diff options
author | Nguyễn Gia Phong <mcsinyx@disroot.org> | 2020-05-17 21:35:30 +0700 |
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committer | Nguyễn Gia Phong <mcsinyx@disroot.org> | 2020-05-17 21:35:30 +0700 |
commit | 7f87ac2f813da186d2c9fffa3460161d262ec6c7 (patch) | |
tree | 5326da29053049b23db1fa658f965fb2f26b2de6 /usth | |
parent | 743056f7631e1af196f040ca2099eb95bb44b83c (diff) | |
download | cp-7f87ac2f813da186d2c9fffa3460161d262ec6c7.tar.gz |
[usth/ICT2.9] Process discrete signals
Diffstat (limited to 'usth')
-rw-r--r-- | usth/ICT2.9/blue-ocean-floor.wav | bin | 0 -> 740622 bytes | |||
-rw-r--r-- | usth/ICT2.9/dsp.ipynb | 1387 | ||||
-rw-r--r-- | usth/ICT2.9/filters.ipynb | 812 | ||||
-rw-r--r-- | usth/ICT2.9/output_bartlett.wav | bin | 0 -> 740222 bytes | |||
-rw-r--r-- | usth/ICT2.9/output_bessel.wav | bin | 0 -> 740022 bytes | |||
-rw-r--r-- | usth/ICT2.9/output_blackman.wav | bin | 0 -> 740222 bytes | |||
-rw-r--r-- | usth/ICT2.9/output_butterworth.wav | bin | 0 -> 740022 bytes | |||
-rw-r--r-- | usth/ICT2.9/output_chebyshev.wav | bin | 0 -> 740022 bytes | |||
-rw-r--r-- | usth/ICT2.9/output_hamming.wav | bin | 0 -> 740222 bytes | |||
-rw-r--r-- | usth/ICT2.9/output_sinc.wav | bin | 0 -> 740222 bytes |
10 files changed, 2199 insertions, 0 deletions
diff --git a/usth/ICT2.9/blue-ocean-floor.wav b/usth/ICT2.9/blue-ocean-floor.wav new file mode 100644 index 0000000..4208cd0 --- /dev/null +++ b/usth/ICT2.9/blue-ocean-floor.wav Binary files differdiff --git a/usth/ICT2.9/dsp.ipynb b/usth/ICT2.9/dsp.ipynb new file mode 100644 index 0000000..e217f43 --- /dev/null +++ b/usth/ICT2.9/dsp.ipynb @@ -0,0 +1,1387 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "FTq58_r1KXZd" + }, + "source": [ + "# DSP Labwork" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "nB6RL9TOKm9D" + }, + "source": [ + "Given the following signals:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "colab": {}, + "colab_type": "code", + "id": "rqw23aUkKqS2" + }, + "outputs": [], + "source": [ + "input_1kHz_15kHz = [\n", + " +0.0000000000, +0.5924659585, -0.0947343455, +0.1913417162, +1.0000000000,\n", + " +0.4174197128, +0.3535533906, +1.2552931065, +0.8660254038, +0.4619397663,\n", + " +1.3194792169, +1.1827865776, +0.5000000000, +1.1827865776, +1.3194792169,\n", + " +0.4619397663, +0.8660254038, +1.2552931065, +0.3535533906, +0.4174197128,\n", + " +1.0000000000, +0.1913417162, -0.0947343455, +0.5924659585, -0.0000000000,\n", + " -0.5924659585, +0.0947343455, -0.1913417162, -1.0000000000, -0.4174197128,\n", + " -0.3535533906, -1.2552931065, -0.8660254038, -0.4619397663, -1.3194792169,\n", + " -1.1827865776, -0.5000000000, -1.1827865776, -1.3194792169, -0.4619397663,\n", + " -0.8660254038, -1.2552931065, -0.3535533906, -0.4174197128, -1.0000000000,\n", + " -0.1913417162, +0.0947343455, -0.5924659585, +0.0000000000, +0.5924659585,\n", + " -0.0947343455, +0.1913417162, +1.0000000000, +0.4174197128, +0.3535533906,\n", + " +1.2552931065, +0.8660254038, +0.4619397663, +1.3194792169, +1.1827865776,\n", + " +0.5000000000, +1.1827865776, +1.3194792169, +0.4619397663, +0.8660254038,\n", + " +1.2552931065, +0.3535533906, +0.4174197128, +1.0000000000, +0.1913417162,\n", + " -0.0947343455, +0.5924659585, +0.0000000000, -0.5924659585, +0.0947343455,\n", + " -0.1913417162, -1.0000000000, -0.4174197128, -0.3535533906, -1.2552931065,\n", + " -0.8660254038, -0.4619397663, -1.3194792169, -1.1827865776, -0.5000000000,\n", + " -1.1827865776, -1.3194792169, -0.4619397663, -0.8660254038, -1.2552931065,\n", + " -0.3535533906, -0.4174197128, -1.0000000000, -0.1913417162, +0.0947343455,\n", + " -0.5924659585, +0.0000000000, +0.5924659585, -0.0947343455, +0.1913417162,\n", + " +1.0000000000, +0.4174197128, +0.3535533906, +1.2552931065, +0.8660254038,\n", + " +0.4619397663, +1.3194792169, +1.1827865776, +0.5000000000, +1.1827865776,\n", + " +1.3194792169, +0.4619397663, +0.8660254038, +1.2552931065, +0.3535533906,\n", + " +0.4174197128, +1.0000000000, +0.1913417162, -0.0947343455, +0.5924659585,\n", + " +0.0000000000, -0.5924659585, +0.0947343455, -0.1913417162, -1.0000000000,\n", + " -0.4174197128, -0.3535533906, -1.2552931065, -0.8660254038, -0.4619397663,\n", + " -1.3194792169, -1.1827865776, -0.5000000000, -1.1827865776, -1.3194792169,\n", + " -0.4619397663, -0.8660254038, -1.2552931065, -0.3535533906, -0.4174197128,\n", + " -1.0000000000, -0.1913417162, +0.0947343455, -0.5924659585, -0.0000000000,\n", + " +0.5924659585, -0.0947343455, +0.1913417162, +1.0000000000, +0.4174197128,\n", + " +0.3535533906, +1.2552931065, +0.8660254038, +0.4619397663, +1.3194792169,\n", + " +1.1827865776, +0.5000000000, +1.1827865776, +1.3194792169, +0.4619397663,\n", + " +0.8660254038, +1.2552931065, +0.3535533906, +0.4174197128, +1.0000000000,\n", + " +0.1913417162, -0.0947343455, +0.5924659585, -0.0000000000, -0.5924659585,\n", + " +0.0947343455, -0.1913417162, -1.0000000000, -0.4174197128, -0.3535533906,\n", + " -1.2552931065, -0.8660254038, -0.4619397663, -1.3194792169, -1.1827865776,\n", + " -0.5000000000, -1.1827865776, -1.3194792169, -0.4619397663, -0.8660254038,\n", + " -1.2552931065, -0.3535533906, -0.4174197128, -1.0000000000, -0.1913417162,\n", + " +0.0947343455, -0.5924659585, +0.0000000000, +0.5924659585, -0.0947343455,\n", + " +0.1913417162, +1.0000000000, +0.4174197128, +0.3535533906, +1.2552931065,\n", + " +0.8660254038, +0.4619397663, +1.3194792169, +1.1827865776, +0.5000000000,\n", + " +1.1827865776, +1.3194792169, +0.4619397663, +0.8660254038, +1.2552931065,\n", + " +0.3535533906, +0.4174197128, +1.0000000000, +0.1913417162, -0.0947343455,\n", + " +0.5924659585, +0.0000000000, -0.5924659585, +0.0947343455, -0.1913417162,\n", + " -1.0000000000, -0.4174197128, -0.3535533906, -1.2552931065, -0.8660254038,\n", + " -0.4619397663, -1.3194792169, -1.1827865776, -0.5000000000, -1.1827865776,\n", + " -1.3194792169, -0.4619397663, -0.8660254038, -1.2552931065, -0.3535533906,\n", + " -0.4174197128, -1.0000000000, -0.1913417162, +0.0947343455, -0.5924659585,\n", + " -0.0000000000, +0.5924659585, -0.0947343455, +0.1913417162, +1.0000000000,\n", + " +0.4174197128, +0.3535533906, +1.2552931065, +0.8660254038, +0.4619397663,\n", + " +1.3194792169, +1.1827865776, +0.5000000000, +1.1827865776, +1.3194792169,\n", + " +0.4619397663, +0.8660254038, +1.2552931065, +0.3535533906, +0.4174197128,\n", + " +1.0000000000, +0.1913417162, -0.0947343455, +0.5924659585, +0.0000000000,\n", + " -0.5924659585, +0.0947343455, -0.1913417162, -1.0000000000, -0.4174197128,\n", + " -0.3535533906, -1.2552931065, -0.8660254038, -0.4619397663, -1.3194792169,\n", + " -1.1827865776, -0.5000000000, -1.1827865776, -1.3194792169, -0.4619397663,\n", + " -0.8660254038, -1.2552931065, -0.3535533906, -0.4174197128, -1.0000000000,\n", + " -0.1913417162, +0.0947343455, -0.5924659585, -0.0000000000, +0.5924659585,\n", + " -0.0947343455, +0.1913417162, +1.0000000000, +0.4174197128, +0.3535533906,\n", + " +1.2552931065, +0.8660254038, +0.4619397663, +1.3194792169, +1.1827865776,\n", + " +0.5000000000, +1.1827865776, +1.3194792169, +0.4619397663, +0.8660254038,\n", + " +1.2552931065, +0.3535533906, +0.4174197128, +1.0000000000, +0.1913417162,\n", + " -0.0947343455, +0.5924659585, +0.0000000000, -0.5924659585, +0.0947343455,\n", + " -0.1913417162, -1.0000000000, -0.4174197128, -0.3535533906, -1.2552931065]\n", + "impulse_response = [\n", + " -0.0018225230, -0.0015879294, +0.0000000000, +0.0036977508, +0.0080754303,\n", + " +0.0085302217, -0.0000000000, -0.0173976984, -0.0341458607, -0.0333591565,\n", + " +0.0000000000, +0.0676308395, +0.1522061835, +0.2229246956, +0.2504960933,\n", + " +0.2229246956, +0.1522061835, +0.0676308395, +0.0000000000, -0.0333591565,\n", + " -0.0341458607, -0.0173976984, -0.0000000000, +0.0085302217, +0.0080754303,\n", + " +0.0036977508, +0.0000000000, -0.0015879294, -0.0018225230]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "Su7BkK-hNrRr" + }, + "source": [ + "## Signals" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "7ywQ1k6SMjB1" + }, + "source": [ + "Then the input signal can be plotted as following\n", + "(the x-axis is wrong of course, we will tackle this later on).\n", + "At first glance, it might be obvious (not for me though)\n", + "that the input is a superposition of two sine waves." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "colab_type": "code", + "id": "NVOkSo_RMcNW", + "outputId": "5d8993db-acf2-4591-a501-8ece487993b4", + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "\n", + "def quickplt(sequence):\n", + " \"\"\"Plot the signal as-is.\"\"\"\n", + " plt.plot(sequence)\n", + " plt.show()\n", + "\n", + "\n", + "quickplt(input_1kHz_15kHz)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "lk2QtF8INxxn" + }, + "source": [ + "To confirm this suspection, we apply FFT on the signals\n", + "and plot the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 281 + }, + "colab_type": "code", + "id": "PwoTNVzAOBb9", + "outputId": "3200e5ca-4b15-4ae9-df41-7f13bb31b849", + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from math import pi\n", + "\n", + "import numpy as np\n", + "from numpy.fft import fft\n", + "\n", + "\n", + "def plt_polar(sequence):\n", + " \"\"\"Plot the complex signal in polar coordinate, from 0 to pi*2.\"\"\"\n", + " fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2)\n", + " domain = np.linspace(0, pi*2, len(sequence))\n", + " ax1.plot(domain, np.abs(sequence))\n", + " ax1.set_title('magnitude')\n", + " ax2.plot(domain, np.angle(sequence))\n", + " ax2.set_title('phase')\n", + " plt.show()\n", + "\n", + "\n", + "inpft = fft(input_1kHz_15kHz)\n", + "plt_polar(inpft)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "IVXjR_4vchPw" + }, + "source": [ + "Since the low frequencies are lurking around `k*pi*2` and the high frequencies are around `k*pi*2 + pi`, we can make a good guess that the higher peak is of 1 kHz and the lower one is of 15 kHz. The sample rate would be at exactly`k*pi*2 + pi` and can be calculated as" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "colab_type": "code", + "id": "ePfjHH_Adju4", + "outputId": "cd35dd14-e771-42d3-b6f3-68b1ce6bc96d" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "26666.666666666668\n" + ] + } + ], + "source": [ + "sample_rate = (len(inpft)/2) / np.argmax(inpft) * 1000\n", + "print(sample_rate)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "rnHm4xSld9h2" + }, + "source": [ + "We can then replot the signal with the correct scaling" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "colab_type": "code", + "id": "t1zuXQQWeH8o", + "outputId": "236316d3-89ff-4e0f-88e0-0f7e529543f5", + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def plt_time(sequence):\n", + " \"\"\"Plot the signal in time domain.\"\"\"\n", + " length = len(sequence)\n", + " plt.plot(np.linspace(0, length/sample_rate, length), sequence)\n", + " plt.show()\n", + "\n", + "\n", + "plt_time(input_1kHz_15kHz)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "WscxWf4PP0dN" + }, + "source": [ + "The plot of these in cartesian coordinates doesn't give me any further understanding, however:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 281 + }, + "colab_type": "code", + "id": "hyV1DJzaQLad", + "outputId": "68b6097b-0d80-4fd2-babb-0dd3efbfa38e" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def plt_rect(sequence):\n", + " \"\"\"Plot the complex signal in rectangular coordinate, from 0 to pi*2.\"\"\" \n", + " fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2)\n", + " domain = np.linspace(0, pi*2, len(sequence))\n", + " ax1.plot(domain, np.real(sequence))\n", + " ax1.set_title('real')\n", + " ax2.plot(domain, np.imag(sequence))\n", + " ax2.set_title('imaginary')\n", + " plt.show()\n", + "\n", + "\n", + "plt_rect(inpft)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "-IiQK8jyUWaJ" + }, + "source": [ + "## Systems" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "p9V5bnZ4-E2K" + }, + "source": [ + "### Low-pass Filter" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "Vgs77T9yUhAU" + }, + "source": [ + "In this section, we also try to do the same thing\n", + "for the impulse response, which seems to be a sinc function." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 793 + }, + "colab_type": "code", + "id": "fh5OzwtRUv54", + "outputId": "727ad099-50c3-4ebc-bb50-7fd096d55ed3" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "quickplt(impulse_response)\n", + "lfft = fft(impulse_response)\n", + "plt_polar(lfft)\n", + "plt_rect(lfft)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "3VGWOQv-VREF" + }, + "source": [ + "As shown in the graphs, the system is a low-pass filter." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "q70T5CckfPwf" + }, + "source": [ + "Applying the system to the input we get what is undeniably the sinusoidal signal of frequency of 1 kHz:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "colab_type": "code", + "id": "153JptX0fPYL", + "outputId": "8b688ebd-10bf-408b-9d40-6e0ed1c633d3" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "output = np.convolve(input_1kHz_15kHz, impulse_response)\n", + "plt_time(output)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "q0m_kWbQfy-1" + }, + "source": [ + "Alternative to convolution in time domain, we can multiply the FTs:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "colab_type": "code", + "id": "EFZ0F9gTivdG", + "outputId": "536337f3-821e-4f63-ea2d-c62c966003a7" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from numpy.fft import ifft\n", + "from scipy import interpolate\n", + "\n", + "f = interpolate.interp1d(np.linspace(0, pi*2, len(lfft)), lfft, kind='zero')\n", + "plt_time(np.real(ifft(inpft*f(np.linspace(0, pi*2, len(inpft))))))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "eoTRi4pfj3mD" + }, + "source": [ + "It is noticeable that the wave is now distorted in shape. Funny enough, using other interpolation methods, the result is much worse (using the convoluted one as the reference), for example the linear one:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "colab_type": "code", + "id": "4JbRKH-zkGZx", + "outputId": "715bdc0a-f48f-4a26-b20e-095516f5bf61" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "f = interpolate.interp1d(np.linspace(0, pi*2, len(lfft)), lfft, kind='linear')\n", + "plt_time(np.real(ifft(inpft*f(np.linspace(0, pi*2, len(inpft))))))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "YP4VVonnyIfq" + }, + "source": [ + "Notice that the low-pass filter filtered out the 15 kHz wave:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 545 + }, + "colab_type": "code", + "id": "c7_k8qUAyLTi", + "outputId": "73ac8110-c9b8-4ec6-cbf8-d3907fd72d8b" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt_polar(fft(output))\n", + "plt_rect(fft(output))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "ywBqbDYo-O8c" + }, + "source": [ + "### High-pass filter" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "WTJ256AU-UeI" + }, + "source": [ + "To turn the given low-pass filter to a high-pass one,\n", + "we subtract it from the impulse signal (which is equivalent to\n", + "subtracting it from 1 in the frequency domain thanks to linearity):" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 793 + }, + "colab_type": "code", + "id": "TGtdsdLi-jmX", + "outputId": "f9720e14-eb43-4368-b514-07cd7d1e8a76" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "high_pass = ((lambda m: [0]*m + [1] + [0]*m)(np.argmax(impulse_response))\n", + " - np.array(impulse_response))\n", + "quickplt(high_pass)\n", + "plt_polar(fft(high_pass))\n", + "plt_rect(fft(high_pass))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "ScsGWwmIAP6E" + }, + "source": [ + "We then apply it to the input and get the high frequency signal of 15 kHz:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 793 + }, + "colab_type": "code", + "id": "OVMsNKwgAk6b", + "outputId": "6810e7a3-8db3-4853-e19d-30551a4e4ece" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "outputhf = np.convolve(input_1kHz_15kHz, high_pass)\n", + "plt_time(outputhf)\n", + "plt_polar(fft(outputhf))\n", + "plt_rect(fft(outputhf))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "JUMVl3wrBAFX" + }, + "source": [ + "Other methods to create a HF filter have been tried, however the result is nowhere as good:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "nAg7C28hBNKd" + }, + "source": [ + "1. Shifting the low-pass filter by pi in frequency domain:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 545 + }, + "colab_type": "code", + "id": "Cib04NkFBIVD", + "outputId": "9166d52e-c8e4-49f7-e2aa-ddf1978cb885" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "high_pass_bad = ifft(np.roll(lfft, len(impulse_response)>>1))\n", + "outputhf_bad = np.convolve(input_1kHz_15kHz, high_pass_bad)\n", + "plt_rect(outputhf_bad)\n", + "plt_polar(fft(outputhf_bad))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "CbW0fDIQCTfP" + }, + "source": [ + "2. Multiply the low-pass in time domain with (-1)^n (which effectively also shift it by pi):" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 529 + }, + "colab_type": "code", + "id": "3UYAyK6eC-Yg", + "outputId": "7d0c08c1-589c-4326-bc25-17a29c457ed9" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "high_pass_worse = np.fromiter(((-1)**n for n in range(len(impulse_response))),\n", + " dtype=float) * impulse_response\n", + "outputhf_worse = np.convolve(input_1kHz_15kHz, high_pass_worse)\n", + "plt_time(outputhf_worse)\n", + "plt_polar(fft(outputhf_worse))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "l1qP70KvDvIO" + }, + "source": [ + "While both of these produce a high frequency signal for most of the interval, at the start and end the *volume* is significantly higher and there are many different frequencies instead of just 15 kHz. This seems disagrees with the theory at first, but the theory is only supposed to apply to infinite length impulse response; manipulate a rather small in size sample cannot give perfect results." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "p2H5i0CX5OSY" + }, + "source": [ + "## Electrocardiogram" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "zf8MKQ_p5b5t" + }, + "source": [ + "Given the following ECG signal:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 793 + }, + "colab_type": "code", + "id": "ulTRe5DT5rNV", + "outputId": "25dae93f-6ffe-4e13-dcc1-de77564d87b8" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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aRURriGgMETVzZ4KG8sXqpRFBCBkVAU2UqVOchJIQ0NSq6zOIJcM/N4qzKJTkWHX3bTYdn3Gs1ifB2GUIRyzd5TWtbbrBFXuqXYV1qrhQrJLb/xXA08zcC8AuALc5bl0QBEsSr9e2WIiUuQtFw/cYcJ0tNhkkt+jLpCUPpjq3RTk80KWCp54e47n069TV1jc0LpV3zUsz8YqL7Ii2Ap4huf0QAO/p218DcIXj1gUhD1EVrDYtipXKJSTKzt/L4EACBhI1vj+vFN8dOQVz1lsnl7ru5ZlJx3htUyODC8XJAGsG6hVUu8Fh2OYXq7YlRQ5NL9nu6HhAcRAzNbk9gLUAKpk5sZBcKYCuFscqJb1PvahlsFKIPS5VKnGYMdIik37YiZTRR93YA4d/GQkTujVz3Q4AwLpt9lPgPT9IAg4jTK1SJaZeReQBf+1VGsRk5noA/fUUm2MBnKDaADO/AuAVABg4cKCp6VEM9REEzyikVzWDTMIIM5ZvFGjzI5Lur8YwQv9UJJHDO5HfurjQvl/odSamchRKyt9//mQ5OrRpblt/6vlREvAGxher1FKC+IWjKBRmriSiqQAGAziciIr0Xng3AJv9NEzCCIV8x6ghk1ZYC0Nj/m8bUX5i/Cr0bN/Kk02bKw+gx/BPTfcl3AEqAu7ViUIu305GzfjWvKANZgJeW9eQlMOpgRk//fdcV/W7RSUKxSy5/Qpoq5Rcoxe7BcCHQRkpCLHEowtFNVY7UT5VZMzebNdt15IsrSjb47vrYXGplrlPRcA9e1CS8prbf5FJy8sxOcNDMJXUGs1+i2cmrcadrzel3rXqpVcfrMdP/z0X6/Vz7+dpV+mBdwHwGhEVQhP8d5j5EyJaDuBtInoEwAIAozxZImGEguCKhMvF6i3f7J75xVsLMO6XZwdiT7OilCFGE7s8u1BUe+D6t/+Jx55xncnJLd2VHHHTYBH1+fXa7Zi4vBx19Q149UeDPNmRiq2AM/NiAANMtq8D4Is14gMXBPc09tgdRkF4ycGRieLCAtTVN+CSv0/H8EvMh8vchvc1Hd9ExmRWLpsxVllVfRC3jJ5te4zqIKafRHYqvSDkIswqg5ja/5X1ODHxx+IAKxEr9DWnaxPFhQXYsa8WJRV7cf/YJabtq0bYhMFUfZHlBNNXp4f31dU3YMPO5Ak9dgOdib1+ft/ICLhkIxQEjcaoEsW7wKnPPEFRYVACTo0RKUUFBaaC5TWMUHUmp5tWfvLaXIXl4VZi0abKpG1WAu71bSMTkRDwIL+gIISF5+s6LZeJVQ9b94GnCMh/Zm5Aj+Gf4kCtuXO2sCCo258a3waCekjApAd/9uNT8Ni4FSnlnLdf38C2veREzLuROisneApWDwc3z7RICLgZIulC3HE9USYRq52yORHlkVbcIoxw5dY9AIBdFr7uooBcKLV1DRi/TFthSy2k0B827TyAl1OmowelI2Zi63UBDTeulchkIwwqN4MgRA3bRY0tyln6uPX/WwmIsZ7E6j2Jz0Hwl3ErGhcDtnpIeA8jbMKvGaVOMHPhqOp3zvnAM/2YoutCtiGi7kQ0lYiW6xk4f+WqIgfX7qad9hnumheZ365NYYQWAm4sa9we0L21unxP42crF4qfK/JkLqdW3xPjVzlr32Sb3RhEYrdVKTfnJDI9cEGIEHUAfsvM84moDYB5RDSRmZc7qcSJPv7oX3PSj0+pYPveGtNjm3rg9u0UEAWymIORmromQ1RcKG6sOVBb1/hZJQ7cKbanyERtrY45cLA+pZzVm5KKZclEogfuBOmQC0HDzGXMPF//vAfazGPTZG1+caC26SYnCx/4ra+mi7yxvEocuFF3ghZyACi2GCj1OsA70rB484w12313wdq5Zcys/2jRlrRt9Q2Mu96Yb1LaHyIj4BJGKEQRIuoBbSLbLJN9GTNtqmpK5f5abDbk0V6ur1avrknulknLhnsyqFjzfYYH3gfzN+PzpVtNywXl5zf7Ws9OLknbphqZAsQ4CiWj3SkXmUSnCNmCiFoDeB/APcxclbqfmV9h5oHMPLBDhw5px1v14lK3JhY5SFBVrbkHlHOh2CSzMm5OziESPIGFEaZQtrvadLtd61an+Os16WGCSfUqx6Gru1rcEAkBN0OEWggTIiqGJt5vMPMH/tXrV02GOvX/K4WxZdmF4nXpNOt6k//2uxk3q+OEQWQEXPVa+nL1NoyZszFYY4SsUbGnGmc/PjVsM5IgrXs1CsAKZn7KbT3ZiqBy5AM3fM6GfWz4b5IdEYtCScXOB+7GM9Q4ld7Hd59ICHimH8Psyz47eU2Q5ghZZOlm88kpIXMmgJsADCGihfq/S51WYnWbqgqnejpZ7f6pt1pAwvA5uUccjZGmIB8kbqfs2+UY9zIIm/UVeQQhn2DmGQjIi8fctIKNSlkVGn3gCgNmyVEoavV7weok+n1yreobNeNbHNuhteP6bE+N4hcw64DmpA/c6jtNWJ7dJYqE8FliMWU8bngNbXOezEq9LJBNF4r/qLowdu6rxZ2vz3Ncv+psWTtKytPXB/3tu4sc22NFJATc7GQkTt+97y3GKsPMLiH3+f5zM8I2wRec9qBTUe0hJ9wEalPpyXR7tvG8qHHAZDozzOqDszeNSos+9ZVICLgd+2rq7AsJQgx445sNymWd6qvKIOY+4wxGZ9W7IrBkUik1+/1AUM3ZbofxJwnigRlZAY/281kQ3LHHUWdE7YZPTAJSWRHGWCQbYYRWeL6/AxYIFzPpzesJ+BxHRsBTv2g0xscFwT1e710Hk/gytmdpRkRuMjdhdYF38DL8eMzqUShBPyOjIeDS3RaENFSEraauaUq5095etvQ7CBFL7QG79aC89OVa0+2+9cCdmeMYWwG3Sq1JRA8R0WYvcbIZ2/WzMkEIAa8TNjIJ39BnpuF7T0/D3uoml4zKoOc5xzdN+Q/ThRJ1Mp0aBiv73IN2oajEgZum1tT3Pc3Mf/PDELmUhFzD67377rxSy32J1XZ+ZwhJe26q+QS3TxeXNX4uLjBGoXizTxWzZtZt34cJy7bi4hM7u6ozbRDTVS3WZHr4nvvEF0p1/HrMwsBj7W174NlIrZkpjFAQBGumrkrPgqhKtu4xq56+l3wjEY9CBACMXbA58NWCHPnATVJr3k1Ei4loNBEd4bNtghBrotgJyXY+cMDF4KoCQeu3X6cmMoOYJqk1XwRwLID+AMoAPGlxXMacyY1I2lghx4j8Oq/ZcqFYprl1b0DQE4F8E3B/qrFEScDNUmsyczkz1zNzA4B/ABhkdqxdzmS9/vTjMtgT+RtDEBwQljsgjMWAk9t3T9DnzLe3k7B74FapNYmoi6HYlQCW+mXU6BnfYq/MvhQA/PCf34Rtgmui3s1wGmfulkxZGeeu34lZ63Z6byRARfdSddBuKpUolERqzSVEtFDfdj+AG4ioP7TfZz2AO/wyasQnmdeOjXoeBcE/vrJZGSXKRP1FMWvmZfCBX/PSTF/q9D0KxVD/5BUV7usxfJ5esh0vfOFvKmxbAc+QWnOcn4Y4eZ0TF4oguGP9jv2Nn7NxH2Xqa8XlPn5/vnU4px2p3/Hxz1d5NSeJSMzElP60kJtET6DWVDSlN81GPnBm67Pgxb0QtOl+jQ+EHgceRfbW1KGuPksOPCFQdh84GLYJgRH9Dma2wgitolD8a8Nvr2r0fzuNyAi4kxNWVV2He8YstC8oRJpZ63bg12P8S24vOCMbIkXkfWm5MIiwaUlEQsDtnp6fLd2atu0Tw/RgIZ4s3FQZtgmBEnURyIYLBQhmIk/QxCVPTCQEXBCE7BN6HLgXH3jKsV4WGTZvwN/qgkIEXBACIuqduOwls/K/oeAHMeNBZAQ86he7IDhFfVHicOKwwnYTRHkQMy5EQsDDuoAFQQgeax+4FxeK60MV649HjzISAi4IUULPrllBRJ7SQ0RdA8LMB57N9t0QYdOSiIyAhz2gIggG/gVgqNdKoixQgD/33NptezPuX7alCrV15nM2vLR+4GC9fSEPRP23SxAJAc9X/5UQTZh5GgAfMixFGz+SWd366uyM+7ftqbHcF2U3RdjjA6pEQsAFIY7Y5bqP+lulH9bV10fDjx1kMqts4SZJX2QEPCYPPEFoxC7XfdSvaT96wF4yg/p5evL1LT4yAi4IQnYJ+wETZRdKXBABF4Q8xQ8/r5eeb5TlOy4Pl1gL+DqbEXAhutTU1WPM3E1hm2EKEb0FYCaA3kRUSkS3uakn6hrgh3meBNxXH7i/PpSI/3SNREbA3ZywIU9+6bsdQnZ4emIJ1m3bF7YZpjDzDczchZmLmbkbM48Ksr2w/Le+9MA9CGeUB3mj/vBNEAkBlyXS8o/te63Dy3KFKAsU4I9IRaUH7ncYioQRCkKeo6oBE5eXB2uIBX5I1AbDEm2O24+HRkaayAi4/JhCvrKirCqUduMyUBcGcTkzkRBwcaAIuUjURSBs/fbzAfK5yaIvXgj73KhiK+BE1J2IphLRciJaRkS/0re3JaKJRFSi//+I4M0VhPgQ9R5u2Pb5uR7qlJUVvtWlEe3fLoFKD7wOwG+ZuQ+AMwD8nIj6ABgOYDIzHwdgsv63Bxjb99agvKraWzVCLHCiHQdq6yVkNACytaSaFftqg01I5YWwz40qRXYFmLkMQJn+eQ8RrQDQFcAwAOfpxV4D8AWA37sxIjGSPfCRSW4OF3Kcu96Yh6mrtqHk0UtQXBgJr58SUdeAqNsn2OPobiCiHgAGAJgFoJMu7gCwFUAni2MyJvwR8hMn4WdfrdkBID6hXQmibm7YLpQoE5dzoyzgRNQawPsA7mHmpGFz1r6t6Te2S/gjCEI4xESjQiEup0ZJwImoGJp4v8HMH+iby4moi76/CwBPowhyMQm5h9pF/cniMvtCARD1iUZhEhc9UolCIQCjAKxg5qcMuz4CcIv++RYAH7o1QiZiCrlI1EUg6vaFSRjuOjcyaDuICeBMADcBWEJEC/Vt9wMYCeAdPdHPBgDXuWhfEISQiEukRSjE5NyoRKHMgPXD4QK/DInJ+RIEZaJ+TYsLJf5EIibL71SQghAFou6iiLp9YRKXUxMJARfyDzfiIYLjL3EJlQuDuJwbEXBBCIioi0DEzQuVuIwPREbAo36xC/6SD5FHUb+in5y4OmwTIktcxgciIeD5cDMLghAf4tKfjISAC0IuEhcRiCJ/vLxP2CbEgsgIuFzrgh1xE8S4vIZHkQ5tmofaflx+uUgIuHhQBEGIFDFR8EgIuCCoELsebczMjRJhd+rikvkyMgIek/Ml5AlENJSIVhHRGiJytViJXNLxJS6/XTQEXMJQ8o4oT+QhokIAzwO4BEAfADfoq1AJeUJcwpqjIeCCEC0GAVjDzOuYuRbA29BWoHJETDRAMEEm8giCz2TxnuoKYJPh71J9WxKy2pQQNpERcLc3Z/XB6C6MKpjDzKiq9m9F8rCwW21q8LHtQrAqNxCvqhqREHAvv9U5j0/1zQ4hO7z45VpMXF7u+Lgs+iU3A+hu+Lubvs0RhQWiQoI6bh5akRBwL1TsqQnbBMEh45c5F+8sMwfAcUR0DBE1A3A9tBWoBCFSqKzIkxXiMuorhEe2rhBmriOiuwGMB1AIYDQzL8tS8wJkjQBVIiHg4u8SogYzjwMwLmw7BCETsXehCIIg5Csi4ELkqa1vACBx1fmEvJWrYSvgRDSaiCqIaKlh20NEtJmIFur/LvVihPxWgiAYkYe1Gio98H8BGGqy/Wlm7q//E1+hEDxyU+cN0gNXw1bAmXkagJ1ZsEUQBAFAfr6VX9K3s+NjvPjA7yaixbqL5QirQqrTjeWVSbAjdulkBdfkYw/8u8e2d3yMWwF/EcCxAPoDKAPwpFVBu+nGAED5+GvlM/K0FoQ0sjYTk5nLmbmemRsA/ANa9jZBCBTR/XxCOnUquBJwIupi+PNKAEutyqoir8d5hLxxCUIabjwRtjMxiegtAOcBaE9EpQAeBHAeEfWHFhewHsAdjls2tuHlYCFvkEd8/pCPecDcfGVbAWfmG0w2j3LRliAIghIyLqaGzMQUYoMkPBNymVink5V7UxCEBLnW/y5S8Am5ycAYCQGXt6U8w+XTWp7x+UOuaYLK94l1D1wQhPzhvTsHh0ytfsYAABpaSURBVG1CThAZARcXSh6Ra90rwTH9ux+ecX+uXSIq+ubmK0dCwGX1DUEFecjnDnZRJrmmCUqXrrhQBEGIA7klz+ERGQGXmZh5hOtBTLlGcgVbF0mOKbxKCGxso1By7ccSBCEz9i6U/EOiUITcRjrgodCsUGTCK0FduvLLCIKQkYYQRo/zcSp9bKNQAIkwyCtc3pxyiYRDvdycWcHNQysSAp5/z1ohqhDRtUS0jIgaiGhg2PZEAbf6XeghpWCuaUJQz8BICLggqJCljuBSAFcBmJaV1nKYQg9ukDz0oASTTjZbyEtaHhHhV3JmXgHkpw/WbwoKANSHbUV8iG0Uitd7pXJ/rT+GCIFTW9eArVXVro6NWhy46oLd+YqnHnjOOVGCIRIC7pX+IyaGbYKgyL3vLUJ5VU2oNhDRJCJaavJvmJN6VBbszmcKxIXiCDcPrci4ULbtCfemFrLDxOXlro9dW7EPXQ5r6dkGZr7QcyWCLV5EOA/1O765UAiEb7fvC9sMIeLcOGoWNlceCNsMQRFP4wh5qOCx9YELgiq79gU73kFEV+qLdw8G8CkRjQ+0wRzGy8LEcfaBDzmhY9bashVwIhpNRBVEtNSwrS0RTSSiEv3/RwRrpiBkB2Yey8zdmLk5M3di5u+FbVNcyddIHrffOqiZmP8CMDRl23AAk5n5OACT9b8FQRAa8SLf+aj9gczEZOZpAHambB4G4DX982sArnDcsoF8/LEEIa6ce7xaxE2+usCzqWdufeCdmLlM/7wVQCerghIrKwjqPH7NyWGbYMs5igIebxn2grvvHUoyK9YylVvOsJBYWUHILVSFxtMgZh6+lmczCqWciLpojVIXABUu64FWh5ejhTgRrbmUghtU71dPLpQYa4KXB5fjtlwe9xGAW/TPtwD40B9zBEHwk2ZF/kcKq/fAY6zCHigqdOtCCWAQk4jeAjATQG8iKiWi2wCMBHAREZUAuFD/WxBsyc9bOjyKA+gOqro3PEWheDg2bAoL3D003TzvbKfSM/MNFrsucN6cOXEO2heEKFNU6H9KQHUXSlPBVY8MRe8HPvfVjqgSBxeKIAgxoNjl63wq/bod1vjZTY3NiwodlY+z98XLQhZOEQEXhBymyOXrfEZUXSiedIxwwQkdccpRh3upJBSKXAq45EIRBCGJbPYGU/Haix5162kYMayvP8ZkkWyuVxIJAY/z65LgDAkjzC5+uVCMN6lqjV7GtlI1oU+XQ/HJL85yXV82MbvGVX6HQKJQBEHIDo9cYd3bvPqUbvjlBcfhygFdHdV5aMtiy33djnCXWz0bHa7UJjhL7QbBZSd1we3n9LQtJy4UIfLE9B7MCid0bmN5fn5wWnf85qLj0dxhXPdjV51kue+6gd2V6vh+vyOT/lbtKfohuMY64hKtlupCue3sY1BcaP+7hTKVXhCE7OFUFNu2ama63RhVYsdT1/VLEhdVt7q3bITpR8elB566dmtxQUFgfnERcEGICGoC5UzFrGZDfnj3Wco1pfYe3cSBOyXNhcIcGwFPdYKrDiQHkk5WEITo4PQez1Q8yoKYsC0ubhMjqZ1t1YFkcaEIkUeiULzh+CbPcIDbHnI2RDUqwn3Xecc6PoZT/CWFBRTYdR8JAc/H1JGCkI5CqJnDWyWQhFJZ8YGb1Ze+8a2fnuGhFXtaNbfNNpJGeg9cTWYlCkUQchyVnun0e883lM9Ql0uFzWZ3KykKxaThQ5o5m6KfDVIHLAsLSGl2j/jAhcgj71reULnHu7c9xFDenzPepoXznqjVjz37fud58Kz0L4ov76mRP0WFyS6UTKGdTomEgPvxGzw3pcSHWoQgmV6yDftq/c2Ml0uk+k7NcHqvZOyBO6jt6R/0bzrOo2p2PLSFctnkOPB4cMt3e6B3pzaNf6fmoxlw1OGYed8QX9qKhID7wd8mrA7bBMGGm0bNDtsEW4joCSJaSUSLiWgsEWUtm1KDwkiXnXiOTOndZfKBO9Hh9q2bNx2neIzvPnBFv7gXTujcxr6QDUUFhOsHNU2SKiqktDeILoe5mwWbSs4IuCD4xEQAfZn5ZACrAdyXrYbrVRTchj5HHpq8IYgxzCx0hQ9tkZwCIHVyTFC2BJH8y212QhUiIeBR9GMJ+QkzT2DmOv3PbwB0y2LbtmWs7pW+XTXhTu2RZrq3Mt12Q0/s7NgGK16/7XRH5d//2eBGP362wwlTBVzlN0mFKPncFhUUWD6AvBIJAReEiPJjAJ9Z7SSi24loLhHN3bZtm+fG6j3Mt04cmiqublwoJ3U9DCOvth5oUw1NTLh7Oh3a3KZkMqce3daqRkf1uMGPQd/UOnK+By4IqviRU4KIJhHRUpN/wwxl/gCgDsAb1rbwK8w8kJkHdujQwbTMAAcLEmRyoSQyBzrtkbodxPRzboYffU9mdb+4F/zLvttUUUGAAu4iNkgQ4g0zX5hpPxHdCuByABewm3doA+/cMRgry/bg+8/NULDLfPvSh7+H1vqEEivBchJm1/Xw5AG0C7/TEZNWVCRt80Nz/JAtM/uPad8K327fp7fhrzj6MfHJrIagkll5EnAiWg9gD7RVU+uYeaCrerwYIeQVQfkSExDRUAD3AjiXmfd7ra+4sAAtm6m96DZY3OWtDbMBnYcRph/x1XAthC2hVUe1bZW0n8E2rpfs37GMpu/u8ZmakdTv7aYpoqZze+lJ1mMJfuCHC+V8Zu7vVrwFwQlZWK7qOQBtAEwkooVE9JLXClUFTy2M0Hy71aFutTajgDusS+U3e/9n37VtKxspZv2qL1GNWTpfP98actaFsnv/QRx2iPVqJELw7KupQ3FhAZo5XIQgE0HrNzP38rtO1dtVJYzQae9XpXjqWw2BMkevKKeTVSsHAL06tFYua7Q26DBCN/UbBTrx8IpqMisGMIGI5hHR7W4r8fuV7IP5peg3YgKWbdnta72CM058cDyufXmmr3UG+focFOo9cLbtrdrVlNqUykBlapt2LhSnqLi9CmyUiJkDc7UaQyZ/mrL0WeLcOIkPJ4L/TxYLvAr4Wcx8CoBLAPyciM5JLeB3qJUK00u2AwAue3YGlm62FvEDtfXYtqcmKzblEvtq6rBjb+bz1vsBLfpu0aZKX9uOn3yrDwg2MLsOJbR6sGVqO5NZ/gxiqldSQIQ/DzsRY+9KdqWY6aDxq3p1R1w1oCtevPGUxr/P793RtNzPzlVPK2u0KGFqJFfkYebN+v8rAIwFMMikjG2oVZB8vHiL6fZ5G3bhO3/6HKc9OinLFsWf7z0zDac+MgnvzSu1LFNT1xBI2zHsgCuLTH0DWw5kGipz1Jbbt9vMPnBndar8ZgVEuGlwDww46gjzOhBMGGFBAQUyKJtaY+Qm8hBRKyJqk/gM4GIAS13V5dYIl8zbsBNXv/h1llvNHUp3HQAA/O7dRRi7wFrEgyF+Cq6qD8xAg40fvIuDRFCAWjpZs9673wsS22HtQkmvxE8xNDPx4j6dfKs06A6Hlx54JwAziGgRgNkAPmXmz/0xK1iufjHZL7t7/8GQLIkfB1KyCf56zCJUVWfv/MWxB66K1gPPXOamwT3w/P+ekrTtsJZNg/VpPvAMInrikdrCxqf2SJ/5mKlXGoR7V8Xnnuj5J7tQ7DkxNT+MsU6TCu46v2kc283lZjoIHDUXCjOvY+Z++r8TmflRPw3LJv1GTPAlkVA+MMjE5cQp3pI4DjQGSZ3itVXP9i6UwgLCZSd3SdrGhsHPdAG3lrhBx7TFrPsvwP/0O1LJvsY6HZVWe+gW2gm4h5mYHdpYT+U3cwc1N4macvLQSi4bzNtNgrybSj/7252m20XA1dhTU5e27YMUN0qQ+h3HX6muXm08oFfH1mk98Acu+47tcV7OSSeHLpmgsBK1RPSHMRTV6fWVcbDWRAH9CHtNfTBENYzQF7I5ses6i7C2oGf45TIPf7w8KdrHdiDOA3Hs3Kv0wGfeNwSnHHVEmg/c6B6xgjna16+VbTcMOqrxs9WbQo92h+CXQ3rhHzerzRM076VnzgiTSnMPD4vUGs2O93MZuEgIuN8YT+DLX65Dj+Gf4tWvvs14zKx15j1zoYl12/Za7qs+WI/yqmr0GP4pev3BMoGfZ+LonlG5YRMJ/lMffioREsZzkpUV4zM08eqtpxnKZbZFZWkxIsJvLu6N7m0PsWhXxXdujVm4ZPOi9N/LyVklsp4IdX7vDuh2xCHmO12QcwLe0MCoMIntfvWr9RmPu3n0bGza6Tn1RU4z5MkvM+5fXb7HdPs+E7eLW+In38DR7Vrh9dtOxykKmQlT48BVhMPvc3JIM7sJ2tZWmT2sgnzmpgplsYlPJNNzpGObdBdS82JzWRxz+xmY8ttzk7aZfV/jQ6FxJqb+4Yye7ayNcUFEBNy/XsMzk1Zjxprtro7dU+2f0OQjVjfqGY9NDryNqHPWce3RUqEnnvr9VNyLZjM4H7vqJDz0/T4OLNT4/dAT8NwNAzKWyWRT0jR3x62rkfzGkcxowxuAHY9ffTLuOj99gk6zwnRZZACn92yHnilT/hMrBxnXuCwqLLD87n67i3MqF8qQJ7+wfF3duHM/vlm3I8sW5Q97quvw8zfnW+57bNwKX9qJsq/XD+ziwBNc3KcTJiwvBwAcaVhfMSEQRv+yE352nvqMQzNaFDv377aw6PGm0jj1P0OZs45rb3akadkrT+mKYhOxNotCscLsejQu4BD09ZpTAr5u277GpaXMuP6Vb7JoTX4xZs4m7M+w4vzL09b501Bu63daFIpVj+35H56C/bX1mF6yDQOPboubRs0K3rgMnNC5DX585jHo373JTdQ0Ucj6uFduOhXf6WJ9zxoxOxVOZ1H++Yq++ON/M883NM16aFG2MXzTUKK4sCDtd4vkVPpco6bOWoDynVqbqfGfL9uaJUtyD+PNnu4DN5eO4sICHNayGJeffCQ6H9Yiq881M4vatCjCdad1Ty6noK0Xn9i5cf1LVZxO5DE+9W8642iHx6bTUY8rLzYs32P8rsbEV2kuMb8XoPC1NpdEZVHjK1/4GiUWA3H5zvEPBBdZ4oRc7IAnh52lRqG4r8tvxtx+Bn585jGm+zL1MP1yIzT26B3W53fv98oBXQEAv724t3Uedos4cKvfUyXe34yccqH4wfKyKhzXqU3YZggWxHUQE1CzPTGh7IZB3bF1dzUu/I5aXo6E3zbIztDpPdvh9J7tMFH3vRsx+2p+9zbN6jO2e3tKKljb+lRCNG0eFk0uFKvjk8tZ8ZOzndmeQARciBW5OIhpFJKED7zbEYfgsatOVq7jpRtPxbvzSnGsg4UR3OJ2Kv01p3bDeb39zUhqjJu/6pSu5u3r/79l8NGm+63obezIWYq9hYKn/J2YkGVcHs8PIiHgfj6n49xDE+zJxd/XzIXidEGF7m0PwW8uOt5Hq5yhktHwb9f286mtps8qKTCYGetHXuaojRUjhqKwgPDCF2sylvv79QPw7OQStGtlnm8lYeud5/XEoS2LcO3A7qbl3BIJAfcTyWmS2+Tir3vbWU1+5cQkmtYt4nVrmv0uXQ5rgcWlu5Xi31Vo8oE3UVdvPwvV2k9tTcJmsw6DcdOZvdrjzF7poYupdTcvKsSPLMYPvBCvq0SBqPXQKvZUo7q2AUe1yzzSPnVVBbof0RJHt2uVFpvKzKiqrsNnS8pw7cDuGZd3qqo+iLLKavTunJt+/DhOpbfj50Oa0pfecW5PNC8uwA2n+dtTA4CP7j7Tl6XSVKt44tp+uPSkChzv05iSsdn2rZth+95apbw7flwypiGMCscpLSfn4SeJhID7OfCyymMUybfb9/lkCfDdxyZjy+5qALB9hfvRq3MAaLmLP/3l2Un7xszZhOEfLGn8+/oMkzRu/OcsLC7VEkstH/E9hWnR9mypPOC5Dr/IPflOnvjRorgQdzpYvssJJ3ezn8qvgt0yZwkObVGMYf3N/dJeYG4aN1BJFGbZA3epOwP0WPc+KXnGWxYX4sDBer1uk9cFC9Y95sy9YyQSYYRR4plJJfhsSZnnepZu3t0o3gAsk2kxM24wTDBatqUKADCjZDte/nItAGC8IcZ6+AdLsNYiqdTMtTsaxRsA/rvAfDk5p3x35BRf6vGFHFPwt28/w5eHrFf+fn1//OQs96/4WflZGgWXcd3AbgCA1s1V0hPYW3f7OT3x5k9PVzLjkpO64OvhQ3D2cckDsl8NH4Lp956fZGqmlm8ZfDR+4NEnHv6VE0GWbanCJSdpSfNr6upRVFCAwgLCUxNWYc22vXjhh6daHvva1+vx4EfL0rY//PFy3DK4BwpS3pdWlO3BzJQp/uc+MRUbdmiJteas34mpq5IXg/7du4vw7h2DUVRoTHvJuOEfyTNN7x+7BPePXYJLT+qMx6/pZzkC/vbsjXhr9kZ8ePdZALRVd5p8gDmmmBHD7+RGbhnWv6tpb/kok0k2Zr7mqy0iQPwkkaOk6xGH4HcX98YvhhyH7TaLawPA8EtOsC1z/6XO4rCPPLxl2ra2rZqhbatmANR69w8P6+uoTTOkB27Cc1PXYOGmSuyvrUPvBz7HT/89F3PW78SzU9Zg3JKteGfuprRjDtTWo++D403FO0HP+8clCeKWygO49NnpaeUS4g0Ak1ZUpO1fsLESj49flbTtsmdnWLY7bslW9H1wPGaUpCf5mr9xF4Z/sASLSnfjvXmlmLS8HN/50+f4eu12HKxvwODHItT7RvBhhET0ZyJaTEQLiWgCETlbrkaBMKNFnLD4oYsx4dfnWO4f3LMdPr77LKz7y6VJMxzvOLdnIN/x8EOa4aUbT8HoWwaCiNCiuNA09es9Fx6X9Hdi6bhUgljMOJWgO0CR6IFnI4exU178Yg3GL9MmLExZWYEpK5uE9N73FqNXx9bYubcWRMB5vTvid+8twl6FtKmV+w/iCP0p7TZrIgC8NWsjfnPR8WhRXIjqg/VYXlZle8yNo2Zh+r3no3L/QWzbW42WxUVJvfbfvbsIA/SUp//7j1l49Mq+2FpVbVVdKGThheAJZv4jABDRLwH8CcCdflR86Uld8PXaHbjqlK6Yt2GX64RT2SKRaS8N/XZtVlSAk7qli+N9l7ibVajC0L7Jy8mZLZd2z4XH45lJJYHZoEK2ZpdHQsCjODkjId5WXPWCu1XtB/x5Ihb+6SKsqdiLe99b7KoOQFva7FdvL8DLNw1E3wfHKx939uNTM+5fsLGy8fMfxmZO+hMGQQs4MxufhK3go3v3h6cfhWtO7YYWxYV47ceD/Ko2NKJy1x7XsTVKKvaaimavjt4mNnn9jkGfo0gIeL5RXlWDjT4sHjG9ZDvq6huUF83NBbLxTYnoUQA3A9gN4PwM5W4HcDsAHHWUfW868dofdxoH6CI8PjLr/gvw2ZIyXO5wwWYrnPaoWxZr0mr5FuMTnnzgRDSUiFYR0RoiGu62nghfB4HwvWemmfqjnbK/tj7Q5cuiiB+iQUSTiGipyb9heht/YObuAN4AcHcGW15h5oHMPLBDB3+niEeZxGBiywg/jDod2gK3nnkM2re2XpFehUTIYD+HIZgX9+mEP17eB/ddaj+A6gXXPXAiKgTwPICLAJQCmENEHzHzcqd15Zl+AwA+WLA5bBNiiR/XCjNfqFj0DQDjADzoQ7M5wxk92+FXFxyHmx3mFokj55/QEbPvvwAdD01fei0TBQWUNMM2KLz0wAcBWMPM65i5FsDbAIa5qSh6Q5hCVLnjP/MCrZ+IjCEMwwCsDLTBLNCzfSs0c7DKjB0FBYRfX3Q82nns3fpFIuRVVUdUVwBK4FS8s4kXH3hXAMZ4ulIAaZHwKn7CG04/Cks270bZ7mhFPAjRY1h/36P6UhlJRL0BNADYAJ8iUMJk0m/Ozem33BdvPBXvzt2kPGD5yS/O8sWFGQUCH8Rk5lcAvAIAAwcONL2Ozu/dETPvuyBoUwTBFma+Omwb/CZ18liu0fXwlrjnQvW4814d26BXx9zIFeTlvWozAOM80G76NkEQBCELeBHwOQCOI6JjiKgZgOsBfOSPWYIgCIIdrl0ozFxHRHcDGA+gEMBoZraeRy4IgiD4iicfODOPgxZmJQiCIGQZSWYlCIIQU0TABUEQYooIuCAIQkwRARcEQYgplM2MYkS0DdrsNjPaA4jT9CixN1jc2Hs0M4eSVSrDtR238w7Ez+Z8sNf02s6qgGeCiOYy88Cw7VBF7A2WuNlrRRy/R9xszmd7xYUiCIIQU0TABUEQYkqUBPyVsA1wiNgbLHGz14o4fo+42Zy39kbGBy4IgiA4I0o9cEEQBMEBIuCCIAgxJXQB92th5GxARN2JaCoRLSeiZUT0q7BtUoGIColoARF9ErYtKhDR4UT0HhGtJKIVRDQ4bJvcINd28MTp2g7iug7VB64vjLwahoWRAdzgZmHkbEBEXQB0Yeb5RNQGwDwAV0TV3gRE9BsAAwEcysyXh22PHUT0GoDpzPxPPdf8IcxcGbZdTpBrOzvE6doO4roOuwfu28LI2YCZy5h5vv55D4AV0NYGjSxE1A3AZQD+GbYtKhDRYQDOATAKAJi5Nm7irSPXdsDE6doO6roOW8DNFkaO9EWTgIh6ABgAYFa4ltjyDIB7oS3SGweOAbANwKv6q/E/iahV2Ea5QK7t4InTtR3IdR22gMcSImoN4H0A9zBzVdj2WEFElwOoYOZ5YdvigCIApwB4kZkHANgHINL+41xCru3ACOS6DlvAY7cwMhEVQ7vA32DmD8K2x4YzAfwPEa2H9go/hIheD9ckW0oBlDJzovf3HrQLP27ItR0scbu2A7muwxbwWC2MTEQEzYe1gpmfCtseO5j5Pmbuxsw9oJ3bKcx8Y8hmZYSZtwLYRES99U0XAIj0QJoFcm0HSNyu7aCua09rYnolhgsjnwngJgBLiGihvu1+fW1QwT9+AeANXfjWAfhRyPY4Rq5twQTfr2uZSi8IghBTwnahCIIgCC4RARcEQYgpIuCCIAgxRQRcEAQhpoiAC4IgxBQRcEEQhJgiAi4IghBT/j96XfNcwyiAUQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ecg = [\n", + " 0, 0.0010593, 0.0021186, 0.003178, 0.0042373, 0.0052966, 0.0063559,\n", + " 0.0074153, 0.0084746, 0.045198, 0.081921, 0.11864, 0.15537, 0.19209,\n", + " 0.22881, 0.26554, 0.30226, 0.33898, 0.30226, 0.26554, 0.22881, 0.19209,\n", + " 0.15537, 0.11864, 0.081921, 0.045198, 0.0084746, 0.0077684, 0.0070621,\n", + " 0.0063559, 0.0056497, 0.0049435, 0.0042373, 0.0035311, 0.0028249,\n", + " 0.0021186, 0.0014124, 0.00070621, 0, -0.096045, -0.19209, -0.28814,\n", + " -0.073446, 0.14124, 0.35593, 0.57062, 0.78531, 1, 0.73729, 0.47458,\n", + " 0.21186, -0.050847, -0.31356, -0.57627, -0.83898, -0.55932, -0.27966, 0,\n", + " 0.00073692, 0.0014738, 0.0022108, 0.0029477, 0.0036846, 0.0044215,\n", + " 0.0051584, 0.0058954, 0.0066323, 0.0073692, 0.0081061, 0.008843, 0.00958,\n", + " 0.010317, 0.011054, 0.011791, 0.012528, 0.013265, 0.014001, 0.014738,\n", + " 0.015475, 0.016212, 0.016949, 0.03484, 0.052731, 0.070621, 0.088512,\n", + " 0.1064, 0.12429, 0.14218, 0.16008, 0.17797, 0.16186, 0.14576, 0.12966,\n", + " 0.11356, 0.097458, 0.081356, 0.065254, 0.049153, 0.033051, 0.016949,\n", + " 0.013559, 0.010169, 0.0067797, 0.0033898, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0010593, 0.0021186, 0.003178,\n", + " 0.0042373, 0.0052966, 0.0063559, 0.0074153, 0.0084746, 0.045198, 0.081921,\n", + " 0.11864, 0.15537, 0.19209, 0.22881, 0.26554, 0.30226, 0.33898, 0.30226,\n", + " 0.26554, 0.22881, 0.19209, 0.15537, 0.11864, 0.081921, 0.045198, 0.0084746,\n", + " 0.0077684, 0.0070621, 0.0063559, 0.0056497, 0.0049435, 0.0042373,\n", + " 0.0035311, 0.0028249, 0.0021186, 0.0014124, 0.00070621, 0, -0.096045,\n", + " -0.19209, -0.28814, -0.073446, 0.14124, 0.35593, 0.57062, 0.78531, 1,\n", + " 0.73729, 0.47458, 0.21186, -0.050847, -0.31356, -0.57627, -0.83898,\n", + " -0.55932, -0.27966, 0, 0.00073692, 0.0014738, 0.0022108, 0.0029477,\n", + " 0.0036846, 0.0044215, 0.0051584, 0.0058954, 0.0066323, 0.0073692,\n", + " 0.0081061, 0.008843, 0.00958, 0.010317, 0.011054, 