverse Clarke transform for Q31 version
-   * @param[in]  Ialpha  input two-phase orthogonal vector axis alpha
-   * @param[in]  Ibeta   input two-phase orthogonal vector axis beta
-   * @param[out] pIa     points to output three-phase coordinate <code>a</code>
-   * @param[out] pIb     points to output three-phase coordinate <code>b</code>
-   *
-   * <b>Scaling and Overflow Behavior:</b>
-   * \par
-   * The function is implemented using an internal 32-bit accumulator.
-   * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
-   * There is saturation on the subtraction, hence there is no risk of overflow.
-   */
-  static __INLINE void arm_inv_clarke_q31(
-  q31_t Ialpha,
-  q31_t Ibeta,
-  q31_t * pIa,
-  q31_t * pIb)
-  {
-    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
-
-    /* Calculating pIa from Ialpha by equation pIa = Ialpha */
-    *pIa = Ialpha;
-
-    /* Intermediate product is calculated by (1/(2*sqrt(3)) * Ia) */
-    product1 = (q31_t) (((q63_t) (Ialpha) * (0x40000000)) >> 31);
-
-    /* Intermediate product is calculated by (1/sqrt(3) * pIb) */
-    product2 = (q31_t) (((q63_t) (Ibeta) * (0x6ED9EBA1)) >> 31);
-
-    /* pIb is calculated by subtracting the products */
-    *pIb = __QSUB(product2, product1);
-  }
-
-  /**
-   * @} end of inv_clarke group
-   */
-
-  /**
-   * @brief  Converts the elements of the Q7 vector to Q15 vector.
-   * @param[in]  pSrc       input pointer
-   * @param[out] pDst       output pointer
-   * @param[in]  blockSize  number of samples to process
-   */
-  void arm_q7_to_q15(
-  q7_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-
-  /**
-   * @ingroup groupController
-   */
-
-  /**
-   * @defgroup park Vector Park Transform
-   *
-   * Forward Park transform converts the input two-coordinate vector to flux and torque components.
-   * The Park transform can be used to realize the transformation of the <code>Ialpha</code> and the <code>Ibeta</code> currents
-   * from the stationary to the moving reference frame and control the spatial relationship between
-   * the stator vector current and rotor flux vector.
-   * If we consider the d axis aligned with the rotor flux, the diagram below shows the
-   * current vector and the relationship from the two reference frames:
-   * \image html park.gif "Stator current space vector and its component in (a,b) and in the d,q rotating reference frame"
-   *
-   * The function operates on a single sample of data and each call to the function returns the processed output.
-   * The library provides separate functions for Q31 and floating-point data types.
-   * \par Algorithm
-   * \image html parkFormula.gif
-   * where <code>Ialpha</code> and <code>Ibeta</code> are the stator vector components,
-   * <code>pId</code> and <code>pIq</code> are rotor vector components and <code>cosVal</code> and <code>sinVal</code> are the
-   * cosine and sine values of theta (rotor flux position).
-   * \par Fixed-Point Behavior
-   * Care must be taken when using the Q31 version of the Park transform.
-   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
-   * Refer to the function specific documentation below for usage guidelines.
-   */
-
-  /**
-   * @addtogroup park
-   * @{
-   */
-
-  /**
-   * @brief Floating-point Park transform
-   * @param[in]  Ialpha  input two-phase vector coordinate alpha
-   * @param[in]  Ibeta   input two-phase vector coordinate beta
-   * @param[out] pId     points to output   rotor reference frame d
-   * @param[out] pIq     points to output   rotor reference frame q
-   * @param[in]  sinVal  sine value of rotation angle theta
-   * @param[in]  cosVal  cosine value of rotation angle theta
-   *
-   * The function implements the forward Park transform.
-   *
-   */
-  static __INLINE void arm_park_f32(
-  float32_t Ialpha,
-  float32_t Ibeta,
-  float32_t * pId,
-  float32_t * pIq,
-  float32_t sinVal,
-  float32_t cosVal)
-  {
-    /* Calculate pId using the equation, pId = Ialpha * cosVal + Ibeta * sinVal */
-    *pId = Ialpha * cosVal + Ibeta * sinVal;
-
-    /* Calculate pIq using the equation, pIq = - Ialpha * sinVal + Ibeta * cosVal */
-    *pIq = -Ialpha * sinVal + Ibeta * cosVal;
-  }
-
-
-  /**
-   * @brief  Park transform for Q31 version
-   * @param[in]  Ialpha  input two-phase vector coordinate alpha
-   * @param[in]  Ibeta   input two-phase vector coordinate beta
-   * @param[out] pId     points to output rotor reference frame d
-   * @param[out] pIq     points to output rotor reference frame q
-   * @param[in]  sinVal  sine value of rotation angle theta
-   * @param[in]  cosVal  cosine value of rotation angle theta
-   *
-   * <b>Scaling and Overflow Behavior:</b>
-   * \par
-   * The function is implemented using an internal 32-bit accumulator.
-   * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
-   * There is saturation on the addition and subtraction, hence there is no risk of overflow.
-   */
-  static __INLINE void arm_park_q31(
-  q31_t Ialpha,
-  q31_t Ibeta,
-  q31_t * pId,
-  q31_t * pIq,
-  q31_t sinVal,
-  q31_t cosVal)
-  {
-    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
-    q31_t product3, product4;                    /* Temporary variables used to store intermediate results */
-
-    /* Intermediate product is calculated by (Ialpha * cosVal) */
-    product1 = (q31_t) (((q63_t) (Ialpha) * (cosVal)) >> 31);
-
-    /* Intermediate product is calculated by (Ibeta * sinVal) */
-    product2 = (q31_t) (((q63_t) (Ibeta) * (sinVal)) >> 31);
-
-
-    /* Intermediate product is calculated by (Ialpha * sinVal) */
-    product3 = (q31_t) (((q63_t) (Ialpha) * (sinVal)) >> 31);
-
-    /* Intermediate product is calculated by (Ibeta * cosVal) */
-    product4 = (q31_t) (((q63_t) (Ibeta) * (cosVal)) >> 31);
-
-    /* Calculate pId by adding the two intermediate products 1 and 2 */
-    *pId = __QADD(product1, product2);
-
-    /* Calculate pIq by subtracting the two intermediate products 3 from 4 */
-    *pIq = __QSUB(product4, product3);
-  }
-
-  /**
-   * @} end of park group
-   */
-
-  /**
-   * @brief  Converts the elements of the Q7 vector to floating-point vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[out] pDst       is output pointer
-   * @param[in]  blockSize  is the number of samples to process
-   */
-  void arm_q7_to_float(
-  q7_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @ingroup groupController
-   */
-
-  /**
-   * @defgroup inv_park Vector Inverse Park transform
-   * Inverse Park transform converts the input flux and torque components to two-coordinate vector.
-   *
-   * The function operates on a single sample of data and each call to the function returns the processed output.
-   * The library provides separate functions for Q31 and floating-point data types.
-   * \par Algorithm
-   * \image html parkInvFormula.gif
-   * where <code>pIalpha</code> and <code>pIbeta</code> are the stator vector components,
-   * <code>Id</code> and <code>Iq</code> are rotor vector components and <code>cosVal</code> and <code>sinVal</code> are the
-   * cosine and sine values of theta (rotor flux position).
-   * \par Fixed-Point Behavior
-   * Care must be taken when using the Q31 version of the Park transform.
-   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
-   * Refer to the function specific documentation below for usage guidelines.
-   */
-
-  /**
-   * @addtogroup inv_park
-   * @{
-   */
-
-   /**
-   * @brief  Floating-point Inverse Park transform
-   * @param[in]  Id       input coordinate of rotor reference frame d
-   * @param[in]  Iq       input coordinate of rotor reference frame q
-   * @param[out] pIalpha  points to output two-phase orthogonal vector axis alpha
-   * @param[out] pIbeta   points to output two-phase orthogonal vector axis beta
-   * @param[in]  sinVal   sine value of rotation angle theta
-   * @param[in]  cosVal   cosine value of rotation angle theta
-   */
-  static __INLINE void arm_inv_park_f32(
-  float32_t Id,
-  float32_t Iq,
-  float32_t * pIalpha,
-  float32_t * pIbeta,
-  float32_t sinVal,
-  float32_t cosVal)
-  {
-    /* Calculate pIalpha using the equation, pIalpha = Id * cosVal - Iq * sinVal */
-    *pIalpha = Id * cosVal - Iq * sinVal;
-
-    /* Calculate pIbeta using the equation, pIbeta = Id * sinVal + Iq * cosVal */
-    *pIbeta = Id * sinVal + Iq * cosVal;
-  }
-
-
-  /**
-   * @brief  Inverse Park transform for   Q31 version
-   * @param[in]  Id       input coordinate of rotor reference frame d
-   * @param[in]  Iq       input coordinate of rotor reference frame q
-   * @param[out] pIalpha  points to output two-phase orthogonal vector axis alpha
-   * @param[out] pIbeta   points to output two-phase orthogonal vector axis beta
-   * @param[in]  sinVal   sine value of rotation angle theta
-   * @param[in]  cosVal   cosine value of rotation angle theta
-   *
-   * <b>Scaling and Overflow Behavior:</b>
-   * \par
-   * The function is implemented using an internal 32-bit accumulator.
-   * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
-   * There is saturation on the addition, hence there is no risk of overflow.
-   */
-  static __INLINE void arm_inv_park_q31(
-  q31_t Id,
-  q31_t Iq,
-  q31_t * pIalpha,
-  q31_t * pIbeta,
-  q31_t sinVal,
-  q31_t cosVal)
-  {
-    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
-    q31_t product3, product4;                    /* Temporary variables used to store intermediate results */
-
-    /* Intermediate product is calculated by (Id * cosVal) */
-    product1 = (q31_t) (((q63_t) (Id) * (cosVal)) >> 31);
-
-    /* Intermediate product is calculated by (Iq * sinVal) */
-    product2 = (q31_t) (((q63_t) (Iq) * (sinVal)) >> 31);
-
-
-    /* Intermediate product is calculated by (Id * sinVal) */
-    product3 = (q31_t) (((q63_t) (Id) * (sinVal)) >> 31);
-
-    /* Intermediate product is calculated by (Iq * cosVal) */
-    product4 = (q31_t) (((q63_t) (Iq) * (cosVal)) >> 31);
-
-    /* Calculate pIalpha by using the two intermediate products 1 and 2 */
-    *pIalpha = __QSUB(product1, product2);
-
-    /* Calculate pIbeta by using the two intermediate products 3 and 4 */
-    *pIbeta = __QADD(product4, product3);
-  }
-
-  /**
-   * @} end of Inverse park group
-   */
-
-
-  /**
-   * @brief  Converts the elements of the Q31 vector to floating-point vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[out] pDst       is output pointer
-   * @param[in]  blockSize  is the number of samples to process
-   */
-  void arm_q31_to_float(
-  q31_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-  /**
-   * @ingroup groupInterpolation
-   */
-
-  /**
-   * @defgroup LinearInterpolate Linear Interpolation
-   *
-   * Linear interpolation is a method of curve fitting using linear polynomials.
-   * Linear interpolation works by effectively drawing a straight line between two neighboring samples and returning the appropriate point along that line
-   *
-   * \par
-   * \image html LinearInterp.gif "Linear interpolation"
-   *
-   * \par
-   * A  Linear Interpolate function calculates an output value(y), for the input(x)
-   * using linear interpolation of the input values x0, x1( nearest input values) and the output values y0 and y1(nearest output values)
-   *
-   * \par Algorithm:
-   * <pre>
-   *       y = y0 + (x - x0) * ((y1 - y0)/(x1-x0))
-   *       where x0, x1 are nearest values of input x
-   *             y0, y1 are nearest values to output y
-   * </pre>
-   *
-   * \par
-   * This set of functions implements Linear interpolation process
-   * for Q7, Q15, Q31, and floating-point data types.  The functions operate on a single
-   * sample of data and each call to the function returns a single processed value.
-   * <code>S</code> points to an instance of the Linear Interpolate function data structure.
-   * <code>x</code> is the input sample value. The functions returns the output value.
-   *
-   * \par
-   * if x is outside of the table boundary, Linear interpolation returns first value of the table
-   * if x is below input range and returns last value of table if x is above range.
-   */
-
-  /**
-   * @addtogroup LinearInterpolate
-   * @{
-   */
-
-  /**
-   * @brief  Process function for the floating-point Linear Interpolation Function.
-   * @param[in,out] S  is an instance of the floating-point Linear Interpolation structure
-   * @param[in]     x  input sample to process
-   * @return y processed output sample.
-   *
-   */
-  static __INLINE float32_t arm_linear_interp_f32(
-  arm_linear_interp_instance_f32 * S,
-  float32_t x)
-  {
-    float32_t y;
-    float32_t x0, x1;                            /* Nearest input values */
-    float32_t y0, y1;                            /* Nearest output values */
-    float32_t xSpacing = S->xSpacing;            /* spacing between input values */
-    int32_t i;                                   /* Index variable */
-    float32_t *pYData = S->pYData;               /* pointer to output table */
-
-    /* Calculation of index */
-    i = (int32_t) ((x - S->x1) / xSpacing);
-
-    if(i < 0)
-    {
-      /* Iniatilize output for below specified range as least output value of table */
-      y = pYData[0];
-    }
-    else if((uint32_t)i >= S->nValues)
-    {
-      /* Iniatilize output for above specified range as last output value of table */
-      y = pYData[S->nValues - 1];
-    }
-    else
-    {
-      /* Calculation of nearest input values */
-      x0 = S->x1 +  i      * xSpacing;
-      x1 = S->x1 + (i + 1) * xSpacing;
-
-      /* Read of nearest output values */
-      y0 = pYData[i];
-      y1 = pYData[i + 1];
-
-      /* Calculation of output */
-      y = y0 + (x - x0) * ((y1 - y0) / (x1 - x0));
-
-    }
-
-    /* returns output value */
-    return (y);
-  }
-
-
-   /**
-   *
-   * @brief  Process function for the Q31 Linear Interpolation Function.
-   * @param[in] pYData   pointer to Q31 Linear Interpolation table
-   * @param[in] x        input sample to process
-   * @param[in] nValues  number of table values
-   * @return y processed output sample.
-   *
-   * \par
-   * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
-   * This function can support maximum of table size 2^12.
-   *
-   */
-  static __INLINE q31_t arm_linear_interp_q31(
-  q31_t * pYData,
-  q31_t x,
-  uint32_t nValues)
-  {
-    q31_t y;                                     /* output */
-    q31_t y0, y1;                                /* Nearest output values */
-    q31_t fract;                                 /* fractional part */
-    int32_t index;                               /* Index to read nearest output values */
-
-    /* Input is in 12.20 format */
-    /* 12 bits for the table index */
-    /* Index value calculation */
-    index = ((x & (q31_t)0xFFF00000) >> 20);
-
-    if(index >= (int32_t)(nValues - 1))
-    {
-      return (pYData[nValues - 1]);
-    }
-    else if(index < 0)
-    {
-      return (pYData[0]);
-    }
-    else
-    {
-      /* 20 bits for the fractional part */
-      /* shift left by 11 to keep fract in 1.31 format */
-      fract = (x & 0x000FFFFF) << 11;
-
-      /* Read two nearest output values from the index in 1.31(q31) format */
-      y0 = pYData[index];
-      y1 = pYData[index + 1];
-
-      /* Calculation of y0 * (1-fract) and y is in 2.30 format */
-      y = ((q31_t) ((q63_t) y0 * (0x7FFFFFFF - fract) >> 32));
-
-      /* Calculation of y0 * (1-fract) + y1 *fract and y is in 2.30 format */
-      y += ((q31_t) (((q63_t) y1 * fract) >> 32));
-
-      /* Convert y to 1.31 format */
-      return (y << 1u);
-    }
-  }
-
-
-  /**
-   *
-   * @brief  Process function for the Q15 Linear Interpolation Function.
-   * @param[in] pYData   pointer to Q15 Linear Interpolation table
-   * @param[in] x        input sample to process
-   * @param[in] nValues  number of table values
-   * @return y processed output sample.
-   *
-   * \par
-   * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
-   * This function can support maximum of table size 2^12.
-   *
-   */
-  static __INLINE q15_t arm_linear_interp_q15(
-  q15_t * pYData,
-  q31_t x,
-  uint32_t nValues)
-  {
-    q63_t y;                                     /* output */
-    q15_t y0, y1;                                /* Nearest output values */
-    q31_t fract;                                 /* fractional part */
-    int32_t index;                               /* Index to read nearest output values */
-
-    /* Input is in 12.20 format */
-    /* 12 bits for the table index */
-    /* Index value calculation */
-    index = ((x & (int32_t)0xFFF00000) >> 20);
-
-    if(index >= (int32_t)(nValues - 1))
-    {
-      return (pYData[nValues - 1]);
-    }
-    else if(index < 0)
-    {
-      return (pYData[0]);
-    }
-    else
-    {
-      /* 20 bits for the fractional part */
-      /* fract is in 12.20 format */
-      fract = (x & 0x000FFFFF);
-
-      /* Read two nearest output values from the index */
-      y0 = pYData[index];
-      y1 = pYData[index + 1];
-
-      /* Calculation of y0 * (1-fract) and y is in 13.35 format */
-      y = ((q63_t) y0 * (0xFFFFF - fract));
-
-      /* Calculation of (y0 * (1-fract) + y1 * fract) and y is in 13.35 format */
-      y += ((q63_t) y1 * (fract));
-
-      /* convert y to 1.15 format */
-      return (q15_t) (y >> 20);
-    }
-  }
-
-
-  /**
-   *
-   * @brief  Process function for the Q7 Linear Interpolation Function.
-   * @param[in] pYData   pointer to Q7 Linear Interpolation table
-   * @param[in] x        input sample to process
-   * @param[in] nValues  number of table values
-   * @return y processed output sample.
-   *
-   * \par
-   * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
-   * This function can support maximum of table size 2^12.
-   */
-  static __INLINE q7_t arm_linear_interp_q7(
-  q7_t * pYData,
-  q31_t x,
-  uint32_t nValues)
-  {
-    q31_t y;                                     /* output */
-    q7_t y0, y1;                                 /* Nearest output values */
-    q31_t fract;                                 /* fractional part */
-    uint32_t index;                              /* Index to read nearest output values */
-
-    /* Input is in 12.20 format */
-    /* 12 bits for the table index */
-    /* Index value calculation */
-    if (x < 0)
-    {
-      return (pYData[0]);
-    }
-    index = (x >> 20) & 0xfff;
-
-    if(index >= (nValues - 1))
-    {
-      return (pYData[nValues - 1]);
-    }
-    else
-    {
-      /* 20 bits for the fractional part */
-      /* fract is in 12.20 format */
-      fract = (x & 0x000FFFFF);
-
-      /* Read two nearest output values from the index and are in 1.7(q7) format */
-      y0 = pYData[index];
-      y1 = pYData[index + 1];
-
-      /* Calculation of y0 * (1-fract ) and y is in 13.27(q27) format */
-      y = ((y0 * (0xFFFFF - fract)));
-
-      /* Calculation of y1 * fract + y0 * (1-fract) and y is in 13.27(q27) format */
-      y += (y1 * fract);
-
-      /* convert y to 1.7(q7) format */
-      return (q7_t) (y >> 20);
-     }
-  }
-
-  /**
-   * @} end of LinearInterpolate group
-   */
-
-  /**
-   * @brief  Fast approximation to the trigonometric sine function for floating-point data.
-   * @param[in] x  input value in radians.
-   * @return  sin(x).
-   */
-  float32_t arm_sin_f32(
-  float32_t x);
-
-
-  /**
-   * @brief  Fast approximation to the trigonometric sine function for Q31 data.
-   * @param[in] x  Scaled input value in radians.
-   * @return  sin(x).
-   */
-  q31_t arm_sin_q31(
-  q31_t x);
-
-
-  /**
-   * @brief  Fast approximation to the trigonometric sine function for Q15 data.
-   * @param[in] x  Scaled input value in radians.
-   * @return  sin(x).
-   */
-  q15_t arm_sin_q15(
-  q15_t x);
-
-
-  /**
-   * @brief  Fast approximation to the trigonometric cosine function for floating-point data.
-   * @param[in] x  input value in radians.
-   * @return  cos(x).
-   */
-  float32_t arm_cos_f32(
-  float32_t x);
-
-
-  /**
-   * @brief Fast approximation to the trigonometric cosine function for Q31 data.
-   * @param[in] x  Scaled input value in radians.
-   * @return  cos(x).
-   */
-  q31_t arm_cos_q31(
-  q31_t x);
-
-
-  /**
-   * @brief  Fast approximation to the trigonometric cosine function for Q15 data.
-   * @param[in] x  Scaled input value in radians.
-   * @return  cos(x).
-   */
-  q15_t arm_cos_q15(
-  q15_t x);
-
-
-  /**
-   * @ingroup groupFastMath
-   */
-
-
-  /**
-   * @defgroup SQRT Square Root
-   *
-   * Computes the square root of a number.
-   * There are separate functions for Q15, Q31, and floating-point data types.
-   * The square root function is computed using the Newton-Raphson algorithm.
-   * This is an iterative algorithm of the form:
-   * <pre>
-   *      x1 = x0 - f(x0)/f'(x0)
-   * </pre>
-   * where <code>x1</code> is the current estimate,
-   * <code>x0</code> is the previous estimate, and
-   * <code>f'(x0)</code> is the derivative of <code>f()</code> evaluated at <code>x0</code>.
-   * For the square root function, the algorithm reduces to:
-   * <pre>
-   *     x0 = in/2                         [initial guess]
-   *     x1 = 1/2 * ( x0 + in / x0)        [each iteration]
-   * </pre>
-   */
-
-
-  /**
-   * @addtogroup SQRT
-   * @{
-   */
-
-  /**
-   * @brief  Floating-point square root function.
-   * @param[in]  in    input value.
-   * @param[out] pOut  square root of input value.
-   * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
-   * <code>in</code> is negative value and returns zero output for negative values.
-   */
-  static __INLINE arm_status arm_sqrt_f32(
-  float32_t in,
-  float32_t * pOut)
-  {
-    if(in >= 0.0f)
-    {
-
-#if   (__FPU_USED == 1) && defined ( __CC_ARM   )
-      *pOut = __sqrtf(in);
-#elif (__FPU_USED == 1) && (defined(__ARMCC_VERSION) && (__ARMCC_VERSION >= 6010050))
-      *pOut = __builtin_sqrtf(in);
-#elif (__FPU_USED == 1) && defined(__GNUC__)
-      *pOut = __builtin_sqrtf(in);
-#elif (__FPU_USED == 1) && defined ( __ICCARM__ ) && (__VER__ >= 6040000)
-      __ASM("VSQRT.F32 %0,%1" : "=t"(*pOut) : "t"(in));
-#else
-      *pOut = sqrtf(in);
-#endif
-
-      return (ARM_MATH_SUCCESS);
-    }
-    else
-    {
-      *pOut = 0.0f;
-      return (ARM_MATH_ARGUMENT_ERROR);
-    }
-  }
-
-
-  /**
-   * @brief Q31 square root function.
-   * @param[in]  in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF.
-   * @param[out] pOut  square root of input value.
-   * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
-   * <code>in</code> is negative value and returns zero output for negative values.
-   */
-  arm_status arm_sqrt_q31(
-  q31_t in,
-  q31_t * pOut);
-
-
-  /**
-   * @brief  Q15 square root function.
-   * @param[in]  in    input value.  The range of the input value is [0 +1) or 0x0000 to 0x7FFF.
-   * @param[out] pOut  square root of input value.
-   * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
-   * <code>in</code> is negative value and returns zero output for negative values.
-   */
-  arm_status arm_sqrt_q15(
-  q15_t in,
-  q15_t * pOut);
-
-  /**
-   * @} end of SQRT group
-   */
-
-
-  /**
-   * @brief floating-point Circular write function.
-   */
-  static __INLINE void arm_circularWrite_f32(
-  int32_t * circBuffer,
-  int32_t L,
-  uint16_t * writeOffset,
-  int32_t bufferInc,
-  const int32_t * src,
-  int32_t srcInc,
-  uint32_t blockSize)
-  {
-    uint32_t i = 0u;
-    int32_t wOffset;
-
-    /* Copy the value of Index pointer that points
-     * to the current location where the input samples to be copied */
-    wOffset = *writeOffset;
-
-    /* Loop over the blockSize */
-    i = blockSize;
-
-    while(i > 0u)
-    {
-      /* copy the input sample to the circular buffer */
-      circBuffer[wOffset] = *src;
-
-      /* Update the input pointer */
-      src += srcInc;
-
-      /* Circularly update wOffset.  Watch out for positive and negative value */
-      wOffset += bufferInc;
-      if(wOffset >= L)
-        wOffset -= L;
-
-      /* Decrement the loop counter */
-      i--;
-    }
-
-    /* Update the index pointer */
-    *writeOffset = (uint16_t)wOffset;
-  }
-
-
-
-  /**
-   * @brief floating-point Circular Read function.
-   */
-  static __INLINE void arm_circularRead_f32(
-  int32_t * circBuffer,
-  int32_t L,
-  int32_t * readOffset,
-  int32_t bufferInc,
-  int32_t * dst,
-  int32_t * dst_base,
-  int32_t dst_length,
-  int32_t dstInc,
-  uint32_t blockSize)
-  {
-    uint32_t i = 0u;
-    int32_t rOffset, dst_end;
-
-    /* Copy the value of Index pointer that points
-     * to the current location from where the input samples to be read */
-    rOffset = *readOffset;
-    dst_end = (int32_t) (dst_base + dst_length);
-
-    /* Loop over the blockSize */
-    i = blockSize;
-
-    while(i > 0u)
-    {
-      /* copy the sample from the circular buffer to the destination buffer */
-      *dst = circBuffer[rOffset];
-
-      /* Update the input pointer */
-      dst += dstInc;
-
-      if(dst == (int32_t *) dst_end)
-      {
-        dst = dst_base;
-      }
-
-      /* Circularly update rOffset.  Watch out for positive and negative value  */
-      rOffset += bufferInc;
-
-      if(rOffset >= L)
-      {
-        rOffset -= L;
-      }
-
-      /* Decrement the loop counter */
-      i--;
-    }
-
-    /* Update the index pointer */
-    *readOffset = rOffset;
-  }
-
-
-  /**
-   * @brief Q15 Circular write function.
-   */
-  static __INLINE void arm_circularWrite_q15(
-  q15_t * circBuffer,
-  int32_t L,
-  uint16_t * writeOffset,
-  int32_t bufferInc,
-  const q15_t * src,
-  int32_t srcInc,
-  uint32_t blockSize)
-  {
-    uint32_t i = 0u;
-    int32_t wOffset;
-
-    /* Copy the value of Index pointer that points
-     * to the current location where the input samples to be copied */
-    wOffset = *writeOffset;
-
-    /* Loop over the blockSize */
-    i = blockSize;
-
-    while(i > 0u)
-    {
-      /* copy the input sample to the circular buffer */
-      circBuffer[wOffset] = *src;
-
-      /* Update the input pointer */
-      src += srcInc;
-
-      /* Circularly update wOffset.  Watch out for positive and negative value */
-      wOffset += bufferInc;
-      if(wOffset >= L)
-        wOffset -= L;
-
-      /* Decrement the loop counter */
-      i--;
-    }
-
-    /* Update the index pointer */
-    *writeOffset = (uint16_t)wOffset;
-  }
-
-
-  /**
-   * @brief Q15 Circular Read function.
-   */
-  static __INLINE void arm_circularRead_q15(
-  q15_t * circBuffer,
-  int32_t L,
-  int32_t * readOffset,
-  int32_t bufferInc,
-  q15_t * dst,
-  q15_t * dst_base,
-  int32_t dst_length,
-  int32_t dstInc,
-  uint32_t blockSize)
-  {
-    uint32_t i = 0;
-    int32_t rOffset, dst_end;
-
-    /* Copy the value of Index pointer that points
-     * to the current location from where the input samples to be read */
-    rOffset = *readOffset;
-
-    dst_end = (int32_t) (dst_base + dst_length);
-
-    /* Loop over the blockSize */
-    i = blockSize;
-
-    while(i > 0u)
-    {
-      /* copy the sample from the circular buffer to the destination buffer */
-      *dst = circBuffer[rOffset];
-
-      /* Update the input pointer */
-      dst += dstInc;
-
-      if(dst == (q15_t *) dst_end)
-      {
-        dst = dst_base;
-      }
-
-      /* Circularly update wOffset.  Watch out for positive and negative value */
-      rOffset += bufferInc;
-
-      if(rOffset >= L)
-      {
-        rOffset -= L;
-      }
-
-      /* Decrement the loop counter */
-      i--;
-    }
-
-    /* Update the index pointer */
-    *readOffset = rOffset;
-  }
-
-
-  /**
-   * @brief Q7 Circular write function.
-   */
-  static __INLINE void arm_circularWrite_q7(
-  q7_t * circBuffer,
-  int32_t L,
-  uint16_t * writeOffset,
-  int32_t bufferInc,
-  const q7_t * src,
-  int32_t srcInc,
-  uint32_t blockSize)
-  {
-    uint32_t i = 0u;
-    int32_t wOffset;
-
-    /* Copy the value of Index pointer that points
-     * to the current location where the input samples to be copied */
-    wOffset = *writeOffset;
-
-    /* Loop over the blockSize */
-    i = blockSize;
-
-    while(i > 0u)
-    {
-      /* copy the input sample to the circular buffer */
-      circBuffer[wOffset] = *src;
-
-      /* Update the input pointer */
-      src += srcInc;
-
-      /* Circularly update wOffset.  Watch out for positive and negative value */
-      wOffset += bufferInc;
-      if(wOffset >= L)
-        wOffset -= L;
-
-      /* Decrement the loop counter */
-      i--;
-    }
-
-    /* Update the index pointer */
-    *writeOffset = (uint16_t)wOffset;
-  }
-
-
-  /**
-   * @brief Q7 Circular Read function.
-   */
-  static __INLINE void arm_circularRead_q7(
-  q7_t * circBuffer,
-  int32_t L,
-  int32_t * readOffset,
-  int32_t bufferInc,
-  q7_t * dst,
-  q7_t * dst_base,
-  int32_t dst_length,
-  int32_t dstInc,
-  uint32_t blockSize)
-  {
-    uint32_t i = 0;
-    int32_t rOffset, dst_end;
-
-    /* Copy the value of Index pointer that points
-     * to the current location from where the input samples to be read */
-    rOffset = *readOffset;
-
-    dst_end = (int32_t) (dst_base + dst_length);
-
-    /* Loop over the blockSize */
-    i = blockSize;
-
-    while(i > 0u)
-    {
-      /* copy the sample from the circular buffer to the destination buffer */
-      *dst = circBuffer[rOffset];
-
-      /* Update the input pointer */
-      dst += dstInc;
-
-      if(dst == (q7_t *) dst_end)
-      {
-        dst = dst_base;
-      }
-
-      /* Circularly update rOffset.  Watch out for positive and negative value */
-      rOffset += bufferInc;
-
-      if(rOffset >= L)
-      {
-        rOffset -= L;
-      }
-
-      /* Decrement the loop counter */
-      i--;
-    }
-
-    /* Update the index pointer */
-    *readOffset = rOffset;
-  }
-
-
-  /**
-   * @brief  Sum of the squares of the elements of a Q31 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_power_q31(
-  q31_t * pSrc,
-  uint32_t blockSize,
-  q63_t * pResult);
-
-
-  /**
-   * @brief  Sum of the squares of the elements of a floating-point vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_power_f32(
-  float32_t * pSrc,
-  uint32_t blockSize,
-  float32_t * pResult);
-
-
-  /**
-   * @brief  Sum of the squares of the elements of a Q15 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_power_q15(
-  q15_t * pSrc,
-  uint32_t blockSize,
-  q63_t * pResult);
-
-
-  /**
-   * @brief  Sum of the squares of the elements of a Q7 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_power_q7(
-  q7_t * pSrc,
-  uint32_t blockSize,
-  q31_t * pResult);
-
-
-  /**
-   * @brief  Mean value of a Q7 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_mean_q7(
-  q7_t * pSrc,
-  uint32_t blockSize,
-  q7_t * pResult);
-
-
-  /**
-   * @brief  Mean value of a Q15 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_mean_q15(
-  q15_t * pSrc,
-  uint32_t blockSize,
-  q15_t * pResult);
-
-
-  /**
-   * @brief  Mean value of a Q31 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_mean_q31(
-  q31_t * pSrc,
-  uint32_t blockSize,
-  q31_t * pResult);
-
-
-  /**
-   * @brief  Mean value of a floating-point vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_mean_f32(
-  float32_t * pSrc,
-  uint32_t blockSize,
-  float32_t * pResult);
-
-
-  /**
-   * @brief  Variance of the elements of a floating-point vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_var_f32(
-  float32_t * pSrc,
-  uint32_t blockSize,
-  float32_t * pResult);
-
-
-  /**
-   * @brief  Variance of the elements of a Q31 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_var_q31(
-  q31_t * pSrc,
-  uint32_t blockSize,
-  q31_t * pResult);
-
-
-  /**
-   * @brief  Variance of the elements of a Q15 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_var_q15(
-  q15_t * pSrc,
-  uint32_t blockSize,
-  q15_t * pResult);
-
-
-  /**
-   * @brief  Root Mean Square of the elements of a floating-point vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_rms_f32(
-  float32_t * pSrc,
-  uint32_t blockSize,
-  float32_t * pResult);
-
-
-  /**
-   * @brief  Root Mean Square of the elements of a Q31 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_rms_q31(
-  q31_t * pSrc,
-  uint32_t blockSize,
-  q31_t * pResult);
-
-
-  /**
-   * @brief  Root Mean Square of the elements of a Q15 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_rms_q15(
-  q15_t * pSrc,
-  uint32_t blockSize,
-  q15_t * pResult);
-
-
-  /**
-   * @brief  Standard deviation of the elements of a floating-point vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_std_f32(
-  float32_t * pSrc,
-  uint32_t blockSize,
-  float32_t * pResult);
-
-
-  /**
-   * @brief  Standard deviation of the elements of a Q31 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_std_q31(
-  q31_t * pSrc,
-  uint32_t blockSize,
-  q31_t * pResult);
-
-
-  /**
-   * @brief  Standard deviation of the elements of a Q15 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output value.
-   */
-  void arm_std_q15(
-  q15_t * pSrc,
-  uint32_t blockSize,
-  q15_t * pResult);
-
-
-  /**
-   * @brief  Floating-point complex magnitude
-   * @param[in]  pSrc        points to the complex input vector
-   * @param[out] pDst        points to the real output vector
-   * @param[in]  numSamples  number of complex samples in the input vector
-   */
-  void arm_cmplx_mag_f32(
-  float32_t * pSrc,
-  float32_t * pDst,
-  uint32_t numSamples);
-
-
-  /**
-   * @brief  Q31 complex magnitude
-   * @param[in]  pSrc        points to the complex input vector
-   * @param[out] pDst        points to the real output vector
-   * @param[in]  numSamples  number of complex samples in the input vector
-   */
-  void arm_cmplx_mag_q31(
-  q31_t * pSrc,
-  q31_t * pDst,
-  uint32_t numSamples);
-
-
-  /**
-   * @brief  Q15 complex magnitude
-   * @param[in]  pSrc        points to the complex input vector
-   * @param[out] pDst        points to the real output vector
-   * @param[in]  numSamples  number of complex samples in the input vector
-   */
-  void arm_cmplx_mag_q15(
-  q15_t * pSrc,
-  q15_t * pDst,
-  uint32_t numSamples);
-
-
-  /**
-   * @brief  Q15 complex dot product
-   * @param[in]  pSrcA       points to the first input vector
-   * @param[in]  pSrcB       points to the second input vector
-   * @param[in]  numSamples  number of complex samples in each vector
-   * @param[out] realResult  real part of the result returned here
-   * @param[out] imagResult  imaginary part of the result returned here
-   */
-  void arm_cmplx_dot_prod_q15(
-  q15_t * pSrcA,
-  q15_t * pSrcB,
-  uint32_t numSamples,
-  q31_t * realResult,
-  q31_t * imagResult);
-
-
-  /**
-   * @brief  Q31 complex dot product
-   * @param[in]  pSrcA       points to the first input vector
-   * @param[in]  pSrcB       points to the second input vector
-   * @param[in]  numSamples  number of complex samples in each vector
-   * @param[out] realResult  real part of the result returned here
-   * @param[out] imagResult  imaginary part of the result returned here
-   */
-  void arm_cmplx_dot_prod_q31(
-  q31_t * pSrcA,
-  q31_t * pSrcB,
-  uint32_t numSamples,
-  q63_t * realResult,
-  q63_t * imagResult);
-
-
-  /**
-   * @brief  Floating-point complex dot product
-   * @param[in]  pSrcA       points to the first input vector
-   * @param[in]  pSrcB       points to the second input vector
-   * @param[in]  numSamples  number of complex samples in each vector
-   * @param[out] realResult  real part of the result returned here
-   * @param[out] imagResult  imaginary part of the result returned here
-   */
-  void arm_cmplx_dot_prod_f32(
-  float32_t * pSrcA,
-  float32_t * pSrcB,
-  uint32_t numSamples,
-  float32_t * realResult,
-  float32_t * imagResult);
-
-
-  /**
-   * @brief  Q15 complex-by-real multiplication
-   * @param[in]  pSrcCmplx   points to the complex input vector
-   * @param[in]  pSrcReal    points to the real input vector
-   * @param[out] pCmplxDst   points to the complex output vector
-   * @param[in]  numSamples  number of samples in each vector
-   */
-  void arm_cmplx_mult_real_q15(
-  q15_t * pSrcCmplx,
-  q15_t * pSrcReal,
-  q15_t * pCmplxDst,
-  uint32_t numSamples);
-
-
-  /**
-   * @brief  Q31 complex-by-real multiplication
-   * @param[in]  pSrcCmplx   points to the complex input vector
-   * @param[in]  pSrcReal    points to the real input vector
-   * @param[out] pCmplxDst   points to the complex output vector
-   * @param[in]  numSamples  number of samples in each vector
-   */
-  void arm_cmplx_mult_real_q31(
-  q31_t * pSrcCmplx,
-  q31_t * pSrcReal,
-  q31_t * pCmplxDst,
-  uint32_t numSamples);
-
-
-  /**
-   * @brief  Floating-point complex-by-real multiplication
-   * @param[in]  pSrcCmplx   points to the complex input vector
-   * @param[in]  pSrcReal    points to the real input vector
-   * @param[out] pCmplxDst   points to the complex output vector
-   * @param[in]  numSamples  number of samples in each vector
-   */
-  void arm_cmplx_mult_real_f32(
-  float32_t * pSrcCmplx,
-  float32_t * pSrcReal,
-  float32_t * pCmplxDst,
-  uint32_t numSamples);
-
-
-  /**
-   * @brief  Minimum value of a Q7 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] result     is output pointer
-   * @param[in]  index      is the array index of the minimum value in the input buffer.
-   */
-  void arm_min_q7(
-  q7_t * pSrc,
-  uint32_t blockSize,
-  q7_t * result,
-  uint32_t * index);
-
-
-  /**
-   * @brief  Minimum value of a Q15 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output pointer
-   * @param[in]  pIndex     is the array index of the minimum value in the input buffer.
-   */
-  void arm_min_q15(
-  q15_t * pSrc,
-  uint32_t blockSize,
-  q15_t * pResult,
-  uint32_t * pIndex);
-
-
-  /**
-   * @brief  Minimum value of a Q31 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output pointer
-   * @param[out] pIndex     is the array index of the minimum value in the input buffer.
-   */
-  void arm_min_q31(
-  q31_t * pSrc,
-  uint32_t blockSize,
-  q31_t * pResult,
-  uint32_t * pIndex);
-
-
-  /**
-   * @brief  Minimum value of a floating-point vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[in]  blockSize  is the number of samples to process
-   * @param[out] pResult    is output pointer
-   * @param[out] pIndex     is the array index of the minimum value in the input buffer.
-   */
-  void arm_min_f32(
-  float32_t * pSrc,
-  uint32_t blockSize,
-  float32_t * pResult,
-  uint32_t * pIndex);
-
-
-/**
- * @brief Maximum value of a Q7 vector.
- * @param[in]  pSrc       points to the input buffer
- * @param[in]  blockSize  length of the input vector
- * @param[out] pResult    maximum value returned here
- * @param[out] pIndex     index of maximum value returned here
- */
-  void arm_max_q7(
-  q7_t * pSrc,
-  uint32_t blockSize,
-  q7_t * pResult,
-  uint32_t * pIndex);
-
-
-/**
- * @brief Maximum value of a Q15 vector.
- * @param[in]  pSrc       points to the input buffer
- * @param[in]  blockSize  length of the input vector
- * @param[out] pResult    maximum value returned here
- * @param[out] pIndex     index of maximum value returned here
- */
-  void arm_max_q15(
-  q15_t * pSrc,
-  uint32_t blockSize,
-  q15_t * pResult,
-  uint32_t * pIndex);
-
-
-/**
- * @brief Maximum value of a Q31 vector.
- * @param[in]  pSrc       points to the input buffer
- * @param[in]  blockSize  length of the input vector
- * @param[out] pResult    maximum value returned here
- * @param[out] pIndex     index of maximum value returned here
- */
-  void arm_max_q31(
-  q31_t * pSrc,
-  uint32_t blockSize,
-  q31_t * pResult,
-  uint32_t * pIndex);
-
-
-/**
- * @brief Maximum value of a floating-point vector.
- * @param[in]  pSrc       points to the input buffer
- * @param[in]  blockSize  length of the input vector
- * @param[out] pResult    maximum value returned here
- * @param[out] pIndex     index of maximum value returned here
- */
-  void arm_max_f32(
-  float32_t * pSrc,
-  uint32_t blockSize,
-  float32_t * pResult,
-  uint32_t * pIndex);
-
-
-  /**
-   * @brief  Q15 complex-by-complex multiplication
-   * @param[in]  pSrcA       points to the first input vector
-   * @param[in]  pSrcB       points to the second input vector
-   * @param[out] pDst        points to the output vector
-   * @param[in]  numSamples  number of complex samples in each vector
-   */
-  void arm_cmplx_mult_cmplx_q15(
-  q15_t * pSrcA,
-  q15_t * pSrcB,
-  q15_t * pDst,
-  uint32_t numSamples);
-
-
-  /**
-   * @brief  Q31 complex-by-complex multiplication
-   * @param[in]  pSrcA       points to the first input vector
-   * @param[in]  pSrcB       points to the second input vector
-   * @param[out] pDst        points to the output vector
-   * @param[in]  numSamples  number of complex samples in each vector
-   */
-  void arm_cmplx_mult_cmplx_q31(
-  q31_t * pSrcA,
-  q31_t * pSrcB,
-  q31_t * pDst,
-  uint32_t numSamples);
-
-
-  /**
-   * @brief  Floating-point complex-by-complex multiplication
-   * @param[in]  pSrcA       points to the first input vector
-   * @param[in]  pSrcB       points to the second input vector
-   * @param[out] pDst        points to the output vector
-   * @param[in]  numSamples  number of complex samples in each vector
-   */
-  void arm_cmplx_mult_cmplx_f32(
-  float32_t * pSrcA,
-  float32_t * pSrcB,
-  float32_t * pDst,
-  uint32_t numSamples);
-
-
-  /**
-   * @brief Converts the elements of the floating-point vector to Q31 vector.
-   * @param[in]  pSrc       points to the floating-point input vector
-   * @param[out] pDst       points to the Q31 output vector
-   * @param[in]  blockSize  length of the input vector
-   */
-  void arm_float_to_q31(
-  float32_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Converts the elements of the floating-point vector to Q15 vector.
-   * @param[in]  pSrc       points to the floating-point input vector
-   * @param[out] pDst       points to the Q15 output vector
-   * @param[in]  blockSize  length of the input vector
-   */
-  void arm_float_to_q15(
-  float32_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief Converts the elements of the floating-point vector to Q7 vector.
-   * @param[in]  pSrc       points to the floating-point input vector
-   * @param[out] pDst       points to the Q7 output vector
-   * @param[in]  blockSize  length of the input vector
-   */
-  void arm_float_to_q7(
-  float32_t * pSrc,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Converts the elements of the Q31 vector to Q15 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[out] pDst       is output pointer
-   * @param[in]  blockSize  is the number of samples to process
-   */
-  void arm_q31_to_q15(
-  q31_t * pSrc,
-  q15_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Converts the elements of the Q31 vector to Q7 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[out] pDst       is output pointer
-   * @param[in]  blockSize  is the number of samples to process
-   */
-  void arm_q31_to_q7(
-  q31_t * pSrc,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Converts the elements of the Q15 vector to floating-point vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[out] pDst       is output pointer
-   * @param[in]  blockSize  is the number of samples to process
-   */
-  void arm_q15_to_float(
-  q15_t * pSrc,
-  float32_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Converts the elements of the Q15 vector to Q31 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[out] pDst       is output pointer
-   * @param[in]  blockSize  is the number of samples to process
-   */
-  void arm_q15_to_q31(
-  q15_t * pSrc,
-  q31_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @brief  Converts the elements of the Q15 vector to Q7 vector.
-   * @param[in]  pSrc       is input pointer
-   * @param[out] pDst       is output pointer
-   * @param[in]  blockSize  is the number of samples to process
-   */
-  void arm_q15_to_q7(
-  q15_t * pSrc,
-  q7_t * pDst,
-  uint32_t blockSize);
-
-
-  /**
-   * @ingroup groupInterpolation
-   */
-
-  /**
-   * @defgroup BilinearInterpolate Bilinear Interpolation
-   *
-   * Bilinear interpolation is an extension of linear interpolation applied to a two dimensional grid.
-   * The underlying function <code>f(x, y)</code> is sampled on a regular grid and the interpolation process
-   * determines values between the grid points.
-   * Bilinear interpolation is equivalent to two step linear interpolation, first in the x-dimension and then in the y-dimension.
-   * Bilinear interpolation is often used in image processing to rescale images.
-   * The CMSIS DSP library provides bilinear interpolation functions for Q7, Q15, Q31, and floating-point data types.
-   *
-   * <b>Algorithm</b>
-   * \par
-   * The instance structure used by the bilinear interpolation functions describes a two dimensional data table.
-   * For floating-point, the instance structure is defined as:
-   * <pre>
-   *   typedef struct
-   *   {
-   *     uint16_t numRows;
-   *     uint16_t numCols;
-   *     float32_t *pData;
-   * } arm_bilinear_interp_instance_f32;
-   * </pre>
-   *
-   * \par
-   * where <code>numRows</code> specifies the number of rows in the table;
-   * <code>numCols</code> specifies the number of columns in the table;
-   * and <code>pData</code> points to an array of size <code>numRows*numCols</code> values.
-   * The data table <code>pTable</code> is organized in row order and the supplied data values fall on integer indexes.
-   * That is, table element (x,y) is located at <code>pTable[x + y*numCols]</code> where x and y are integers.
-   *
-   * \par
-   * Let <code>(x, y)</code> specify the desired interpolation point.  Then define:
-   * <pre>
-   *     XF = floor(x)
-   *     YF = floor(y)
-   * </pre>
-   * \par
-   * The interpolated output point is computed as:
-   * <pre>
-   *  f(x, y) = f(XF, YF) * (1-(x-XF)) * (1-(y-YF))
-   *           + f(XF+1, YF) * (x-XF)*(1-(y-YF))
-   *           + f(XF, YF+1) * (1-(x-XF))*(y-YF)
-   *           + f(XF+1, YF+1) * (x-XF)*(y-YF)
-   * </pre>
-   * Note that the coordinates (x, y) contain integer and fractional components.
-   * The integer components specify which portion of the table to use while the
-   * fractional components control the interpolation processor.
-   *
-   * \par
-   * if (x,y) are outside of the table boundary, Bilinear interpolation returns zero output.
-   */
-
-  /**
-   * @addtogroup BilinearInterpolate
-   * @{
-   */
-
-
-  /**
-  *
-  * @brief  Floating-point bilinear interpolation.
-  * @param[in,out] S  points to an instance of the interpolation structure.
