From 93252dc4b6703c9ee0beb437c1bbf34711528899 Mon Sep 17 00:00:00 2001 From: mamutalib Date: Fri, 28 Jul 2023 23:31:53 +0600 Subject: [PATCH] initial commit --- 1-sinusoid.ipynb | 446 ++++++++++++++++++ ...1_6_23).ipynb => 10-Divide _ Conquer.ipynb | 46 +- 11-MovingAverage.ipynb | 159 +++++++ 2-signal.ipynb | 157 ++++++ 3-convolution.ipynb | 111 +++++ 4-Convolution-np.ipynb | 158 +++++++ 5-MovingAverage(6_6_23).ipynb | 150 ------ 5-correlation.ipynb | 205 ++++++++ 1-DSP(15_5_23).ipynb => 6-DFT.ipynb | 0 2-DSP-DFT(18_5_23).ipynb => 7-DFT-fft.ipynb | 0 ...yDFTs(25_5_23).ipynb => 8-ConvByDFTs.ipynb | 0 ..._add(25_5_23).ipynb => 9-Overlap_add.ipynb | 0 DSP_After Mid.pdf | Bin 12882161 -> 0 bytes README.md | 12 + 14 files changed, 1264 insertions(+), 180 deletions(-) create mode 100644 1-sinusoid.ipynb rename 4-DSPL_Divide _ Conquer(1_6_23).ipynb => 10-Divide _ Conquer.ipynb (87%) create mode 100644 11-MovingAverage.ipynb create mode 100644 2-signal.ipynb create mode 100644 3-convolution.ipynb create mode 100644 4-Convolution-np.ipynb delete mode 100644 5-MovingAverage(6_6_23).ipynb create mode 100644 5-correlation.ipynb rename 1-DSP(15_5_23).ipynb => 6-DFT.ipynb (100%) rename 2-DSP-DFT(18_5_23).ipynb => 7-DFT-fft.ipynb (100%) rename 3-ConvByDFTs(25_5_23).ipynb => 8-ConvByDFTs.ipynb (100%) rename 3-Overlap_add(25_5_23).ipynb => 9-Overlap_add.ipynb (100%) delete mode 100644 DSP_After Mid.pdf create mode 100644 README.md diff --git a/1-sinusoid.ipynb b/1-sinusoid.ipynb new file mode 100644 index 0000000..5fb4d7b --- /dev/null +++ b/1-sinusoid.ipynb @@ -0,0 +1,446 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 15, + "id": "906acde9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-2, 0, 1, 10, 23, 34, 99]\n" + ] + } + ], + "source": [ + "def sort(x):\n", + " for i in range(len(x)):\n", + " for j in range(len(x) - 1):\n", + " if x[j]>x[j+1]:\n", + " temp = x[j]\n", + " x[j] = x[j+1]\n", + " x[j + 1] = temp\n", + " return x\n", + " \n", + "x = [34, 0, -2, 99, 10, 23, 1]\n", + "y= sort(x)\n", + "print(y)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "f01aca31", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0, 1, 2, 3, 4]\n", + "[2, 3]\n", + "[2, 3, 4]\n", + "[0, 1, 2, 3]\n", + "[0, 1, 2, 3]\n", + "[0, 1, 8, 9, 4]\n" + ] + } + ], + "source": [ + "nums = list(range(5))\n", + "print(nums)\n", + "print(nums[2:4])\n", + "print(nums[2:])\n", + "print(nums[:4])\n", + "print(nums[:-1])\n", + "nums[2:4] = [8,9]\n", + "print(nums)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "8075236e", + "metadata": {}, + "outputs": [], + "source": [ + "#3rd part -1\n", + "#DSP start from here" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "5de515b1", + "metadata": {}, + "outputs": [], + "source": [ + "#1. Genarate |* a sinusoid, x(n) = cos(2pifn) or x(n) = cos(2piFn/Fs)\n", + "# plot |* a DT signal x(n)\n", + " # *unit impulse d(n)\n", + " # *\n", + " # *\n", + " # *" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "5e445017", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#1. Generate sinusoid\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "F = 10 #Set the frequency \n", + "Fs = 400 # Set the sampling frequency\n", + "L = 50 # Set the size of line\n", + "x = np.zeros(L) # initialize the zero(0)\n", + "\n", + "for n in range(L):\n", + " x[n] = np.sin(2*np.pi*F*n/Fs)\n", + "\n", + "# print(x)\n", + "plt.plot(x)\n", + "plt.stem(x)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "80db45d4", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# unit impulse\n", + "d = np.zeros(10)\n", + "d[0] = 1 \n", + "\n", + "# plt.plot(d)\n", + "plt.stem(d)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "d7c37ff2", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# unit