0.011791, 0.012528,\n", + " 0.013265, 0.014001, 0.014738, 0.015475, 0.016212, 0.016949, 0.03484,\n", + " 0.052731, 0.070621, 0.088512, 0.1064, 0.12429, 0.14218, 0.16008, 0.17797,\n", + " 0.16186, 0.14576, 0.12966, 0.11356, 0.097458, 0.081356, 0.065254, 0.049153,\n", + " 0.033051, 0.016949, 0.013559, 0.010169, 0.0067797, 0.0033898, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0010593,\n", + " 0.0021186, 0.003178, 0.0042373, 0.0052966, 0.0063559, 0.0074153, 0.0084746,\n", + " 0.045198, 0.081921, 0.11864, 0.15537, 0.19209, 0.22881, 0.26554, 0.30226,\n", + " 0.33898, 0.30226, 0.26554, 0.22881, 0.19209, 0.15537, 0.11864, 0.081921,\n", + " 0.045198, 0.0084746, 0.0077684, 0.0070621, 0.0063559, 0.0056497, 0.0049435,\n", + " 0.0042373, 0.0035311, 0.0028249, 0.0021186, 0.0014124, 0.00070621, 0,\n", + " -0.096045, -0.19209, -0.28814, -0.073446, 0.14124, 0.35593, 0.57062,\n", + " 0.78531, 1, 0.73729, 0.47458, 0.21186, -0.050847, -0.31356, -0.57627,\n", + " -0.83898, -0.55932, -0.27966, 0, 0.00073692, 0.0014738, 0.0022108,\n", + " 0.0029477, 0.0036846, 0.0044215, 0.0051584, 0.0058954, 0.0066323,\n", + " 0.0073692, 0.0081061, 0.008843, 0.00958, 0.010317, 0.011054, 0.011791,\n", + " 0.012528, 0.013265, 0.014001, 0.014738, 0.015475, 0.016212, 0.016949,\n", + " 0.03484, 0.052731, 0.070621, 0.088512, 0.1064, 0.12429, 0.14218, 0.16008,\n", + " 0.17797, 0.16186, 0.14576, 0.12966, 0.11356, 0.097458, 0.081356, 0.065254,\n", + " 0.049153, 0.033051, 0.016949, 0.013559, 0.010169, 0.0067797, 0.0033898, 0,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0.0010593, 0.0021186, 0.003178, 0.0042373, 0.0052966, 0.0063559, 0.0074153,\n", + " 0.0084746, 0.045198, 0.081921, 0.11864, 0.15537, 0.19209, 0.22881, 0.26554,\n", + " 0.30226, 0.33898, 0.30226, 0.26554, 0.22881, 0.19209, 0.15537, 0.11864,\n", + " 0.081921, 0.045198, 0.0084746, 0.0077684, 0.0070621, 0.0063559, 0.0056497,\n", + " 0.0049435, 0.0042373, 0.0035311, 0.0028249, 0.0021186, 0.0014124,\n", + " 0.00070621, 0, -0.096045, -0.19209, -0.28814, -0.073446, 0.14124, 0.35593,\n", + " 0.57062, 0.78531, 1, 0.73729, 0.47458, 0.21186, -0.050847, -0.31356,\n", + " -0.57627, -0.83898, -0.55932, -0.27966, 0, 0.00073692, 0.0014738,\n", + " 0.0022108, 0.0029477, 0.0036846, 0.0044215, 0.0051584, 0.0058954,\n", + " 0.0066323, 0.0073692, 0.0081061, 0.008843, 0.00958, 0.010317, 0.011054,\n", + " 0.011791, 0.012528, 0.013265, 0.014001, 0.014738, 0.015475, 0.016212,\n", + " 0.016949, 0.03484, 0.052731, 0.070621, 0.088512, 0.1064, 0.12429, 0.14218,\n", + " 0.16008, 0.17797, 0.16186, 0.14576, 0.12966, 0.11356, 0.097458, 0.081356,\n", + " 0.065254, 0.049153, 0.033051, 0.016949, 0.013559, 0.010169, 0.0067797,\n", + " 0.0033898, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0.0010593, 0.0021186, 0.003178, 0.0042373, 0.0052966,\n", + " 0.0063559, 0.0074153, 0.0084746, 0.045198, 0.081921, 0.11864, 0.15537,\n", + " 0.19209, 0.22881, 0.26554, 0.30226, 0.33898, 0.30226, 0.26554, 0.22881,\n", + " 0.19209, 0.15537, 0.11864, 0.081921, 0.045198, 0.0084746, 0.0077684,\n", + " 0.0070621, 0.0063559, 0.0056497, 0.0049435, 0.0042373, 0.0035311,\n", + " 0.0028249, 0.0021186, 0.0014124, 0.00070621, 0, -0.096045, -0.19209,\n", + " -0.28814, -0.073446, 0.14124, 0.35593, 0.57062, 0.78531, 1, 0.73729,\n", + " 0.47458, 0.21186, -0.050847, -0.31356, -0.57627, -0.83898, -0.55932,\n", + " -0.27966, 0, 0.00073692, 0.0014738, 0.0022108, 0.0029477, 0.0036846,\n", + " 0.0044215, 0.0051584, 0.0058954, 0.0066323, 0.0073692, 0.0081061, 0.008843,\n", + " 0.00958, 0.010317, 0.011054, 0.011791, 0.012528, 0.013265, 0.014001,\n", + " 0.014738, 0.015475, 0.016212, 0.016949, 0.03484, 0.052731, 0.070621,\n", + " 0.088512, 0.1064, 0.12429, 0.14218, 0.16008, 0.17797, 0.16186, 0.14576,\n", + " 0.12966, 0.11356, 0.097458, 0.081356, 0.065254, 0.049153, 0.033051,\n", + " 0.016949, 0.013559, 0.010169, 0.0067797, 0.0033898, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n", + "quickplt(ecg)\n", + "plt_polar(fft(ecg))\n", + "plt_rect(fft(ecg))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "Aw8a-DUZFS6m" + }, + "source": [ + "The plots of the ECG gives us the initial intuition that it's a rather low frequency signal (in fact we have the heartrate of somewhere between 50 to 500 Hz) with multiple face each priod. This is confirmed by the low-passed response, which looks surprisingly similar to the original in time domain" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 793 + }, + "colab_type": "code", + "id": "uTj33b3YF2Ij", + "outputId": "f1677908-82a9-47c3-cb40-f2cbbdf7068d" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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FjCbaGmZzTbln0El9QCRuJ7sktFm02+Il2vL9rk7drthQ51dN/k8IcAadrDdec7xXXwJuynXYOh/X6B/j6H/CeMm3Hp+6XajNNaHOoJMzGASSqgQs1w31uDXTqRxHS1UeVfmfPf5mp3JeiW3yec2gU8jsOZlq5bmCgc6NaEot8HEKgDfPfivsLIgP0mP89BeXd9nmt8++2+l1JQb5dpaIzhlzaGbTzKzRzBobGhoyvj/7E6850843m1JBdNhEOqvELpS+z6DTPhJf6s2IXO8pNVEJRa7j1qkmH2xWRHxXTB+pSqzJ+zaDTrbuRrk+uEbvc1OuK7C4tcmL29rarFMXyFufXlbwPortQunLsAbeDDonABhIciWAa5GYMed+bzad5QC+5kda6XI31wSRqoTNYtomL276xu3z8GKGgecKUWw59yXIl2sGnUyf8YEFK/1MQhzx/Dvrws6CSN5KDfBAZTbX+CbbjdfXckz4rOYaN+U6bN+9+5WObR1vlZ/5evdjiIskbWluKep9TgT5pCcWf4wRVz2KNSkD7eeiGB9dyWP7+KJEuVi7Kf9yUUkuv/fVsLMgDihkMLNUTgT5ZEX+3pdXAAAWf7Qp7/cqxrupkNr5XXM/BAC8+fHmoLJT0TS2fGVav6UZzS2tvu1vTZGVGCeCfFL7bCpeFS6fk1r95N2Uz2FbtyVRs0mWh3yeIvQLyQkk3yK5jGTRQ3b4YfQ1j8HMih5vXIJxxA1zcElKs2Kp1m6KcE0+KX2SnL/n0Zapcu+mwoYa7phQoxxIVgP4NYDTARwI4BySB5Yn9cxGTp2Ffa+ehRWfbMP9L6/Atp3Ftd+KP5J//zlL12L6Pz8oah+11Z0L9Afrtxa1HzdmhmLyZ+KXgm6mKshHXrL/cBkr8uMALDOz9xLpcgYSYzUtKWQnm3bswrUPL/Y1Y8f9v2cAAFc+uBBk4sty/Jg9UVcT/hDF2U7brOuynMTZ31dcetne2d37dra24d21W/BRhvuF18705xiv9Cb/LpQTQT4p2VxTWIxXlHdRYRN5J36WsblmCIAVKa9XAjgyfSOSUwBMAYDhw4d32UnvuhrMWbomoCx2/F2Wrt6EnnXVRT1l6bdshyjbQ4/FHtps4+9n22XWfGZY17yrLWOAL8Wu1s5nwWPfO66o/TgV5NE+jnz+IUBN8m4q5BiH0SafDzObBmAaADQ2Nnb5QFVVxOHD++N/384+MF8+xo8ZhDlLEyOHvPKjU9Cjtgo9a6vR2maoqXaqVdZpu1rbsHz9Vsx4aQUmjN0LX/3di77tu9gJY5w4+