-  * @param[in]     X  interpolation coordinate.
-  * @param[in]     Y  interpolation coordinate.
-  * @return out interpolated value.
-  */
-  static __INLINE float32_t arm_bilinear_interp_f32(
-  const arm_bilinear_interp_instance_f32 * S,
-  float32_t X,
-  float32_t Y)
-  {
-    float32_t out;
-    float32_t f00, f01, f10, f11;
-    float32_t *pData = S->pData;
-    int32_t xIndex, yIndex, index;
-    float32_t xdiff, ydiff;
-    float32_t b1, b2, b3, b4;
-
-    xIndex = (int32_t) X;
-    yIndex = (int32_t) Y;
-
-    /* Care taken for table outside boundary */
-    /* Returns zero output when values are outside table boundary */
-    if(xIndex < 0 || xIndex > (S->numRows - 1) || yIndex < 0 || yIndex > (S->numCols - 1))
-    {
-      return (0);
-    }
-
-    /* Calculation of index for two nearest points in X-direction */
-    index = (xIndex - 1) + (yIndex - 1) * S->numCols;
-
-
-    /* Read two nearest points in X-direction */
-    f00 = pData[index];
-    f01 = pData[index + 1];
-
-    /* Calculation of index for two nearest points in Y-direction */
-    index = (xIndex - 1) + (yIndex) * S->numCols;
-
-
-    /* Read two nearest points in Y-direction */
-    f10 = pData[index];
-    f11 = pData[index + 1];
-
-    /* Calculation of intermediate values */
-    b1 = f00;
-    b2 = f01 - f00;
-    b3 = f10 - f00;
-    b4 = f00 - f01 - f10 + f11;
-
-    /* Calculation of fractional part in X */
-    xdiff = X - xIndex;
-
-    /* Calculation of fractional part in Y */
-    ydiff = Y - yIndex;
-
-    /* Calculation of bi-linear interpolated output */
-    out = b1 + b2 * xdiff + b3 * ydiff + b4 * xdiff * ydiff;
-
-    /* return to application */
-    return (out);
-  }
-
-
-  /**
-  *
-  * @brief  Q31 bilinear interpolation.
-  * @param[in,out] S  points to an instance of the interpolation structure.
-  * @param[in]     X  interpolation coordinate in 12.20 format.
-  * @param[in]     Y  interpolation coordinate in 12.20 format.
-  * @return out interpolated value.
-  */
-  static __INLINE q31_t arm_bilinear_interp_q31(
-  arm_bilinear_interp_instance_q31 * S,
-  q31_t X,
-  q31_t Y)
-  {
-    q31_t out;                                   /* Temporary output */
-    q31_t acc = 0;                               /* output */
-    q31_t xfract, yfract;                        /* X, Y fractional parts */
-    q31_t x1, x2, y1, y2;                        /* Nearest output values */
-    int32_t rI, cI;                              /* Row and column indices */
-    q31_t *pYData = S->pData;                    /* pointer to output table values */
-    uint32_t nCols = S->numCols;                 /* num of rows */
-
-    /* Input is in 12.20 format */
-    /* 12 bits for the table index */
-    /* Index value calculation */
-    rI = ((X & (q31_t)0xFFF00000) >> 20);
-
-    /* Input is in 12.20 format */
-    /* 12 bits for the table index */
-    /* Index value calculation */
-    cI = ((Y & (q31_t)0xFFF00000) >> 20);
-
-    /* Care taken for table outside boundary */
-    /* Returns zero output when values are outside table boundary */
-    if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
-    {
-      return (0);
-    }
-
-    /* 20 bits for the fractional part */
-    /* shift left xfract by 11 to keep 1.31 format */
-    xfract = (X & 0x000FFFFF) << 11u;
-
-    /* Read two nearest output values from the index */
-    x1 = pYData[(rI) + (int32_t)nCols * (cI)    ];
-    x2 = pYData[(rI) + (int32_t)nCols * (cI) + 1];
-
-    /* 20 bits for the fractional part */
-    /* shift left yfract by 11 to keep 1.31 format */
-    yfract = (Y & 0x000FFFFF) << 11u;
-
-    /* Read two nearest output values from the index */
-    y1 = pYData[(rI) + (int32_t)nCols * (cI + 1)    ];
-    y2 = pYData[(rI) + (int32_t)nCols * (cI + 1) + 1];
-
-    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 3.29(q29) format */
-    out = ((q31_t) (((q63_t) x1  * (0x7FFFFFFF - xfract)) >> 32));
-    acc = ((q31_t) (((q63_t) out * (0x7FFFFFFF - yfract)) >> 32));
-
-    /* x2 * (xfract) * (1-yfract)  in 3.29(q29) and adding to acc */
-    out = ((q31_t) ((q63_t) x2 * (0x7FFFFFFF - yfract) >> 32));
-    acc += ((q31_t) ((q63_t) out * (xfract) >> 32));
-
-    /* y1 * (1 - xfract) * (yfract)  in 3.29(q29) and adding to acc */
-    out = ((q31_t) ((q63_t) y1 * (0x7FFFFFFF - xfract) >> 32));
-    acc += ((q31_t) ((q63_t) out * (yfract) >> 32));
-
-    /* y2 * (xfract) * (yfract)  in 3.29(q29) and adding to acc */
-    out = ((q31_t) ((q63_t) y2 * (xfract) >> 32));
-    acc += ((q31_t) ((q63_t) out * (yfract) >> 32));
-
-    /* Convert acc to 1.31(q31) format */
-    return ((q31_t)(acc << 2));
-  }
-
-
-  /**
-  * @brief  Q15 bilinear interpolation.
-  * @param[in,out] S  points to an instance of the interpolation structure.
-  * @param[in]     X  interpolation coordinate in 12.20 format.
-  * @param[in]     Y  interpolation coordinate in 12.20 format.
-  * @return out interpolated value.
-  */
-  static __INLINE q15_t arm_bilinear_interp_q15(
-  arm_bilinear_interp_instance_q15 * S,
-  q31_t X,
-  q31_t Y)
-  {
-    q63_t acc = 0;                               /* output */
-    q31_t out;                                   /* Temporary output */
-    q15_t x1, x2, y1, y2;                        /* Nearest output values */
-    q31_t xfract, yfract;                        /* X, Y fractional parts */
-    int32_t rI, cI;                              /* Row and column indices */
-    q15_t *pYData = S->pData;                    /* pointer to output table values */
-    uint32_t nCols = S->numCols;                 /* num of rows */
-
-    /* Input is in 12.20 format */
-    /* 12 bits for the table index */
-    /* Index value calculation */
-    rI = ((X & (q31_t)0xFFF00000) >> 20);
-
-    /* Input is in 12.20 format */
-    /* 12 bits for the table index */
-    /* Index value calculation */
-    cI = ((Y & (q31_t)0xFFF00000) >> 20);
-
-    /* Care taken for table outside boundary */
-    /* Returns zero output when values are outside table boundary */
-    if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
-    {
-      return (0);
-    }
-
-    /* 20 bits for the fractional part */
-    /* xfract should be in 12.20 format */
-    xfract = (X & 0x000FFFFF);
-
-    /* Read two nearest output values from the index */
-    x1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI)    ];
-    x2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI) + 1];
-
-    /* 20 bits for the fractional part */
-    /* yfract should be in 12.20 format */
-    yfract = (Y & 0x000FFFFF);
-
-    /* Read two nearest output values from the index */
-    y1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1)    ];
-    y2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1) + 1];
-
-    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 13.51 format */
-
-    /* x1 is in 1.15(q15), xfract in 12.20 format and out is in 13.35 format */
-    /* convert 13.35 to 13.31 by right shifting  and out is in 1.31 */
-    out = (q31_t) (((q63_t) x1 * (0xFFFFF - xfract)) >> 4u);
-    acc = ((q63_t) out * (0xFFFFF - yfract));
-
-    /* x2 * (xfract) * (1-yfract)  in 1.51 and adding to acc */
-    out = (q31_t) (((q63_t) x2 * (0xFFFFF - yfract)) >> 4u);
-    acc += ((q63_t) out * (xfract));
-
-    /* y1 * (1 - xfract) * (yfract)  in 1.51 and adding to acc */
-    out = (q31_t) (((q63_t) y1 * (0xFFFFF - xfract)) >> 4u);
-    acc += ((q63_t) out * (yfract));
-
-    /* y2 * (xfract) * (yfract)  in 1.51 and adding to acc */
-    out = (q31_t) (((q63_t) y2 * (xfract)) >> 4u);
-    acc += ((q63_t) out * (yfract));
-
-    /* acc is in 13.51 format and down shift acc by 36 times */
-    /* Convert out to 1.15 format */
-    return ((q15_t)(acc >> 36));
-  }
-
-
-  /**
-  * @brief  Q7 bilinear interpolation.
-  * @param[in,out] S  points to an instance of the interpolation structure.
-  * @param[in]     X  interpolation coordinate in 12.20 format.
-  * @param[in]     Y  interpolation coordinate in 12.20 format.
-  * @return out interpolated value.
-  */
-  static __INLINE q7_t arm_bilinear_interp_q7(
-  arm_bilinear_interp_instance_q7 * S,
-  q31_t X,
-  q31_t Y)
-  {
-    q63_t acc = 0;                               /* output */
-    q31_t out;                                   /* Temporary output */
-    q31_t xfract, yfract;                        /* X, Y fractional parts */
-    q7_t x1, x2, y1, y2;                         /* Nearest output values */
-    int32_t rI, cI;                              /* Row and column indices */
-    q7_t *pYData = S->pData;                     /* pointer to output table values */
-    uint32_t nCols = S->numCols;                 /* num of rows */
-
-    /* Input is in 12.20 format */
-    /* 12 bits for the table index */
-    /* Index value calculation */
-    rI = ((X & (q31_t)0xFFF00000) >> 20);
-
-    /* Input is in 12.20 format */
-    /* 12 bits for the table index */
-    /* Index value calculation */
-    cI = ((Y & (q31_t)0xFFF00000) >> 20);
-
-    /* Care taken for table outside boundary */
-    /* Returns zero output when values are outside table boundary */
-    if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
-    {
-      return (0);
-    }
-
-    /* 20 bits for the fractional part */
-    /* xfract should be in 12.20 format */
-    xfract = (X & (q31_t)0x000FFFFF);
-
-    /* Read two nearest output values from the index */
-    x1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI)    ];
-    x2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI) + 1];
-
-    /* 20 bits for the fractional part */
-    /* yfract should be in 12.20 format */
-    yfract = (Y & (q31_t)0x000FFFFF);
-
-    /* Read two nearest output values from the index */
-    y1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1)    ];
-    y2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1) + 1];
-
-    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 16.47 format */
-    out = ((x1 * (0xFFFFF - xfract)));
-    acc = (((q63_t) out * (0xFFFFF - yfract)));
-
-    /* x2 * (xfract) * (1-yfract)  in 2.22 and adding to acc */
-    out = ((x2 * (0xFFFFF - yfract)));
-    acc += (((q63_t) out * (xfract)));
-
-    /* y1 * (1 - xfract) * (yfract)  in 2.22 and adding to acc */
-    out = ((y1 * (0xFFFFF - xfract)));
-    acc += (((q63_t) out * (yfract)));
-
-    /* y2 * (xfract) * (yfract)  in 2.22 and adding to acc */
-    out = ((y2 * (yfract)));
-    acc += (((q63_t) out * (xfract)));
-
-    /* acc in 16.47 format and down shift by 40 to convert to 1.7 format */
-    return ((q7_t)(acc >> 40));
-  }
-
-  /**
-   * @} end of BilinearInterpolate group
-   */
-
-
-/* SMMLAR */
-#define multAcc_32x32_keep32_R(a, x, y) \
-    a = (q31_t) (((((q63_t) a) << 32) + ((q63_t) x * y) + 0x80000000LL ) >> 32)
-
-/* SMMLSR */
-#define multSub_32x32_keep32_R(a, x, y) \
-    a = (q31_t) (((((q63_t) a) << 32) - ((q63_t) x * y) + 0x80000000LL ) >> 32)
-
-/* SMMULR */
-#define mult_32x32_keep32_R(a, x, y) \
-    a = (q31_t) (((q63_t) x * y + 0x80000000LL ) >> 32)
-
-/* SMMLA */
-#define multAcc_32x32_keep32(a, x, y) \
-    a += (q31_t) (((q63_t) x * y) >> 32)
-
-/* SMMLS */
-#define multSub_32x32_keep32(a, x, y) \
-    a -= (q31_t) (((q63_t) x * y) >> 32)
-
-/* SMMUL */
-#define mult_32x32_keep32(a, x, y) \
-    a = (q31_t) (((q63_t) x * y ) >> 32)
-
-
-#if defined ( __CC_ARM )
-  /* Enter low optimization region - place directly above function definition */
-  #if defined( ARM_MATH_CM4 ) || defined( ARM_MATH_CM7)
-    #define LOW_OPTIMIZATION_ENTER \
-       _Pragma ("push")         \
-       _Pragma ("O1")
-  #else
-    #define LOW_OPTIMIZATION_ENTER
-  #endif
-
-  /* Exit low optimization region - place directly after end of function definition */
-  #if defined( ARM_MATH_CM4 ) || defined( ARM_MATH_CM7)
-    #define LOW_OPTIMIZATION_EXIT \
-       _Pragma ("pop")
-  #else
-    #define LOW_OPTIMIZATION_EXIT
-  #endif
-
-  /* Enter low optimization region - place directly above function definition */
-  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
-
-  /* Exit low optimization region - place directly after end of function definition */
-  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
-
-#elif defined(__ARMCC_VERSION) && (__ARMCC_VERSION >= 6010050)
-  #define LOW_OPTIMIZATION_ENTER
-  #define LOW_OPTIMIZATION_EXIT
-  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
-  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
-
-#elif defined(__GNUC__)
-  #define LOW_OPTIMIZATION_ENTER __attribute__(( optimize("-O1") ))
-  #define LOW_OPTIMIZATION_EXIT
-  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
-  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
-
-#elif defined(__ICCARM__)
-  /* Enter low optimization region - place directly above function definition */
-  #if defined( ARM_MATH_CM4 ) || defined( ARM_MATH_CM7)
-    #define LOW_OPTIMIZATION_ENTER \
-       _Pragma ("optimize=low")
-  #else
-    #define LOW_OPTIMIZATION_ENTER
-  #endif
-
-  /* Exit low optimization region - place directly after end of function definition */
-  #define LOW_OPTIMIZATION_EXIT
-
-  /* Enter low optimization region - place directly above function definition */
-  #if defined( ARM_MATH_CM4 ) || defined( ARM_MATH_CM7)
-    #define IAR_ONLY_LOW_OPTIMIZATION_ENTER \
-       _Pragma ("optimize=low")
-  #else
-    #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
-  #endif
-
-  /* Exit low optimization region - place directly after end of function definition */
-  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
-
-#elif defined(__CSMC__)
-  #define LOW_OPTIMIZATION_ENTER
-  #define LOW_OPTIMIZATION_EXIT
-  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
-  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
-
-#elif defined(__TASKING__)
-  #define LOW_OPTIMIZATION_ENTER
-  #define LOW_OPTIMIZATION_EXIT
-  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
-  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
-
-#endif
-
-
-#ifdef   __cplusplus
-}
-#endif
-
-
-#if defined ( __GNUC__ )
-#pragma GCC diagnostic pop
-#endif
-
-#endif /* _ARM_MATH_H */
-
-/**
- *
- * End of file.
- */
+/******************************************************************************
+ * @file     arm_math.h
+ * @brief    Public header file for CMSIS DSP Library
+ * @version  V1.6.0
+ * @date     18. March 2019
+ ******************************************************************************/
+/*
+ * Copyright (c) 2010-2019 Arm Limited or its affiliates. All rights reserved.
+ *
+ * SPDX-License-Identifier: Apache-2.0
+ *
+ * Licensed under the Apache License, Version 2.0 (the License); you may
+ * not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an AS IS BASIS, WITHOUT
+ * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+/**
+   \mainpage CMSIS DSP Software Library
+   *
+   * Introduction
+   * ------------
+   *
+   * This user manual describes the CMSIS DSP software library,
+   * a suite of common signal processing functions for use on Cortex-M processor based devices.
+   *
+   * The library is divided into a number of functions each covering a specific category:
+   * - Basic math functions
+   * - Fast math functions
+   * - Complex math functions
+   * - Filters
+   * - Matrix functions
+   * - Transform functions
+   * - Motor control functions
+   * - Statistical functions
+   * - Support functions
+   * - Interpolation functions
+   *
+   * The library has separate functions for operating on 8-bit integers, 16-bit integers,
+   * 32-bit integer and 32-bit floating-point values.
+   *
+   * Using the Library
+   * ------------
+   *
+   * The library installer contains prebuilt versions of the libraries in the <code>Lib</code> folder.
+   * - arm_cortexM7lfdp_math.lib (Cortex-M7, Little endian, Double Precision Floating Point Unit)
+   * - arm_cortexM7bfdp_math.lib (Cortex-M7, Big endian, Double Precision Floating Point Unit)
+   * - arm_cortexM7lfsp_math.lib (Cortex-M7, Little endian, Single Precision Floating Point Unit)
+   * - arm_cortexM7bfsp_math.lib (Cortex-M7, Big endian and Single Precision Floating Point Unit on)
+   * - arm_cortexM7l_math.lib (Cortex-M7, Little endian)
+   * - arm_cortexM7b_math.lib (Cortex-M7, Big endian)
+   * - arm_cortexM4lf_math.lib (Cortex-M4, Little endian, Floating Point Unit)
+   * - arm_cortexM4bf_math.lib (Cortex-M4, Big endian, Floating Point Unit)
+   * - arm_cortexM4l_math.lib (Cortex-M4, Little endian)
+   * - arm_cortexM4b_math.lib (Cortex-M4, Big endian)
+   * - arm_cortexM3l_math.lib (Cortex-M3, Little endian)
+   * - arm_cortexM3b_math.lib (Cortex-M3, Big endian)
+   * - arm_cortexM0l_math.lib (Cortex-M0 / Cortex-M0+, Little endian)
+   * - arm_cortexM0b_math.lib (Cortex-M0 / Cortex-M0+, Big endian)
+   * - arm_ARMv8MBLl_math.lib (Armv8-M Baseline, Little endian)
+   * - arm_ARMv8MMLl_math.lib (Armv8-M Mainline, Little endian)
+   * - arm_ARMv8MMLlfsp_math.lib (Armv8-M Mainline, Little endian, Single Precision Floating Point Unit)
+   * - arm_ARMv8MMLld_math.lib (Armv8-M Mainline, Little endian, DSP instructions)
+   * - arm_ARMv8MMLldfsp_math.lib (Armv8-M Mainline, Little endian, DSP instructions, Single Precision Floating Point Unit)
+   *
+   * The library functions are declared in the public file <code>arm_math.h</code> which is placed in the <code>Include</code> folder.
+   * Simply include this file and link the appropriate library in the application and begin calling the library functions. The Library supports single
+   * public header file <code> arm_math.h</code> for Cortex-M cores with little endian and big endian. Same header file will be used for floating point unit(FPU) variants.
+   *
+   *
+   * Examples
+   * --------
+   *
+   * The library ships with a number of examples which demonstrate how to use the library functions.
+   *
+   * Toolchain Support
+   * ------------
+   *
+   * The library has been developed and tested with MDK version 5.14.0.0
+   * The library is being tested in GCC and IAR toolchains and updates on this activity will be made available shortly.
+   *
+   * Building the Library
+   * ------------
+   *
+   * The library installer contains a project file to rebuild libraries on MDK toolchain in the <code>CMSIS\\DSP\\Projects\\ARM</code> folder.
+   * - arm_cortexM_math.uvprojx
+   *
+   *
+   * The libraries can be built by opening the arm_cortexM_math.uvprojx project in MDK-ARM, selecting a specific target, and defining the optional preprocessor macros detailed above.
+   *
+   * Preprocessor Macros
+   * ------------
+   *
+   * Each library project have different preprocessor macros.
+   *
+   * - ARM_MATH_BIG_ENDIAN:
+   *
+   * Define macro ARM_MATH_BIG_ENDIAN to build the library for big endian targets. By default library builds for little endian targets.
+   *
+   * - ARM_MATH_MATRIX_CHECK:
+   *
+   * Define macro ARM_MATH_MATRIX_CHECK for checking on the input and output sizes of matrices
+   *
+   * - ARM_MATH_ROUNDING:
+   *
+   * Define macro ARM_MATH_ROUNDING for rounding on support functions
+   *
+   * - ARM_MATH_LOOPUNROLL:
+   *
+   * Define macro ARM_MATH_LOOPUNROLL to enable manual loop unrolling in DSP functions
+   *
+   * - ARM_MATH_NEON:
+   *
+   * Define macro ARM_MATH_NEON to enable Neon versions of the DSP functions.
+   * It is not enabled by default when Neon is available because performances are 
+   * dependent on the compiler and target architecture.
+   *
+   * - ARM_MATH_NEON_EXPERIMENTAL:
+   *
+   * Define macro ARM_MATH_NEON_EXPERIMENTAL to enable experimental Neon versions of 
+   * of some DSP functions. Experimental Neon versions currently do not have better
+   * performances than the scalar versions.
+   *
+   * <hr>
+   * CMSIS-DSP in ARM::CMSIS Pack
+   * -----------------------------
+   *
+   * The following files relevant to CMSIS-DSP are present in the <b>ARM::CMSIS</b> Pack directories:
+   * |File/Folder                      |Content                                                                 |
+   * |---------------------------------|------------------------------------------------------------------------|
+   * |\b CMSIS\\Documentation\\DSP     | This documentation                                                     |
+   * |\b CMSIS\\DSP\\DSP_Lib_TestSuite | DSP_Lib test suite                                                     |
+   * |\b CMSIS\\DSP\\Examples          | Example projects demonstrating the usage of the library functions      |
+   * |\b CMSIS\\DSP\\Include           | DSP_Lib include files                                                  |
+   * |\b CMSIS\\DSP\\Lib               | DSP_Lib binaries                                                       |
+   * |\b CMSIS\\DSP\\Projects          | Projects to rebuild DSP_Lib binaries                                   |
+   * |\b CMSIS\\DSP\\Source            | DSP_Lib source files                                                   |
+   *
+   * <hr>
+   * Revision History of CMSIS-DSP
+   * ------------
+   * Please refer to \ref ChangeLog_pg.
+   */
+
+
+/**
+ * @defgroup groupMath Basic Math Functions
+ */
+
+/**
+ * @defgroup groupFastMath Fast Math Functions
+ * This set of functions provides a fast approximation to sine, cosine, and square root.
+ * As compared to most of the other functions in the CMSIS math library, the fast math functions
+ * operate on individual values and not arrays.
+ * There are separate functions for Q15, Q31, and floating-point data.
+ *
+ */
+
+/**
+ * @defgroup groupCmplxMath Complex Math Functions
+ * This set of functions operates on complex data vectors.
+ * The data in the complex arrays is stored in an interleaved fashion
+ * (real, imag, real, imag, ...).
+ * In the API functions, the number of samples in a complex array refers
+ * to the number of complex values; the array contains twice this number of
+ * real values.
+ */
+
+/**
+ * @defgroup groupFilters Filtering Functions
+ */
+
+/**
+ * @defgroup groupMatrix Matrix Functions
+ *
+ * This set of functions provides basic matrix math operations.
+ * The functions operate on matrix data structures.  For example,
+ * the type
+ * definition for the floating-point matrix structure is shown
+ * below:
+ * <pre>
+ *     typedef struct
+ *     {
+ *       uint16_t numRows;     // number of rows of the matrix.
+ *       uint16_t numCols;     // number of columns of the matrix.
+ *       float32_t *pData;     // points to the data of the matrix.
+ *     } arm_matrix_instance_f32;
+ * </pre>
+ * There are similar definitions for Q15 and Q31 data types.
+ *
+ * The structure specifies the size of the matrix and then points to
+ * an array of data.  The array is of size <code>numRows X numCols</code>
+ * and the values are arranged in row order.  That is, the
+ * matrix element (i, j) is stored at:
+ * <pre>
+ *     pData[i*numCols + j]
+ * </pre>
+ *
+ * \par Init Functions
+ * There is an associated initialization function for each type of matrix
+ * data structure.
+ * The initialization function sets the values of the internal structure fields.
+ * Refer to \ref arm_mat_init_f32(), \ref arm_mat_init_q31() and \ref arm_mat_init_q15()
+ * for floating-point, Q31 and Q15 types,  respectively.
+ *
+ * \par
+ * Use of the initialization function is optional. However, if initialization function is used
+ * then the instance structure cannot be placed into a const data section.
+ * To place the instance structure in a const data
+ * section, manually initialize the data structure.  For example:
+ * <pre>
+ * <code>arm_matrix_instance_f32 S = {nRows, nColumns, pData};</code>
+ * <code>arm_matrix_instance_q31 S = {nRows, nColumns, pData};</code>
+ * <code>arm_matrix_instance_q15 S = {nRows, nColumns, pData};</code>
+ * </pre>
+ * where <code>nRows</code> specifies the number of rows, <code>nColumns</code>
+ * specifies the number of columns, and <code>pData</code> points to the
+ * data array.
+ *
+ * \par Size Checking
+ * By default all of the matrix functions perform size checking on the input and
+ * output matrices. For example, the matrix addition function verifies that the
+ * two input matrices and the output matrix all have the same number of rows and
+ * columns. If the size check fails the functions return:
+ * <pre>
+ *     ARM_MATH_SIZE_MISMATCH
+ * </pre>
+ * Otherwise the functions return
+ * <pre>
+ *     ARM_MATH_SUCCESS
+ * </pre>
+ * There is some overhead associated with this matrix size checking.
+ * The matrix size checking is enabled via the \#define
+ * <pre>
+ *     ARM_MATH_MATRIX_CHECK
+ * </pre>
+ * within the library project settings.  By default this macro is defined
+ * and size checking is enabled. By changing the project settings and
+ * undefining this macro size checking is eliminated and the functions
+ * run a bit faster. With size checking disabled the functions always
+ * return <code>ARM_MATH_SUCCESS</code>.
+ */
+
+/**
+ * @defgroup groupTransforms Transform Functions
+ */
+
+/**
+ * @defgroup groupController Controller Functions
+ */
+
+/**
+ * @defgroup groupStats Statistics Functions
+ */
+
+/**
+ * @defgroup groupSupport Support Functions
+ */
+
+/**
+ * @defgroup groupInterpolation Interpolation Functions
+ * These functions perform 1- and 2-dimensional interpolation of data.
+ * Linear interpolation is used for 1-dimensional data and
+ * bilinear interpolation is used for 2-dimensional data.
+ */
+
+/**
+ * @defgroup groupExamples Examples
+ */
+
+
+#ifndef _ARM_MATH_H
+#define _ARM_MATH_H
+
+/* Compiler specific diagnostic adjustment */
+#if   defined ( __CC_ARM )
+
+#elif defined ( __ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 )
+
+#elif defined ( __GNUC__ )
+  #pragma GCC diagnostic push
+  #pragma GCC diagnostic ignored "-Wsign-conversion"
+  #pragma GCC diagnostic ignored "-Wconversion"
+  #pragma GCC diagnostic ignored "-Wunused-parameter"
+
+#elif defined ( __ICCARM__ )
+
+#elif defined ( __TI_ARM__ )
+
+#elif defined ( __CSMC__ )
+
+#elif defined ( __TASKING__ )
+
+#elif defined ( _MSC_VER )
+
+#else
+  #error Unknown compiler
+#endif
+
+
+/* Included for instrinsics definitions */
+#if !defined ( _MSC_VER )
+#include "cmsis_compiler.h"
+#else
+#include <stdint.h>
+#define __STATIC_FORCEINLINE static __forceinline
+#define __ALIGNED(x) __declspec(align(x))
+#define LOW_OPTIMIZATION_ENTER
+#define LOW_OPTIMIZATION_EXIT
+#define IAR_ONLY_LOW_OPTIMIZATION_ENTER 
+#define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+#endif
+
+#include "string.h"
+#include "math.h"
+#include "float.h"
+
+/* evaluate ARM DSP feature */
+#if (defined (__ARM_FEATURE_DSP) && (__ARM_FEATURE_DSP == 1))
+  #define ARM_MATH_DSP                   1
+#endif
+
+#if defined(__ARM_NEON)
+#include <arm_neon.h>
+#endif
+
+
+#ifdef   __cplusplus
+extern "C"
+{
+#endif
+
+
+  /**
+   * @brief Macros required for reciprocal calculation in Normalized LMS
+   */
+
+#define DELTA_Q31          (0x100)
+#define DELTA_Q15          0x5
+#define INDEX_MASK         0x0000003F
+#ifndef PI
+  #define PI               3.14159265358979f
+#endif
+
+  /**
+   * @brief Macros required for SINE and COSINE Fast math approximations
+   */
+
+#define FAST_MATH_TABLE_SIZE  512
+#define FAST_MATH_Q31_SHIFT   (32 - 10)
+#define FAST_MATH_Q15_SHIFT   (16 - 10)
+#define CONTROLLER_Q31_SHIFT  (32 - 9)
+#define TABLE_SPACING_Q31     0x400000
+#define TABLE_SPACING_Q15     0x80
+
+  /**
+   * @brief Macros required for SINE and COSINE Controller functions
+   */
+  /* 1.31(q31) Fixed value of 2/360 */
+  /* -1 to +1 is divided into 360 values so total spacing is (2/360) */
+#define INPUT_SPACING         0xB60B61
+
+
+  /**
+   * @brief Error status returned by some functions in the library.
+   */
+
+  typedef enum
+  {
+    ARM_MATH_SUCCESS        =  0,        /**< No error */
+    ARM_MATH_ARGUMENT_ERROR = -1,        /**< One or more arguments are incorrect */
+    ARM_MATH_LENGTH_ERROR   = -2,        /**< Length of data buffer is incorrect */
+    ARM_MATH_SIZE_MISMATCH  = -3,        /**< Size of matrices is not compatible with the operation */
+    ARM_MATH_NANINF         = -4,        /**< Not-a-number (NaN) or infinity is generated */
+    ARM_MATH_SINGULAR       = -5,        /**< Input matrix is singular and cannot be inverted */
+    ARM_MATH_TEST_FAILURE   = -6         /**< Test Failed */
+  } arm_status;
+
+  /**
+   * @brief 8-bit fractional data type in 1.7 format.
+   */
+  typedef int8_t q7_t;
+
+  /**
+   * @brief 16-bit fractional data type in 1.15 format.
+   */
+  typedef int16_t q15_t;
+
+  /**
+   * @brief 32-bit fractional data type in 1.31 format.
+   */
+  typedef int32_t q31_t;
+
+  /**
+   * @brief 64-bit fractional data type in 1.63 format.
+   */
+  typedef int64_t q63_t;
+
+  /**
+   * @brief 32-bit floating-point type definition.
+   */
+  typedef float float32_t;
+
+  /**
+   * @brief 64-bit floating-point type definition.
+   */
+  typedef double float64_t;
+
+
+/**
+  @brief definition to read/write two 16 bit values.
+  @deprecated
+ */
+#if   defined ( __CC_ARM )
+  #define __SIMD32_TYPE int32_t __packed
+#elif defined ( __ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 )
+  #define __SIMD32_TYPE int32_t
+#elif defined ( __GNUC__ )
+  #define __SIMD32_TYPE int32_t
+#elif defined ( __ICCARM__ )
+  #define __SIMD32_TYPE int32_t __packed
+#elif defined ( __TI_ARM__ )
+  #define __SIMD32_TYPE int32_t
+#elif defined ( __CSMC__ )
+  #define __SIMD32_TYPE int32_t
+#elif defined ( __TASKING__ )
+  #define __SIMD32_TYPE __un(aligned) int32_t
+#elif defined(_MSC_VER )
+  #define __SIMD32_TYPE int32_t
+#else
+  #error Unknown compiler
+#endif
+
+#define __SIMD32(addr)        (*(__SIMD32_TYPE **) & (addr))
+#define __SIMD32_CONST(addr)  ( (__SIMD32_TYPE * )   (addr))
+#define _SIMD32_OFFSET(addr)  (*(__SIMD32_TYPE * )   (addr))
+#define __SIMD64(addr)        (*(      int64_t **) & (addr))
+
+/* SIMD replacement */
+
+
+/**
+  @brief         Read 2 Q15 from Q15 pointer.
+  @param[in]     pQ15      points to input value
+  @return        Q31 value
+ */
+__STATIC_FORCEINLINE q31_t read_q15x2 (
+  q15_t * pQ15)
+{
+  q31_t val;
+
+  memcpy (&val, pQ15, 4);
+
+  return (val);
+}
+
+/**
+  @brief         Read 2 Q15 from Q15 pointer and increment pointer afterwards.
+  @param[in]     pQ15      points to input value
+  @return        Q31 value
+ */
+__STATIC_FORCEINLINE q31_t read_q15x2_ia (
+  q15_t ** pQ15)
+{
+  q31_t val;
+
+  memcpy (&val, *pQ15, 4);
+  *pQ15 += 2;
+
+  return (val);
+}
+
+/**
+  @brief         Read 2 Q15 from Q15 pointer and decrement pointer afterwards.
+  @param[in]     pQ15      points to input value
+  @return        Q31 value
+ */
+__STATIC_FORCEINLINE q31_t read_q15x2_da (
+  q15_t ** pQ15)
+{
+  q31_t val;
+
+  memcpy (&val, *pQ15, 4);
+  *pQ15 -= 2;
+
+  return (val);
+}
+
+/**
+  @brief         Write 2 Q15 to Q15 pointer and increment pointer afterwards.
+  @param[in]     pQ15      points to input value
+  @param[in]     value     Q31 value
+  @return        none
+ */
+__STATIC_FORCEINLINE void write_q15x2_ia (
+  q15_t ** pQ15,
+  q31_t    value)
+{
+  q31_t val = value;
+
+  memcpy (*pQ15, &val, 4);
+  *pQ15 += 2;
+}
+
+/**
+  @brief         Write 2 Q15 to Q15 pointer.
+  @param[in]     pQ15      points to input value
+  @param[in]     value     Q31 value
+  @return        none
+ */
+__STATIC_FORCEINLINE void write_q15x2 (
+  q15_t * pQ15,
+  q31_t   value)
+{
+  q31_t val = value;
+
+  memcpy (pQ15, &val, 4);
+}
+
+
+/**
+  @brief         Read 4 Q7 from Q7 pointer and increment pointer afterwards.
+  @param[in]     pQ7       points to input value
+  @return        Q31 value
+ */
+__STATIC_FORCEINLINE q31_t read_q7x4_ia (
+  q7_t ** pQ7)
+{
+  q31_t val;
+
+  memcpy (&val, *pQ7, 4);
+  *pQ7 += 4;
+
+  return (val);
+}
+
+/**
+  @brief         Read 4 Q7 from Q7 pointer and decrement pointer afterwards.
+  @param[in]     pQ7       points to input value
+  @return        Q31 value
+ */
+__STATIC_FORCEINLINE q31_t read_q7x4_da (
+  q7_t ** pQ7)
+{
+  q31_t val;
+
+  memcpy (&val, *pQ7, 4);
+  *pQ7 -= 4;
+
+  return (val);
+}
+
+/**
+  @brief         Write 4 Q7 to Q7 pointer and increment pointer afterwards.
+  @param[in]     pQ7       points to input value
+  @param[in]     value     Q31 value
+  @return        none
+ */
+__STATIC_FORCEINLINE void write_q7x4_ia (
+  q7_t ** pQ7,
+  q31_t   value)
+{
+  q31_t val = value;
+
+  memcpy (*pQ7, &val, 4);
+  *pQ7 += 4;
+}
+
+/*
+
+Normally those kind of definitions are in a compiler file
+in Core or Core_A.
+
+But for MSVC compiler it is a bit special. The goal is very specific
+to CMSIS-DSP and only to allow the use of this library from other
+systems like Python or Matlab.
+
+MSVC is not going to be used to cross-compile to ARM. So, having a MSVC
+compiler file in Core or Core_A would not make sense.
+
+*/
+#if defined ( _MSC_VER )
+    __STATIC_FORCEINLINE uint8_t __CLZ(uint32_t data)
+    {
+      if (data == 0U) { return 32U; }
+
+      uint32_t count = 0U;
+      uint32_t mask = 0x80000000U;
+
+      while ((data & mask) == 0U)
+      {
+        count += 1U;
+        mask = mask >> 1U;
+      }
+      return count;
+    }
+
+  __STATIC_FORCEINLINE int32_t __SSAT(int32_t val, uint32_t sat)
+  {
+    if ((sat >= 1U) && (sat <= 32U))
+    {
+      const int32_t max = (int32_t)((1U << (sat - 1U)) - 1U);
+      const int32_t min = -1 - max ;
+      if (val > max)
+      {
+        return max;
+      }
+      else if (val < min)
+      {
+        return min;
+      }
+    }
+    return val;
+  }
+
+  __STATIC_FORCEINLINE uint32_t __USAT(int32_t val, uint32_t sat)
+  {
+    if (sat <= 31U)
+    {
+      const uint32_t max = ((1U << sat) - 1U);
+      if (val > (int32_t)max)
+      {
+        return max;
+      }
+      else if (val < 0)
+      {
+        return 0U;
+      }
+    }
+    return (uint32_t)val;
+  }
+#endif
+
+#ifndef ARM_MATH_DSP
+  /**
+   * @brief definition to pack two 16 bit values.
+   */
+  #define __PKHBT(ARG1, ARG2, ARG3) ( (((int32_t)(ARG1) <<    0) & (int32_t)0x0000FFFF) | \
+                                      (((int32_t)(ARG2) << ARG3) & (int32_t)0xFFFF0000)  )
+  #define __PKHTB(ARG1, ARG2, ARG3) ( (((int32_t)(ARG1) <<    0) & (int32_t)0xFFFF0000) | \
+                                      (((int32_t)(ARG2) >> ARG3) & (int32_t)0x0000FFFF)  )
+#endif
+
+   /**
+   * @brief definition to pack four 8 bit values.
+   */
+#ifndef ARM_MATH_BIG_ENDIAN
+  #define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v0) <<  0) & (int32_t)0x000000FF) | \
+                                  (((int32_t)(v1) <<  8) & (int32_t)0x0000FF00) | \
+                                  (((int32_t)(v2) << 16) & (int32_t)0x00FF0000) | \
+                                  (((int32_t)(v3) << 24) & (int32_t)0xFF000000)  )
+#else
+  #define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v3) <<  0) & (int32_t)0x000000FF) | \
+                                  (((int32_t)(v2) <<  8) & (int32_t)0x0000FF00) | \
+                                  (((int32_t)(v1) << 16) & (int32_t)0x00FF0000) | \
+                                  (((int32_t)(v0) << 24) & (int32_t)0xFF000000)  )
+#endif
+
+
+  /**
+   * @brief Clips Q63 to Q31 values.
+   */
+  __STATIC_FORCEINLINE q31_t clip_q63_to_q31(
+  q63_t x)
+  {
+    return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
+      ((0x7FFFFFFF ^ ((q31_t) (x >> 63)))) : (q31_t) x;
+  }
+
+  /**
+   * @brief Clips Q63 to Q15 values.
+   */
+  __STATIC_FORCEINLINE q15_t clip_q63_to_q15(
+  q63_t x)
+  {
+    return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
+      ((0x7FFF ^ ((q15_t) (x >> 63)))) : (q15_t) (x >> 15);
+  }
+
+  /**
+   * @brief Clips Q31 to Q7 values.
+   */
+  __STATIC_FORCEINLINE q7_t clip_q31_to_q7(
+  q31_t x)
+  {
+    return ((q31_t) (x >> 24) != ((q31_t) x >> 23)) ?
+      ((0x7F ^ ((q7_t) (x >> 31)))) : (q7_t) x;
+  }
+
+  /**
+   * @brief Clips Q31 to Q15 values.
+   */
+  __STATIC_FORCEINLINE q15_t clip_q31_to_q15(
+  q31_t x)
+  {
+    return ((q31_t) (x >> 16) != ((q31_t) x >> 15)) ?
+      ((0x7FFF ^ ((q15_t) (x >> 31)))) : (q15_t) x;
+  }
+
+  /**
+   * @brief Multiplies 32 X 64 and returns 32 bit result in 2.30 format.
+   */
+  __STATIC_FORCEINLINE q63_t mult32x64(
+  q63_t x,
+  q31_t y)
+  {
+    return ((((q63_t) (x & 0x00000000FFFFFFFF) * y) >> 32) +
+            (((q63_t) (x >> 32)                * y)      )  );
+  }
+
+  /**
+   * @brief Function to Calculates 1/in (reciprocal) value of Q31 Data type.
+   */
+  __STATIC_FORCEINLINE uint32_t arm_recip_q31(
+        q31_t in,
+        q31_t * dst,
+  const q31_t * pRecipTable)
+  {
+    q31_t out;
+    uint32_t tempVal;
+    uint32_t index, i;
+    uint32_t signBits;
+
+    if (in > 0)
+    {
+      signBits = ((uint32_t) (__CLZ( in) - 1));
+    }
+    else
+    {
+      signBits = ((uint32_t) (__CLZ(-in) - 1));
+    }
+
+    /* Convert input sample to 1.31 format */
+    in = (in << signBits);
+
+    /* calculation of index for initial approximated Val */
+    index = (uint32_t)(in >> 24);
+    index = (index & INDEX_MASK);
+
+    /* 1.31 with exp 1 */
+    out = pRecipTable[index];
+
+    /* calculation of reciprocal value */
+    /* running approximation for two iterations */
+    for (i = 0U; i < 2U; i++)
+    {
+      tempVal = (uint32_t) (((q63_t) in * out) >> 31);
+      tempVal = 0x7FFFFFFFu - tempVal;
+      /*      1.31 with exp 1 */
+      /* out = (q31_t) (((q63_t) out * tempVal) >> 30); */
+      out = clip_q63_to_q31(((q63_t) out * tempVal) >> 30);
+    }
+
+    /* write output */
+    *dst = out;
+
+    /* return num of signbits of out = 1/in value */
+    return (signBits + 1U);
+  }
+
+
+  /**
+   * @brief Function to Calculates 1/in (reciprocal) value of Q15 Data type.
+   */
+  __STATIC_FORCEINLINE uint32_t arm_recip_q15(
+        q15_t in,
+        q15_t * dst,
+  const q15_t * pRecipTable)
+  {
+    q15_t out = 0;
+    uint32_t tempVal = 0;
+    uint32_t index = 0, i = 0;
+    uint32_t signBits = 0;
+
+    if (in > 0)
+    {
+      signBits = ((uint32_t)(__CLZ( in) - 17));
+    }
+    else
+    {
+      signBits = ((uint32_t)(__CLZ(-in) - 17));
+    }
+
+    /* Convert input sample to 1.15 format */
+    in = (in << signBits);
+
+    /* calculation of index for initial approximated Val */
+    index = (uint32_t)(in >>  8);
+    index = (index & INDEX_MASK);
+
+    /*      1.15 with exp 1  */
+    out = pRecipTable[index];
+
+    /* calculation of reciprocal value */
+    /* running approximation for two iterations */
+    for (i = 0U; i < 2U; i++)
+    {
+      tempVal = (uint32_t) (((q31_t) in * out) >> 15);
+      tempVal = 0x7FFFu - tempVal;
+      /*      1.15 with exp 1 */
+      out = (q15_t) (((q31_t) out * tempVal) >> 14);
+      /* out = clip_q31_to_q15(((q31_t) out * tempVal) >> 14); */
+    }
+
+    /* write output */
+    *dst = out;
+
+    /* return num of signbits of out = 1/in value */
+    return (signBits + 1);
+  }
+
+#if defined(ARM_MATH_NEON)
+
+static inline float32x4_t __arm_vec_sqrt_f32_neon(float32x4_t  x)
+{
+    float32x4_t x1 = vmaxq_f32(x, vdupq_n_f32(FLT_MIN));
+    float32x4_t e = vrsqrteq_f32(x1);
+    e = vmulq_f32(vrsqrtsq_f32(vmulq_f32(x1, e), e), e);
+    e = vmulq_f32(vrsqrtsq_f32(vmulq_f32(x1, e), e), e);
+    return vmulq_f32(x, e);
+}
+
+static inline int16x8_t __arm_vec_sqrt_q15_neon(int16x8_t vec)
+{
+    float32x4_t tempF;
+    int32x4_t tempHI,tempLO;
+
+    tempLO = vmovl_s16(vget_low_s16(vec));
+    tempF = vcvtq_n_f32_s32(tempLO,15);
+    tempF = __arm_vec_sqrt_f32_neon(tempF);
+    tempLO = vcvtq_n_s32_f32(tempF,15);
+
+    tempHI = vmovl_s16(vget_high_s16(vec));
+    tempF = vcvtq_n_f32_s32(tempHI,15);
+    tempF = __arm_vec_sqrt_f32_neon(tempF);
+    tempHI = vcvtq_n_s32_f32(tempF,15);
+
+    return(vcombine_s16(vqmovn_s32(tempLO),vqmovn_s32(tempHI)));
+}
+
+static inline int32x4_t __arm_vec_sqrt_q31_neon(int32x4_t vec)
+{
+  float32x4_t temp;
+
+  temp = vcvtq_n_f32_s32(vec,31);
+  temp = __arm_vec_sqrt_f32_neon(temp);
+  return(vcvtq_n_s32_f32(temp,31));
+}
+
+#endif
+
+/*
+ * @brief C custom defined intrinsic functions
+ */
+#if !defined (ARM_MATH_DSP)
+
+  /*
+   * @brief C custom defined QADD8
+   */
+  __STATIC_FORCEINLINE uint32_t __QADD8(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s, t, u;
+
+    r = __SSAT(((((q31_t)x << 24) >> 24) + (((q31_t)y << 24) >> 24)), 8) & (int32_t)0x000000FF;
+    s = __SSAT(((((q31_t)x << 16) >> 24) + (((q31_t)y << 16) >> 24)), 8) & (int32_t)0x000000FF;
+    t = __SSAT(((((q31_t)x <<  8) >> 24) + (((q31_t)y <<  8) >> 24)), 8) & (int32_t)0x000000FF;
+    u = __SSAT(((((q31_t)x      ) >> 24) + (((q31_t)y      ) >> 24)), 8) & (int32_t)0x000000FF;
+
+    return ((uint32_t)((u << 24) | (t << 16) | (s <<  8) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined QSUB8
+   */
+  __STATIC_FORCEINLINE uint32_t __QSUB8(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s, t, u;
+
+    r = __SSAT(((((q31_t)x << 24) >> 24) - (((q31_t)y << 24) >> 24)), 8) & (int32_t)0x000000FF;
+    s = __SSAT(((((q31_t)x << 16) >> 24) - (((q31_t)y << 16) >> 24)), 8) & (int32_t)0x000000FF;
+    t = __SSAT(((((q31_t)x <<  8) >> 24) - (((q31_t)y <<  8) >> 24)), 8) & (int32_t)0x000000FF;
+    u = __SSAT(((((q31_t)x      ) >> 24) - (((q31_t)y      ) >> 24)), 8) & (int32_t)0x000000FF;
+
+    return ((uint32_t)((u << 24) | (t << 16) | (s <<  8) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined QADD16
+   */
+  __STATIC_FORCEINLINE uint32_t __QADD16(
+  uint32_t x,
+  uint32_t y)
+  {
+/*  q31_t r,     s;  without initialisation 'arm_offset_q15 test' fails  but 'intrinsic' tests pass! for armCC */
+    q31_t r = 0, s = 0;
+
+    r = __SSAT(((((q31_t)x << 16) >> 16) + (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
+    s = __SSAT(((((q31_t)x      ) >> 16) + (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined SHADD16
+   */
+  __STATIC_FORCEINLINE uint32_t __SHADD16(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = (((((q31_t)x << 16) >> 16) + (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+    s = (((((q31_t)x      ) >> 16) + (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined QSUB16
+   */
+  __STATIC_FORCEINLINE uint32_t __QSUB16(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = __SSAT(((((q31_t)x << 16) >> 16) - (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
+    s = __SSAT(((((q31_t)x      ) >> 16) - (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined SHSUB16
+   */
+  __STATIC_FORCEINLINE uint32_t __SHSUB16(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = (((((q31_t)x << 16) >> 16) - (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+    s = (((((q31_t)x      ) >> 16) - (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined QASX
+   */
+  __STATIC_FORCEINLINE uint32_t __QASX(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = __SSAT(((((q31_t)x << 16) >> 16) - (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
+    s = __SSAT(((((q31_t)x      ) >> 16) + (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined SHASX
+   */
+  __STATIC_FORCEINLINE uint32_t __SHASX(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = (((((q31_t)x << 16) >> 16) - (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+    s = (((((q31_t)x      ) >> 16) + (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined QSAX
+   */
+  __STATIC_FORCEINLINE uint32_t __QSAX(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = __SSAT(((((q31_t)x << 16) >> 16) + (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
+    s = __SSAT(((((q31_t)x      ) >> 16) - (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined SHSAX
+   */
+  __STATIC_FORCEINLINE uint32_t __SHSAX(
+  uint32_t x,
+  uint32_t y)
+  {
+    q31_t r, s;
+
+    r = (((((q31_t)x << 16) >> 16) + (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+    s = (((((q31_t)x      ) >> 16) - (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
+
+    return ((uint32_t)((s << 16) | (r      )));
+  }
+
+
+  /*
+   * @brief C custom defined SMUSDX
+   */
+  __STATIC_FORCEINLINE uint32_t __SMUSDX(
+  uint32_t x,
+  uint32_t y)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) -
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16))   ));
+  }
+
+  /*
+   * @brief C custom defined SMUADX
+   */
+  __STATIC_FORCEINLINE uint32_t __SMUADX(
+  uint32_t x,
+  uint32_t y)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) +
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16))   ));
+  }
+
+
+  /*
+   * @brief C custom defined QADD
+   */
+  __STATIC_FORCEINLINE int32_t __QADD(
+  int32_t x,
+  int32_t y)
+  {
+    return ((int32_t)(clip_q63_to_q31((q63_t)x + (q31_t)y)));
+  }
+
+
+  /*
+   * @brief C custom defined QSUB
+   */
+  __STATIC_FORCEINLINE int32_t __QSUB(
+  int32_t x,
+  int32_t y)
+  {
+    return ((int32_t)(clip_q63_to_q31((q63_t)x - (q31_t)y)));
+  }
+
+
+  /*
+   * @brief C custom defined SMLAD
+   */
+  __STATIC_FORCEINLINE uint32_t __SMLAD(
+  uint32_t x,
+  uint32_t y,
+  uint32_t sum)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) +
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16)) +
+                       ( ((q31_t)sum    )                                  )   ));
+  }
+
+
+  /*
+   * @brief C custom defined SMLADX
+   */
+  __STATIC_FORCEINLINE uint32_t __SMLADX(
+  uint32_t x,
+  uint32_t y,
+  uint32_t sum)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) +
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16)) +
+                       ( ((q31_t)sum    )                                  )   ));
+  }
+
+
+  /*
+   * @brief C custom defined SMLSDX
+   */
+  __STATIC_FORCEINLINE uint32_t __SMLSDX(
+  uint32_t x,
+  uint32_t y,
+  uint32_t sum)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) -
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16)) +
+                       ( ((q31_t)sum    )                                  )   ));
+  }
+
+
+  /*
+   * @brief C custom defined SMLALD
+   */
+  __STATIC_FORCEINLINE uint64_t __SMLALD(
+  uint32_t x,
+  uint32_t y,
+  uint64_t sum)
+  {
+/*  return (sum + ((q15_t) (x >> 16) * (q15_t) (y >> 16)) + ((q15_t) x * (q15_t) y)); */
+    return ((uint64_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) +
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16)) +
+                       ( ((q63_t)sum    )                                  )   ));
+  }
+
+
+  /*
+   * @brief C custom defined SMLALDX
+   */
+  __STATIC_FORCEINLINE uint64_t __SMLALDX(
+  uint32_t x,
+  uint32_t y,
+  uint64_t sum)
+  {
+/*  return (sum + ((q15_t) (x >> 16) * (q15_t) y)) + ((q15_t) x * (q15_t) (y >> 16)); */
+    return ((uint64_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) +