impulse\n", + "# d = np.zeros(10)\n", + "# d[0] = 1 \n", + "n = range(-10,10)\n", + "d = np.zeros(len(n))\n", + "d[len(n)//2] = 1\n", + "\n", + "plt.stem(n,d)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "bf7091b8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#unit step\n", + "n = range(-10, 11)\n", + "d = np.zeros(len(n))\n", + "for i in range(len(n)//2):\n", + " d[len(n)//2+i] = 1\n", + "plt.stem(n,d)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "b9d60144", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "#ramp \n", + "n = range(-10,11)\n", + "d = np.zeros(len(n))\n", + "\n", + "for i in range(len(n)//2):\n", + " d[len(n)//2+i] = 1+i\n", + "plt.stem(n,d)" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "50843372", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# exponential a > 1\n", + "ur = np.zeros(50)\n", + "a = 0.95\n", + "\n", + "for n in range(50):\n", + " ur[n] = a**n\n", + "plt.stem(ur)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "df76e742", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#emp a < 1\n", + "ur = np.zeros(50)\n", + "a = -0.95\n", + "for n in range(50):\n", + " ur[n] = a**n\n", + "plt.stem(ur)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "781f2a41", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ur = np.zeros(50)\n", + "a = 1.5\n", + "for n in range(50):\n", + " ur[n] = a**n\n", + "plt.stem(ur)" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "eb6b9b9b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#ramp\n", + "r = np.zeros(40)\n", + "for n in range(40):\n", + " r[n] = n\n", + "plt.stem(r)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/4-DSPL_Divide _ Conquer(1_6_23).ipynb b/10-Divide _ Conquer.ipynb similarity index 87% rename from 4-DSPL_Divide _ Conquer(1_6_23).ipynb rename to 10-Divide _ Conquer.ipynb index 61a6466..a033973 100644 --- a/4-DSPL_Divide _ Conquer(1_6_23).ipynb +++ b/10-Divide _ Conquer.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "id": "6a749398", "metadata": {}, "outputs": [], @@ -13,8 +13,8 @@ }, { "cell_type": "code", - "execution_count": 2, - "id": "f8f59a71", + "execution_count": 3, + "id": "7fb2cb10", "metadata": {}, "outputs": [ { @@ -35,21 +35,13 @@ "M = 3\n", "x = np.array([4,2,0,5,7,2,4,9,1,2,3,8,0,2,3])\n", "np.shape(x)\n", - "y = x.reshape(L,M, order='F')\n", + "y = x.reshape(L,M,order='F')\n", "print(y)" ] }, { "cell_type": "code", - "execution_count": null, - "id": "7fb2cb10", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "id": "222ce56e", "metadata": {}, "outputs": [], @@ -65,8 +57,8 @@ }, { "cell_type": "code", - "execution_count": 4, - "id": "4bf3e133", + "execution_count": 9, + "id": "fb11ddff", "metadata": {}, "outputs": [ { @@ -83,17 +75,19 @@ } ], "source": [ - "F = np.zeros((L,M),dtype = 'complex_')\n", + "F = np.zeros((L,M), dtype= 'complex_')\n", "print(np.shape(F))\n", + "\n", "for l in range(L):\n", - " F[l] = DFT(y[l,:],M) #row\n", - " #np.shape(F)\n", - " print(F[l])" + " F[l] = DFT(y[l,:],M) # for Row\n", + " # np.shape(F)\n", + " print(F[l])\n", + "\n" ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 12, "id": "37f26696", "metadata": {}, "outputs": [ @@ -119,7 +113,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 14, "id": "971059df", "metadata": {}, "outputs": [ @@ -144,7 +138,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 16, "id": "b563a847", "metadata": {}, "outputs": [ @@ -161,14 +155,6 @@ "source": [ "print(abs(np.fft.fft(x,N)))" ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "53bef6ec", - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { diff --git a/11-MovingAverage.ipynb b/11-MovingAverage.ipynb new file mode 100644 index 0000000..2534f6c --- /dev/null +++ b/11-MovingAverage.ipynb @@ -0,0 +1,159 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "z29EylnaOAta", + "outputId": "ec0dc12e-43d4-4ae7-e405-0a4b66ca8e23" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#generate an aperiodic signal\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "F = 2\n", + "Fs = 40\n", + "L = 100\n", + "x = np.zeros(L)\n", + "for n in range(L):\n", + " x[n] = np.sin(2*np.pi*F*n/Fs)\n", + "plt.plot(x[0:L//2])" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "ZeDRitc7PV_R", + "outputId": "f0c33f82-e5bb-4bb5-f625-f4c8d9d35df8" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "wn = np.random.normal(0,1,L) \n", + "\n", + "wn = wn/np.max((wn))\n", + "y = x + wn\n", + "\n", + "#plt.plot(wn[0:L])\n", + "plt.plot(y[0:L//2])" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "eZc1ZMZZS3Pg", + "outputId": "aa298832-b4aa-4062-a802-fa0fcbfcc82e" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "M = 7\n", + "s = np.zeros(L)\n", + "for i in range(L-M):\n", + " s[i] = sum(y[i:i+M])/M\n", + "plt.plot(s[0:L//2]) " + ] + } + ], + "metadata": { + "accelerator": "GPU", + "colab": { + "gpuType": "T4", + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.13" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/2-signal.ipynb b/2-signal.ipynb new file mode 100644 index 0000000..d167dce --- /dev/null +++ b/2-signal.ipynb @@ -0,0 +1,157 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 3, + "id": "6d91e573", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0.23987883, 0.64761344],\n", + " [0.91901951, 0.05954873]])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "e = np.random.random((2,2))\n", + "e" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "7869feae", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0.23987883 0.64761344]\n", + " [0.91901951 0.05954873]]\n" + ] + } + ], + "source": [ + "print(e)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "bc5a7498", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[3, 2, 0, 4, 6, -1, 3, -2]\n" + ] + }, + { + "data": { + "text/plain": [ + ", clear=False, **kwargs)>" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt \n", + "x = [3, 2, 0 , 4 , 6, -1 , 3, -2]\n", + "y = range(-3, 5)\n", + "print(x)\n", + "plt.stem(x, y)\n", + "#plt.stem(y)\n", + "k = 1\n", + "plt.figure\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "72b6509e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt \n", + "import numpy as np\n", + "y = [3, 2, 0 , 4 , 6, -1 , 3, -2]\n", + "x = np.arange(-3, 5)\n", + "plt.subplot(3, 1, 1)\n", + "plt.stem(x, y)\n", + "#plt.stem(y)\n", + "plt.subplot(3, 1, 2)\n", + "#plt.figure(figsize=(10,6))\n", + "k = 1\n", + "plt.stem(x+k, y)\n", + "plt.subplot(3, 1, 3)\n", + "k = 1\n", + "plt.stem(x-k, y)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/3-convolution.ipynb b/3-convolution.ipynb new file mode 100644 index 0000000..d975c10 --- /dev/null +++ b/3-convolution.ipynb @@ -0,0 +1,111 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 7, + "id": "3693637f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 4. 8. 8. 3. -2. -1.]\n" + ] + } + ], + "source": [ + "#convulation sum EX: 2.3.2\n", + "#1st method\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "x = [1, 2, 3, 1]\n", + "h = [1, 2, 1, -1]\n", + "lx = len(x)\n", + "lh = len(h)\n", + "y = np.zeros(lx+lh-1)\n", + "\n", + "for m in range(lx):\n", + " for n in range(lh):\n", + " y[m+n] = y[m+n] + x[m]*h[n]\n", + "print(y)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "a84b4ef8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1 4 8 8 3 -2 -1]\n" + ] + } + ], + "source": [ + "#2nd method relates with 1st\n", + "z = np.convolve(x, h, 