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16)) +
+                       ( ((q63_t)sum    )                                  )   ));
+  }
+
+
+  /*
+   * @brief C custom defined SMUAD
+   */
+  __STATIC_FORCEINLINE uint32_t __SMUAD(
+  uint32_t x,
+  uint32_t y)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) +
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16))   ));
+  }
+
+
+  /*
+   * @brief C custom defined SMUSD
+   */
+  __STATIC_FORCEINLINE uint32_t __SMUSD(
+  uint32_t x,
+  uint32_t y)
+  {
+    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) -
+                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16))   ));
+  }
+
+
+  /*
+   * @brief C custom defined SXTB16
+   */
+  __STATIC_FORCEINLINE uint32_t __SXTB16(
+  uint32_t x)
+  {
+    return ((uint32_t)(((((q31_t)x << 24) >> 24) & (q31_t)0x0000FFFF) |
+                       ((((q31_t)x <<  8) >>  8) & (q31_t)0xFFFF0000)  ));
+  }
+
+  /*
+   * @brief C custom defined SMMLA
+   */
+  __STATIC_FORCEINLINE int32_t __SMMLA(
+  int32_t x,
+  int32_t y,
+  int32_t sum)
+  {
+    return (sum + (int32_t) (((int64_t) x * y) >> 32));
+  }
+
+#endif /* !defined (ARM_MATH_DSP) */
+
+
+  /**
+   * @brief Instance structure for the Q7 FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;        /**< number of filter coefficients in the filter. */
+          q7_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    const q7_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
+  } arm_fir_instance_q7;
+
+  /**
+   * @brief Instance structure for the Q15 FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;         /**< number of filter coefficients in the filter. */
+          q15_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    const q15_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
+  } arm_fir_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;         /**< number of filter coefficients in the filter. */
+          q31_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    const q31_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps. */
+  } arm_fir_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;     /**< number of filter coefficients in the filter. */
+          float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+    const float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
+  } arm_fir_instance_f32;
+
+  /**
+   * @brief Processing function for the Q7 FIR filter.
+   * @param[in]  S          points to an instance of the Q7 FIR filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_q7(
+  const arm_fir_instance_q7 * S,
+  const q7_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q7 FIR filter.
+   * @param[in,out] S          points to an instance of the Q7 FIR structure.
+   * @param[in]     numTaps    Number of filter coefficients in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of samples that are processed.
+   */
+  void arm_fir_init_q7(
+        arm_fir_instance_q7 * S,
+        uint16_t numTaps,
+  const q7_t * pCoeffs,
+        q7_t * pState,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q15 FIR filter.
+   * @param[in]  S          points to an instance of the Q15 FIR structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_q15(
+  const arm_fir_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the fast Q15 FIR filter (fast version).
+   * @param[in]  S          points to an instance of the Q15 FIR filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_fast_q15(
+  const arm_fir_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q15 FIR filter.
+   * @param[in,out] S          points to an instance of the Q15 FIR filter structure.
+   * @param[in]     numTaps    Number of filter coefficients in the filter. Must be even and greater than or equal to 4.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of samples that are processed at a time.
+   * @return     The function returns either
+   * <code>ARM_MATH_SUCCESS</code> if initialization was successful or
+   * <code>ARM_MATH_ARGUMENT_ERROR</code> if <code>numTaps</code> is not a supported value.
+   */
+  arm_status arm_fir_init_q15(
+        arm_fir_instance_q15 * S,
+        uint16_t numTaps,
+  const q15_t * pCoeffs,
+        q15_t * pState,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q31 FIR filter.
+   * @param[in]  S          points to an instance of the Q31 FIR filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_q31(
+  const arm_fir_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the fast Q31 FIR filter (fast version).
+   * @param[in]  S          points to an instance of the Q31 FIR filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_fast_q31(
+  const arm_fir_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q31 FIR filter.
+   * @param[in,out] S          points to an instance of the Q31 FIR structure.
+   * @param[in]     numTaps    Number of filter coefficients in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of samples that are processed at a time.
+   */
+  void arm_fir_init_q31(
+        arm_fir_instance_q31 * S,
+        uint16_t numTaps,
+  const q31_t * pCoeffs,
+        q31_t * pState,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the floating-point FIR filter.
+   * @param[in]  S          points to an instance of the floating-point FIR structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_f32(
+  const arm_fir_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the floating-point FIR filter.
+   * @param[in,out] S          points to an instance of the floating-point FIR filter structure.
+   * @param[in]     numTaps    Number of filter coefficients in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of samples that are processed at a time.
+   */
+  void arm_fir_init_f32(
+        arm_fir_instance_f32 * S,
+        uint16_t numTaps,
+  const float32_t * pCoeffs,
+        float32_t * pState,
+        uint32_t blockSize);
+
+  /**
+   * @brief Instance structure for the Q15 Biquad cascade filter.
+   */
+  typedef struct
+  {
+          int8_t numStages;        /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          q15_t *pState;           /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
+    const q15_t *pCoeffs;          /**< Points to the array of coefficients.  The array is of length 5*numStages. */
+          int8_t postShift;        /**< Additional shift, in bits, applied to each output sample. */
+  } arm_biquad_casd_df1_inst_q15;
+
+  /**
+   * @brief Instance structure for the Q31 Biquad cascade filter.
+   */
+  typedef struct
+  {
+          uint32_t numStages;      /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          q31_t *pState;           /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
+    const q31_t *pCoeffs;          /**< Points to the array of coefficients.  The array is of length 5*numStages. */
+          uint8_t postShift;       /**< Additional shift, in bits, applied to each output sample. */
+  } arm_biquad_casd_df1_inst_q31;
+
+  /**
+   * @brief Instance structure for the floating-point Biquad cascade filter.
+   */
+  typedef struct
+  {
+          uint32_t numStages;      /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          float32_t *pState;       /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
+    const float32_t *pCoeffs;      /**< Points to the array of coefficients.  The array is of length 5*numStages. */
+  } arm_biquad_casd_df1_inst_f32;
+
+  /**
+   * @brief Processing function for the Q15 Biquad cascade filter.
+   * @param[in]  S          points to an instance of the Q15 Biquad cascade structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df1_q15(
+  const arm_biquad_casd_df1_inst_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q15 Biquad cascade filter.
+   * @param[in,out] S          points to an instance of the Q15 Biquad cascade structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     postShift  Shift to be applied to the output. Varies according to the coefficients format
+   */
+  void arm_biquad_cascade_df1_init_q15(
+        arm_biquad_casd_df1_inst_q15 * S,
+        uint8_t numStages,
+  const q15_t * pCoeffs,
+        q15_t * pState,
+        int8_t postShift);
+
+  /**
+   * @brief Fast but less precise processing function for the Q15 Biquad cascade filter for Cortex-M3 and Cortex-M4.
+   * @param[in]  S          points to an instance of the Q15 Biquad cascade structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df1_fast_q15(
+  const arm_biquad_casd_df1_inst_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q31 Biquad cascade filter
+   * @param[in]  S          points to an instance of the Q31 Biquad cascade structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df1_q31(
+  const arm_biquad_casd_df1_inst_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief Fast but less precise processing function for the Q31 Biquad cascade filter for Cortex-M3 and Cortex-M4.
+   * @param[in]  S          points to an instance of the Q31 Biquad cascade structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df1_fast_q31(
+  const arm_biquad_casd_df1_inst_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the Q31 Biquad cascade filter.
+   * @param[in,out] S          points to an instance of the Q31 Biquad cascade structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     postShift  Shift to be applied to the output. Varies according to the coefficients format
+   */
+  void arm_biquad_cascade_df1_init_q31(
+        arm_biquad_casd_df1_inst_q31 * S,
+        uint8_t numStages,
+  const q31_t * pCoeffs,
+        q31_t * pState,
+        int8_t postShift);
+
+  /**
+   * @brief Processing function for the floating-point Biquad cascade filter.
+   * @param[in]  S          points to an instance of the floating-point Biquad cascade structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df1_f32(
+  const arm_biquad_casd_df1_inst_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief  Initialization function for the floating-point Biquad cascade filter.
+   * @param[in,out] S          points to an instance of the floating-point Biquad cascade structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   */
+  void arm_biquad_cascade_df1_init_f32(
+        arm_biquad_casd_df1_inst_f32 * S,
+        uint8_t numStages,
+  const float32_t * pCoeffs,
+        float32_t * pState);
+
+  /**
+   * @brief Instance structure for the floating-point matrix structure.
+   */
+  typedef struct
+  {
+    uint16_t numRows;     /**< number of rows of the matrix.     */
+    uint16_t numCols;     /**< number of columns of the matrix.  */
+    float32_t *pData;     /**< points to the data of the matrix. */
+  } arm_matrix_instance_f32;
+
+
+  /**
+   * @brief Instance structure for the floating-point matrix structure.
+   */
+  typedef struct
+  {
+    uint16_t numRows;     /**< number of rows of the matrix.     */
+    uint16_t numCols;     /**< number of columns of the matrix.  */
+    float64_t *pData;     /**< points to the data of the matrix. */
+  } arm_matrix_instance_f64;
+
+  /**
+   * @brief Instance structure for the Q15 matrix structure.
+   */
+  typedef struct
+  {
+    uint16_t numRows;     /**< number of rows of the matrix.     */
+    uint16_t numCols;     /**< number of columns of the matrix.  */
+    q15_t *pData;         /**< points to the data of the matrix. */
+  } arm_matrix_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 matrix structure.
+   */
+  typedef struct
+  {
+    uint16_t numRows;     /**< number of rows of the matrix.     */
+    uint16_t numCols;     /**< number of columns of the matrix.  */
+    q31_t *pData;         /**< points to the data of the matrix. */
+  } arm_matrix_instance_q31;
+
+  /**
+   * @brief Floating-point matrix addition.
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_add_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+        arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix addition.
+   * @param[in]   pSrcA  points to the first input matrix structure
+   * @param[in]   pSrcB  points to the second input matrix structure
+   * @param[out]  pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_add_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+        arm_matrix_instance_q15 * pDst);
+
+  /**
+   * @brief Q31 matrix addition.
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_add_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Floating-point, complex, matrix multiplication.
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_cmplx_mult_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+        arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15, complex,  matrix multiplication.
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_cmplx_mult_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+        arm_matrix_instance_q15 * pDst,
+        q15_t * pScratch);
+
+  /**
+   * @brief Q31, complex, matrix multiplication.
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_cmplx_mult_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Floating-point matrix transpose.
+   * @param[in]  pSrc  points to the input matrix
+   * @param[out] pDst  points to the output matrix
+   * @return    The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
+   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_trans_f32(
+  const arm_matrix_instance_f32 * pSrc,
+        arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix transpose.
+   * @param[in]  pSrc  points to the input matrix
+   * @param[out] pDst  points to the output matrix
+   * @return    The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
+   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_trans_q15(
+  const arm_matrix_instance_q15 * pSrc,
+        arm_matrix_instance_q15 * pDst);
+
+  /**
+   * @brief Q31 matrix transpose.
+   * @param[in]  pSrc  points to the input matrix
+   * @param[out] pDst  points to the output matrix
+   * @return    The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
+   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_trans_q31(
+  const arm_matrix_instance_q31 * pSrc,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Floating-point matrix multiplication
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_mult_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+        arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix multiplication
+   * @param[in]  pSrcA   points to the first input matrix structure
+   * @param[in]  pSrcB   points to the second input matrix structure
+   * @param[out] pDst    points to output matrix structure
+   * @param[in]  pState  points to the array for storing intermediate results
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_mult_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+        arm_matrix_instance_q15 * pDst,
+        q15_t * pState);
+
+  /**
+   * @brief Q15 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA   points to the first input matrix structure
+   * @param[in]  pSrcB   points to the second input matrix structure
+   * @param[out] pDst    points to output matrix structure
+   * @param[in]  pState  points to the array for storing intermediate results
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_mult_fast_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+        arm_matrix_instance_q15 * pDst,
+        q15_t * pState);
+
+  /**
+   * @brief Q31 matrix multiplication
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_mult_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Q31 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_mult_fast_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Floating-point matrix subtraction
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_sub_f32(
+  const arm_matrix_instance_f32 * pSrcA,
+  const arm_matrix_instance_f32 * pSrcB,
+        arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix subtraction
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_sub_q15(
+  const arm_matrix_instance_q15 * pSrcA,
+  const arm_matrix_instance_q15 * pSrcB,
+        arm_matrix_instance_q15 * pDst);
+
+  /**
+   * @brief Q31 matrix subtraction
+   * @param[in]  pSrcA  points to the first input matrix structure
+   * @param[in]  pSrcB  points to the second input matrix structure
+   * @param[out] pDst   points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_sub_q31(
+  const arm_matrix_instance_q31 * pSrcA,
+  const arm_matrix_instance_q31 * pSrcB,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief Floating-point matrix scaling.
+   * @param[in]  pSrc   points to the input matrix
+   * @param[in]  scale  scale factor
+   * @param[out] pDst   points to the output matrix
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_scale_f32(
+  const arm_matrix_instance_f32 * pSrc,
+        float32_t scale,
+        arm_matrix_instance_f32 * pDst);
+
+  /**
+   * @brief Q15 matrix scaling.
+   * @param[in]  pSrc        points to input matrix
+   * @param[in]  scaleFract  fractional portion of the scale factor
+   * @param[in]  shift       number of bits to shift the result by
+   * @param[out] pDst        points to output matrix
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_scale_q15(
+  const arm_matrix_instance_q15 * pSrc,
+        q15_t scaleFract,
+        int32_t shift,
+        arm_matrix_instance_q15 * pDst);
+
+  /**
+   * @brief Q31 matrix scaling.
+   * @param[in]  pSrc        points to input matrix
+   * @param[in]  scaleFract  fractional portion of the scale factor
+   * @param[in]  shift       number of bits to shift the result by
+   * @param[out] pDst        points to output matrix structure
+   * @return     The function returns either
+   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
+   */
+arm_status arm_mat_scale_q31(
+  const arm_matrix_instance_q31 * pSrc,
+        q31_t scaleFract,
+        int32_t shift,
+        arm_matrix_instance_q31 * pDst);
+
+  /**
+   * @brief  Q31 matrix initialization.
+   * @param[in,out] S         points to an instance of the floating-point matrix structure.
+   * @param[in]     nRows     number of rows in the matrix.
+   * @param[in]     nColumns  number of columns in the matrix.
+   * @param[in]     pData     points to the matrix data array.
+   */
+void arm_mat_init_q31(
+        arm_matrix_instance_q31 * S,
+        uint16_t nRows,
+        uint16_t nColumns,
+        q31_t * pData);
+
+  /**
+   * @brief  Q15 matrix initialization.
+   * @param[in,out] S         points to an instance of the floating-point matrix structure.
+   * @param[in]     nRows     number of rows in the matrix.
+   * @param[in]     nColumns  number of columns in the matrix.
+   * @param[in]     pData     points to the matrix data array.
+   */
+void arm_mat_init_q15(
+        arm_matrix_instance_q15 * S,
+        uint16_t nRows,
+        uint16_t nColumns,
+        q15_t * pData);
+
+  /**
+   * @brief  Floating-point matrix initialization.
+   * @param[in,out] S         points to an instance of the floating-point matrix structure.
+   * @param[in]     nRows     number of rows in the matrix.
+   * @param[in]     nColumns  number of columns in the matrix.
+   * @param[in]     pData     points to the matrix data array.
+   */
+void arm_mat_init_f32(
+        arm_matrix_instance_f32 * S,
+        uint16_t nRows,
+        uint16_t nColumns,
+        float32_t * pData);
+
+
+  /**
+   * @brief Instance structure for the Q15 PID Control.
+   */
+  typedef struct
+  {
+          q15_t A0;           /**< The derived gain, A0 = Kp + Ki + Kd . */
+#if !defined (ARM_MATH_DSP)
+          q15_t A1;
+          q15_t A2;
+#else
+          q31_t A1;           /**< The derived gain A1 = -Kp - 2Kd | Kd.*/
+#endif
+          q15_t state[3];     /**< The state array of length 3. */
+          q15_t Kp;           /**< The proportional gain. */
+          q15_t Ki;           /**< The integral gain. */
+          q15_t Kd;           /**< The derivative gain. */
+  } arm_pid_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 PID Control.
+   */
+  typedef struct
+  {
+          q31_t A0;            /**< The derived gain, A0 = Kp + Ki + Kd . */
+          q31_t A1;            /**< The derived gain, A1 = -Kp - 2Kd. */
+          q31_t A2;            /**< The derived gain, A2 = Kd . */
+          q31_t state[3];      /**< The state array of length 3. */
+          q31_t Kp;            /**< The proportional gain. */
+          q31_t Ki;            /**< The integral gain. */
+          q31_t Kd;            /**< The derivative gain. */
+  } arm_pid_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point PID Control.
+   */
+  typedef struct
+  {
+          float32_t A0;          /**< The derived gain, A0 = Kp + Ki + Kd . */
+          float32_t A1;          /**< The derived gain, A1 = -Kp - 2Kd. */
+          float32_t A2;          /**< The derived gain, A2 = Kd . */
+          float32_t state[3];    /**< The state array of length 3. */
+          float32_t Kp;          /**< The proportional gain. */
+          float32_t Ki;          /**< The integral gain. */
+          float32_t Kd;          /**< The derivative gain. */
+  } arm_pid_instance_f32;
+
+
+
+  /**
+   * @brief  Initialization function for the floating-point PID Control.
+   * @param[in,out] S               points to an instance of the PID structure.
+   * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
+   */
+  void arm_pid_init_f32(
+        arm_pid_instance_f32 * S,
+        int32_t resetStateFlag);
+
+
+  /**
+   * @brief  Reset function for the floating-point PID Control.
+   * @param[in,out] S  is an instance of the floating-point PID Control structure
+   */
+  void arm_pid_reset_f32(
+        arm_pid_instance_f32 * S);
+
+
+  /**
+   * @brief  Initialization function for the Q31 PID Control.
+   * @param[in,out] S               points to an instance of the Q15 PID structure.
+   * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
+   */
+  void arm_pid_init_q31(
+        arm_pid_instance_q31 * S,
+        int32_t resetStateFlag);
+
+
+  /**
+   * @brief  Reset function for the Q31 PID Control.
+   * @param[in,out] S   points to an instance of the Q31 PID Control structure
+   */
+
+  void arm_pid_reset_q31(
+        arm_pid_instance_q31 * S);
+
+
+  /**
+   * @brief  Initialization function for the Q15 PID Control.
+   * @param[in,out] S               points to an instance of the Q15 PID structure.
+   * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
+   */
+  void arm_pid_init_q15(
+        arm_pid_instance_q15 * S,
+        int32_t resetStateFlag);
+
+
+  /**
+   * @brief  Reset function for the Q15 PID Control.
+   * @param[in,out] S  points to an instance of the q15 PID Control structure
+   */
+  void arm_pid_reset_q15(
+        arm_pid_instance_q15 * S);
+
+
+  /**
+   * @brief Instance structure for the floating-point Linear Interpolate function.
+   */
+  typedef struct
+  {
+          uint32_t nValues;           /**< nValues */
+          float32_t x1;               /**< x1 */
+          float32_t xSpacing;         /**< xSpacing */
+          float32_t *pYData;          /**< pointer to the table of Y values */
+  } arm_linear_interp_instance_f32;
+
+  /**
+   * @brief Instance structure for the floating-point bilinear interpolation function.
+   */
+  typedef struct
+  {
+          uint16_t numRows;   /**< number of rows in the data table. */
+          uint16_t numCols;   /**< number of columns in the data table. */
+          float32_t *pData;   /**< points to the data table. */
+  } arm_bilinear_interp_instance_f32;
+
+   /**
+   * @brief Instance structure for the Q31 bilinear interpolation function.
+   */
+  typedef struct
+  {
+          uint16_t numRows;   /**< number of rows in the data table. */
+          uint16_t numCols;   /**< number of columns in the data table. */
+          q31_t *pData;       /**< points to the data table. */
+  } arm_bilinear_interp_instance_q31;
+
+   /**
+   * @brief Instance structure for the Q15 bilinear interpolation function.
+   */
+  typedef struct
+  {
+          uint16_t numRows;   /**< number of rows in the data table. */
+          uint16_t numCols;   /**< number of columns in the data table. */
+          q15_t *pData;       /**< points to the data table. */
+  } arm_bilinear_interp_instance_q15;
+
+   /**
+   * @brief Instance structure for the Q15 bilinear interpolation function.
+   */
+  typedef struct
+  {
+          uint16_t numRows;   /**< number of rows in the data table. */
+          uint16_t numCols;   /**< number of columns in the data table. */
+          q7_t *pData;        /**< points to the data table. */
+  } arm_bilinear_interp_instance_q7;
+
+
+  /**
+   * @brief Q7 vector multiplication.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_mult_q7(
+  const q7_t * pSrcA,
+  const q7_t * pSrcB,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Q15 vector multiplication.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_mult_q15(
+  const q15_t * pSrcA,
+  const q15_t * pSrcB,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Q31 vector multiplication.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_mult_q31(
+  const q31_t * pSrcA,
+  const q31_t * pSrcB,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Floating-point vector multiplication.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_mult_f32(
+  const float32_t * pSrcA,
+  const float32_t * pSrcB,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q15 CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                 /**< length of the FFT. */
+          uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+          uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    const q15_t *pTwiddle;                 /**< points to the Sin twiddle factor table. */
+    const uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
+          uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+          uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+  } arm_cfft_radix2_instance_q15;
+
+/* Deprecated */
+  arm_status arm_cfft_radix2_init_q15(
+        arm_cfft_radix2_instance_q15 * S,
+        uint16_t fftLen,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+/* Deprecated */
+  void arm_cfft_radix2_q15(
+  const arm_cfft_radix2_instance_q15 * S,
+        q15_t * pSrc);
+
+
+  /**
+   * @brief Instance structure for the Q15 CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                 /**< length of the FFT. */
+          uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+          uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    const q15_t *pTwiddle;                 /**< points to the twiddle factor table. */
+    const uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
+          uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+          uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+  } arm_cfft_radix4_instance_q15;
+
+/* Deprecated */
+  arm_status arm_cfft_radix4_init_q15(
+        arm_cfft_radix4_instance_q15 * S,
+        uint16_t fftLen,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+/* Deprecated */
+  void arm_cfft_radix4_q15(
+  const arm_cfft_radix4_instance_q15 * S,
+        q15_t * pSrc);
+
+  /**
+   * @brief Instance structure for the Radix-2 Q31 CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                 /**< length of the FFT. */
+          uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+          uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    const q31_t *pTwiddle;                 /**< points to the Twiddle factor table. */
+    const uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
+          uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+          uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+  } arm_cfft_radix2_instance_q31;
+
+/* Deprecated */
+  arm_status arm_cfft_radix2_init_q31(
+        arm_cfft_radix2_instance_q31 * S,
+        uint16_t fftLen,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+/* Deprecated */
+  void arm_cfft_radix2_q31(
+  const arm_cfft_radix2_instance_q31 * S,
+        q31_t * pSrc);
+
+  /**
+   * @brief Instance structure for the Q31 CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                 /**< length of the FFT. */
+          uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+          uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    const q31_t *pTwiddle;                 /**< points to the twiddle factor table. */
+    const uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
+          uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+          uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+  } arm_cfft_radix4_instance_q31;
+
+/* Deprecated */
+  void arm_cfft_radix4_q31(
+  const arm_cfft_radix4_instance_q31 * S,
+        q31_t * pSrc);
+
+/* Deprecated */
+  arm_status arm_cfft_radix4_init_q31(
+        arm_cfft_radix4_instance_q31 * S,
+        uint16_t fftLen,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+  /**
+   * @brief Instance structure for the floating-point CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                   /**< length of the FFT. */
+          uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+          uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    const float32_t *pTwiddle;               /**< points to the Twiddle factor table. */
+    const uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
+          uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+          uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+          float32_t onebyfftLen;             /**< value of 1/fftLen. */
+  } arm_cfft_radix2_instance_f32;
+
+/* Deprecated */
+  arm_status arm_cfft_radix2_init_f32(
+        arm_cfft_radix2_instance_f32 * S,
+        uint16_t fftLen,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+/* Deprecated */
+  void arm_cfft_radix2_f32(
+  const arm_cfft_radix2_instance_f32 * S,
+        float32_t * pSrc);
+
+  /**
+   * @brief Instance structure for the floating-point CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                   /**< length of the FFT. */
+          uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
+          uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
+    const float32_t *pTwiddle;               /**< points to the Twiddle factor table. */
+    const uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
+          uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+          uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
+          float32_t onebyfftLen;             /**< value of 1/fftLen. */
+  } arm_cfft_radix4_instance_f32;
+
+/* Deprecated */
+  arm_status arm_cfft_radix4_init_f32(
+        arm_cfft_radix4_instance_f32 * S,
+        uint16_t fftLen,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+/* Deprecated */
+  void arm_cfft_radix4_f32(
+  const arm_cfft_radix4_instance_f32 * S,
+        float32_t * pSrc);
+
+  /**
+   * @brief Instance structure for the fixed-point CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                   /**< length of the FFT. */
+    const q15_t *pTwiddle;             /**< points to the Twiddle factor table. */
+    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
+          uint16_t bitRevLength;             /**< bit reversal table length. */
+  } arm_cfft_instance_q15;
+
+void arm_cfft_q15(
+    const arm_cfft_instance_q15 * S,
+          q15_t * p1,
+          uint8_t ifftFlag,
+          uint8_t bitReverseFlag);
+
+  /**
+   * @brief Instance structure for the fixed-point CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                   /**< length of the FFT. */
+    const q31_t *pTwiddle;             /**< points to the Twiddle factor table. */
+    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
+          uint16_t bitRevLength;             /**< bit reversal table length. */
+  } arm_cfft_instance_q31;
+
+void arm_cfft_q31(
+    const arm_cfft_instance_q31 * S,
+          q31_t * p1,
+          uint8_t ifftFlag,
+          uint8_t bitReverseFlag);
+
+  /**
+   * @brief Instance structure for the floating-point CFFT/CIFFT function.
+   */
+  typedef struct
+  {
+          uint16_t fftLen;                   /**< length of the FFT. */
+    const float32_t *pTwiddle;         /**< points to the Twiddle factor table. */
+    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
+          uint16_t bitRevLength;             /**< bit reversal table length. */
+  } arm_cfft_instance_f32;
+
+  void arm_cfft_f32(
+  const arm_cfft_instance_f32 * S,
+        float32_t * p1,
+        uint8_t ifftFlag,
+        uint8_t bitReverseFlag);
+
+  /**
+   * @brief Instance structure for the Q15 RFFT/RIFFT function.
+   */
+  typedef struct
+  {
+          uint32_t fftLenReal;                      /**< length of the real FFT. */
+          uint8_t ifftFlagR;                        /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
+          uint8_t bitReverseFlagR;                  /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
+          uint32_t twidCoefRModifier;               /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    const q15_t *pTwiddleAReal;                     /**< points to the real twiddle factor table. */
+    const q15_t *pTwiddleBReal;                     /**< points to the imag twiddle factor table. */
+    const arm_cfft_instance_q15 *pCfft;       /**< points to the complex FFT instance. */
+  } arm_rfft_instance_q15;
+
+  arm_status arm_rfft_init_q15(
+        arm_rfft_instance_q15 * S,
+        uint32_t fftLenReal,
+        uint32_t ifftFlagR,
+        uint32_t bitReverseFlag);
+
+  void arm_rfft_q15(
+  const arm_rfft_instance_q15 * S,
+        q15_t * pSrc,
+        q15_t * pDst);
+
+  /**
+   * @brief Instance structure for the Q31 RFFT/RIFFT function.
+   */
+  typedef struct
+  {
+          uint32_t fftLenReal;                        /**< length of the real FFT. */
+          uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
+          uint8_t bitReverseFlagR;                    /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
+          uint32_t twidCoefRModifier;                 /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    const q31_t *pTwiddleAReal;                       /**< points to the real twiddle factor table. */
+    const q31_t *pTwiddleBReal;                       /**< points to the imag twiddle factor table. */
+    const arm_cfft_instance_q31 *pCfft;         /**< points to the complex FFT instance. */
+  } arm_rfft_instance_q31;
+
+  arm_status arm_rfft_init_q31(
+        arm_rfft_instance_q31 * S,
+        uint32_t fftLenReal,
+        uint32_t ifftFlagR,
+        uint32_t bitReverseFlag);
+
+  void arm_rfft_q31(
+  const arm_rfft_instance_q31 * S,
+        q31_t * pSrc,
+        q31_t * pDst);
+
+  /**
+   * @brief Instance structure for the floating-point RFFT/RIFFT function.
+   */
+  typedef struct
+  {
+          uint32_t fftLenReal;                        /**< length of the real FFT. */
+          uint16_t fftLenBy2;                         /**< length of the complex FFT. */
+          uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
+          uint8_t bitReverseFlagR;                    /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
+          uint32_t twidCoefRModifier;                     /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
+    const float32_t *pTwiddleAReal;                   /**< points to the real twiddle factor table. */
+    const float32_t *pTwiddleBReal;                   /**< points to the imag twiddle factor table. */
+          arm_cfft_radix4_instance_f32 *pCfft;        /**< points to the complex FFT instance. */
+  } arm_rfft_instance_f32;
+
+  arm_status arm_rfft_init_f32(
+        arm_rfft_instance_f32 * S,
+        arm_cfft_radix4_instance_f32 * S_CFFT,
+        uint32_t fftLenReal,
+        uint32_t ifftFlagR,
+        uint32_t bitReverseFlag);
+
+  void arm_rfft_f32(
+  const arm_rfft_instance_f32 * S,
+        float32_t * pSrc,
+        float32_t * pDst);
+
+  /**
+   * @brief Instance structure for the floating-point RFFT/RIFFT function.
+   */
+typedef struct
+  {
+          arm_cfft_instance_f32 Sint;      /**< Internal CFFT structure. */
+          uint16_t fftLenRFFT;             /**< length of the real sequence */
+    const float32_t * pTwiddleRFFT;        /**< Twiddle factors real stage  */
+  } arm_rfft_fast_instance_f32 ;
+
+arm_status arm_rfft_fast_init_f32 (
+         arm_rfft_fast_instance_f32 * S,
+         uint16_t fftLen);
+
+arm_status arm_rfft_32_fast_init_f32 ( arm_rfft_fast_instance_f32 * S );
+
+arm_status arm_rfft_64_fast_init_f32 ( arm_rfft_fast_instance_f32 * S );
+
+arm_status arm_rfft_128_fast_init_f32 ( arm_rfft_fast_instance_f32 * S );
+
+arm_status arm_rfft_256_fast_init_f32 ( arm_rfft_fast_instance_f32 * S );
+
+arm_status arm_rfft_512_fast_init_f32 ( arm_rfft_fast_instance_f32 * S );
+
+arm_status arm_rfft_1024_fast_init_f32 ( arm_rfft_fast_instance_f32 * S );
+
+arm_status arm_rfft_2048_fast_init_f32 ( arm_rfft_fast_instance_f32 * S );
+
+arm_status arm_rfft_4096_fast_init_f32 ( arm_rfft_fast_instance_f32 * S );
+
+
+  void arm_rfft_fast_f32(
+        arm_rfft_fast_instance_f32 * S,
+        float32_t * p, float32_t * pOut,
+        uint8_t ifftFlag);
+
+  /**
+   * @brief Instance structure for the floating-point DCT4/IDCT4 function.
+   */
+  typedef struct
+  {
+          uint16_t N;                          /**< length of the DCT4. */
+          uint16_t Nby2;                       /**< half of the length of the DCT4. */
+          float32_t normalize;                 /**< normalizing factor. */
+    const float32_t *pTwiddle;                 /**< points to the twiddle factor table. */
+    const float32_t *pCosFactor;               /**< points to the cosFactor table. */
+          arm_rfft_instance_f32 *pRfft;        /**< points to the real FFT instance. */
+          arm_cfft_radix4_instance_f32 *pCfft; /**< points to the complex FFT instance. */
+  } arm_dct4_instance_f32;
+
+
+  /**
+   * @brief  Initialization function for the floating-point DCT4/IDCT4.
+   * @param[in,out] S          points to an instance of floating-point DCT4/IDCT4 structure.
+   * @param[in]     S_RFFT     points to an instance of floating-point RFFT/RIFFT structure.
+   * @param[in]     S_CFFT     points to an instance of floating-point CFFT/CIFFT structure.
+   * @param[in]     N          length of the DCT4.
+   * @param[in]     Nby2       half of the length of the DCT4.
+   * @param[in]     normalize  normalizing factor.
+   * @return      arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported transform length.
+   */
+  arm_status arm_dct4_init_f32(
+        arm_dct4_instance_f32 * S,
+        arm_rfft_instance_f32 * S_RFFT,
+        arm_cfft_radix4_instance_f32 * S_CFFT,
+        uint16_t N,
+        uint16_t Nby2,
+        float32_t normalize);
+
+
+  /**
+   * @brief Processing function for the floating-point DCT4/IDCT4.
+   * @param[in]     S              points to an instance of the floating-point DCT4/IDCT4 structure.
+   * @param[in]     pState         points to state buffer.
+   * @param[in,out] pInlineBuffer  points to the in-place input and output buffer.
+   */
+  void arm_dct4_f32(
+  const arm_dct4_instance_f32 * S,
+        float32_t * pState,
+        float32_t * pInlineBuffer);
+
+
+  /**
+   * @brief Instance structure for the Q31 DCT4/IDCT4 function.
+   */
+  typedef struct
+  {
+          uint16_t N;                          /**< length of the DCT4. */
+          uint16_t Nby2;                       /**< half of the length of the DCT4. */
+          q31_t normalize;                     /**< normalizing factor. */
+    const q31_t *pTwiddle;                     /**< points to the twiddle factor table. */
+    const q31_t *pCosFactor;                   /**< points to the cosFactor table. */
+          arm_rfft_instance_q31 *pRfft;        /**< points to the real FFT instance. */
+          arm_cfft_radix4_instance_q31 *pCfft; /**< points to the complex FFT instance. */
+  } arm_dct4_instance_q31;
+
+
+  /**
+   * @brief  Initialization function for the Q31 DCT4/IDCT4.
+   * @param[in,out] S          points to an instance of Q31 DCT4/IDCT4 structure.
+   * @param[in]     S_RFFT     points to an instance of Q31 RFFT/RIFFT structure
+   * @param[in]     S_CFFT     points to an instance of Q31 CFFT/CIFFT structure
+   * @param[in]     N          length of the DCT4.
+   * @param[in]     Nby2       half of the length of the DCT4.
+   * @param[in]     normalize  normalizing factor.
+   * @return      arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
+   */
+  arm_status arm_dct4_init_q31(
+        arm_dct4_instance_q31 * S,
+        arm_rfft_instance_q31 * S_RFFT,
+        arm_cfft_radix4_instance_q31 * S_CFFT,
+        uint16_t N,
+        uint16_t Nby2,
+        q31_t normalize);
+
+
+  /**
+   * @brief Processing function for the Q31 DCT4/IDCT4.
+   * @param[in]     S              points to an instance of the Q31 DCT4 structure.
+   * @param[in]     pState         points to state buffer.
+   * @param[in,out] pInlineBuffer  points to the in-place input and output buffer.
+   */
+  void arm_dct4_q31(
+  const arm_dct4_instance_q31 * S,
+        q31_t * pState,
+        q31_t * pInlineBuffer);
+
+
+  /**
+   * @brief Instance structure for the Q15 DCT4/IDCT4 function.
+   */
+  typedef struct
+  {
+          uint16_t N;                          /**< length of the DCT4. */
+          uint16_t Nby2;                       /**< half of the length of the DCT4. */
+          q15_t normalize;                     /**< normalizing factor. */
+    const q15_t *pTwiddle;                     /**< points to the twiddle factor table. */
+    const q15_t *pCosFactor;                   /**< points to the cosFactor table. */
+          arm_rfft_instance_q15 *pRfft;        /**< points to the real FFT instance. */
+          arm_cfft_radix4_instance_q15 *pCfft; /**< points to the complex FFT instance. */
+  } arm_dct4_instance_q15;
+
+
+  /**
+   * @brief  Initialization function for the Q15 DCT4/IDCT4.
+   * @param[in,out] S          points to an instance of Q15 DCT4/IDCT4 structure.
+   * @param[in]     S_RFFT     points to an instance of Q15 RFFT/RIFFT structure.
+   * @param[in]     S_CFFT     points to an instance of Q15 CFFT/CIFFT structure.
+   * @param[in]     N          length of the DCT4.
+   * @param[in]     Nby2       half of the length of the DCT4.
+   * @param[in]     normalize  normalizing factor.
+   * @return      arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
+   */
+  arm_status arm_dct4_init_q15(
+        arm_dct4_instance_q15 * S,
+        arm_rfft_instance_q15 * S_RFFT,
+        arm_cfft_radix4_instance_q15 * S_CFFT,
+        uint16_t N,
+        uint16_t Nby2,
+        q15_t normalize);
+
+
+  /**
+   * @brief Processing function for the Q15 DCT4/IDCT4.
+   * @param[in]     S              points to an instance of the Q15 DCT4 structure.
+   * @param[in]     pState         points to state buffer.
+   * @param[in,out] pInlineBuffer  points to the in-place input and output buffer.
+   */
+  void arm_dct4_q15(
+  const arm_dct4_instance_q15 * S,
+        q15_t * pState,
+        q15_t * pInlineBuffer);
+
+
+  /**
+   * @brief Floating-point vector addition.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_add_f32(
+  const float32_t * pSrcA,
+  const float32_t * pSrcB,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Q7 vector addition.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_add_q7(
+  const q7_t * pSrcA,
+  const q7_t * pSrcB,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Q15 vector addition.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_add_q15(
+  const q15_t * pSrcA,
+  const q15_t * pSrcB,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Q31 vector addition.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_add_q31(
+  const q31_t * pSrcA,
+  const q31_t * pSrcB,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Floating-point vector subtraction.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_sub_f32(
+  const float32_t * pSrcA,
+  const float32_t * pSrcB,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Q7 vector subtraction.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_sub_q7(
+  const q7_t * pSrcA,
+  const q7_t * pSrcB,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Q15 vector subtraction.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_sub_q15(
+  const q15_t * pSrcA,
+  const q15_t * pSrcB,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Q31 vector subtraction.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_sub_q31(
+  const q31_t * pSrcA,
+  const q31_t * pSrcB,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Multiplies a floating-point vector by a scalar.
+   * @param[in]  pSrc       points to the input vector
+   * @param[in]  scale      scale factor to be applied
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in the vector
+   */
+  void arm_scale_f32(
+  const float32_t * pSrc,
+        float32_t scale,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Multiplies a Q7 vector by a scalar.
+   * @param[in]  pSrc        points to the input vector
+   * @param[in]  scaleFract  fractional portion of the scale value
+   * @param[in]  shift       number of bits to shift the result by
+   * @param[out] pDst        points to the output vector
+   * @param[in]  blockSize   number of samples in the vector
+   */
+  void arm_scale_q7(
+  const q7_t * pSrc,
+        q7_t scaleFract,
+        int8_t shift,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Multiplies a Q15 vector by a scalar.
+   * @param[in]  pSrc        points to the input vector
+   * @param[in]  scaleFract  fractional portion of the scale value
+   * @param[in]  shift       number of bits to shift the result by
+   * @param[out] pDst        points to the output vector
+   * @param[in]  blockSize   number of samples in the vector
+   */
+  void arm_scale_q15(
+  const q15_t * pSrc,
+        q15_t scaleFract,
+        int8_t shift,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Multiplies a Q31 vector by a scalar.
+   * @param[in]  pSrc        points to the input vector
+   * @param[in]  scaleFract  fractional portion of the scale value
+   * @param[in]  shift       number of bits to shift the result by
+   * @param[out] pDst        points to the output vector
+   * @param[in]  blockSize   number of samples in the vector
+   */
+  void arm_scale_q31(
+  const q31_t * pSrc,
+        q31_t scaleFract,
+        int8_t shift,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Q7 vector absolute value.
+   * @param[in]  pSrc       points to the input buffer
+   * @param[out] pDst       points to the output buffer
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_abs_q7(
+  const q7_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Floating-point vector absolute value.
+   * @param[in]  pSrc       points to the input buffer
+   * @param[out] pDst       points to the output buffer
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_abs_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Q15 vector absolute value.
+   * @param[in]  pSrc       points to the input buffer
+   * @param[out] pDst       points to the output buffer
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_abs_q15(
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Q31 vector absolute value.
+   * @param[in]  pSrc       points to the input buffer
+   * @param[out] pDst       points to the output buffer
+   * @param[in]  blockSize  number of samples in each vector
+   */
+  void arm_abs_q31(
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Dot product of floating-point vectors.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[in]  blockSize  number of samples in each vector
+   * @param[out] result     output result returned here
+   */
+  void arm_dot_prod_f32(
+  const float32_t * pSrcA,
+  const float32_t * pSrcB,
+        uint32_t blockSize,
+        float32_t * result);
+
+
+  /**
+   * @brief Dot product of Q7 vectors.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[in]  blockSize  number of samples in each vector
+   * @param[out] result     output result returned here
+   */
+  void arm_dot_prod_q7(
+  const q7_t * pSrcA,
+  const q7_t * pSrcB,
+        uint32_t blockSize,
+        q31_t * result);
+
+
+  /**
+   * @brief Dot product of Q15 vectors.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[in]  blockSize  number of samples in each vector
+   * @param[out] result     output result returned here
+   */
+  void arm_dot_prod_q15(
+  const q15_t * pSrcA,
+  const q15_t * pSrcB,
+        uint32_t blockSize,
+        q63_t * result);
+
+
+  /**
+   * @brief Dot product of Q31 vectors.
+   * @param[in]  pSrcA      points to the first input vector
+   * @param[in]  pSrcB      points to the second input vector
+   * @param[in]  blockSize  number of samples in each vector
+   * @param[out] result     output result returned here
+   */
+  void arm_dot_prod_q31(
+  const q31_t * pSrcA,
+  const q31_t * pSrcB,
+        uint32_t blockSize,
+        q63_t * result);
+
+
+  /**
+   * @brief  Shifts the elements of a Q7 vector a specified number of bits.
+   * @param[in]  pSrc       points to the input vector
+   * @param[in]  shiftBits  number of bits to shift.  A positive value shifts left; a negative value shifts right.
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in the vector
+   */
+  void arm_shift_q7(
+  const q7_t * pSrc,
+        int8_t shiftBits,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Shifts the elements of a Q15 vector a specified number of bits.
+   * @param[in]  pSrc       points to the input vector
+   * @param[in]  shiftBits  number of bits to shift.  A positive value shifts left; a negative value shifts right.
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in the vector
+   */
+  void arm_shift_q15(
+  const q15_t * pSrc,
+        int8_t shiftBits,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Shifts the elements of a Q31 vector a specified number of bits.
+   * @param[in]  pSrc       points to the input vector
+   * @param[in]  shiftBits  number of bits to shift.  A positive value shifts left; a negative value shifts right.
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in the vector
+   */
+  void arm_shift_q31(
+  const q31_t * pSrc,
+        int8_t shiftBits,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Adds a constant offset to a floating-point vector.
+   * @param[in]  pSrc       points to the input vector
+   * @param[in]  offset     is the offset to be added
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in the vector
+   */
+  void arm_offset_f32(
+  const float32_t * pSrc,
+        float32_t offset,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Adds a constant offset to a Q7 vector.
+   * @param[in]  pSrc       points to the input vector
+   * @param[in]  offset     is the offset to be added
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in the vector
+   */
+  void arm_offset_q7(
+  const q7_t * pSrc,
+        q7_t offset,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Adds a constant offset to a Q15 vector.
+   * @param[in]  pSrc       points to the input vector
+   * @param[in]  offset     is the offset to be added
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in the vector
+   */
+  void arm_offset_q15(
+  const q15_t * pSrc,
+        q15_t offset,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Adds a constant offset to a Q31 vector.
+   * @param[in]  pSrc       points to the input vector
+   * @param[in]  offset     is the offset to be added
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in the vector
+   */
+  void arm_offset_q31(
+  const q31_t * pSrc,
+        q31_t offset,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Negates the elements of a floating-point vector.
+   * @param[in]  pSrc       points to the input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in the vector
+   */
+  void arm_negate_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Negates the elements of a Q7 vector.
+   * @param[in]  pSrc       points to the input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in the vector
+   */
+  void arm_negate_q7(
+  const q7_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Negates the elements of a Q15 vector.
+   * @param[in]  pSrc       points to the input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in the vector
+   */
+  void arm_negate_q15(
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Negates the elements of a Q31 vector.
+   * @param[in]  pSrc       points to the input vector
+   * @param[out] pDst       points to the output vector
+   * @param[in]  blockSize  number of samples in the vector
+   */
+  void arm_negate_q31(
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Copies the elements of a floating-point vector.
+   * @param[in]  pSrc       input pointer
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_copy_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Copies the elements of a Q7 vector.
+   * @param[in]  pSrc       input pointer
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_copy_q7(
+  const q7_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Copies the elements of a Q15 vector.
+   * @param[in]  pSrc       input pointer
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_copy_q15(
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Copies the elements of a Q31 vector.
+   * @param[in]  pSrc       input pointer
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_copy_q31(
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Fills a constant value into a floating-point vector.
+   * @param[in]  value      input value to be filled
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_fill_f32(
+        float32_t value,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Fills a constant value into a Q7 vector.
+   * @param[in]  value      input value to be filled
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_fill_q7(
+        q7_t value,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Fills a constant value into a Q15 vector.
+   * @param[in]  value      input value to be filled
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_fill_q15(
+        q15_t value,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Fills a constant value into a Q31 vector.
+   * @param[in]  value      input value to be filled
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_fill_q31(
+        q31_t value,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+/**
+ * @brief Convolution of floating-point sequences.
+ * @param[in]  pSrcA    points to the first input sequence.
+ * @param[in]  srcALen  length of the first input sequence.
+ * @param[in]  pSrcB    points to the second input sequence.
+ * @param[in]  srcBLen  length of the second input sequence.
+ * @param[out] pDst     points to the location where the output result is written.  Length srcALen+srcBLen-1.
+ */
+  void arm_conv_f32(
+  const float32_t * pSrcA,
+        uint32_t srcALen,
+  const float32_t * pSrcB,
+        uint32_t srcBLen,
+        float32_t * pDst);
+
+
+  /**
+   * @brief Convolution of Q15 sequences.
+   * @param[in]  pSrcA      points to the first input sequence.
+   * @param[in]  srcALen    length of the first input sequence.
+   * @param[in]  pSrcB      points to the second input sequence.
+   * @param[in]  srcBLen    length of the second input sequence.
+   * @param[out] pDst       points to the block of output data  Length srcALen+srcBLen-1.
+   * @param[in]  pScratch1  points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2  points to scratch buffer of size min(srcALen, srcBLen).
+   */
+  void arm_conv_opt_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+/**
+ * @brief Convolution of Q15 sequences.
+ * @param[in]  pSrcA    points to the first input sequence.
+ * @param[in]  srcALen  length of the first input sequence.
+ * @param[in]  pSrcB    points to the second input sequence.
+ * @param[in]  srcBLen  length of the second input sequence.
+ * @param[out] pDst     points to the location where the output result is written.  Length srcALen+srcBLen-1.
+ */
+  void arm_conv_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst);
+
+
+  /**
+   * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length srcALen+srcBLen-1.
+   */
+  void arm_conv_fast_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst);
+
+
+  /**
+   * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA      points to the first input sequence.
+   * @param[in]  srcALen    length of the first input sequence.
+   * @param[in]  pSrcB      points to the second input sequence.
+   * @param[in]  srcBLen    length of the second input sequence.
+   * @param[out] pDst       points to the block of output data  Length srcALen+srcBLen-1.
+   * @param[in]  pScratch1  points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2  points to scratch buffer of size min(srcALen, srcBLen).
+   */
+  void arm_conv_fast_opt_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+  /**
+   * @brief Convolution of Q31 sequences.
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length srcALen+srcBLen-1.
+   */
+  void arm_conv_q31(
+  const q31_t * pSrcA,
+        uint32_t srcALen,
+  const q31_t * pSrcB,
+        uint32_t srcBLen,
+        q31_t * pDst);
+
+
+  /**
+   * @brief Convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length srcALen+srcBLen-1.
+   */
+  void arm_conv_fast_q31(
+  const q31_t * pSrcA,
+        uint32_t srcALen,
+  const q31_t * pSrcB,
+        uint32_t srcBLen,
+        q31_t * pDst);
+
+
+    /**
+   * @brief Convolution of Q7 sequences.
+   * @param[in]  pSrcA      points to the first input sequence.
+   * @param[in]  srcALen    length of the first input sequence.
+   * @param[in]  pSrcB      points to the second input sequence.
+   * @param[in]  srcBLen    length of the second input sequence.
+   * @param[out] pDst       points to the block of output data  Length srcALen+srcBLen-1.
+   * @param[in]  pScratch1  points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2  points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
+   */
+  void arm_conv_opt_q7(
+  const q7_t * pSrcA,
+        uint32_t srcALen,
+  const q7_t * pSrcB,
+        uint32_t srcBLen,
+        q7_t * pDst,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+  /**
+   * @brief Convolution of Q7 sequences.
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length srcALen+srcBLen-1.
+   */
+  void arm_conv_q7(
+  const q7_t * pSrcA,
+        uint32_t srcALen,
+  const q7_t * pSrcB,
+        uint32_t srcBLen,
+        q7_t * pDst);
+
+
+  /**
+   * @brief Partial convolution of floating-point sequences.
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_f32(
+  const float32_t * pSrcA,
+        uint32_t srcALen,
+  const float32_t * pSrcB,
+        uint32_t srcBLen,
+        float32_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints);
+
+
+  /**
+   * @brief Partial convolution of Q15 sequences.
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @param[in]  pScratch1   points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2   points to scratch buffer of size min(srcALen, srcBLen).
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_opt_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+  /**
+   * @brief Partial convolution of Q15 sequences.
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints);
+
+
+  /**
+   * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_fast_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints);
+
+
+  /**
+   * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @param[in]  pScratch1   points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2   points to scratch buffer of size min(srcALen, srcBLen).
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_fast_opt_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+  /**
+   * @brief Partial convolution of Q31 sequences.
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_q31(
+  const q31_t * pSrcA,
+        uint32_t srcALen,
+  const q31_t * pSrcB,
+        uint32_t srcBLen,
+        q31_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints);
+
+
+  /**
+   * @brief Partial convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_fast_q31(
+  const q31_t * pSrcA,
+        uint32_t srcALen,
+  const q31_t * pSrcB,
+        uint32_t srcBLen,
+        q31_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints);
+
+
+  /**
+   * @brief Partial convolution of Q7 sequences
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @param[in]  pScratch1   points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2   points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_opt_q7(
+  const q7_t * pSrcA,
+        uint32_t srcALen,
+  const q7_t * pSrcB,
+        uint32_t srcBLen,
+        q7_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+/**
+   * @brief Partial convolution of Q7 sequences.
+   * @param[in]  pSrcA       points to the first input sequence.
+   * @param[in]  srcALen     length of the first input sequence.
+   * @param[in]  pSrcB       points to the second input sequence.
+   * @param[in]  srcBLen     length of the second input sequence.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  firstIndex  is the first output sample to start with.
+   * @param[in]  numPoints   is the number of output points to be computed.
+   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
+   */
+  arm_status arm_conv_partial_q7(
+  const q7_t * pSrcA,
+        uint32_t srcALen,
+  const q7_t * pSrcB,
+        uint32_t srcBLen,
+        q7_t * pDst,
+        uint32_t firstIndex,
+        uint32_t numPoints);
+
+
+  /**
+   * @brief Instance structure for the Q15 FIR decimator.
+   */
+  typedef struct
+  {
+          uint8_t M;                  /**< decimation factor. */
+          uint16_t numTaps;           /**< number of coefficients in the filter. */
+    const q15_t *pCoeffs;             /**< points to the coefficient array. The array is of length numTaps.*/
+          q15_t *pState;              /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+  } arm_fir_decimate_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 FIR decimator.
+   */
+  typedef struct
+  {
+          uint8_t M;                  /**< decimation factor. */
+          uint16_t numTaps;           /**< number of coefficients in the filter. */
+    const q31_t *pCoeffs;             /**< points to the coefficient array. The array is of length numTaps.*/
+          q31_t *pState;              /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+  } arm_fir_decimate_instance_q31;
+
+/**
+  @brief Instance structure for floating-point FIR decimator.
+ */
+typedef struct
+  {
+          uint8_t M;                  /**< decimation factor. */
+          uint16_t numTaps;           /**< number of coefficients in the filter. */
+    const float32_t *pCoeffs;         /**< points to the coefficient array. The array is of length numTaps.*/
+          float32_t *pState;          /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+  } arm_fir_decimate_instance_f32;
+
+
+/**
+  @brief         Processing function for floating-point FIR decimator.
+  @param[in]     S         points to an instance of the floating-point FIR decimator structure
+  @param[in]     pSrc      points to the block of input data
+  @param[out]    pDst      points to the block of output data
+  @param[in]     blockSize number of samples to process
+ */
+void arm_fir_decimate_f32(
+  const arm_fir_decimate_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+/**
+  @brief         Initialization function for the floating-point FIR decimator.
+  @param[in,out] S          points to an instance of the floating-point FIR decimator structure
+  @param[in]     numTaps    number of coefficients in the filter
+  @param[in]     M          decimation factor
+  @param[in]     pCoeffs    points to the filter coefficients
+  @param[in]     pState     points to the state buffer
+  @param[in]     blockSize  number of input samples to process per call
+  @return        execution status
+                   - \ref ARM_MATH_SUCCESS      : Operation successful
+                   - \ref ARM_MATH_LENGTH_ERROR : <code>blockSize</code> is not a multiple of <code>M</code>
+ */
+arm_status arm_fir_decimate_init_f32(
+        arm_fir_decimate_instance_f32 * S,
+        uint16_t numTaps,
+        uint8_t M,
+  const float32_t * pCoeffs,
+        float32_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q15 FIR decimator.
+   * @param[in]  S          points to an instance of the Q15 FIR decimator structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of input samples to process per call.
+   */
+  void arm_fir_decimate_q15(
+  const arm_fir_decimate_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q15 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
+   * @param[in]  S          points to an instance of the Q15 FIR decimator structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of input samples to process per call.
+   */
+  void arm_fir_decimate_fast_q15(
+  const arm_fir_decimate_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q15 FIR decimator.
+   * @param[in,out] S          points to an instance of the Q15 FIR decimator structure.
+   * @param[in]     numTaps    number of coefficients in the filter.
+   * @param[in]     M          decimation factor.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of input samples to process per call.
+   * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * <code>blockSize</code> is not a multiple of <code>M</code>.
+   */
+  arm_status arm_fir_decimate_init_q15(
+        arm_fir_decimate_instance_q15 * S,
+        uint16_t numTaps,
+        uint8_t M,
+  const q15_t * pCoeffs,
+        q15_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q31 FIR decimator.
+   * @param[in]  S     points to an instance of the Q31 FIR decimator structure.
+   * @param[in]  pSrc  points to the block of input data.
+   * @param[out] pDst  points to the block of output data
+   * @param[in] blockSize number of input samples to process per call.
+   */
+  void arm_fir_decimate_q31(
+  const arm_fir_decimate_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+  /**
+   * @brief Processing function for the Q31 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
+   * @param[in]  S          points to an instance of the Q31 FIR decimator structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of input samples to process per call.
+   */
+  void arm_fir_decimate_fast_q31(
+  const arm_fir_decimate_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q31 FIR decimator.
+   * @param[in,out] S          points to an instance of the Q31 FIR decimator structure.
+   * @param[in]     numTaps    number of coefficients in the filter.
+   * @param[in]     M          decimation factor.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of input samples to process per call.
+   * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * <code>blockSize</code> is not a multiple of <code>M</code>.
+   */
+  arm_status arm_fir_decimate_init_q31(
+        arm_fir_decimate_instance_q31 * S,
+        uint16_t numTaps,
+        uint8_t M,
+  const q31_t * pCoeffs,
+        q31_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q15 FIR interpolator.
+   */
+  typedef struct
+  {
+        uint8_t L;                      /**< upsample factor. */
+        uint16_t phaseLength;           /**< length of each polyphase filter component. */
+  const q15_t *pCoeffs;                 /**< points to the coefficient array. The array is of length L*phaseLength. */
+        q15_t *pState;                  /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
+  } arm_fir_interpolate_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 FIR interpolator.
+   */
+  typedef struct
+  {
+        uint8_t L;                      /**< upsample factor. */
+        uint16_t phaseLength;           /**< length of each polyphase filter component. */
+  const q31_t *pCoeffs;                 /**< points to the coefficient array. The array is of length L*phaseLength. */
+        q31_t *pState;                  /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
+  } arm_fir_interpolate_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point FIR interpolator.
+   */
+  typedef struct
+  {
+        uint8_t L;                     /**< upsample factor. */
+        uint16_t phaseLength;          /**< length of each polyphase filter component. */
+  const float32_t *pCoeffs;            /**< points to the coefficient array. The array is of length L*phaseLength. */
+        float32_t *pState;             /**< points to the state variable array. The array is of length phaseLength+numTaps-1. */
+  } arm_fir_interpolate_instance_f32;
+
+
+  /**
+   * @brief Processing function for the Q15 FIR interpolator.
+   * @param[in]  S          points to an instance of the Q15 FIR interpolator structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of input samples to process per call.
+   */
+  void arm_fir_interpolate_q15(
+  const arm_fir_interpolate_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q15 FIR interpolator.
+   * @param[in,out] S          points to an instance of the Q15 FIR interpolator structure.
+   * @param[in]     L          upsample factor.
+   * @param[in]     numTaps    number of filter coefficients in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficient buffer.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of input samples to process per call.
+   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
+   */
+  arm_status arm_fir_interpolate_init_q15(
+        arm_fir_interpolate_instance_q15 * S,
+        uint8_t L,
+        uint16_t numTaps,
+  const q15_t * pCoeffs,
+        q15_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q31 FIR interpolator.
+   * @param[in]  S          points to an instance of the Q15 FIR interpolator structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of input samples to process per call.
+   */
+  void arm_fir_interpolate_q31(
+  const arm_fir_interpolate_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q31 FIR interpolator.
+   * @param[in,out] S          points to an instance of the Q31 FIR interpolator structure.
+   * @param[in]     L          upsample factor.
+   * @param[in]     numTaps    number of filter coefficients in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficient buffer.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of input samples to process per call.
+   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
+   */
+  arm_status arm_fir_interpolate_init_q31(
+        arm_fir_interpolate_instance_q31 * S,
+        uint8_t L,
+        uint16_t numTaps,
+  const q31_t * pCoeffs,
+        q31_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the floating-point FIR interpolator.
+   * @param[in]  S          points to an instance of the floating-point FIR interpolator structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of input samples to process per call.
+   */
+  void arm_fir_interpolate_f32(
+  const arm_fir_interpolate_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the floating-point FIR interpolator.
+   * @param[in,out] S          points to an instance of the floating-point FIR interpolator structure.
+   * @param[in]     L          upsample factor.
+   * @param[in]     numTaps    number of filter coefficients in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficient buffer.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     blockSize  number of input samples to process per call.
+   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
+   * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
+   */
+  arm_status arm_fir_interpolate_init_f32(
+        arm_fir_interpolate_instance_f32 * S,
+        uint8_t L,
+        uint16_t numTaps,
+  const float32_t * pCoeffs,
+        float32_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the high precision Q31 Biquad cascade filter.
+   */
+  typedef struct
+  {
+          uint8_t numStages;       /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          q63_t *pState;           /**< points to the array of state coefficients.  The array is of length 4*numStages. */
+    const q31_t *pCoeffs;          /**< points to the array of coefficients.  The array is of length 5*numStages. */
+          uint8_t postShift;       /**< additional shift, in bits, applied to each output sample. */
+  } arm_biquad_cas_df1_32x64_ins_q31;
+
+
+  /**
+   * @param[in]  S          points to an instance of the high precision Q31 Biquad cascade filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cas_df1_32x64_q31(
+  const arm_biquad_cas_df1_32x64_ins_q31 * S,
+        q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @param[in,out] S          points to an instance of the high precision Q31 Biquad cascade filter structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     postShift  shift to be applied to the output. Varies according to the coefficients format
+   */
+  void arm_biquad_cas_df1_32x64_init_q31(
+        arm_biquad_cas_df1_32x64_ins_q31 * S,
+        uint8_t numStages,
+  const q31_t * pCoeffs,
+        q63_t * pState,
+        uint8_t postShift);
+
+
+  /**
+   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
+   */
+  typedef struct
+  {
+          uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          float32_t *pState;         /**< points to the array of state coefficients.  The array is of length 2*numStages. */
+    const float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
+  } arm_biquad_cascade_df2T_instance_f32;
+
+  /**
+   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
+   */
+  typedef struct
+  {
+          uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          float32_t *pState;         /**< points to the array of state coefficients.  The array is of length 4*numStages. */
+    const float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
+  } arm_biquad_cascade_stereo_df2T_instance_f32;
+
+  /**
+   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
+   */
+  typedef struct
+  {
+          uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
+          float64_t *pState;         /**< points to the array of state coefficients.  The array is of length 2*numStages. */
+          float64_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
+  } arm_biquad_cascade_df2T_instance_f64;
+
+
+  /**
+   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
+   * @param[in]  S          points to an instance of the filter data structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df2T_f32(
+  const arm_biquad_cascade_df2T_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. 2 channels
+   * @param[in]  S          points to an instance of the filter data structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_stereo_df2T_f32(
+  const arm_biquad_cascade_stereo_df2T_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
+   * @param[in]  S          points to an instance of the filter data structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_biquad_cascade_df2T_f64(
+  const arm_biquad_cascade_df2T_instance_f64 * S,
+        float64_t * pSrc,
+        float64_t * pDst,
+        uint32_t blockSize);
+
+
+#if defined(ARM_MATH_NEON) 
+void arm_biquad_cascade_df2T_compute_coefs_f32(
+  arm_biquad_cascade_df2T_instance_f32 * S,
+  uint8_t numStages,
+  float32_t * pCoeffs);
+#endif
+  /**
+   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
+   * @param[in,out] S          points to an instance of the filter data structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   */
+  void arm_biquad_cascade_df2T_init_f32(
+        arm_biquad_cascade_df2T_instance_f32 * S,
+        uint8_t numStages,
+  const float32_t * pCoeffs,
+        float32_t * pState);
+
+
+  /**
+   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
+   * @param[in,out] S          points to an instance of the filter data structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   */
+  void arm_biquad_cascade_stereo_df2T_init_f32(
+        arm_biquad_cascade_stereo_df2T_instance_f32 * S,
+        uint8_t numStages,
+  const float32_t * pCoeffs,
+        float32_t * pState);
+
+
+  /**
+   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
+   * @param[in,out] S          points to an instance of the filter data structure.
+   * @param[in]     numStages  number of 2nd order stages in the filter.
+   * @param[in]     pCoeffs    points to the filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   */
+  void arm_biquad_cascade_df2T_init_f64(
+        arm_biquad_cascade_df2T_instance_f64 * S,
+        uint8_t numStages,
+        float64_t * pCoeffs,
+        float64_t * pState);
+
+
+  /**
+   * @brief Instance structure for the Q15 FIR lattice filter.
+   */
+  typedef struct
+  {
+          uint16_t numStages;                  /**< number of filter stages. */
+          q15_t *pState;                       /**< points to the state variable array. The array is of length numStages. */
+    const q15_t *pCoeffs;                      /**< points to the coefficient array. The array is of length numStages. */
+  } arm_fir_lattice_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 FIR lattice filter.
+   */
+  typedef struct
+  {
+          uint16_t numStages;                  /**< number of filter stages. */
+          q31_t *pState;                       /**< points to the state variable array. The array is of length numStages. */
+    const q31_t *pCoeffs;                      /**< points to the coefficient array. The array is of length numStages. */
+  } arm_fir_lattice_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point FIR lattice filter.
+   */
+  typedef struct
+  {
+          uint16_t numStages;                  /**< number of filter stages. */
+          float32_t *pState;                   /**< points to the state variable array. The array is of length numStages. */
+    const float32_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numStages. */
+  } arm_fir_lattice_instance_f32;
+
+
+  /**
+   * @brief Initialization function for the Q15 FIR lattice filter.
+   * @param[in] S          points to an instance of the Q15 FIR lattice structure.
+   * @param[in] numStages  number of filter stages.
+   * @param[in] pCoeffs    points to the coefficient buffer.  The array is of length numStages.
+   * @param[in] pState     points to the state buffer.  The array is of length numStages.
+   */
+  void arm_fir_lattice_init_q15(
+        arm_fir_lattice_instance_q15 * S,
+        uint16_t numStages,
+  const q15_t * pCoeffs,
+        q15_t * pState);
+
+
+  /**
+   * @brief Processing function for the Q15 FIR lattice filter.
+   * @param[in]  S          points to an instance of the Q15 FIR lattice structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_lattice_q15(
+  const arm_fir_lattice_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for the Q31 FIR lattice filter.
+   * @param[in] S          points to an instance of the Q31 FIR lattice structure.
+   * @param[in] numStages  number of filter stages.
+   * @param[in] pCoeffs    points to the coefficient buffer.  The array is of length numStages.
+   * @param[in] pState     points to the state buffer.   The array is of length numStages.
+   */
+  void arm_fir_lattice_init_q31(
+        arm_fir_lattice_instance_q31 * S,
+        uint16_t numStages,
+  const q31_t * pCoeffs,
+        q31_t * pState);
+
+
+  /**
+   * @brief Processing function for the Q31 FIR lattice filter.
+   * @param[in]  S          points to an instance of the Q31 FIR lattice structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_lattice_q31(
+  const arm_fir_lattice_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+/**
+ * @brief Initialization function for the floating-point FIR lattice filter.
+ * @param[in] S          points to an instance of the floating-point FIR lattice structure.
+ * @param[in] numStages  number of filter stages.
+ * @param[in] pCoeffs    points to the coefficient buffer.  The array is of length numStages.
+ * @param[in] pState     points to the state buffer.  The array is of length numStages.
+ */
+  void arm_fir_lattice_init_f32(
+        arm_fir_lattice_instance_f32 * S,
+        uint16_t numStages,
+  const float32_t * pCoeffs,
+        float32_t * pState);
+
+
+  /**
+   * @brief Processing function for the floating-point FIR lattice filter.
+   * @param[in]  S          points to an instance of the floating-point FIR lattice structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_fir_lattice_f32(
+  const arm_fir_lattice_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q15 IIR lattice filter.
+   */
+  typedef struct
+  {
+          uint16_t numStages;                  /**< number of stages in the filter. */
+          q15_t *pState;                       /**< points to the state variable array. The array is of length numStages+blockSize. */
+          q15_t *pkCoeffs;                     /**< points to the reflection coefficient array. The array is of length numStages. */
+          q15_t *pvCoeffs;                     /**< points to the ladder coefficient array. The array is of length numStages+1. */
+  } arm_iir_lattice_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q31 IIR lattice filter.
+   */
+  typedef struct
+  {
+          uint16_t numStages;                  /**< number of stages in the filter. */
+          q31_t *pState;                       /**< points to the state variable array. The array is of length numStages+blockSize. */
+          q31_t *pkCoeffs;                     /**< points to the reflection coefficient array. The array is of length numStages. */
+          q31_t *pvCoeffs;                     /**< points to the ladder coefficient array. The array is of length numStages+1. */
+  } arm_iir_lattice_instance_q31;
+
+  /**
+   * @brief Instance structure for the floating-point IIR lattice filter.
+   */
+  typedef struct
+  {
+          uint16_t numStages;                  /**< number of stages in the filter. */
+          float32_t *pState;                   /**< points to the state variable array. The array is of length numStages+blockSize. */
+          float32_t *pkCoeffs;                 /**< points to the reflection coefficient array. The array is of length numStages. */
+          float32_t *pvCoeffs;                 /**< points to the ladder coefficient array. The array is of length numStages+1. */
+  } arm_iir_lattice_instance_f32;
+
+
+  /**
+   * @brief Processing function for the floating-point IIR lattice filter.
+   * @param[in]  S          points to an instance of the floating-point IIR lattice structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_iir_lattice_f32(
+  const arm_iir_lattice_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for the floating-point IIR lattice filter.
+   * @param[in] S          points to an instance of the floating-point IIR lattice structure.
+   * @param[in] numStages  number of stages in the filter.
+   * @param[in] pkCoeffs   points to the reflection coefficient buffer.  The array is of length numStages.
+   * @param[in] pvCoeffs   points to the ladder coefficient buffer.  The array is of length numStages+1.
+   * @param[in] pState     points to the state buffer.  The array is of length numStages+blockSize-1.
+   * @param[in] blockSize  number of samples to process.
+   */
+  void arm_iir_lattice_init_f32(
+        arm_iir_lattice_instance_f32 * S,
+        uint16_t numStages,
+        float32_t * pkCoeffs,
+        float32_t * pvCoeffs,
+        float32_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q31 IIR lattice filter.
+   * @param[in]  S          points to an instance of the Q31 IIR lattice structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_iir_lattice_q31(
+  const arm_iir_lattice_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for the Q31 IIR lattice filter.
+   * @param[in] S          points to an instance of the Q31 IIR lattice structure.
+   * @param[in] numStages  number of stages in the filter.
+   * @param[in] pkCoeffs   points to the reflection coefficient buffer.  The array is of length numStages.
+   * @param[in] pvCoeffs   points to the ladder coefficient buffer.  The array is of length numStages+1.
+   * @param[in] pState     points to the state buffer.  The array is of length numStages+blockSize.
+   * @param[in] blockSize  number of samples to process.
+   */
+  void arm_iir_lattice_init_q31(
+        arm_iir_lattice_instance_q31 * S,
+        uint16_t numStages,
+        q31_t * pkCoeffs,
+        q31_t * pvCoeffs,
+        q31_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q15 IIR lattice filter.
+   * @param[in]  S          points to an instance of the Q15 IIR lattice structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[out] pDst       points to the block of output data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_iir_lattice_q15(
+  const arm_iir_lattice_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+/**
+ * @brief Initialization function for the Q15 IIR lattice filter.
+ * @param[in] S          points to an instance of the fixed-point Q15 IIR lattice structure.
+ * @param[in] numStages  number of stages in the filter.
+ * @param[in] pkCoeffs   points to reflection coefficient buffer.  The array is of length numStages.
+ * @param[in] pvCoeffs   points to ladder coefficient buffer.  The array is of length numStages+1.
+ * @param[in] pState     points to state buffer.  The array is of length numStages+blockSize.
+ * @param[in] blockSize  number of samples to process per call.
+ */
+  void arm_iir_lattice_init_q15(
+        arm_iir_lattice_instance_q15 * S,
+        uint16_t numStages,
+        q15_t * pkCoeffs,
+        q15_t * pvCoeffs,
+        q15_t * pState,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the floating-point LMS filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;    /**< number of coefficients in the filter. */
+          float32_t *pState;   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+          float32_t *pCoeffs;  /**< points to the coefficient array. The array is of length numTaps. */
+          float32_t mu;        /**< step size that controls filter coefficient updates. */
+  } arm_lms_instance_f32;
+
+
+  /**
+   * @brief Processing function for floating-point LMS filter.
+   * @param[in]  S          points to an instance of the floating-point LMS filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[in]  pRef       points to the block of reference data.
+   * @param[out] pOut       points to the block of output data.
+   * @param[out] pErr       points to the block of error data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_lms_f32(
+  const arm_lms_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pRef,
+        float32_t * pOut,
+        float32_t * pErr,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for floating-point LMS filter.
+   * @param[in] S          points to an instance of the floating-point LMS filter structure.
+   * @param[in] numTaps    number of filter coefficients.
+   * @param[in] pCoeffs    points to the coefficient buffer.
+   * @param[in] pState     points to state buffer.
+   * @param[in] mu         step size that controls filter coefficient updates.
+   * @param[in] blockSize  number of samples to process.
+   */
+  void arm_lms_init_f32(
+        arm_lms_instance_f32 * S,
+        uint16_t numTaps,
+        float32_t * pCoeffs,
+        float32_t * pState,
+        float32_t mu,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q15 LMS filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;    /**< number of coefficients in the filter. */
+          q15_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+          q15_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
+          q15_t mu;            /**< step size that controls filter coefficient updates. */
+          uint32_t postShift;  /**< bit shift applied to coefficients. */
+  } arm_lms_instance_q15;
+
+
+  /**
+   * @brief Initialization function for the Q15 LMS filter.
+   * @param[in] S          points to an instance of the Q15 LMS filter structure.
+   * @param[in] numTaps    number of filter coefficients.
+   * @param[in] pCoeffs    points to the coefficient buffer.
+   * @param[in] pState     points to the state buffer.
+   * @param[in] mu         step size that controls filter coefficient updates.
+   * @param[in] blockSize  number of samples to process.
+   * @param[in] postShift  bit shift applied to coefficients.
+   */
+  void arm_lms_init_q15(
+        arm_lms_instance_q15 * S,
+        uint16_t numTaps,
+        q15_t * pCoeffs,
+        q15_t * pState,
+        q15_t mu,
+        uint32_t blockSize,
+        uint32_t postShift);
+
+
+  /**
+   * @brief Processing function for Q15 LMS filter.
+   * @param[in]  S          points to an instance of the Q15 LMS filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[in]  pRef       points to the block of reference data.
+   * @param[out] pOut       points to the block of output data.
+   * @param[out] pErr       points to the block of error data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_lms_q15(
+  const arm_lms_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pRef,
+        q15_t * pOut,
+        q15_t * pErr,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q31 LMS filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;    /**< number of coefficients in the filter. */
+          q31_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+          q31_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
+          q31_t mu;            /**< step size that controls filter coefficient updates. */
+          uint32_t postShift;  /**< bit shift applied to coefficients. */
+  } arm_lms_instance_q31;
+
+
+  /**
+   * @brief Processing function for Q31 LMS filter.
+   * @param[in]  S          points to an instance of the Q15 LMS filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[in]  pRef       points to the block of reference data.
+   * @param[out] pOut       points to the block of output data.
+   * @param[out] pErr       points to the block of error data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_lms_q31(
+  const arm_lms_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pRef,
+        q31_t * pOut,
+        q31_t * pErr,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for Q31 LMS filter.
+   * @param[in] S          points to an instance of the Q31 LMS filter structure.
+   * @param[in] numTaps    number of filter coefficients.
+   * @param[in] pCoeffs    points to coefficient buffer.
+   * @param[in] pState     points to state buffer.
+   * @param[in] mu         step size that controls filter coefficient updates.
+   * @param[in] blockSize  number of samples to process.
+   * @param[in] postShift  bit shift applied to coefficients.
+   */
+  void arm_lms_init_q31(
+        arm_lms_instance_q31 * S,
+        uint16_t numTaps,
+        q31_t * pCoeffs,
+        q31_t * pState,
+        q31_t mu,
+        uint32_t blockSize,
+        uint32_t postShift);
+
+
+  /**
+   * @brief Instance structure for the floating-point normalized LMS filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;     /**< number of coefficients in the filter. */
+          float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+          float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
+          float32_t mu;         /**< step size that control filter coefficient updates. */
+          float32_t energy;     /**< saves previous frame energy. */
+          float32_t x0;         /**< saves previous input sample. */
+  } arm_lms_norm_instance_f32;
+
+
+  /**
+   * @brief Processing function for floating-point normalized LMS filter.
+   * @param[in]  S          points to an instance of the floating-point normalized LMS filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[in]  pRef       points to the block of reference data.
+   * @param[out] pOut       points to the block of output data.
+   * @param[out] pErr       points to the block of error data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_lms_norm_f32(
+        arm_lms_norm_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pRef,
+        float32_t * pOut,
+        float32_t * pErr,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for floating-point normalized LMS filter.
+   * @param[in] S          points to an instance of the floating-point LMS filter structure.
+   * @param[in] numTaps    number of filter coefficients.
+   * @param[in] pCoeffs    points to coefficient buffer.
+   * @param[in] pState     points to state buffer.
+   * @param[in] mu         step size that controls filter coefficient updates.
+   * @param[in] blockSize  number of samples to process.
+   */
+  void arm_lms_norm_init_f32(
+        arm_lms_norm_instance_f32 * S,
+        uint16_t numTaps,
+        float32_t * pCoeffs,
+        float32_t * pState,
+        float32_t mu,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Instance structure for the Q31 normalized LMS filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;     /**< number of coefficients in the filter. */
+          q31_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+          q31_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
+          q31_t mu;             /**< step size that controls filter coefficient updates. */
+          uint8_t postShift;    /**< bit shift applied to coefficients. */
+    const q31_t *recipTable;    /**< points to the reciprocal initial value table. */
+          q31_t energy;         /**< saves previous frame energy. */
+          q31_t x0;             /**< saves previous input sample. */
+  } arm_lms_norm_instance_q31;
+
+
+  /**
+   * @brief Processing function for Q31 normalized LMS filter.
+   * @param[in]  S          points to an instance of the Q31 normalized LMS filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[in]  pRef       points to the block of reference data.
+   * @param[out] pOut       points to the block of output data.
+   * @param[out] pErr       points to the block of error data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_lms_norm_q31(
+        arm_lms_norm_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pRef,
+        q31_t * pOut,
+        q31_t * pErr,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for Q31 normalized LMS filter.
+   * @param[in] S          points to an instance of the Q31 normalized LMS filter structure.
+   * @param[in] numTaps    number of filter coefficients.
+   * @param[in] pCoeffs    points to coefficient buffer.
+   * @param[in] pState     points to state buffer.
+   * @param[in] mu         step size that controls filter coefficient updates.
+   * @param[in] blockSize  number of samples to process.
+   * @param[in] postShift  bit shift applied to coefficients.
+   */
+  void arm_lms_norm_init_q31(
+        arm_lms_norm_instance_q31 * S,
+        uint16_t numTaps,
+        q31_t * pCoeffs,
+        q31_t * pState,
+        q31_t mu,
+        uint32_t blockSize,
+        uint8_t postShift);
+
+
+  /**
+   * @brief Instance structure for the Q15 normalized LMS filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;     /**< Number of coefficients in the filter. */
+          q15_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
+          q15_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
+          q15_t mu;             /**< step size that controls filter coefficient updates. */
+          uint8_t postShift;    /**< bit shift applied to coefficients. */
+    const q15_t *recipTable;    /**< Points to the reciprocal initial value table. */
+          q15_t energy;         /**< saves previous frame energy. */
+          q15_t x0;             /**< saves previous input sample. */
+  } arm_lms_norm_instance_q15;
+
+
+  /**
+   * @brief Processing function for Q15 normalized LMS filter.
+   * @param[in]  S          points to an instance of the Q15 normalized LMS filter structure.
+   * @param[in]  pSrc       points to the block of input data.
+   * @param[in]  pRef       points to the block of reference data.
+   * @param[out] pOut       points to the block of output data.
+   * @param[out] pErr       points to the block of error data.
+   * @param[in]  blockSize  number of samples to process.
+   */
+  void arm_lms_norm_q15(
+        arm_lms_norm_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pRef,
+        q15_t * pOut,
+        q15_t * pErr,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Initialization function for Q15 normalized LMS filter.
+   * @param[in] S          points to an instance of the Q15 normalized LMS filter structure.
+   * @param[in] numTaps    number of filter coefficients.
+   * @param[in] pCoeffs    points to coefficient buffer.
+   * @param[in] pState     points to state buffer.
+   * @param[in] mu         step size that controls filter coefficient updates.
+   * @param[in] blockSize  number of samples to process.
+   * @param[in] postShift  bit shift applied to coefficients.
+   */
+  void arm_lms_norm_init_q15(
+        arm_lms_norm_instance_q15 * S,
+        uint16_t numTaps,
+        q15_t * pCoeffs,
+        q15_t * pState,
+        q15_t mu,
+        uint32_t blockSize,
+        uint8_t postShift);
+
+
+  /**
+   * @brief Correlation of floating-point sequences.
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   */
+  void arm_correlate_f32(
+  const float32_t * pSrcA,
+        uint32_t srcALen,
+  const float32_t * pSrcB,
+        uint32_t srcBLen,
+        float32_t * pDst);
+
+
+/**
+ @brief Correlation of Q15 sequences
+ @param[in]  pSrcA     points to the first input sequence
+ @param[in]  srcALen   length of the first input sequence
+ @param[in]  pSrcB     points to the second input sequence
+ @param[in]  srcBLen   length of the second input sequence
+ @param[out] pDst      points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+ @param[in]  pScratch  points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+*/
+void arm_correlate_opt_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        q15_t * pScratch);
+
+
+/**
+  @brief Correlation of Q15 sequences.
+  @param[in]  pSrcA    points to the first input sequence
+  @param[in]  srcALen  length of the first input sequence
+  @param[in]  pSrcB    points to the second input sequence
+  @param[in]  srcBLen  length of the second input sequence
+  @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+ */
+  void arm_correlate_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst);
+
+
+/**
+  @brief         Correlation of Q15 sequences (fast version).
+  @param[in]     pSrcA      points to the first input sequence
+  @param[in]     srcALen    length of the first input sequence
+  @param[in]     pSrcB      points to the second input sequence
+  @param[in]     srcBLen    length of the second input sequence
+  @param[out]    pDst       points to the location where the output result is written.  Length 2 * max(srcALen, srcBLen) - 1.
+  @return        none
+ */
+void arm_correlate_fast_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst);
+
+
+/**
+  @brief Correlation of Q15 sequences (fast version).
+  @param[in]  pSrcA     points to the first input sequence.
+  @param[in]  srcALen   length of the first input sequence.
+  @param[in]  pSrcB     points to the second input sequence.
+  @param[in]  srcBLen   length of the second input sequence.
+  @param[out] pDst      points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+  @param[in]  pScratch  points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+ */
+void arm_correlate_fast_opt_q15(
+  const q15_t * pSrcA,
+        uint32_t srcALen,
+  const q15_t * pSrcB,
+        uint32_t srcBLen,
+        q15_t * pDst,
+        q15_t * pScratch);
+
+
+  /**
+   * @brief Correlation of Q31 sequences.
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   */
+  void arm_correlate_q31(
+  const q31_t * pSrcA,
+        uint32_t srcALen,
+  const q31_t * pSrcB,
+        uint32_t srcBLen,
+        q31_t * pDst);
+
+
+/**
+  @brief Correlation of Q31 sequences (fast version).
+  @param[in]  pSrcA    points to the first input sequence
+  @param[in]  srcALen  length of the first input sequence
+  @param[in]  pSrcB    points to the second input sequence
+  @param[in]  srcBLen  length of the second input sequence
+  @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+ */
+void arm_correlate_fast_q31(
+  const q31_t * pSrcA,
+        uint32_t srcALen,
+  const q31_t * pSrcB,
+        uint32_t srcBLen,
+        q31_t * pDst);
+
+
+ /**
+   * @brief Correlation of Q7 sequences.
+   * @param[in]  pSrcA      points to the first input sequence.
+   * @param[in]  srcALen    length of the first input sequence.
+   * @param[in]  pSrcB      points to the second input sequence.
+   * @param[in]  srcBLen    length of the second input sequence.
+   * @param[out] pDst       points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   * @param[in]  pScratch1  points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
+   * @param[in]  pScratch2  points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
+   */
+  void arm_correlate_opt_q7(
+  const q7_t * pSrcA,
+        uint32_t srcALen,
+  const q7_t * pSrcB,
+        uint32_t srcBLen,
+        q7_t * pDst,
+        q15_t * pScratch1,
+        q15_t * pScratch2);
+
+
+  /**
+   * @brief Correlation of Q7 sequences.
+   * @param[in]  pSrcA    points to the first input sequence.
+   * @param[in]  srcALen  length of the first input sequence.
+   * @param[in]  pSrcB    points to the second input sequence.
+   * @param[in]  srcBLen  length of the second input sequence.
+   * @param[out] pDst     points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
+   */
+  void arm_correlate_q7(
+  const q7_t * pSrcA,
+        uint32_t srcALen,
+  const q7_t * pSrcB,
+        uint32_t srcBLen,
+        q7_t * pDst);
+
+
+  /**
+   * @brief Instance structure for the floating-point sparse FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;             /**< number of coefficients in the filter. */
+          uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
+          float32_t *pState;            /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
+    const float32_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
+          uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
+          int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
+  } arm_fir_sparse_instance_f32;
+
+  /**
+   * @brief Instance structure for the Q31 sparse FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;             /**< number of coefficients in the filter. */
+          uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
+          q31_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
+    const q31_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
+          uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
+          int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
+  } arm_fir_sparse_instance_q31;
+
+  /**
+   * @brief Instance structure for the Q15 sparse FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;             /**< number of coefficients in the filter. */
+          uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
+          q15_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
+    const q15_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
+          uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
+          int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
+  } arm_fir_sparse_instance_q15;
+
+  /**
+   * @brief Instance structure for the Q7 sparse FIR filter.
+   */
+  typedef struct
+  {
+          uint16_t numTaps;             /**< number of coefficients in the filter. */
+          uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
+          q7_t *pState;                 /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
+    const q7_t *pCoeffs;                /**< points to the coefficient array. The array is of length numTaps.*/
+          uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
+          int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
+  } arm_fir_sparse_instance_q7;
+
+
+  /**
+   * @brief Processing function for the floating-point sparse FIR filter.
+   * @param[in]  S           points to an instance of the floating-point sparse FIR structure.
+   * @param[in]  pSrc        points to the block of input data.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  pScratchIn  points to a temporary buffer of size blockSize.
+   * @param[in]  blockSize   number of input samples to process per call.
+   */
+  void arm_fir_sparse_f32(
+        arm_fir_sparse_instance_f32 * S,
+  const float32_t * pSrc,
+        float32_t * pDst,
+        float32_t * pScratchIn,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the floating-point sparse FIR filter.
+   * @param[in,out] S          points to an instance of the floating-point sparse FIR structure.
+   * @param[in]     numTaps    number of nonzero coefficients in the filter.
+   * @param[in]     pCoeffs    points to the array of filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     pTapDelay  points to the array of offset times.
+   * @param[in]     maxDelay   maximum offset time supported.
+   * @param[in]     blockSize  number of samples that will be processed per block.
+   */
+  void arm_fir_sparse_init_f32(
+        arm_fir_sparse_instance_f32 * S,
+        uint16_t numTaps,
+  const float32_t * pCoeffs,
+        float32_t * pState,
+        int32_t * pTapDelay,
+        uint16_t maxDelay,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q31 sparse FIR filter.
+   * @param[in]  S           points to an instance of the Q31 sparse FIR structure.
+   * @param[in]  pSrc        points to the block of input data.
+   * @param[out] pDst        points to the block of output data
+   * @param[in]  pScratchIn  points to a temporary buffer of size blockSize.
+   * @param[in]  blockSize   number of input samples to process per call.
+   */
+  void arm_fir_sparse_q31(
+        arm_fir_sparse_instance_q31 * S,
+  const q31_t * pSrc,
+        q31_t * pDst,
+        q31_t * pScratchIn,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q31 sparse FIR filter.
+   * @param[in,out] S          points to an instance of the Q31 sparse FIR structure.
+   * @param[in]     numTaps    number of nonzero coefficients in the filter.
+   * @param[in]     pCoeffs    points to the array of filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     pTapDelay  points to the array of offset times.
+   * @param[in]     maxDelay   maximum offset time supported.
+   * @param[in]     blockSize  number of samples that will be processed per block.
+   */
+  void arm_fir_sparse_init_q31(
+        arm_fir_sparse_instance_q31 * S,
+        uint16_t numTaps,
+  const q31_t * pCoeffs,
+        q31_t * pState,
+        int32_t * pTapDelay,
+        uint16_t maxDelay,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q15 sparse FIR filter.
+   * @param[in]  S            points to an instance of the Q15 sparse FIR structure.
+   * @param[in]  pSrc         points to the block of input data.
+   * @param[out] pDst         points to the block of output data
+   * @param[in]  pScratchIn   points to a temporary buffer of size blockSize.
+   * @param[in]  pScratchOut  points to a temporary buffer of size blockSize.
+   * @param[in]  blockSize    number of input samples to process per call.
+   */
+  void arm_fir_sparse_q15(
+        arm_fir_sparse_instance_q15 * S,
+  const q15_t * pSrc,
+        q15_t * pDst,
+        q15_t * pScratchIn,
+        q31_t * pScratchOut,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q15 sparse FIR filter.
+   * @param[in,out] S          points to an instance of the Q15 sparse FIR structure.
+   * @param[in]     numTaps    number of nonzero coefficients in the filter.
+   * @param[in]     pCoeffs    points to the array of filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     pTapDelay  points to the array of offset times.
+   * @param[in]     maxDelay   maximum offset time supported.
+   * @param[in]     blockSize  number of samples that will be processed per block.
+   */
+  void arm_fir_sparse_init_q15(
+        arm_fir_sparse_instance_q15 * S,
+        uint16_t numTaps,
+  const q15_t * pCoeffs,
+        q15_t * pState,
+        int32_t * pTapDelay,
+        uint16_t maxDelay,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Processing function for the Q7 sparse FIR filter.
+   * @param[in]  S            points to an instance of the Q7 sparse FIR structure.
+   * @param[in]  pSrc         points to the block of input data.
+   * @param[out] pDst         points to the block of output data
+   * @param[in]  pScratchIn   points to a temporary buffer of size blockSize.
+   * @param[in]  pScratchOut  points to a temporary buffer of size blockSize.
+   * @param[in]  blockSize    number of input samples to process per call.
+   */
+  void arm_fir_sparse_q7(
+        arm_fir_sparse_instance_q7 * S,
+  const q7_t * pSrc,
+        q7_t * pDst,
+        q7_t * pScratchIn,
+        q31_t * pScratchOut,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Initialization function for the Q7 sparse FIR filter.
+   * @param[in,out] S          points to an instance of the Q7 sparse FIR structure.
+   * @param[in]     numTaps    number of nonzero coefficients in the filter.
+   * @param[in]     pCoeffs    points to the array of filter coefficients.
+   * @param[in]     pState     points to the state buffer.
+   * @param[in]     pTapDelay  points to the array of offset times.
+   * @param[in]     maxDelay   maximum offset time supported.
+   * @param[in]     blockSize  number of samples that will be processed per block.
+   */
+  void arm_fir_sparse_init_q7(
+        arm_fir_sparse_instance_q7 * S,
+        uint16_t numTaps,
+  const q7_t * pCoeffs,
+        q7_t * pState,
+        int32_t * pTapDelay,
+        uint16_t maxDelay,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Floating-point sin_cos function.
+   * @param[in]  theta   input value in degrees
+   * @param[out] pSinVal  points to the processed sine output.
+   * @param[out] pCosVal  points to the processed cos output.
+   */
+  void arm_sin_cos_f32(
+        float32_t theta,
+        float32_t * pSinVal,
+        float32_t * pCosVal);
+
+
+  /**
+   * @brief  Q31 sin_cos function.
+   * @param[in]  theta    scaled input value in degrees
+   * @param[out] pSinVal  points to the processed sine output.
+   * @param[out] pCosVal  points to the processed cosine output.
+   */
+  void arm_sin_cos_q31(
+        q31_t theta,
+        q31_t * pSinVal,
+        q31_t * pCosVal);
+
+
+  /**
+   * @brief  Floating-point complex conjugate.
+   * @param[in]  pSrc        points to the input vector
+   * @param[out] pDst        points to the output vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   */
+  void arm_cmplx_conj_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t numSamples);
+
+  /**
+   * @brief  Q31 complex conjugate.
+   * @param[in]  pSrc        points to the input vector
+   * @param[out] pDst        points to the output vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   */
+  void arm_cmplx_conj_q31(
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q15 complex conjugate.
+   * @param[in]  pSrc        points to the input vector
+   * @param[out] pDst        points to the output vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   */
+  void arm_cmplx_conj_q15(
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Floating-point complex magnitude squared
+   * @param[in]  pSrc        points to the complex input vector
+   * @param[out] pDst        points to the real output vector
+   * @param[in]  numSamples  number of complex samples in the input vector
+   */
+  void arm_cmplx_mag_squared_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q31 complex magnitude squared
+   * @param[in]  pSrc        points to the complex input vector
+   * @param[out] pDst        points to the real output vector
+   * @param[in]  numSamples  number of complex samples in the input vector
+   */
+  void arm_cmplx_mag_squared_q31(
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q15 complex magnitude squared
+   * @param[in]  pSrc        points to the complex input vector
+   * @param[out] pDst        points to the real output vector
+   * @param[in]  numSamples  number of complex samples in the input vector
+   */
+  void arm_cmplx_mag_squared_q15(
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t numSamples);
+
+
+ /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup PID PID Motor Control
+   *
+   * A Proportional Integral Derivative (PID) controller is a generic feedback control
+   * loop mechanism widely used in industrial control systems.
+   * A PID controller is the most commonly used type of feedback controller.
+   *
+   * This set of functions implements (PID) controllers
+   * for Q15, Q31, and floating-point data types.  The functions operate on a single sample
+   * of data and each call to the function returns a single processed value.
+   * <code>S</code> points to an instance of the PID control data structure.  <code>in</code>
+   * is the input sample value. The functions return the output value.
+   *
+   * \par Algorithm:
+   * <pre>
+   *    y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]
+   *    A0 = Kp + Ki + Kd
+   *    A1 = (-Kp ) - (2 * Kd )
+   *    A2 = Kd
+   * </pre>
+   *
+   * \par
+   * where \c Kp is proportional constant, \c Ki is Integral constant and \c Kd is Derivative constant
+   *
+   * \par
+   * \image html PID.gif "Proportional Integral Derivative Controller"
+   *
+   * \par
+   * The PID controller calculates an "error" value as the difference between
+   * the measured output and the reference input.
+   * The controller attempts to minimize the error by adjusting the process control inputs.
+   * The proportional value determines the reaction to the current error,
+   * the integral value determines the reaction based on the sum of recent errors,
+   * and the derivative value determines the reaction based on the rate at which the error has been changing.
+   *
+   * \par Instance Structure
+   * The Gains A0, A1, A2 and state variables for a PID controller are stored together in an instance data structure.
+   * A separate instance structure must be defined for each PID Controller.
+   * There are separate instance structure declarations for each of the 3 supported data types.
+   *
+   * \par Reset Functions
+   * There is also an associated reset function for each data type which clears the state array.
+   *
+   * \par Initialization Functions
+   * There is also an associated initialization function for each data type.
+   * The initialization function performs the following operations:
+   * - Initializes the Gains A0, A1, A2 from Kp,Ki, Kd gains.
+   * - Zeros out the values in the state buffer.
+   *
+   * \par
+   * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.
+   *
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the fixed-point versions of the PID Controller functions.
+   * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup PID
+   * @{
+   */
+
+  /**
+   * @brief         Process function for the floating-point PID Control.
+   * @param[in,out] S   is an instance of the floating-point PID Control structure
+   * @param[in]     in  input sample to process
+   * @return        processed output sample.
+   */
+  __STATIC_FORCEINLINE float32_t arm_pid_f32(
+  arm_pid_instance_f32 * S,
+  float32_t in)
+  {
+    float32_t out;
+
+    /* y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]  */
+    out = (S->A0 * in) +
+      (S->A1 * S->state[0]) + (S->A2 * S->state[1]) + (S->state[2]);
+
+    /* Update state */
+    S->state[1] = S->state[0];
+    S->state[0] = in;
+    S->state[2] = out;
+
+    /* return to application */
+    return (out);
+
+  }
+
+/**
+  @brief         Process function for the Q31 PID Control.
+  @param[in,out] S  points to an instance of the Q31 PID Control structure
+  @param[in]     in  input sample to process
+  @return        processed output sample.
+
+  \par Scaling and Overflow Behavior
+         The function is implemented using an internal 64-bit accumulator.
+         The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
+         Thus, if the accumulator result overflows it wraps around rather than clip.
+         In order to avoid overflows completely the input signal must be scaled down by 2 bits as there are four additions.
+         After all multiply-accumulates are performed, the 2.62 accumulator is truncated to 1.32 format and then saturated to 1.31 format.
+ */
+__STATIC_FORCEINLINE q31_t arm_pid_q31(
+  arm_pid_instance_q31 * S,
+  q31_t in)
+  {
+    q63_t acc;
+    q31_t out;
+
+    /* acc = A0 * x[n]  */
+    acc = (q63_t) S->A0 * in;
+
+    /* acc += A1 * x[n-1] */
+    acc += (q63_t) S->A1 * S->state[0];
+
+    /* acc += A2 * x[n-2]  */
+    acc += (q63_t) S->A2 * S->state[1];
+
+    /* convert output to 1.31 format to add y[n-1] */
+    out = (q31_t) (acc >> 31U);
+
+    /* out += y[n-1] */
+    out += S->state[2];
+
+    /* Update state */
+    S->state[1] = S->state[0];
+    S->state[0] = in;
+    S->state[2] = out;
+
+    /* return to application */
+    return (out);
+  }
+
+
+/**
+  @brief         Process function for the Q15 PID Control.
+  @param[in,out] S   points to an instance of the Q15 PID Control structure
+  @param[in]     in  input sample to process
+  @return        processed output sample.
+
+  \par Scaling and Overflow Behavior
+         The function is implemented using a 64-bit internal accumulator.
+         Both Gains and state variables are represented in 1.15 format and multiplications yield a 2.30 result.
+         The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.
+         There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.
+         After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits.
+         Lastly, the accumulator is saturated to yield a result in 1.15 format.
+ */
+__STATIC_FORCEINLINE q15_t arm_pid_q15(
+  arm_pid_instance_q15 * S,
+  q15_t in)
+  {
+    q63_t acc;
+    q15_t out;
+
+#if defined (ARM_MATH_DSP)
+    /* Implementation of PID controller */
+
+    /* acc = A0 * x[n]  */
+    acc = (q31_t) __SMUAD((uint32_t)S->A0, (uint32_t)in);
+
+    /* acc += A1 * x[n-1] + A2 * x[n-2]  */
+    acc = (q63_t)__SMLALD((uint32_t)S->A1, (uint32_t)read_q15x2 (S->state), (uint64_t)acc);
+#else
+    /* acc = A0 * x[n]  */
+    acc = ((q31_t) S->A0) * in;
+
+    /* acc += A1 * x[n-1] + A2 * x[n-2]  */
+    acc += (q31_t) S->A1 * S->state[0];
+    acc += (q31_t) S->A2 * S->state[1];
+#endif
+
+    /* acc += y[n-1] */
+    acc += (q31_t) S->state[2] << 15;
+
+    /* saturate the output */
+    out = (q15_t) (__SSAT((acc >> 15), 16));
+
+    /* Update state */
+    S->state[1] = S->state[0];
+    S->state[0] = in;
+    S->state[2] = out;
+
+    /* return to application */
+    return (out);
+  }
+
+  /**
+   * @} end of PID group
+   */
+
+
+  /**
+   * @brief Floating-point matrix inverse.
+   * @param[in]  src   points to the instance of the input floating-point matrix structure.
+   * @param[out] dst   points to the instance of the output floating-point matrix structure.
+   * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
+   * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR.
+   */
+  arm_status arm_mat_inverse_f32(
+  const arm_matrix_instance_f32 * src,
+  arm_matrix_instance_f32 * dst);
+
+
+  /**
+   * @brief Floating-point matrix inverse.
+   * @param[in]  src   points to the instance of the input floating-point matrix structure.
+   * @param[out] dst   points to the instance of the output floating-point matrix structure.
+   * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
+   * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR.
+   */
+  arm_status arm_mat_inverse_f64(
+  const arm_matrix_instance_f64 * src,
+  arm_matrix_instance_f64 * dst);
+
+
+
+  /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup clarke Vector Clarke Transform
+   * Forward Clarke transform converts the instantaneous stator phases into a two-coordinate time invariant vector.
+   * Generally the Clarke transform uses three-phase currents <code>Ia, Ib and Ic</code> to calculate currents
+   * in the two-phase orthogonal stator axis <code>Ialpha</code> and <code>Ibeta</code>.
+   * When <code>Ialpha</code> is superposed with <code>Ia</code> as shown in the figure below
+   * \image html clarke.gif Stator current space vector and its components in (a,b).
+   * and <code>Ia + Ib + Ic = 0</code>, in this condition <code>Ialpha</code> and <code>Ibeta</code>
+   * can be calculated using only <code>Ia</code> and <code>Ib</code>.
+   *
+   * The function operates on a single sample of data and each call to the function returns the processed output.
+   * The library provides separate functions for Q31 and floating-point data types.
+   * \par Algorithm
+   * \image html clarkeFormula.gif
+   * where <code>Ia</code> and <code>Ib</code> are the instantaneous stator phases and
+   * <code>pIalpha</code> and <code>pIbeta</code> are the two coordinates of time invariant vector.
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the Q31 version of the Clarke transform.
+   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup clarke
+   * @{
+   */
+
+  /**
+   *
+   * @brief  Floating-point Clarke transform
+   * @param[in]  Ia       input three-phase coordinate <code>a</code>
+   * @param[in]  Ib       input three-phase coordinate <code>b</code>
+   * @param[out] pIalpha  points to output two-phase orthogonal vector axis alpha
+   * @param[out] pIbeta   points to output two-phase orthogonal vector axis beta
+   * @return        none
+   */
+  __STATIC_FORCEINLINE void arm_clarke_f32(
+  float32_t Ia,
+  float32_t Ib,
+  float32_t * pIalpha,
+  float32_t * pIbeta)
+  {
+    /* Calculate pIalpha using the equation, pIalpha = Ia */
+    *pIalpha = Ia;
+
+    /* Calculate pIbeta using the equation, pIbeta = (1/sqrt(3)) * Ia + (2/sqrt(3)) * Ib */
+    *pIbeta = ((float32_t) 0.57735026919 * Ia + (float32_t) 1.15470053838 * Ib);
+  }
+
+
+/**
+  @brief  Clarke transform for Q31 version
+  @param[in]  Ia       input three-phase coordinate <code>a</code>
+  @param[in]  Ib       input three-phase coordinate <code>b</code>
+  @param[out] pIalpha  points to output two-phase orthogonal vector axis alpha
+  @param[out] pIbeta   points to output two-phase orthogonal vector axis beta
+  @return     none
+
+  \par Scaling and Overflow Behavior
+         The function is implemented using an internal 32-bit accumulator.
+         The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
+         There is saturation on the addition, hence there is no risk of overflow.
+ */
+__STATIC_FORCEINLINE void arm_clarke_q31(
+  q31_t Ia,
+  q31_t Ib,
+  q31_t * pIalpha,
+  q31_t * pIbeta)
+  {
+    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
+
+    /* Calculating pIalpha from Ia by equation pIalpha = Ia */
+    *pIalpha = Ia;
+
+    /* Intermediate product is calculated by (1/(sqrt(3)) * Ia) */
+    product1 = (q31_t) (((q63_t) Ia * 0x24F34E8B) >> 30);
+
+    /* Intermediate product is calculated by (2/sqrt(3) * Ib) */
+    product2 = (q31_t) (((q63_t) Ib * 0x49E69D16) >> 30);
+
+    /* pIbeta is calculated by adding the intermediate products */
+    *pIbeta = __QADD(product1, product2);
+  }
+
+  /**
+   * @} end of clarke group
+   */
+
+
+  /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup inv_clarke Vector Inverse Clarke Transform
+   * Inverse Clarke transform converts the two-coordinate time invariant vector into instantaneous stator phases.
+   *
+   * The function operates on a single sample of data and each call to the function returns the processed output.
+   * The library provides separate functions for Q31 and floating-point data types.
+   * \par Algorithm
+   * \image html clarkeInvFormula.gif
+   * where <code>pIa</code> and <code>pIb</code> are the instantaneous stator phases and
+   * <code>Ialpha</code> and <code>Ibeta</code> are the two coordinates of time invariant vector.
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the Q31 version of the Clarke transform.
+   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup inv_clarke
+   * @{
+   */
+
+   /**
+   * @brief  Floating-point Inverse Clarke transform
+   * @param[in]  Ialpha  input two-phase orthogonal vector axis alpha
+   * @param[in]  Ibeta   input two-phase orthogonal vector axis beta
+   * @param[out] pIa     points to output three-phase coordinate <code>a</code>
+   * @param[out] pIb     points to output three-phase coordinate <code>b</code>
+   * @return     none
+   */
+  __STATIC_FORCEINLINE void arm_inv_clarke_f32(
+  float32_t Ialpha,
+  float32_t Ibeta,
+  float32_t * pIa,
+  float32_t * pIb)
+  {
+    /* Calculating pIa from Ialpha by equation pIa = Ialpha */
+    *pIa = Ialpha;
+
+    /* Calculating pIb from Ialpha and Ibeta by equation pIb = -(1/2) * Ialpha + (sqrt(3)/2) * Ibeta */
+    *pIb = -0.5f * Ialpha + 0.8660254039f * Ibeta;
+  }
+
+
+/**
+  @brief  Inverse Clarke transform for Q31 version
+  @param[in]  Ialpha  input two-phase orthogonal vector axis alpha
+  @param[in]  Ibeta   input two-phase orthogonal vector axis beta
+  @param[out] pIa     points to output three-phase coordinate <code>a</code>
+  @param[out] pIb     points to output three-phase coordinate <code>b</code>
+  @return     none
+
+  \par Scaling and Overflow Behavior
+         The function is implemented using an internal 32-bit accumulator.
+         The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
+         There is saturation on the subtraction, hence there is no risk of overflow.
+ */
+__STATIC_FORCEINLINE void arm_inv_clarke_q31(
+  q31_t Ialpha,
+  q31_t Ibeta,
+  q31_t * pIa,
+  q31_t * pIb)
+  {
+    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
+
+    /* Calculating pIa from Ialpha by equation pIa = Ialpha */
+    *pIa = Ialpha;
+
+    /* Intermediate product is calculated by (1/(2*sqrt(3)) * Ia) */
+    product1 = (q31_t) (((q63_t) (Ialpha) * (0x40000000)) >> 31);
+
+    /* Intermediate product is calculated by (1/sqrt(3) * pIb) */
+    product2 = (q31_t) (((q63_t) (Ibeta) * (0x6ED9EBA1)) >> 31);
+
+    /* pIb is calculated by subtracting the products */
+    *pIb = __QSUB(product2, product1);
+  }
+
+  /**
+   * @} end of inv_clarke group
+   */
+
+
+
+  /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup park Vector Park Transform
+   *
+   * Forward Park transform converts the input two-coordinate vector to flux and torque components.
+   * The Park transform can be used to realize the transformation of the <code>Ialpha</code> and the <code>Ibeta</code> currents
+   * from the stationary to the moving reference frame and control the spatial relationship between
+   * the stator vector current and rotor flux vector.
+   * If we consider the d axis aligned with the rotor flux, the diagram below shows the
+   * current vector and the relationship from the two reference frames:
+   * \image html park.gif "Stator current space vector and its component in (a,b) and in the d,q rotating reference frame"
+   *
+   * The function operates on a single sample of data and each call to the function returns the processed output.
+   * The library provides separate functions for Q31 and floating-point data types.
+   * \par Algorithm
+   * \image html parkFormula.gif
+   * where <code>Ialpha</code> and <code>Ibeta</code> are the stator vector components,
+   * <code>pId</code> and <code>pIq</code> are rotor vector components and <code>cosVal</code> and <code>sinVal</code> are the
+   * cosine and sine values of theta (rotor flux position).
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the Q31 version of the Park transform.
+   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup park
+   * @{
+   */
+
+  /**
+   * @brief Floating-point Park transform
+   * @param[in]  Ialpha  input two-phase vector coordinate alpha
+   * @param[in]  Ibeta   input two-phase vector coordinate beta
+   * @param[out] pId     points to output   rotor reference frame d
+   * @param[out] pIq     points to output   rotor reference frame q
+   * @param[in]  sinVal  sine value of rotation angle theta
+   * @param[in]  cosVal  cosine value of rotation angle theta
+   * @return     none
+   *
+   * The function implements the forward Park transform.
+   *
+   */
+  __STATIC_FORCEINLINE void arm_park_f32(
+  float32_t Ialpha,
+  float32_t Ibeta,
+  float32_t * pId,
+  float32_t * pIq,
+  float32_t sinVal,
+  float32_t cosVal)
+  {
+    /* Calculate pId using the equation, pId = Ialpha * cosVal + Ibeta * sinVal */
+    *pId = Ialpha * cosVal + Ibeta * sinVal;
+
+    /* Calculate pIq using the equation, pIq = - Ialpha * sinVal + Ibeta * cosVal */
+    *pIq = -Ialpha * sinVal + Ibeta * cosVal;
+  }
+
+
+/**
+  @brief  Park transform for Q31 version
+  @param[in]  Ialpha  input two-phase vector coordinate alpha
+  @param[in]  Ibeta   input two-phase vector coordinate beta
+  @param[out] pId     points to output rotor reference frame d
+  @param[out] pIq     points to output rotor reference frame q
+  @param[in]  sinVal  sine value of rotation angle theta
+  @param[in]  cosVal  cosine value of rotation angle theta
+  @return     none
+
+  \par Scaling and Overflow Behavior
+         The function is implemented using an internal 32-bit accumulator.
+         The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
+         There is saturation on the addition and subtraction, hence there is no risk of overflow.
+ */
+__STATIC_FORCEINLINE void arm_park_q31(
+  q31_t Ialpha,
+  q31_t Ibeta,
+  q31_t * pId,
+  q31_t * pIq,
+  q31_t sinVal,
+  q31_t cosVal)
+  {
+    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
+    q31_t product3, product4;                    /* Temporary variables used to store intermediate results */
+
+    /* Intermediate product is calculated by (Ialpha * cosVal) */
+    product1 = (q31_t) (((q63_t) (Ialpha) * (cosVal)) >> 31);
+
+    /* Intermediate product is calculated by (Ibeta * sinVal) */
+    product2 = (q31_t) (((q63_t) (Ibeta) * (sinVal)) >> 31);
+
+
+    /* Intermediate product is calculated by (Ialpha * sinVal) */
+    product3 = (q31_t) (((q63_t) (Ialpha) * (sinVal)) >> 31);
+
+    /* Intermediate product is calculated by (Ibeta * cosVal) */
+    product4 = (q31_t) (((q63_t) (Ibeta) * (cosVal)) >> 31);
+
+    /* Calculate pId by adding the two intermediate products 1 and 2 */
+    *pId = __QADD(product1, product2);
+
+    /* Calculate pIq by subtracting the two intermediate products 3 from 4 */
+    *pIq = __QSUB(product4, product3);
+  }
+
+  /**
+   * @} end of park group
+   */
+
+
+  /**
+   * @ingroup groupController
+   */
+
+  /**
+   * @defgroup inv_park Vector Inverse Park transform
+   * Inverse Park transform converts the input flux and torque components to two-coordinate vector.
+   *
+   * The function operates on a single sample of data and each call to the function returns the processed output.
+   * The library provides separate functions for Q31 and floating-point data types.
+   * \par Algorithm
+   * \image html parkInvFormula.gif
+   * where <code>pIalpha</code> and <code>pIbeta</code> are the stator vector components,
+   * <code>Id</code> and <code>Iq</code> are rotor vector components and <code>cosVal</code> and <code>sinVal</code> are the
+   * cosine and sine values of theta (rotor flux position).
+   * \par Fixed-Point Behavior
+   * Care must be taken when using the Q31 version of the Park transform.
+   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
+   * Refer to the function specific documentation below for usage guidelines.
+   */
+
+  /**
+   * @addtogroup inv_park
+   * @{
+   */
+
+   /**
+   * @brief  Floating-point Inverse Park transform
+   * @param[in]  Id       input coordinate of rotor reference frame d
+   * @param[in]  Iq       input coordinate of rotor reference frame q
+   * @param[out] pIalpha  points to output two-phase orthogonal vector axis alpha
+   * @param[out] pIbeta   points to output two-phase orthogonal vector axis beta
+   * @param[in]  sinVal   sine value of rotation angle theta
+   * @param[in]  cosVal   cosine value of rotation angle theta
+   * @return     none
+   */
+  __STATIC_FORCEINLINE void arm_inv_park_f32(
+  float32_t Id,
+  float32_t Iq,
+  float32_t * pIalpha,
+  float32_t * pIbeta,
+  float32_t sinVal,
+  float32_t cosVal)
+  {
+    /* Calculate pIalpha using the equation, pIalpha = Id * cosVal - Iq * sinVal */
+    *pIalpha = Id * cosVal - Iq * sinVal;
+
+    /* Calculate pIbeta using the equation, pIbeta = Id * sinVal + Iq * cosVal */
+    *pIbeta = Id * sinVal + Iq * cosVal;
+  }
+
+
+/**
+  @brief  Inverse Park transform for   Q31 version
+  @param[in]  Id       input coordinate of rotor reference frame d
+  @param[in]  Iq       input coordinate of rotor reference frame q
+  @param[out] pIalpha  points to output two-phase orthogonal vector axis alpha
+  @param[out] pIbeta   points to output two-phase orthogonal vector axis beta
+  @param[in]  sinVal   sine value of rotation angle theta
+  @param[in]  cosVal   cosine value of rotation angle theta
+  @return     none
+
+  @par Scaling and Overflow Behavior
+         The function is implemented using an internal 32-bit accumulator.
+         The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
+         There is saturation on the addition, hence there is no risk of overflow.
+ */
+__STATIC_FORCEINLINE void arm_inv_park_q31(
+  q31_t Id,
+  q31_t Iq,
+  q31_t * pIalpha,
+  q31_t * pIbeta,
+  q31_t sinVal,
+  q31_t cosVal)
+  {
+    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
+    q31_t product3, product4;                    /* Temporary variables used to store intermediate results */
+
+    /* Intermediate product is calculated by (Id * cosVal) */
+    product1 = (q31_t) (((q63_t) (Id) * (cosVal)) >> 31);
+
+    /* Intermediate product is calculated by (Iq * sinVal) */
+    product2 = (q31_t) (((q63_t) (Iq) * (sinVal)) >> 31);
+
+
+    /* Intermediate product is calculated by (Id * sinVal) */
+    product3 = (q31_t) (((q63_t) (Id) * (sinVal)) >> 31);
+
+    /* Intermediate product is calculated by (Iq * cosVal) */
+    product4 = (q31_t) (((q63_t) (Iq) * (cosVal)) >> 31);
+
+    /* Calculate pIalpha by using the two intermediate products 1 and 2 */
+    *pIalpha = __QSUB(product1, product2);
+
+    /* Calculate pIbeta by using the two intermediate products 3 and 4 */
+    *pIbeta = __QADD(product4, product3);
+  }
+
+  /**
+   * @} end of Inverse park group
+   */
+
+
+  /**
+   * @ingroup groupInterpolation
+   */
+
+  /**
+   * @defgroup LinearInterpolate Linear Interpolation
+   *
+   * Linear interpolation is a method of curve fitting using linear polynomials.
+   * Linear interpolation works by effectively drawing a straight line between two neighboring samples and returning the appropriate point along that line
+   *
+   * \par
+   * \image html LinearInterp.gif "Linear interpolation"
+   *
+   * \par
+   * A  Linear Interpolate function calculates an output value(y), for the input(x)
+   * using linear interpolation of the input values x0, x1( nearest input values) and the output values y0 and y1(nearest output values)
+   *
+   * \par Algorithm:
+   * <pre>
+   *       y = y0 + (x - x0) * ((y1 - y0)/(x1-x0))
+   *       where x0, x1 are nearest values of input x
+   *             y0, y1 are nearest values to output y
+   * </pre>
+   *
+   * \par
+   * This set of functions implements Linear interpolation process
+   * for Q7, Q15, Q31, and floating-point data types.  The functions operate on a single
+   * sample of data and each call to the function returns a single processed value.
+   * <code>S</code> points to an instance of the Linear Interpolate function data structure.
+   * <code>x</code> is the input sample value. The functions returns the output value.
+   *
+   * \par
+   * if x is outside of the table boundary, Linear interpolation returns first value of the table
+   * if x is below input range and returns last value of table if x is above range.
+   */
+
+  /**
+   * @addtogroup LinearInterpolate
+   * @{
+   */
+
+  /**
+   * @brief  Process function for the floating-point Linear Interpolation Function.
+   * @param[in,out] S  is an instance of the floating-point Linear Interpolation structure
+   * @param[in]     x  input sample to process
+   * @return y processed output sample.
+   *
+   */
+  __STATIC_FORCEINLINE float32_t arm_linear_interp_f32(
+  arm_linear_interp_instance_f32 * S,
+  float32_t x)
+  {
+    float32_t y;
+    float32_t x0, x1;                            /* Nearest input values */
+    float32_t y0, y1;                            /* Nearest output values */
+    float32_t xSpacing = S->xSpacing;            /* spacing between input values */
+    int32_t i;                                   /* Index variable */
+    float32_t *pYData = S->pYData;               /* pointer to output table */
+
+    /* Calculation of index */
+    i = (int32_t) ((x - S->x1) / xSpacing);
+
+    if (i < 0)
+    {
+      /* Iniatilize output for below specified range as least output value of table */
+      y = pYData[0];
+    }
+    else if ((uint32_t)i >= S->nValues)
+    {
+      /* Iniatilize output for above specified range as last output value of table */
+      y = pYData[S->nValues - 1];
+    }
+    else
+    {
+      /* Calculation of nearest input values */
+      x0 = S->x1 +  i      * xSpacing;
+      x1 = S->x1 + (i + 1) * xSpacing;
+
+      /* Read of nearest output values */
+      y0 = pYData[i];
+      y1 = pYData[i + 1];
+
+      /* Calculation of output */
+      y = y0 + (x - x0) * ((y1 - y0) / (x1 - x0));
+
+    }
+
+    /* returns output value */
+    return (y);
+  }
+
+
+   /**
+   *
+   * @brief  Process function for the Q31 Linear Interpolation Function.
+   * @param[in] pYData   pointer to Q31 Linear Interpolation table
+   * @param[in] x        input sample to process
+   * @param[in] nValues  number of table values
+   * @return y processed output sample.
+   *
+   * \par
+   * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
+   * This function can support maximum of table size 2^12.
+   *
+   */
+  __STATIC_FORCEINLINE q31_t arm_linear_interp_q31(
+  q31_t * pYData,
+  q31_t x,
+  uint32_t nValues)
+  {
+    q31_t y;                                     /* output */
+    q31_t y0, y1;                                /* Nearest output values */
+    q31_t fract;                                 /* fractional part */
+    int32_t index;                               /* Index to read nearest output values */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    index = ((x & (q31_t)0xFFF00000) >> 20);
+
+    if (index >= (int32_t)(nValues - 1))
+    {
+      return (pYData[nValues - 1]);
+    }
+    else if (index < 0)
+    {
+      return (pYData[0]);
+    }
+    else
+    {
+      /* 20 bits for the fractional part */
+      /* shift left by 11 to keep fract in 1.31 format */