'full')\n", + "print(z)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "b78f4be2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1 4 8 8 3 -2 -1]\n" + ] + } + ], + "source": [ + "#3rd method indivitual\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "x = [1, 2, 3, 1]\n", + "h = [1, 2, 1, -1]\n", + "\n", + "z = np.convolve(x, h, 'full')\n", + "print(z)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "58064ae7", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/4-Convolution-np.ipynb b/4-Convolution-np.ipynb new file mode 100644 index 0000000..950d040 --- /dev/null +++ b/4-Convolution-np.ipynb @@ -0,0 +1,158 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def conv(x, h):\n", + " lx = len(x)\n", + " lh = len(h)\n", + " y = np.zeros(lx+lh-1)\n", + " \n", + " for m in range(lx):\n", + " for n in range(lh):\n", + " y[m+n] = y[m+n] + x[m]*h[n]\n", + " return y\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 4. 8. 8. 3. -2. -1.]\n", + "[ 2. 8. 18. 22. 16. 4. 0.]\n" + ] + } + ], + "source": [ + "x = [1,2,3,1]\n", + "h = [1, 2, 1, -1]\n", + "\n", + "y = conv(x, h)\n", + "print(y)\n", + "\n", + "\n", + "\n", + "yd2 = conv(x, h) + conv(x, h2)\n", + "print(yd2)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1. 2. 3. 1.]\n" + ] + } + ], + "source": [ + "d = np.zeros(1)\n", + "d[0] = 1\n", + "\n", + "#identity law\n", + "yi = conv(x, d)\n", + "print(yi)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 4. 8. 8. 3. -2. -1.]\n" + ] + } + ], + "source": [ + "\n", + "#communitative property\n", + "yc = conv(h, x)\n", + "print(yc) \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 6. 19. 37. 47. 36. 12. -5. -5. -1.]\n", + "[ 1. 6. 19. 37. 47. 36. 12. -5. -5. -1.]\n" + ] + } + ], + "source": [ + "#assosiative law \n", + "h2 = [1,2 ,3, 1]\n", + "ya = conv(yc, h2)\n", + "print(ya) \n", + "yb = conv(h2, yc)\n", + "print(yb)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 4. 8. 8. 4. 2. 9. 14. 13. 6. 1.]\n" + ] + } + ], + "source": [ + "\n", + "#distributive law \n", + "yd1 = conv(x, h + h2)\n", + "print(yd1)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.13" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/5-MovingAverage(6_6_23).ipynb b/5-MovingAverage(6_6_23).ipynb deleted file mode 100644 index 903e22f..0000000 --- a/5-MovingAverage(6_6_23).ipynb +++ /dev/null @@ -1,150 +0,0 @@ -{ - "nbformat": 4, - "nbformat_minor": 0, - "metadata": { - "colab": { - "provenance": [], - "gpuType": "T4" - }, - "kernelspec": { - "name": "python3", - "display_name": "Python 3" - }, - "language_info": { - "name": "python" - }, - "accelerator": "GPU" - }, - "cells": [ - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 447 - }, - "id": "z29EylnaOAta", - "outputId": "ec0dc12e-43d4-4ae7-e405-0a4b66ca8e23" - }, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "[]" - ] - }, - "metadata": {}, - "execution_count": 21 - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
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\n" - }, - "metadata": {} - } - ], - "source": [ - "#generate an aperiodic signal\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "F = 2\n", - "Fs = 40\n", - "L = 100\n", - "x = np.zeros(L)\n", - "for n in range(L):\n", - " x[n] = np.sin(2*np.pi*F*n/Fs)\n", - "plt.plot(x[0:L//2])" - ] - }, - { - "cell_type": "code", - "source": [ - "wn = np.random.normal(0,1,L) \n", - "\n", - "wn = wn/np.max((wn))\n", - "y = x + wn\n", - "\n", - "#plt.plot(wn[0:L])\n", - "plt.plot(y[0:L//2])" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 447 - }, - "id": "ZeDRitc7PV_R", - "outputId": "f0c33f82-e5bb-4bb5-f625-f4c8d9d35df8" - }, - "execution_count": 26, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "[]" - ] - }, - "metadata": {}, - "execution_count": 26 - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "M = 7\n", - "s = np.zeros(L)\n", - "for i in range(L-M):\n", - " s[i] = sum(y[i:i+M])/M\n", - "plt.plot(s[0:L//2]) " - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 447 - }, - "id": "eZc1ZMZZS3Pg", - "outputId": "aa298832-b4aa-4062-a802-fa0fcbfcc82e" - }, - "execution_count": 30, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "[]" - ] - }, - "metadata": {}, - "execution_count": 30 - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - } - ] -} \ No newline at end of file diff --git a/5-correlation.ipynb b/5-correlation.ipynb new file mode 100644 index 0000000..c96d2f2 --- /dev/null +++ b/5-correlation.ipynb @@ -0,0 +1,205 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 14, + "id": "4197536d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 4. 8. 6. 10. -12. 13. -9. -1. 1.]\n", + "[ 4 8 6 10 -12 13 -9 -1 1]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def conv(x,h):\n", + " lx = len(x)\n", + " lh = len(h)\n", + " \n", + " y = np.zeros(lx+lh-1)\n", + " \n", + " for m in range(lx):\n", + " for n in range(lh):\n", + " y[m+n] = y[m+n] + x[m]*h[n]\n", + " return y\n", + "\n", + "x = [2,0,3,-4,1]\n", + "h = [1,3,0,4,2]\n", + "\n", + "# cross-correlation\n", + "y = conv(x,np.flip(h))\n", + "print(y)\n", + "\n", + "z = np.correlate(x, h, 'full')\n", + "print(z)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "f623ee67", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 4. 8. 6. 10. -12. 13. -9. -1. 1.]\n", + "[ 4 8 6 10 -12 13 -9 -1 1]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def conv(x, h):\n", + " lx = len(x)\n", + " lh = len(h)\n", + " y = np.zeros(lx+lh-1)\n", + " \n", + " for m in range(lx):\n", + " for n in range(lh):\n", + " y[m+n] = y[m+n] + x[m]*h[n]\n", + " return y\n", + "\n", + "x = [2, 0, 3, -4, 1]\n", + "h = [1, 3, 0, 4, 2]\n", + "\n", + "#cross-correlation\n", + "y = conv(x,np.flip(h))\n", + "print(y)\n", + "\n", + "z = np.correlate(x, h, 'full')\n", + "print(z)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "c6eb1a19", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 4. 11. 6. 14. 30. 14. 6. 11. 4.]\n", + "[ 4 11 6 14 30 14 6 11 4]\n" + ] + } + ], + "source": [ + "# auto-corellation\n", + "x = [1,2,0,3,4]\n", + "y = conv(x,np.flip(x))\n", + "print(y)\n", + "\n", + "z = np.correlate(x,x,'full')\n", + "print(z)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f02c6549", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-1. -2. 2. 2. 1. 12. 11. 13. 12.]\n", + "[-1 -2 2 2 1 12 11 13 12]\n" + ] + } + ], + "source": [ + "#cross-corellation\n", + "def cross(x, h):\n", + " lx = len(x)\n", + " h = np.flip(h)\n", + " lh = len(h)\n", + " y = np.zeros(lx+lh-1)\n", + " \n", + " for m in range(lx):\n", + " for n in range(lh):\n", + " y[m+n] = y[m+n] + x[m]*h[n]\n", + " return y\n", + "x = [1, 2, 0, 3, 4]\n", + "y = [3,1,2,0,-1]\n", + "\n", + "rxy = cross(x, y)\n", + "print(rxy)\n", + "\n", + "z = np.correlate(x, y, 'full')\n", + "print(z)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3febd008", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 4. 11. 6. 14. 30. 14. 6. 11. 4.]\n", + "[ 4 11 6 14 30 14 6 11 4]\n" + ] + } + ], + "source": [ + "#cross-corellation\n", + "def cross(x, h):\n", + " lx = len(x)\n", + " h = np.flip(h)\n", + " lh = len(h)\n", + " y = np.zeros(lx+lh-1)\n", + " \n", + " for m in range(lx):\n", + " for n in range(lh):\n", + " y[m+n] = y[m+n] + x[m]*h[n]\n", + " return y\n", + "x = [1, 2, 0, 3, 4]\n", + "#y = [3,1,2,0,-1]\n", + "\n", + "rxy = cross(x, x)\n", + "print(rxy)\n", + "\n", + "z = np.correlate(x, x, 'full')\n", + "print(z)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.13" + } + }, + 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