+      fract = (x & 0x000FFFFF) << 11;
+
+      /* Read two nearest output values from the index in 1.31(q31) format */
+      y0 = pYData[index];
+      y1 = pYData[index + 1];
+
+      /* Calculation of y0 * (1-fract) and y is in 2.30 format */
+      y = ((q31_t) ((q63_t) y0 * (0x7FFFFFFF - fract) >> 32));
+
+      /* Calculation of y0 * (1-fract) + y1 *fract and y is in 2.30 format */
+      y += ((q31_t) (((q63_t) y1 * fract) >> 32));
+
+      /* Convert y to 1.31 format */
+      return (y << 1U);
+    }
+  }
+
+
+  /**
+   *
+   * @brief  Process function for the Q15 Linear Interpolation Function.
+   * @param[in] pYData   pointer to Q15 Linear Interpolation table
+   * @param[in] x        input sample to process
+   * @param[in] nValues  number of table values
+   * @return y processed output sample.
+   *
+   * \par
+   * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
+   * This function can support maximum of table size 2^12.
+   *
+   */
+  __STATIC_FORCEINLINE q15_t arm_linear_interp_q15(
+  q15_t * pYData,
+  q31_t x,
+  uint32_t nValues)
+  {
+    q63_t y;                                     /* output */
+    q15_t y0, y1;                                /* Nearest output values */
+    q31_t fract;                                 /* fractional part */
+    int32_t index;                               /* Index to read nearest output values */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    index = ((x & (int32_t)0xFFF00000) >> 20);
+
+    if (index >= (int32_t)(nValues - 1))
+    {
+      return (pYData[nValues - 1]);
+    }
+    else if (index < 0)
+    {
+      return (pYData[0]);
+    }
+    else
+    {
+      /* 20 bits for the fractional part */
+      /* fract is in 12.20 format */
+      fract = (x & 0x000FFFFF);
+
+      /* Read two nearest output values from the index */
+      y0 = pYData[index];
+      y1 = pYData[index + 1];
+
+      /* Calculation of y0 * (1-fract) and y is in 13.35 format */
+      y = ((q63_t) y0 * (0xFFFFF - fract));
+
+      /* Calculation of (y0 * (1-fract) + y1 * fract) and y is in 13.35 format */
+      y += ((q63_t) y1 * (fract));
+
+      /* convert y to 1.15 format */
+      return (q15_t) (y >> 20);
+    }
+  }
+
+
+  /**
+   *
+   * @brief  Process function for the Q7 Linear Interpolation Function.
+   * @param[in] pYData   pointer to Q7 Linear Interpolation table
+   * @param[in] x        input sample to process
+   * @param[in] nValues  number of table values
+   * @return y processed output sample.
+   *
+   * \par
+   * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
+   * This function can support maximum of table size 2^12.
+   */
+  __STATIC_FORCEINLINE q7_t arm_linear_interp_q7(
+  q7_t * pYData,
+  q31_t x,
+  uint32_t nValues)
+  {
+    q31_t y;                                     /* output */
+    q7_t y0, y1;                                 /* Nearest output values */
+    q31_t fract;                                 /* fractional part */
+    uint32_t index;                              /* Index to read nearest output values */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    if (x < 0)
+    {
+      return (pYData[0]);
+    }
+    index = (x >> 20) & 0xfff;
+
+    if (index >= (nValues - 1))
+    {
+      return (pYData[nValues - 1]);
+    }
+    else
+    {
+      /* 20 bits for the fractional part */
+      /* fract is in 12.20 format */
+      fract = (x & 0x000FFFFF);
+
+      /* Read two nearest output values from the index and are in 1.7(q7) format */
+      y0 = pYData[index];
+      y1 = pYData[index + 1];
+
+      /* Calculation of y0 * (1-fract ) and y is in 13.27(q27) format */
+      y = ((y0 * (0xFFFFF - fract)));
+
+      /* Calculation of y1 * fract + y0 * (1-fract) and y is in 13.27(q27) format */
+      y += (y1 * fract);
+
+      /* convert y to 1.7(q7) format */
+      return (q7_t) (y >> 20);
+     }
+  }
+
+  /**
+   * @} end of LinearInterpolate group
+   */
+
+  /**
+   * @brief  Fast approximation to the trigonometric sine function for floating-point data.
+   * @param[in] x  input value in radians.
+   * @return  sin(x).
+   */
+  float32_t arm_sin_f32(
+  float32_t x);
+
+
+  /**
+   * @brief  Fast approximation to the trigonometric sine function for Q31 data.
+   * @param[in] x  Scaled input value in radians.
+   * @return  sin(x).
+   */
+  q31_t arm_sin_q31(
+  q31_t x);
+
+
+  /**
+   * @brief  Fast approximation to the trigonometric sine function for Q15 data.
+   * @param[in] x  Scaled input value in radians.
+   * @return  sin(x).
+   */
+  q15_t arm_sin_q15(
+  q15_t x);
+
+
+  /**
+   * @brief  Fast approximation to the trigonometric cosine function for floating-point data.
+   * @param[in] x  input value in radians.
+   * @return  cos(x).
+   */
+  float32_t arm_cos_f32(
+  float32_t x);
+
+
+  /**
+   * @brief Fast approximation to the trigonometric cosine function for Q31 data.
+   * @param[in] x  Scaled input value in radians.
+   * @return  cos(x).
+   */
+  q31_t arm_cos_q31(
+  q31_t x);
+
+
+  /**
+   * @brief  Fast approximation to the trigonometric cosine function for Q15 data.
+   * @param[in] x  Scaled input value in radians.
+   * @return  cos(x).
+   */
+  q15_t arm_cos_q15(
+  q15_t x);
+
+
+  /**
+   * @ingroup groupFastMath
+   */
+
+
+  /**
+   * @defgroup SQRT Square Root
+   *
+   * Computes the square root of a number.
+   * There are separate functions for Q15, Q31, and floating-point data types.
+   * The square root function is computed using the Newton-Raphson algorithm.
+   * This is an iterative algorithm of the form:
+   * <pre>
+   *      x1 = x0 - f(x0)/f'(x0)
+   * </pre>
+   * where <code>x1</code> is the current estimate,
+   * <code>x0</code> is the previous estimate, and
+   * <code>f'(x0)</code> is the derivative of <code>f()</code> evaluated at <code>x0</code>.
+   * For the square root function, the algorithm reduces to:
+   * <pre>
+   *     x0 = in/2                         [initial guess]
+   *     x1 = 1/2 * ( x0 + in / x0)        [each iteration]
+   * </pre>
+   */
+
+
+  /**
+   * @addtogroup SQRT
+   * @{
+   */
+
+/**
+  @brief         Floating-point square root function.
+  @param[in]     in    input value
+  @param[out]    pOut  square root of input value
+  @return        execution status
+                   - \ref ARM_MATH_SUCCESS        : input value is positive
+                   - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0
+ */
+__STATIC_FORCEINLINE arm_status arm_sqrt_f32(
+  float32_t in,
+  float32_t * pOut)
+  {
+    if (in >= 0.0f)
+    {
+#if defined ( __CC_ARM )
+  #if defined __TARGET_FPU_VFP
+      *pOut = __sqrtf(in);
+  #else
+      *pOut = sqrtf(in);
+  #endif
+
+#elif defined ( __ICCARM__ )
+  #if defined __ARMVFP__
+      __ASM("VSQRT.F32 %0,%1" : "=t"(*pOut) : "t"(in));
+  #else
+      *pOut = sqrtf(in);
+  #endif
+
+#else
+      *pOut = sqrtf(in);
+#endif
+
+      return (ARM_MATH_SUCCESS);
+    }
+    else
+    {
+      *pOut = 0.0f;
+      return (ARM_MATH_ARGUMENT_ERROR);
+    }
+  }
+
+
+/**
+  @brief         Q31 square root function.
+  @param[in]     in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF
+  @param[out]    pOut  points to square root of input value
+  @return        execution status
+                   - \ref ARM_MATH_SUCCESS        : input value is positive
+                   - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0
+ */
+arm_status arm_sqrt_q31(
+  q31_t in,
+  q31_t * pOut);
+
+
+/**
+  @brief         Q15 square root function.
+  @param[in]     in    input value.  The range of the input value is [0 +1) or 0x0000 to 0x7FFF
+  @param[out]    pOut  points to square root of input value
+  @return        execution status
+                   - \ref ARM_MATH_SUCCESS        : input value is positive
+                   - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0
+ */
+arm_status arm_sqrt_q15(
+  q15_t in,
+  q15_t * pOut);
+
+  /**
+   * @brief  Vector Floating-point square root function.
+   * @param[in]  pIn   input vector.
+   * @param[out] pOut  vector of square roots of input elements.
+   * @param[in]  len   length of input vector.
+   * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
+   * <code>in</code> is negative value and returns zero output for negative values.
+   */
+  void arm_vsqrt_f32(
+  float32_t * pIn,
+  float32_t * pOut,
+  uint16_t len);
+
+  void arm_vsqrt_q31(
+  q31_t * pIn,
+  q31_t * pOut,
+  uint16_t len);
+
+  void arm_vsqrt_q15(
+  q15_t * pIn,
+  q15_t * pOut,
+  uint16_t len);
+
+  /**
+   * @} end of SQRT group
+   */
+
+
+  /**
+   * @brief floating-point Circular write function.
+   */
+  __STATIC_FORCEINLINE void arm_circularWrite_f32(
+  int32_t * circBuffer,
+  int32_t L,
+  uint16_t * writeOffset,
+  int32_t bufferInc,
+  const int32_t * src,
+  int32_t srcInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0U;
+    int32_t wOffset;
+
+    /* Copy the value of Index pointer that points
+     * to the current location where the input samples to be copied */
+    wOffset = *writeOffset;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while (i > 0U)
+    {
+      /* copy the input sample to the circular buffer */
+      circBuffer[wOffset] = *src;
+
+      /* Update the input pointer */
+      src += srcInc;
+
+      /* Circularly update wOffset.  Watch out for positive and negative value */
+      wOffset += bufferInc;
+      if (wOffset >= L)
+        wOffset -= L;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *writeOffset = (uint16_t)wOffset;
+  }
+
+
+
+  /**
+   * @brief floating-point Circular Read function.
+   */
+  __STATIC_FORCEINLINE void arm_circularRead_f32(
+  int32_t * circBuffer,
+  int32_t L,
+  int32_t * readOffset,
+  int32_t bufferInc,
+  int32_t * dst,
+  int32_t * dst_base,
+  int32_t dst_length,
+  int32_t dstInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0U;
+    int32_t rOffset;
+    int32_t* dst_end;
+
+    /* Copy the value of Index pointer that points
+     * to the current location from where the input samples to be read */
+    rOffset = *readOffset;
+    dst_end = dst_base + dst_length;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while (i > 0U)
+    {
+      /* copy the sample from the circular buffer to the destination buffer */
+      *dst = circBuffer[rOffset];
+
+      /* Update the input pointer */
+      dst += dstInc;
+
+      if (dst == dst_end)
+      {
+        dst = dst_base;
+      }
+
+      /* Circularly update rOffset.  Watch out for positive and negative value  */
+      rOffset += bufferInc;
+
+      if (rOffset >= L)
+      {
+        rOffset -= L;
+      }
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *readOffset = rOffset;
+  }
+
+
+  /**
+   * @brief Q15 Circular write function.
+   */
+  __STATIC_FORCEINLINE void arm_circularWrite_q15(
+  q15_t * circBuffer,
+  int32_t L,
+  uint16_t * writeOffset,
+  int32_t bufferInc,
+  const q15_t * src,
+  int32_t srcInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0U;
+    int32_t wOffset;
+
+    /* Copy the value of Index pointer that points
+     * to the current location where the input samples to be copied */
+    wOffset = *writeOffset;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while (i > 0U)
+    {
+      /* copy the input sample to the circular buffer */
+      circBuffer[wOffset] = *src;
+
+      /* Update the input pointer */
+      src += srcInc;
+
+      /* Circularly update wOffset.  Watch out for positive and negative value */
+      wOffset += bufferInc;
+      if (wOffset >= L)
+        wOffset -= L;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *writeOffset = (uint16_t)wOffset;
+  }
+
+
+  /**
+   * @brief Q15 Circular Read function.
+   */
+  __STATIC_FORCEINLINE void arm_circularRead_q15(
+  q15_t * circBuffer,
+  int32_t L,
+  int32_t * readOffset,
+  int32_t bufferInc,
+  q15_t * dst,
+  q15_t * dst_base,
+  int32_t dst_length,
+  int32_t dstInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0;
+    int32_t rOffset;
+    q15_t* dst_end;
+
+    /* Copy the value of Index pointer that points
+     * to the current location from where the input samples to be read */
+    rOffset = *readOffset;
+
+    dst_end = dst_base + dst_length;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while (i > 0U)
+    {
+      /* copy the sample from the circular buffer to the destination buffer */
+      *dst = circBuffer[rOffset];
+
+      /* Update the input pointer */
+      dst += dstInc;
+
+      if (dst == dst_end)
+      {
+        dst = dst_base;
+      }
+
+      /* Circularly update wOffset.  Watch out for positive and negative value */
+      rOffset += bufferInc;
+
+      if (rOffset >= L)
+      {
+        rOffset -= L;
+      }
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *readOffset = rOffset;
+  }
+
+
+  /**
+   * @brief Q7 Circular write function.
+   */
+  __STATIC_FORCEINLINE void arm_circularWrite_q7(
+  q7_t * circBuffer,
+  int32_t L,
+  uint16_t * writeOffset,
+  int32_t bufferInc,
+  const q7_t * src,
+  int32_t srcInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0U;
+    int32_t wOffset;
+
+    /* Copy the value of Index pointer that points
+     * to the current location where the input samples to be copied */
+    wOffset = *writeOffset;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while (i > 0U)
+    {
+      /* copy the input sample to the circular buffer */
+      circBuffer[wOffset] = *src;
+
+      /* Update the input pointer */
+      src += srcInc;
+
+      /* Circularly update wOffset.  Watch out for positive and negative value */
+      wOffset += bufferInc;
+      if (wOffset >= L)
+        wOffset -= L;
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *writeOffset = (uint16_t)wOffset;
+  }
+
+
+  /**
+   * @brief Q7 Circular Read function.
+   */
+  __STATIC_FORCEINLINE void arm_circularRead_q7(
+  q7_t * circBuffer,
+  int32_t L,
+  int32_t * readOffset,
+  int32_t bufferInc,
+  q7_t * dst,
+  q7_t * dst_base,
+  int32_t dst_length,
+  int32_t dstInc,
+  uint32_t blockSize)
+  {
+    uint32_t i = 0;
+    int32_t rOffset;
+    q7_t* dst_end;
+
+    /* Copy the value of Index pointer that points
+     * to the current location from where the input samples to be read */
+    rOffset = *readOffset;
+
+    dst_end = dst_base + dst_length;
+
+    /* Loop over the blockSize */
+    i = blockSize;
+
+    while (i > 0U)
+    {
+      /* copy the sample from the circular buffer to the destination buffer */
+      *dst = circBuffer[rOffset];
+
+      /* Update the input pointer */
+      dst += dstInc;
+
+      if (dst == dst_end)
+      {
+        dst = dst_base;
+      }
+
+      /* Circularly update rOffset.  Watch out for positive and negative value */
+      rOffset += bufferInc;
+
+      if (rOffset >= L)
+      {
+        rOffset -= L;
+      }
+
+      /* Decrement the loop counter */
+      i--;
+    }
+
+    /* Update the index pointer */
+    *readOffset = rOffset;
+  }
+
+
+  /**
+   * @brief  Sum of the squares of the elements of a Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_power_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q63_t * pResult);
+
+
+  /**
+   * @brief  Sum of the squares of the elements of a floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_power_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult);
+
+
+  /**
+   * @brief  Sum of the squares of the elements of a Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_power_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q63_t * pResult);
+
+
+  /**
+   * @brief  Sum of the squares of the elements of a Q7 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_power_q7(
+  const q7_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult);
+
+
+  /**
+   * @brief  Mean value of a Q7 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_mean_q7(
+  const q7_t * pSrc,
+        uint32_t blockSize,
+        q7_t * pResult);
+
+
+  /**
+   * @brief  Mean value of a Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_mean_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q15_t * pResult);
+
+
+  /**
+   * @brief  Mean value of a Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_mean_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult);
+
+
+  /**
+   * @brief  Mean value of a floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_mean_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult);
+
+
+  /**
+   * @brief  Variance of the elements of a floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_var_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult);
+
+
+  /**
+   * @brief  Variance of the elements of a Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_var_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult);
+
+
+  /**
+   * @brief  Variance of the elements of a Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_var_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q15_t * pResult);
+
+
+  /**
+   * @brief  Root Mean Square of the elements of a floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_rms_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult);
+
+
+  /**
+   * @brief  Root Mean Square of the elements of a Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_rms_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult);
+
+
+  /**
+   * @brief  Root Mean Square of the elements of a Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_rms_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q15_t * pResult);
+
+
+  /**
+   * @brief  Standard deviation of the elements of a floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_std_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult);
+
+
+  /**
+   * @brief  Standard deviation of the elements of a Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_std_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult);
+
+
+  /**
+   * @brief  Standard deviation of the elements of a Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output value.
+   */
+  void arm_std_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q15_t * pResult);
+
+
+  /**
+   * @brief  Floating-point complex magnitude
+   * @param[in]  pSrc        points to the complex input vector
+   * @param[out] pDst        points to the real output vector
+   * @param[in]  numSamples  number of complex samples in the input vector
+   */
+  void arm_cmplx_mag_f32(
+  const float32_t * pSrc,
+        float32_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q31 complex magnitude
+   * @param[in]  pSrc        points to the complex input vector
+   * @param[out] pDst        points to the real output vector
+   * @param[in]  numSamples  number of complex samples in the input vector
+   */
+  void arm_cmplx_mag_q31(
+  const q31_t * pSrc,
+        q31_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q15 complex magnitude
+   * @param[in]  pSrc        points to the complex input vector
+   * @param[out] pDst        points to the real output vector
+   * @param[in]  numSamples  number of complex samples in the input vector
+   */
+  void arm_cmplx_mag_q15(
+  const q15_t * pSrc,
+        q15_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q15 complex dot product
+   * @param[in]  pSrcA       points to the first input vector
+   * @param[in]  pSrcB       points to the second input vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   * @param[out] realResult  real part of the result returned here
+   * @param[out] imagResult  imaginary part of the result returned here
+   */
+  void arm_cmplx_dot_prod_q15(
+  const q15_t * pSrcA,
+  const q15_t * pSrcB,
+        uint32_t numSamples,
+        q31_t * realResult,
+        q31_t * imagResult);
+
+
+  /**
+   * @brief  Q31 complex dot product
+   * @param[in]  pSrcA       points to the first input vector
+   * @param[in]  pSrcB       points to the second input vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   * @param[out] realResult  real part of the result returned here
+   * @param[out] imagResult  imaginary part of the result returned here
+   */
+  void arm_cmplx_dot_prod_q31(
+  const q31_t * pSrcA,
+  const q31_t * pSrcB,
+        uint32_t numSamples,
+        q63_t * realResult,
+        q63_t * imagResult);
+
+
+  /**
+   * @brief  Floating-point complex dot product
+   * @param[in]  pSrcA       points to the first input vector
+   * @param[in]  pSrcB       points to the second input vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   * @param[out] realResult  real part of the result returned here
+   * @param[out] imagResult  imaginary part of the result returned here
+   */
+  void arm_cmplx_dot_prod_f32(
+  const float32_t * pSrcA,
+  const float32_t * pSrcB,
+        uint32_t numSamples,
+        float32_t * realResult,
+        float32_t * imagResult);
+
+
+  /**
+   * @brief  Q15 complex-by-real multiplication
+   * @param[in]  pSrcCmplx   points to the complex input vector
+   * @param[in]  pSrcReal    points to the real input vector
+   * @param[out] pCmplxDst   points to the complex output vector
+   * @param[in]  numSamples  number of samples in each vector
+   */
+  void arm_cmplx_mult_real_q15(
+  const q15_t * pSrcCmplx,
+  const q15_t * pSrcReal,
+        q15_t * pCmplxDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q31 complex-by-real multiplication
+   * @param[in]  pSrcCmplx   points to the complex input vector
+   * @param[in]  pSrcReal    points to the real input vector
+   * @param[out] pCmplxDst   points to the complex output vector
+   * @param[in]  numSamples  number of samples in each vector
+   */
+  void arm_cmplx_mult_real_q31(
+  const q31_t * pSrcCmplx,
+  const q31_t * pSrcReal,
+        q31_t * pCmplxDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Floating-point complex-by-real multiplication
+   * @param[in]  pSrcCmplx   points to the complex input vector
+   * @param[in]  pSrcReal    points to the real input vector
+   * @param[out] pCmplxDst   points to the complex output vector
+   * @param[in]  numSamples  number of samples in each vector
+   */
+  void arm_cmplx_mult_real_f32(
+  const float32_t * pSrcCmplx,
+  const float32_t * pSrcReal,
+        float32_t * pCmplxDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Minimum value of a Q7 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] result     is output pointer
+   * @param[in]  index      is the array index of the minimum value in the input buffer.
+   */
+  void arm_min_q7(
+  const q7_t * pSrc,
+        uint32_t blockSize,
+        q7_t * result,
+        uint32_t * index);
+
+
+  /**
+   * @brief  Minimum value of a Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output pointer
+   * @param[in]  pIndex     is the array index of the minimum value in the input buffer.
+   */
+  void arm_min_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q15_t * pResult,
+        uint32_t * pIndex);
+
+
+  /**
+   * @brief  Minimum value of a Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output pointer
+   * @param[out] pIndex     is the array index of the minimum value in the input buffer.
+   */
+  void arm_min_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult,
+        uint32_t * pIndex);
+
+
+  /**
+   * @brief  Minimum value of a floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[in]  blockSize  is the number of samples to process
+   * @param[out] pResult    is output pointer
+   * @param[out] pIndex     is the array index of the minimum value in the input buffer.
+   */
+  void arm_min_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult,
+        uint32_t * pIndex);
+
+
+/**
+ * @brief Maximum value of a Q7 vector.
+ * @param[in]  pSrc       points to the input buffer
+ * @param[in]  blockSize  length of the input vector
+ * @param[out] pResult    maximum value returned here
+ * @param[out] pIndex     index of maximum value returned here
+ */
+  void arm_max_q7(
+  const q7_t * pSrc,
+        uint32_t blockSize,
+        q7_t * pResult,
+        uint32_t * pIndex);
+
+
+/**
+ * @brief Maximum value of a Q15 vector.
+ * @param[in]  pSrc       points to the input buffer
+ * @param[in]  blockSize  length of the input vector
+ * @param[out] pResult    maximum value returned here
+ * @param[out] pIndex     index of maximum value returned here
+ */
+  void arm_max_q15(
+  const q15_t * pSrc,
+        uint32_t blockSize,
+        q15_t * pResult,
+        uint32_t * pIndex);
+
+
+/**
+ * @brief Maximum value of a Q31 vector.
+ * @param[in]  pSrc       points to the input buffer
+ * @param[in]  blockSize  length of the input vector
+ * @param[out] pResult    maximum value returned here
+ * @param[out] pIndex     index of maximum value returned here
+ */
+  void arm_max_q31(
+  const q31_t * pSrc,
+        uint32_t blockSize,
+        q31_t * pResult,
+        uint32_t * pIndex);
+
+
+/**
+ * @brief Maximum value of a floating-point vector.
+ * @param[in]  pSrc       points to the input buffer
+ * @param[in]  blockSize  length of the input vector
+ * @param[out] pResult    maximum value returned here
+ * @param[out] pIndex     index of maximum value returned here
+ */
+  void arm_max_f32(
+  const float32_t * pSrc,
+        uint32_t blockSize,
+        float32_t * pResult,
+        uint32_t * pIndex);
+
+
+  /**
+   * @brief  Q15 complex-by-complex multiplication
+   * @param[in]  pSrcA       points to the first input vector
+   * @param[in]  pSrcB       points to the second input vector
+   * @param[out] pDst        points to the output vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   */
+  void arm_cmplx_mult_cmplx_q15(
+  const q15_t * pSrcA,
+  const q15_t * pSrcB,
+        q15_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Q31 complex-by-complex multiplication
+   * @param[in]  pSrcA       points to the first input vector
+   * @param[in]  pSrcB       points to the second input vector
+   * @param[out] pDst        points to the output vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   */
+  void arm_cmplx_mult_cmplx_q31(
+  const q31_t * pSrcA,
+  const q31_t * pSrcB,
+        q31_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief  Floating-point complex-by-complex multiplication
+   * @param[in]  pSrcA       points to the first input vector
+   * @param[in]  pSrcB       points to the second input vector
+   * @param[out] pDst        points to the output vector
+   * @param[in]  numSamples  number of complex samples in each vector
+   */
+  void arm_cmplx_mult_cmplx_f32(
+  const float32_t * pSrcA,
+  const float32_t * pSrcB,
+        float32_t * pDst,
+        uint32_t numSamples);
+
+
+  /**
+   * @brief Converts the elements of the floating-point vector to Q31 vector.
+   * @param[in]  pSrc       points to the floating-point input vector
+   * @param[out] pDst       points to the Q31 output vector
+   * @param[in]  blockSize  length of the input vector
+   */
+  void arm_float_to_q31(
+  const float32_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Converts the elements of the floating-point vector to Q15 vector.
+   * @param[in]  pSrc       points to the floating-point input vector
+   * @param[out] pDst       points to the Q15 output vector
+   * @param[in]  blockSize  length of the input vector
+   */
+  void arm_float_to_q15(
+  const float32_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief Converts the elements of the floating-point vector to Q7 vector.
+   * @param[in]  pSrc       points to the floating-point input vector
+   * @param[out] pDst       points to the Q7 output vector
+   * @param[in]  blockSize  length of the input vector
+   */
+  void arm_float_to_q7(
+  const float32_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q31 vector to floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q31_to_float(
+  const q31_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q31 vector to Q15 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q31_to_q15(
+  const q31_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q31 vector to Q7 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q31_to_q7(
+  const q31_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q15 vector to floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q15_to_float(
+  const q15_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q15 vector to Q31 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q15_to_q31(
+  const q15_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q15 vector to Q7 vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q15_to_q7(
+  const q15_t * pSrc,
+        q7_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q7 vector to floating-point vector.
+   * @param[in]  pSrc       is input pointer
+   * @param[out] pDst       is output pointer
+   * @param[in]  blockSize  is the number of samples to process
+   */
+  void arm_q7_to_float(
+  const q7_t * pSrc,
+        float32_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q7 vector to Q31 vector.
+   * @param[in]  pSrc       input pointer
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_q7_to_q31(
+  const q7_t * pSrc,
+        q31_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @brief  Converts the elements of the Q7 vector to Q15 vector.
+   * @param[in]  pSrc       input pointer
+   * @param[out] pDst       output pointer
+   * @param[in]  blockSize  number of samples to process
+   */
+  void arm_q7_to_q15(
+  const q7_t * pSrc,
+        q15_t * pDst,
+        uint32_t blockSize);
+
+
+  /**
+   * @ingroup groupInterpolation
+   */
+
+  /**
+   * @defgroup BilinearInterpolate Bilinear Interpolation
+   *
+   * Bilinear interpolation is an extension of linear interpolation applied to a two dimensional grid.
+   * The underlying function <code>f(x, y)</code> is sampled on a regular grid and the interpolation process
+   * determines values between the grid points.
+   * Bilinear interpolation is equivalent to two step linear interpolation, first in the x-dimension and then in the y-dimension.
+   * Bilinear interpolation is often used in image processing to rescale images.
+   * The CMSIS DSP library provides bilinear interpolation functions for Q7, Q15, Q31, and floating-point data types.
+   *
+   * <b>Algorithm</b>
+   * \par
+   * The instance structure used by the bilinear interpolation functions describes a two dimensional data table.
+   * For floating-point, the instance structure is defined as:
+   * <pre>
+   *   typedef struct
+   *   {
+   *     uint16_t numRows;
+   *     uint16_t numCols;
+   *     float32_t *pData;
+   * } arm_bilinear_interp_instance_f32;
+   * </pre>
+   *
+   * \par
+   * where <code>numRows</code> specifies the number of rows in the table;
+   * <code>numCols</code> specifies the number of columns in the table;
+   * and <code>pData</code> points to an array of size <code>numRows*numCols</code> values.
+   * The data table <code>pTable</code> is organized in row order and the supplied data values fall on integer indexes.
+   * That is, table element (x,y) is located at <code>pTable[x + y*numCols]</code> where x and y are integers.
+   *
+   * \par
+   * Let <code>(x, y)</code> specify the desired interpolation point.  Then define:
+   * <pre>
+   *     XF = floor(x)
+   *     YF = floor(y)
+   * </pre>
+   * \par
+   * The interpolated output point is computed as:
+   * <pre>
+   *  f(x, y) = f(XF, YF) * (1-(x-XF)) * (1-(y-YF))
+   *           + f(XF+1, YF) * (x-XF)*(1-(y-YF))
+   *           + f(XF, YF+1) * (1-(x-XF))*(y-YF)
+   *           + f(XF+1, YF+1) * (x-XF)*(y-YF)
+   * </pre>
+   * Note that the coordinates (x, y) contain integer and fractional components.
+   * The integer components specify which portion of the table to use while the
+   * fractional components control the interpolation processor.
+   *
+   * \par
+   * if (x,y) are outside of the table boundary, Bilinear interpolation returns zero output.
+   */
+
+
+  /**
+   * @addtogroup BilinearInterpolate
+   * @{
+   */
+
+  /**
+  * @brief  Floating-point bilinear interpolation.
+  * @param[in,out] S  points to an instance of the interpolation structure.
+  * @param[in]     X  interpolation coordinate.
+  * @param[in]     Y  interpolation coordinate.
+  * @return out interpolated value.
+  */
+  __STATIC_FORCEINLINE float32_t arm_bilinear_interp_f32(
+  const arm_bilinear_interp_instance_f32 * S,
+  float32_t X,
+  float32_t Y)
+  {
+    float32_t out;
+    float32_t f00, f01, f10, f11;
+    float32_t *pData = S->pData;
+    int32_t xIndex, yIndex, index;
+    float32_t xdiff, ydiff;
+    float32_t b1, b2, b3, b4;
+
+    xIndex = (int32_t) X;
+    yIndex = (int32_t) Y;
+
+    /* Care taken for table outside boundary */
+    /* Returns zero output when values are outside table boundary */
+    if (xIndex < 0 || xIndex > (S->numRows - 1) || yIndex < 0 || yIndex > (S->numCols - 1))
+    {
+      return (0);
+    }
+
+    /* Calculation of index for two nearest points in X-direction */
+    index = (xIndex - 1) + (yIndex - 1) * S->numCols;
+
+
+    /* Read two nearest points in X-direction */
+    f00 = pData[index];
+    f01 = pData[index + 1];
+
+    /* Calculation of index for two nearest points in Y-direction */
+    index = (xIndex - 1) + (yIndex) * S->numCols;
+
+
+    /* Read two nearest points in Y-direction */
+    f10 = pData[index];
+    f11 = pData[index + 1];
+
+    /* Calculation of intermediate values */
+    b1 = f00;
+    b2 = f01 - f00;
+    b3 = f10 - f00;
+    b4 = f00 - f01 - f10 + f11;
+
+    /* Calculation of fractional part in X */
+    xdiff = X - xIndex;
+
+    /* Calculation of fractional part in Y */
+    ydiff = Y - yIndex;
+
+    /* Calculation of bi-linear interpolated output */
+    out = b1 + b2 * xdiff + b3 * ydiff + b4 * xdiff * ydiff;
+
+    /* return to application */
+    return (out);
+  }
+
+
+  /**
+  * @brief  Q31 bilinear interpolation.
+  * @param[in,out] S  points to an instance of the interpolation structure.
+  * @param[in]     X  interpolation coordinate in 12.20 format.
+  * @param[in]     Y  interpolation coordinate in 12.20 format.
+  * @return out interpolated value.
+  */
+  __STATIC_FORCEINLINE q31_t arm_bilinear_interp_q31(
+  arm_bilinear_interp_instance_q31 * S,
+  q31_t X,
+  q31_t Y)
+  {
+    q31_t out;                                   /* Temporary output */
+    q31_t acc = 0;                               /* output */
+    q31_t xfract, yfract;                        /* X, Y fractional parts */
+    q31_t x1, x2, y1, y2;                        /* Nearest output values */
+    int32_t rI, cI;                              /* Row and column indices */
+    q31_t *pYData = S->pData;                    /* pointer to output table values */
+    uint32_t nCols = S->numCols;                 /* num of rows */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    rI = ((X & (q31_t)0xFFF00000) >> 20);
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    cI = ((Y & (q31_t)0xFFF00000) >> 20);
+
+    /* Care taken for table outside boundary */
+    /* Returns zero output when values are outside table boundary */
+    if (rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
+    {
+      return (0);
+    }
+
+    /* 20 bits for the fractional part */
+    /* shift left xfract by 11 to keep 1.31 format */
+    xfract = (X & 0x000FFFFF) << 11U;
+
+    /* Read two nearest output values from the index */
+    x1 = pYData[(rI) + (int32_t)nCols * (cI)    ];
+    x2 = pYData[(rI) + (int32_t)nCols * (cI) + 1];
+
+    /* 20 bits for the fractional part */
+    /* shift left yfract by 11 to keep 1.31 format */
+    yfract = (Y & 0x000FFFFF) << 11U;
+
+    /* Read two nearest output values from the index */
+    y1 = pYData[(rI) + (int32_t)nCols * (cI + 1)    ];
+    y2 = pYData[(rI) + (int32_t)nCols * (cI + 1) + 1];
+
+    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 3.29(q29) format */
+    out = ((q31_t) (((q63_t) x1  * (0x7FFFFFFF - xfract)) >> 32));
+    acc = ((q31_t) (((q63_t) out * (0x7FFFFFFF - yfract)) >> 32));
+
+    /* x2 * (xfract) * (1-yfract)  in 3.29(q29) and adding to acc */
+    out = ((q31_t) ((q63_t) x2 * (0x7FFFFFFF - yfract) >> 32));
+    acc += ((q31_t) ((q63_t) out * (xfract) >> 32));
+
+    /* y1 * (1 - xfract) * (yfract)  in 3.29(q29) and adding to acc */
+    out = ((q31_t) ((q63_t) y1 * (0x7FFFFFFF - xfract) >> 32));
+    acc += ((q31_t) ((q63_t) out * (yfract) >> 32));
+
+    /* y2 * (xfract) * (yfract)  in 3.29(q29) and adding to acc */
+    out = ((q31_t) ((q63_t) y2 * (xfract) >> 32));
+    acc += ((q31_t) ((q63_t) out * (yfract) >> 32));
+
+    /* Convert acc to 1.31(q31) format */
+    return ((q31_t)(acc << 2));
+  }
+
+
+  /**
+  * @brief  Q15 bilinear interpolation.
+  * @param[in,out] S  points to an instance of the interpolation structure.
+  * @param[in]     X  interpolation coordinate in 12.20 format.
+  * @param[in]     Y  interpolation coordinate in 12.20 format.
+  * @return out interpolated value.
+  */
+  __STATIC_FORCEINLINE q15_t arm_bilinear_interp_q15(
+  arm_bilinear_interp_instance_q15 * S,
+  q31_t X,
+  q31_t Y)
+  {
+    q63_t acc = 0;                               /* output */
+    q31_t out;                                   /* Temporary output */
+    q15_t x1, x2, y1, y2;                        /* Nearest output values */
+    q31_t xfract, yfract;                        /* X, Y fractional parts */
+    int32_t rI, cI;                              /* Row and column indices */
+    q15_t *pYData = S->pData;                    /* pointer to output table values */
+    uint32_t nCols = S->numCols;                 /* num of rows */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    rI = ((X & (q31_t)0xFFF00000) >> 20);
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    cI = ((Y & (q31_t)0xFFF00000) >> 20);
+
+    /* Care taken for table outside boundary */
+    /* Returns zero output when values are outside table boundary */
+    if (rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
+    {
+      return (0);
+    }
+
+    /* 20 bits for the fractional part */
+    /* xfract should be in 12.20 format */
+    xfract = (X & 0x000FFFFF);
+
+    /* Read two nearest output values from the index */
+    x1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI)    ];
+    x2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI) + 1];
+
+    /* 20 bits for the fractional part */
+    /* yfract should be in 12.20 format */
+    yfract = (Y & 0x000FFFFF);
+
+    /* Read two nearest output values from the index */
+    y1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1)    ];
+    y2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1) + 1];
+
+    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 13.51 format */
+
+    /* x1 is in 1.15(q15), xfract in 12.20 format and out is in 13.35 format */
+    /* convert 13.35 to 13.31 by right shifting  and out is in 1.31 */
+    out = (q31_t) (((q63_t) x1 * (0xFFFFF - xfract)) >> 4U);
+    acc = ((q63_t) out * (0xFFFFF - yfract));
+
+    /* x2 * (xfract) * (1-yfract)  in 1.51 and adding to acc */
+    out = (q31_t) (((q63_t) x2 * (0xFFFFF - yfract)) >> 4U);
+    acc += ((q63_t) out * (xfract));
+
+    /* y1 * (1 - xfract) * (yfract)  in 1.51 and adding to acc */
+    out = (q31_t) (((q63_t) y1 * (0xFFFFF - xfract)) >> 4U);
+    acc += ((q63_t) out * (yfract));
+
+    /* y2 * (xfract) * (yfract)  in 1.51 and adding to acc */
+    out = (q31_t) (((q63_t) y2 * (xfract)) >> 4U);
+    acc += ((q63_t) out * (yfract));
+
+    /* acc is in 13.51 format and down shift acc by 36 times */
+    /* Convert out to 1.15 format */
+    return ((q15_t)(acc >> 36));
+  }
+
+
+  /**
+  * @brief  Q7 bilinear interpolation.
+  * @param[in,out] S  points to an instance of the interpolation structure.
+  * @param[in]     X  interpolation coordinate in 12.20 format.
+  * @param[in]     Y  interpolation coordinate in 12.20 format.
+  * @return out interpolated value.
+  */
+  __STATIC_FORCEINLINE q7_t arm_bilinear_interp_q7(
+  arm_bilinear_interp_instance_q7 * S,
+  q31_t X,
+  q31_t Y)
+  {
+    q63_t acc = 0;                               /* output */
+    q31_t out;                                   /* Temporary output */
+    q31_t xfract, yfract;                        /* X, Y fractional parts */
+    q7_t x1, x2, y1, y2;                         /* Nearest output values */
+    int32_t rI, cI;                              /* Row and column indices */
+    q7_t *pYData = S->pData;                     /* pointer to output table values */
+    uint32_t nCols = S->numCols;                 /* num of rows */
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    rI = ((X & (q31_t)0xFFF00000) >> 20);
+
+    /* Input is in 12.20 format */
+    /* 12 bits for the table index */
+    /* Index value calculation */
+    cI = ((Y & (q31_t)0xFFF00000) >> 20);
+
+    /* Care taken for table outside boundary */
+    /* Returns zero output when values are outside table boundary */
+    if (rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
+    {
+      return (0);
+    }
+
+    /* 20 bits for the fractional part */
+    /* xfract should be in 12.20 format */
+    xfract = (X & (q31_t)0x000FFFFF);
+
+    /* Read two nearest output values from the index */
+    x1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI)    ];
+    x2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI) + 1];
+
+    /* 20 bits for the fractional part */
+    /* yfract should be in 12.20 format */
+    yfract = (Y & (q31_t)0x000FFFFF);
+
+    /* Read two nearest output values from the index */
+    y1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1)    ];
+    y2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1) + 1];
+
+    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 16.47 format */
+    out = ((x1 * (0xFFFFF - xfract)));
+    acc = (((q63_t) out * (0xFFFFF - yfract)));
+
+    /* x2 * (xfract) * (1-yfract)  in 2.22 and adding to acc */
+    out = ((x2 * (0xFFFFF - yfract)));
+    acc += (((q63_t) out * (xfract)));
+
+    /* y1 * (1 - xfract) * (yfract)  in 2.22 and adding to acc */
+    out = ((y1 * (0xFFFFF - xfract)));
+    acc += (((q63_t) out * (yfract)));
+
+    /* y2 * (xfract) * (yfract)  in 2.22 and adding to acc */
+    out = ((y2 * (yfract)));
+    acc += (((q63_t) out * (xfract)));
+
+    /* acc in 16.47 format and down shift by 40 to convert to 1.7 format */
+    return ((q7_t)(acc >> 40));
+  }
+
+  /**
+   * @} end of BilinearInterpolate group
+   */
+
+
+/* SMMLAR */
+#define multAcc_32x32_keep32_R(a, x, y) \
+    a = (q31_t) (((((q63_t) a) << 32) + ((q63_t) x * y) + 0x80000000LL ) >> 32)
+
+/* SMMLSR */
+#define multSub_32x32_keep32_R(a, x, y) \
+    a = (q31_t) (((((q63_t) a) << 32) - ((q63_t) x * y) + 0x80000000LL ) >> 32)
+
+/* SMMULR */
+#define mult_32x32_keep32_R(a, x, y) \
+    a = (q31_t) (((q63_t) x * y + 0x80000000LL ) >> 32)
+
+/* SMMLA */
+#define multAcc_32x32_keep32(a, x, y) \
+    a += (q31_t) (((q63_t) x * y) >> 32)
+
+/* SMMLS */
+#define multSub_32x32_keep32(a, x, y) \
+    a -= (q31_t) (((q63_t) x * y) >> 32)
+
+/* SMMUL */
+#define mult_32x32_keep32(a, x, y) \
+    a = (q31_t) (((q63_t) x * y ) >> 32)
+
+
+#if   defined ( __CC_ARM )
+  /* Enter low optimization region - place directly above function definition */
+  #if defined( __ARM_ARCH_7EM__ )
+    #define LOW_OPTIMIZATION_ENTER \
+       _Pragma ("push")         \
+       _Pragma ("O1")
+  #else
+    #define LOW_OPTIMIZATION_ENTER
+  #endif
+
+  /* Exit low optimization region - place directly after end of function definition */
+  #if defined ( __ARM_ARCH_7EM__ )
+    #define LOW_OPTIMIZATION_EXIT \
+       _Pragma ("pop")
+  #else
+    #define LOW_OPTIMIZATION_EXIT
+  #endif
+
+  /* Enter low optimization region - place directly above function definition */
+  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+
+  /* Exit low optimization region - place directly after end of function definition */
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+
+#elif defined (__ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 )
+  #define LOW_OPTIMIZATION_ENTER
+  #define LOW_OPTIMIZATION_EXIT
+  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+
+#elif defined ( __GNUC__ )
+  #define LOW_OPTIMIZATION_ENTER \
+       __attribute__(( optimize("-O1") ))
+  #define LOW_OPTIMIZATION_EXIT
+  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+
+#elif defined ( __ICCARM__ )
+  /* Enter low optimization region - place directly above function definition */
+  #if defined ( __ARM_ARCH_7EM__ )
+    #define LOW_OPTIMIZATION_ENTER \
+       _Pragma ("optimize=low")
+  #else
+    #define LOW_OPTIMIZATION_ENTER
+  #endif
+
+  /* Exit low optimization region - place directly after end of function definition */
+  #define LOW_OPTIMIZATION_EXIT
+
+  /* Enter low optimization region - place directly above function definition */
+  #if defined ( __ARM_ARCH_7EM__ )
+    #define IAR_ONLY_LOW_OPTIMIZATION_ENTER \
+       _Pragma ("optimize=low")
+  #else
+    #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+  #endif
+
+  /* Exit low optimization region - place directly after end of function definition */
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+
+#elif defined ( __TI_ARM__ )
+  #define LOW_OPTIMIZATION_ENTER
+  #define LOW_OPTIMIZATION_EXIT
+  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+
+#elif defined ( __CSMC__ )
+  #define LOW_OPTIMIZATION_ENTER
+  #define LOW_OPTIMIZATION_EXIT
+  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+
+#elif defined ( __TASKING__ )
+  #define LOW_OPTIMIZATION_ENTER
+  #define LOW_OPTIMIZATION_EXIT
+  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
+  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
+
+#endif
+
+
+#ifdef   __cplusplus
+}
+#endif
+
+/* Compiler specific diagnostic adjustment */
+#if   defined ( __CC_ARM )
+
+#elif defined ( __ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 )
+
+#elif defined ( __GNUC__ )
+#pragma GCC diagnostic pop
+
+#elif defined ( __ICCARM__ )
+
+#elif defined ( __TI_ARM__ )
+
+#elif defined ( __CSMC__ )
+
+#elif defined ( __TASKING__ )
+
+#elif defined ( _MSC_VER )
+
+#else
+  #error Unknown compiler
+#endif
+
+#endif /* _ARM_MATH_H */
+
+/**
+ *
+ * End of file.
+ */
diff --git a/cmsis/libarm_cortexM4lf_math.a b/cmsis/libarm_cortexM4lf_math.a
index d8c36583072fbd0ad929fe470a19e31e62a94565..66efc87f62cf9d9ef826342e3463df2d6705da20 100644
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diff --git a/drivers/stm32l4/dfsdm.cpp b/drivers/stm32l4/dfsdm.cpp
index 0406222..ae88c1e 100644
--- a/drivers/stm32l4/dfsdm.cpp
+++ b/drivers/stm32l4/dfsdm.cpp
@@ -20,16 +20,21 @@ using namespace drivers;
 namespace
 {
 
-DFSDM_Channel_TypeDef * get_channel_reg(dfsdm::channel::id ch)
+DFSDM_Channel_TypeDef *get_channel_reg(dfsdm::channel::id ch)
 {
     return DFSDM_Channel0 + (DFSDM_Channel1 - DFSDM_Channel0) * static_cast<uint8_t>(ch);
 }
 
-DFSDM_Filter_TypeDef * get_filter_reg(dfsdm::filter::id f)
+DFSDM_Filter_TypeDef *get_filter_reg(dfsdm::filter::id f)
 {
     return DFSDM_Filter0 + (DFSDM_Filter1 - DFSDM_Filter0) * static_cast<uint8_t>(f);
 }
 
+DMA_Channel_TypeDef *get_dma_channel_reg(dfsdm::filter::id f)
+{
+    return DMA1_Channel4 + (DMA1_Channel5 - DMA1_Channel4) * static_cast<uint8_t>(f);
+}
+
 }
 
 //-----------------------------------------------------------------------------
@@ -170,7 +175,58 @@ void dfsdm::filter::enable(id f, bool state)
         filter->FLTCR1 &= ~DFSDM_FLTCR1_DFEN;
 }
 
-void dfsdm::filter::configure(id f, order ord, uint16_t decim, uint8_t avg)
+void dfsdm::filter::enable_dma(id f, int16_t *data_buffer, uint16_t data_buffer_len, data_ready_callback_t data_ready_cb)
+{
+    const uint8_t filter_id = static_cast<uint8_t>(f);
+
+    /* Save output data buffer properties */
+    output_data[filter_id].buffer = data_buffer;
+    output_data[filter_id].buffer_len = data_buffer_len;
+    output_data[filter_id].ready_callback = data_ready_cb;
+
+    /* Enable filter DMA requests */
+    auto filter = get_filter_reg(f);
+    filter->FLTCR1 |= DFSDM_FLTCR1_RDMAEN;
+
+    /* Configure DMA */
+    auto dma_ch = get_dma_channel_reg(f);
+
+    rcc::toggle_periph_clock(RCC_PERIPH_BUS(AHB1, DMA1), true);
+    dma_ch->CCR &= ~DMA_CCR_EN;
+
+    /* Data flow: periph > mem; pDataSize: 16bit; mDataSize: 16bit(increment), circular mode */
+    dma_ch->CCR = DMA_CCR_MINC | DMA_CCR_PSIZE_0 | DMA_CCR_MSIZE_0 | DMA_CCR_CIRC;
+    dma_ch->CCR |= DMA_CCR_HTIE | DMA_CCR_TCIE;
+    dma_ch->CPAR = reinterpret_cast<uint32_t>(&filter->FLTRDATAR) + sizeof(uint16_t);
+    dma_ch->CMAR = reinterpret_cast<uint32_t>(data_buffer);
+    dma_ch->CNDTR = data_buffer_len;
+
+    DMA1_CSELR->CSELR &= ~(0b1111 << (12 + filter_id * 4));
+
+    /* Priority level */
+    IRQn_Type nvic_irq = static_cast<IRQn_Type>(DMA1_Channel4_IRQn + filter_id);
+    NVIC_SetPriority(nvic_irq, NVIC_EncodePriority( NVIC_GetPriorityGrouping(), 0, 0 ));
+
+    /* Enable IRQ */
+    NVIC_EnableIRQ(nvic_irq);
+
+    /* Start DMA */
+    dma_ch->CCR |= DMA_CCR_EN;
+}
+
+void dfsdm::filter::dma_half_transfer_complete(id f)
+{
+    uint8_t filter_id = static_cast<uint8_t>(f);
+    dfsdm::output_data[filter_id].ready_callback(&dfsdm::output_data[filter_id].buffer[dfsdm::output_data[filter_id].buffer_len / 2], dfsdm::output_data[filter_id].buffer_len / 2);
+}
+
+void dfsdm::filter::dma_full_transfer_complete(id f)
+{
+    uint8_t filter_id = static_cast<uint8_t>(f);
+    dfsdm::output_data[filter_id].ready_callback(&dfsdm::output_data[filter_id].buffer[0], dfsdm::output_data[filter_id].buffer_len / 2);
+}
+
+void dfsdm::filter::configure(id f, order ord, uint16_t decim, uint8_t avg, bool continous_mode, bool fast_mode, bool sync_with_f0)
 {
     auto filter = get_filter_reg(f);
 
@@ -185,22 +241,17 @@ void dfsdm::filter::configure(id f, order ord, uint16_t decim, uint8_t avg)
 
     filter->FLTFCR &= ~DFSDM_FLTFCR_IOSR_Msk;
     filter->FLTFCR |= avg << DFSDM_FLTFCR_IOSR_Pos;
-}
 
-void dfsdm::filter::configure_conversions(id f, bool fast_mode, bool continous_mode, bool sync_with_f0)
-{
-    auto filter = get_filter_reg(f);
+    if (continous_mode)
+        filter->FLTCR1 |= DFSDM_FLTCR1_RCONT;
+    else
+        filter->FLTCR1 &= ~DFSDM_FLTCR1_RCONT;
 
     if (fast_mode)
         filter->FLTCR1 |= DFSDM_FLTCR1_FAST;
     else
         filter->FLTCR1 &= ~DFSDM_FLTCR1_FAST;
 
-    if (continous_mode)
-        filter->FLTCR1 |= DFSDM_FLTCR1_RCONT;
-    else
-        filter->FLTCR1 &= ~DFSDM_FLTCR1_RCONT;
-
     if (sync_with_f0)
         filter->FLTCR1 |= DFSDM_FLTCR1_RSYNC;
     else
@@ -221,7 +272,7 @@ void dfsdm::filter::trigger(id f)
     filter->FLTCR1 |= DFSDM_FLTCR1_RSWSTART;
 }
 
-int32_t dfsdm::filter::poll(id f)
+int32_t dfsdm::filter::read(id f)
 {
     auto filter = get_filter_reg(f);
 
@@ -231,3 +282,25 @@ int32_t dfsdm::filter::poll(id f)
     struct int24_t { int32_t value:24; };
     return int24_t{static_cast<int32_t>(filter->FLTRDATAR >> 8)}.value;
 }
+
+//-----------------------------------------------------------------------------
+/* interrupt handlers */
+
+extern "C" void DMA1_Channel4_IRQHandler(void)
+{
+    /* Transfer Complete */
+    if (DMA1->ISR & DMA_ISR_TCIF4)
+    {
+        DMA1->IFCR |= DMA_IFCR_CTCIF4;
+
+        dfsdm::filter::dma_half_transfer_complete(dfsdm::filter::id::f0);
+    }
+
+    /* Half-Transfer Complete */
+    if (DMA1->ISR & DMA_ISR_HTIF4)
+    {
+        DMA1->IFCR |= DMA_IFCR_CHTIF4;
+
+        dfsdm::filter::dma_full_transfer_complete(dfsdm::filter::id::f0);
+    }
+}
diff --git a/drivers/stm32l4/dfsdm.hpp b/drivers/stm32l4/dfsdm.hpp
index 2cda3b6..0fe5133 100644
--- a/drivers/stm32l4/dfsdm.hpp
+++ b/drivers/stm32l4/dfsdm.hpp
@@ -9,17 +9,21 @@
 #define STM32L4_DFSDM_HPP_
 
 #include <cstdint>
+#include <cstddef>
+
 
 namespace drivers
 {
-
 //--------------------------------------------------------------------------------
+/* TODO: Refactor this class to be non-static, add templates for channel & filter classes */
 
 class dfsdm final
 {
 public:
     dfsdm() = delete;
 
+    typedef void (*data_ready_callback_t)(const int16_t *data, uint16_t data_len);
+
     enum class clk_out_src
     {
         apb2, sysclk, sai1
@@ -80,15 +84,26 @@ class dfsdm final
         };
 
         static void enable(id f, bool state);
-        static void configure(id f, order ord, uint16_t decim, uint8_t avg);
-        static void configure_conversions(id f, bool fast_mode, bool continous_mode, bool sync_with_f0);
-//        static void configure_dma(void);
+        static void enable_dma(id f, int16_t *data_buffer, uint16_t data_buffer_len, data_ready_callback_t data_ready_cb);
+        static void dma_half_transfer_complete(id f);
+        static void dma_full_transfer_complete(id f);
+        static void configure(id f, order ord, uint16_t decim, uint8_t avg, bool continous_mode = true, bool fast_mode = true, bool sync_with_f0 = false);
         static void link_channel(id f, channel::id ch);
         static void trigger(id f);
-        static int32_t poll(id f);
+        static int32_t read(id f);
     } filter;
 
 private:
+
+    struct output_data
+    {
+        int16_t *buffer;
+        uint16_t buffer_len;
+        data_ready_callback_t ready_callback;
+    };
+
+    inline static output_data output_data[4] = {0};
+
     static void global_toggle(bool state);
 };
 
diff --git a/main.cpp b/main.cpp
index e054559..696ff89 100644
--- a/main.cpp
+++ b/main.cpp
@@ -15,6 +15,29 @@
 #include <drivers/lcd_gh08172.hpp>
 #include <drivers/stm32l4/dfsdm.hpp>
 
+#include <cmsis/arm_math.h>
+
+static const unsigned buffer_length = 4096;
+static volatile int16_t samples_buffer[buffer_length];
+static volatile float32_t dsp_samples_buffer[buffer_length / 2];
+static volatile float32_t rms = 0;
+
+void dfsdm_data_ready(const int16_t *data, uint16_t data_len)
+{
+    /* Copy integer values to DSP buffer */
+    for (uint32_t i = 0; i < data_len; i++)
+        dsp_samples_buffer[i] = data[i];
+
+    /* Delete offset */
+    float32_t *dsp_buffer = const_cast<float32_t*>(dsp_samples_buffer);
+    float32_t mean;
+    arm_mean_f32(dsp_buffer, data_len, &mean);
+    arm_offset_f32(dsp_buffer, (-1.0f)*mean, const_cast<float32_t*>(dsp_samples_buffer), data_len);
+
+    /* Calculate RMS value */
+    arm_rms_f32(dsp_buffer, data_len, const_cast<float32_t*>(&rms));
+}
+
 int main(void)
 {
     hal::system::init();
@@ -40,32 +63,28 @@ int main(void)
     dfsdm::filter::enable(dfsdm_filter, false);
 
     dfsdm::channel::set_offset(dfsdm_channel, 0);
-    dfsdm::channel::set_bitshift(dfsdm_channel, 0);
+    dfsdm::channel::set_bitshift(dfsdm_channel, 2);
     dfsdm::channel::configure(dfsdm_channel,
                               dfsdm::channel::data_pack::standard,
                               dfsdm::channel::data_input::ext_pin,
                               dfsdm::channel::clk_src::int_ckout,
                               dfsdm::channel::protocol::spi_r_edge);
 
-    dfsdm::filter::configure(dfsdm_filter, dfsdm::filter::order::fast_sinc, 128, 0);
-    dfsdm::filter::configure_conversions(dfsdm_filter, true, true, false);
+    dfsdm::filter::configure(dfsdm_filter, dfsdm::filter::order::sinc4, 64, 2);
     dfsdm::filter::link_channel(dfsdm_filter, dfsdm_channel);
 
     dfsdm::configure_clock_output(dfsdm::clk_out_src::apb2, 2400000, true);
 
+    dfsdm::filter::enable_dma(dfsdm_filter, const_cast<int16_t*>(samples_buffer), buffer_length, dfsdm_data_ready);
     dfsdm::channel::enable(dfsdm_channel, true);
     dfsdm::filter::enable(dfsdm_filter, true);
     dfsdm::filter::trigger(dfsdm_filter);
 
+    debug_led->set(true);
+
     while (true)
     {
-        int32_t data = dfsdm::filter::poll(dfsdm_filter);
-        std::cout << "Data: " << data << std::endl;
+        std::cout << "RMS: " << rms << std::endl;
         hal::delay::delay_ms(50);
-
-//        debug_led->set(true);
-//        hal::delay::delay_ms(500);
-//        debug_led->set(false);
-//        hal::delay::delay_ms(500);
     }
 }
diff --git a/system/startup-cortex-m4.S b/system/startup-cortex-m4.S
index 4a089f2..5187a92 100644
--- a/system/startup-cortex-m4.S
+++ b/system/startup-cortex-m4.S
@@ -87,6 +87,89 @@ __isr_vector:
     .long   SysTick_Handler       /* SysTick Handler */
 
     /* External interrupts */
+    .long   WWDG_IRQHandler
+    .long   PVD_PVM_IRQHandler
+    .long   TAMP_STAMP_IRQHandler
+    .long   RTC_WKUP_IRQHandler
+    .long   FLASH_IRQHandler
+    .long   RCC_IRQHandler
+    .long   EXTI0_IRQHandler
+    .long   EXTI1_IRQHandler
+    .long   EXTI2_IRQHandler
+    .long   EXTI3_IRQHandler
+    .long   EXTI4_IRQHandler
+    .long   DMA1_Channel1_IRQHandler
+    .long   DMA1_Channel2_IRQHandler
+    .long   DMA1_Channel3_IRQHandler
+    .long   DMA1_Channel4_IRQHandler
+    .long   DMA1_Channel5_IRQHandler
+    .long   DMA1_Channel6_IRQHandler
+    .long   DMA1_Channel7_IRQHandler
+    .long   ADC1_2_IRQHandler
+    .long   CAN1_TX_IRQHandler
+    .long   CAN1_RX0_IRQHandler
+    .long   CAN1_RX1_IRQHandler
+    .long   CAN1_SCE_IRQHandler
+    .long   EXTI9_5_IRQHandler
+    .long   TIM1_BRK_TIM15_IRQHandler
+    .long   TIM1_UP_TIM16_IRQHandler
+    .long   TIM1_TRG_COM_TIM17_IRQHandler
+    .long   TIM1_CC_IRQHandler
+    .long   TIM2_IRQHandler
+    .long   TIM3_IRQHandler
+    .long   TIM4_IRQHandler
+    .long   I2C1_EV_IRQHandler
+    .long   I2C1_ER_IRQHandler
+    .long   I2C2_EV_IRQHandler
+    .long   I2C2_ER_IRQHandler
+    .long   SPI1_IRQHandler
+    .long   SPI2_IRQHandler
+    .long   USART1_IRQHandler
+    .long   USART2_IRQHandler
+    .long   USART3_IRQHandler
+    .long   EXTI15_10_IRQHandler
+    .long   RTC_Alarm_IRQHandler
+    .long   DFSDM1_FLT3_IRQHandler
+    .long   TIM8_BRK_IRQHandler
+    .long   TIM8_UP_IRQHandler
+    .long   TIM8_TRG_COM_IRQHandler
+    .long   TIM8_CC_IRQHandler
+    .long   ADC3_IRQHandler
+    .long   FMC_IRQHandler
+    .long   SDMMC1_IRQHandler
+    .long   TIM5_IRQHandler
+    .long   SPI3_IRQHandler
+    .long   UART4_IRQHandler
+    .long   UART5_IRQHandler
+    .long   TIM6_DAC_IRQHandler
+    .long   TIM7_IRQHandler
+    .long   DMA2_Channel1_IRQHandler
+    .long   DMA2_Channel2_IRQHandler
+    .long   DMA2_Channel3_IRQHandler
+    .long   DMA2_Channel4_IRQHandler
+    .long   DMA2_Channel5_IRQHandler
+    .long   DFSDM1_FLT0_IRQHandler
+    .long   DFSDM1_FLT1_IRQHandler
+    .long   DFSDM1_FLT2_IRQHandler
+    .long   COMP_IRQHandler
+    .long   LPTIM1_IRQHandler
+    .long   LPTIM2_IRQHandler
+    .long   OTG_FS_IRQHandler
+    .long   DMA2_Channel6_IRQHandler
+    .long   DMA2_Channel7_IRQHandler
+    .long   LPUART1_IRQHandler
+    .long   QUADSPI_IRQHandler
+    .long   I2C3_EV_IRQHandler
+    .long   I2C3_ER_IRQHandler
+    .long   SAI1_IRQHandler
+    .long   SAI2_IRQHandler
+    .long   SWPMI1_IRQHandler
+    .long   TSC_IRQHandler
+    .long   LCD_IRQHandler
+    .long   0
+    .long   RNG_IRQHandler
+    .long   FPU_IRQHandler
+
     .long   Default_Handler
 
     .size   __isr_vector, . - __isr_vector
@@ -252,6 +335,90 @@ Default_Handler:
     def_irq_handler DebugMon_Handler
     def_irq_handler PendSV_Handler
     def_irq_handler SysTick_Handler
+
+    /* External interrupts */
+    def_irq_handler WWDG_IRQHandler
+    def_irq_handler PVD_PVM_IRQHandler
+    def_irq_handler TAMP_STAMP_IRQHandler
+    def_irq_handler RTC_WKUP_IRQHandler
+    def_irq_handler FLASH_IRQHandler
+    def_irq_handler RCC_IRQHandler
+    def_irq_handler EXTI0_IRQHandler
+    def_irq_handler EXTI1_IRQHandler
+    def_irq_handler EXTI2_IRQHandler
+    def_irq_handler EXTI3_IRQHandler
+    def_irq_handler EXTI4_IRQHandler
+    def_irq_handler DMA1_Channel1_IRQHandler
+    def_irq_handler DMA1_Channel2_IRQHandler
+    def_irq_handler DMA1_Channel3_IRQHandler
+    def_irq_handler DMA1_Channel4_IRQHandler
+    def_irq_handler DMA1_Channel5_IRQHandler
+    def_irq_handler DMA1_Channel6_IRQHandler
+    def_irq_handler DMA1_Channel7_IRQHandler
+    def_irq_handler ADC1_2_IRQHandler
+    def_irq_handler CAN1_TX_IRQHandler
+    def_irq_handler CAN1_RX0_IRQHandler
+    def_irq_handler CAN1_RX1_IRQHandler
+    def_irq_handler CAN1_SCE_IRQHandler
+    def_irq_handler EXTI9_5_IRQHandler
+    def_irq_handler TIM1_BRK_TIM15_IRQHandler
+    def_irq_handler TIM1_UP_TIM16_IRQHandler
+    def_irq_handler TIM1_TRG_COM_TIM17_IRQHandler
+    def_irq_handler TIM1_CC_IRQHandler
+    def_irq_handler TIM2_IRQHandler
+    def_irq_handler TIM3_IRQHandler
+    def_irq_handler TIM4_IRQHandler
+    def_irq_handler I2C1_EV_IRQHandler
+    def_irq_handler I2C1_ER_IRQHandler
+    def_irq_handler I2C2_EV_IRQHandler
+    def_irq_handler I2C2_ER_IRQHandler
+    def_irq_handler SPI1_IRQHandler
+    def_irq_handler SPI2_IRQHandler
+    def_irq_handler USART1_IRQHandler
+    def_irq_handler USART2_IRQHandler
+    def_irq_handler USART3_IRQHandler
+    def_irq_handler EXTI15_10_IRQHandler
+    def_irq_handler RTC_Alarm_IRQHandler
+    def_irq_handler DFSDM1_FLT3_IRQHandler
+    def_irq_handler TIM8_BRK_IRQHandler
+    def_irq_handler TIM8_UP_IRQHandler
+    def_irq_handler TIM8_TRG_COM_IRQHandler
+    def_irq_handler TIM8_CC_IRQHandler
+    def_irq_handler ADC3_IRQHandler
+    def_irq_handler FMC_IRQHandler
+    def_irq_handler SDMMC1_IRQHandler
+    def_irq_handler TIM5_IRQHandler
+    def_irq_handler SPI3_IRQHandler
+    def_irq_handler UART4_IRQHandler
+    def_irq_handler UART5_IRQHandler
+    def_irq_handler TIM6_DAC_IRQHandler
+    def_irq_handler TIM7_IRQHandler
+    def_irq_handler DMA2_Channel1_IRQHandler
+    def_irq_handler DMA2_Channel2_IRQHandler
+    def_irq_handler DMA2_Channel3_IRQHandler
+    def_irq_handler DMA2_Channel4_IRQHandler
+    def_irq_handler DMA2_Channel5_IRQHandler
+    def_irq_handler DFSDM1_FLT0_IRQHandler
+    def_irq_handler DFSDM1_FLT1_IRQHandler
+    def_irq_handler DFSDM1_FLT2_IRQHandler
+    def_irq_handler COMP_IRQHandler
+    def_irq_handler LPTIM1_IRQHandler
+    def_irq_handler LPTIM2_IRQHandler
+    def_irq_handler OTG_FS_IRQHandler
+    def_irq_handler DMA2_Channel6_IRQHandler
+    def_irq_handler DMA2_Channel7_IRQHandler
+    def_irq_handler LPUART1_IRQHandler
+    def_irq_handler QUADSPI_IRQHandler
+    def_irq_handler I2C3_EV_IRQHandler
+    def_irq_handler I2C3_ER_IRQHandler
+    def_irq_handler SAI1_IRQHandler
+    def_irq_handler SAI2_IRQHandler
+    def_irq_handler SWPMI1_IRQHandler
+    def_irq_handler TSC_IRQHandler
+    def_irq_handler LCD_IRQHandler
+    def_irq_handler RNG_IRQHandler
+    def_irq_handler FPU_IRQHandler
+
     def_irq_handler DEF_IRQHandler
 
     .end