skP13HjNf/3qp+8mwo5aq3tQT6YvGSwCsCwlNdDvWUFGztkd18ydPsFn8Mhw/oBAPr2rEWvuhqQVIAvs9rqKowa1Ac/PPNANI4YgJeuPhlLrj8t1Dw5VQKSX2SFNMEoxEdf8ku/jBX5lwGMJjmSZB2As5EYq6lg+wzYzbdM/fnCcfj7pceiuozfdpLdoN17oFddDeZd7evD/wVxqrkmddq/fKki76iCGuUTP8o1/6mZtZC8FMBsANUA/mBmRd1d679bnW/56turFgf36uvb/sQ/e+7eI7S0nQryVd51RzHd68QthVyttYbQJm9mswDMKnU//XvV+pAbibopn9+36Pe61VyD3F0o04O6Qnz0JcuDi40UveqcqmdJSK4+Y0zR73UiyLdX0NKeeM0kfZUq8m4qpkmu0nrX5MOP9vO+PXU1IN1zqhrR/sRrAQ9AqJ+8m4o5ag7G+JJ7BL10zcmor6n2JzMSSW7U5L3wnryxli0ApNfyNayBm4q5AnMxyBdzs/ji4/dr/31Qnx6qyUtWTgT5pI4nXruPAC1pT4npxms05HMc49Jco6tTKYRjQT5xQqzbsrPbbVZt2NbptWK8m9ID2dad/g3ZWkmKaq5RmZYCOBHk2wcoy2Pb8bc8F2hepDzSv5z/84GF4WQkYOlXH8eM2qPLNt9O6z6nGB8NV5/xmbKk40SQb1dErUfDGkRDrmkeATev2tJbmKZfOK7LNlV6gjWSkl/wQbcyOhHkk3+Dv75S+PAgrbrz6qT0Nvia6txnwhm3Po975n0YVJYCkd4mn89YM7rPFA3lekLbiSBfiuaWNmzb2YKFK3PXBCVcZoZ5762HmaG5pfOUdtV5nhAPLFiRe6MKUszNYtVboiXoDgORD/I7drXi8ntfwxdv+wc27dgVdnYkiwdfWYWvT5uLma9/hB27Ot9o3ZznTPWuxb9izm9V5KMl6Pq8E0G+lC+6HbvasGD5JwC6dq+UyvKhN73ZB+u2danJ7zswv9EaXQuA+V6hpNJ9pmgo17SVTgT5Qkw8eHCn1ztaWjumhwsjQ5K3ZBtlq1mXmvyQ/j3z2odr4a+QS/WBvesBqE3edQcP6TxSaLYZsfzgRJAv5I+Q3r+6eVdrextmq06OipYMeG1thh27Otfkd6bV7Lvl2DEuJMgn78mqHLvtnn87Ek/+3893WT5+zKBA0nMiyBdia3PnGuDFd73SfnnbpjtWFS0ZxNrMcOfc5Z3Wbd4RzTb5qgLOwPYvQdc+pHTSp0ctRu/Zp8vy1DHnf3n2ob6lF7kgv3F715uryeYa1YAqW7I/eKbjlOm4ZuLaIc5Wk6+rrsIPTjugy7ZqromWjhnvOkw6dIhv+3ciyBdyY2LDtq5DHiTPCfWZr2zV7UGs67q8g7xjdflsQX7J9afhkhNHtb/u0yMxaGzveqcGj5Uc2oN8N0X36SuOL2n/TgT5Qqz4dHun14cM69deM9we0fFPoqCtzdCSvOLK8GX84SfbuizLvB9fsxW4bM016Q/LTDx4MH44cQy+f8oB3bxDXNRxzzFzlN+3oXdJ+49ckO8SIMzal53yi+fw5JI1IeRKcvnxzEW4efZbADIH+XyvwlzrXljIjdeqKuJbx+2LnnUaP95F//31Q/GNI4d3WZ6rJl+qwIM8yQkk3yK5jORVQaeXLj02PLZodfvvy9ZuQXOLavdh2LBtJz7a0HHVddfcjuEI4nTF5eLwyFKcyYcNwY1fOrj9dTKoB10CAm3cI1kN4NcATgGwEsDLJGea2ZIg0021emPn5pt31mzBGb98HuPHDMKtTy/D+Ufvg2u/cJAv07BJfna1tmHirS9g1YbtuOykUXh7zeZO6++bX/zQBI5V5LMONawSGQ/Mci/KD0HfwRkHYJmZvQcAJGcAmASgoCBfykA+6WPPv7FqIwBgyepNAIA/v7gcs95YjQlj9yq5a1olnpSVVlFc+el2PPtWU/vrXz29zNf9+3XjleRZAK4DMAbAODObn7JuKoCLALQCuNzMZpeQTok5Fdc5XZMHMARAarVsJYAjUzcgOQXAFAAYPrxre1U5rNuyE3979SP0qC2lrbPyqpCVWKvNdwyaYvn4mRcB+DKA36cuJHkggLMBHARgbwBzSO5vZiW3MfXv1XkaP8X/aGuvkDDttc9C74tlZtMATAOAxsbGjJ/Sz7J+3OiB+OoRQ/G9Ga8BAM47ah9cM3EM6muqVKsqg7Y2w/qtO/Gjvy3C44s/BgDMmHIUpv71Dby/bmvJ+/frNDGzpUDGmvYkADPMrBnA+ySXIXHF+mKxaV120ij0rq/B5MP86xst7nB9gLJVAIalvB7qLQvNDZPHYmj/XgCAQ4f1w08nj0WP2moF+DKpqiIa+tTjd+cd0b7sqH33wNcah2V5V/7K8KBQpqvTjNGZ5BSS80nOb2pqyrQJAOCKUw/At4/fr9MTj977fciuuMLV3jUvAxhNciTJOiQuc2cGnGZWNdVVGNw3cTL9y35dp1qT8hk9qKP/r1/DQBdyX4XkHJKLMvyf5EdezGyamTWaWWNDQ4Mfu5QIae9dE/CXeaDNNWbWQvJSALMBVAP4g5ktDjLNXGqriUF9euD5K0/E3v3yG9lQgvG3S47B1p2JNvph3tVVqValPQyXjZmNLyYJVNjVqURDev3k7m8dibqa0uvhgbfJm9ksALNK2Ycf3RuPGz0QFx+/Hwb1SdTihw3wJ6hI8Xarr8Fu3iP654wbhta2Nvzo4dLqADtb2/CPZetwzKiBfmQxk5kA7iF5CxI3XkcDeCmoxCT6unsYyq8y7MQTr5MPG4Ij9ulf0j7+5/zGIE98KRFJnHf0CPxw4piS9vP5/RswbuQAP/LzJZIrARwN4FGSswHAuxK9H4luwI8DuMSPnjUSX653ofRF3561OH3sXliw/NOi91GXxwTJEr6D9u6be6MsLj9pFGp9ONZm9hCAh7pZdyOAG0tOpATnH70Pjhype0pR0P4wVEBdKJ2JfKU8/v3IZce2D2Mrle3o/fbAJSfuV/T749Ij5fpJYzHxs4NzbygVKxnSq7KPT1YyZ4J8KeduQ596/zIigdurb343xIdnuK+i73JxT7ImHwxngnymmvxR++bX9hqTyl3sHDy0a9OOBvwSV3R0oQw2HYeCfNdlPfMchqBaJ75T8j1avTIcfwV5cU17a01AT0M5E+TTJwMBgPqa/IK8Tny35Hu4aqq7bqhDLa5RTd6z5KNNXZbV1+aXfd10dQvzrMtnqvhs36XejOKGZG8aqk0+of9udV2W1ef5NJjGindLvjWbTNtti9GEIxINqsl7rvvCgV2W5d9c43dupFIdpwfexFGuDlDmmz16d+0GmW9NXm3ybsn/aHXesn+vWjXNiXMC7ibvTpDPpCbPJxsV5N2S7+FK742Qb28rkUoy2Bsocf+UUVn95HSQzzcYqE3eLfneeN3Z2tbpdWkze4mUV7KO8rkRA/Dgd47Gd08cFUg6Tgf5fGO3Ynw0jRvR+WE4P4ZlrUSVOI2j+IcEjthnQHtltF/aNJClcmKAskymnv4ZbM1zvtC4jGcSGXkeroOH9sXgvj2weuOOYPMjUiZPX3E8+vXq2pOwFM4GeRJ68iWi8j2qBDvdb9GXubhu3wb/2+Wdvb7Nt91W3DM4zwHK0mO6SoS4yPWJvAND5vfHeeSyYwPPi/jr2NEDcc+/HZlzO7JzoFdFXqQrZ4N8vsYOKW0SCgnHv+yX+6Emggry4qygBiRL52yQJ6mTOuYSV3MpbfJqsBEHaViDbuh0lvR77/rSF5eUq2uss0G+iqq5xV36fRmVBnFR0HHM2SCv7nICsFM5UJkQFwU1gXeSs0G+il0vz79y+NBwMiOhCLJ3DcmbSb5JciHJh0j2S1k3leQykm+RPM2/VEX852yQz3RGl+tutVQGItAmmicBjDWzzwJ4G8BUACB5IICzARwEYAKA35DUoDlSNDXXdCPTCd6mIB8riR5WHaXAz9FGzewJM0uOmzEXQPIycRKAGWbWbGbvA1gGYJxvCYv4zN0gn+F8blWMj5X0L/oA60PfBPCY9/sQACtS1q30lnVBcgrJ+STnNzU1BZc7cVK5wpW7Y9egaz951eTjJb1NvvD3cw6AvTKsusbMHva2uQZAC4C7C92/mU0DMA0AGhsbVTglo6D7C7gb5DP8YdradB7FCb1/SYU215jZ+Kz7J/8VwJkATraOGz6rAAxL2Wyot0ykIOonn0PiQZjOJ3WrgnysdKnJ+9u7ZgKAKwF80cy2payaCeBskvUkRwIYDeAl/1KWuAm642+0avKK8eKf2wDUA3jSq0zMNbOLzWwxyfsBLEGiGecSM2stR4b0GIAUo6SaPMmzSC4m2UayMW1doH2JM3U7UhfKeEnU5FOba/zbt5mNMrNhZnao9//ilHU3mtl+ZnaAmT2WbT8i3Qn6IaikUmvyiwB8GcDvUxem9SXeG8Ackvv7WuPJWJNXkI8Tkmm9a1TVFQcFfIlWUk3ezJaa2VsZVgXel3hIv55d/jbpXSj32aOXn0lKhSGAzw7tGEpazRniktrqRPitCXgS6qBuvAbal/gvFx+NY0Z1HW88vXfNs/9xQp7ZlUp050XZ6wUk8JNJB+GKU/Zvfy3iim8eMxLfPGYkvnXcyEDTyRnkSc4huSjD/0l+ZMDMpplZo5k1NjQ05PWez40YkMhb2uX5yIG7pefdjyxKSKrTjt/uPTq3LhJEfU01Dh3er/21iCt61lXjx184EL3qgu3/kjPIm9l4Mxub4f/DWd4WSl/iayaOCToJKaP0L+k53z8+bX3iZ/JWjL7TRboKqrmmLH2J00/qHrUaJ8G/364AAAcaSURBVCpK0o/voN17dF7v/dQNd5HuldqF8kskVwI4GsCjJGcDgJktBpDsS/w4ytiXWKIj5xOsaavVPCfSVUmNQWb2EICHull3I4AbS9l/Ljqloy13jE9sYO2vRSSds8MaSPSl9iwbNah3l/UdbfLW6bWIdHA6yGc6qRf95DSce9RwDO7bo+tKccqoQX0AAD8/6xA8ctmxXdanH37FeJGunB27pju962tww+SDccPksHMiperbsxYf3DSx2/XJNviO3jUK8yLp3K7Jq+4Wax29azq/FpEOTgd5iTe1yYvk5lRzzbTzjsAzb61tf62TOt6SV3LHjW7AcaMH4uoz9DCcSDqngvypB+2FUw/KNFubxJL3Jd+zrhp3XnRkuHkRqVBqrhFnxeVKrlzjjks0KciLs2IS40VK4nSQV5e5eNPxF8nN6SAv8aYQL5Kb00FeJ3m8qSIvkpvTQV7iTQ/DieTmdJBXTS7edPxFcnM6yIsEheRPSS4k+RrJJ0ju7S0nyVtJLvPWHx52XkWycTrIqyIXbwHX5G82s8+a2aEAHgHwY2/56UjMdDYawBQAvw00FyIlcjrIS7wF2SZvZptSXu6GjrlJJgH4syXMBdCP5ODAMiJSIqeGNUinftLxFvThJ3kjgPMBbARword4CIAVKZut9JatzvD+KUjU9jF8+PBA8yrSncjU5L982JCwsyBl0K9XbfvvpcZ4knNILsrwfxIAmNk1ZjYMwN0ALi10/2Y2zcwazayxoaGhxNyKFCcSQf6cccPx87MOCTsbUgYLfnhK+++lXsmZ2XgzG5vh/8Npm94N4Cve76sADEtZN9RbJlKRnA7yyXO8poqoqlLTTRxUpxznII84ydEpLycBeNP7fSaA871eNkcB2GhmXZpqRCqF023ySRqlL54CbpO/ieQBANoALAdwsbd8FoAzACwDsA3AhX4nvFtdNbbubPV7txJTTgd51d3jLcgb72b2lW6WG4BLAksYwHNXnohNO1qCTEJixOkgn2SqyEuE7NG7Hnv0rg87GxIRTrfJ11ZXdfop8VAXs+Od/Lxx+9ziD6dr8l8+fCjeX7cVl540KuysSBn9/bJj8fw7TWFno2y+c8J+2NnShnOP2ifsrIiDnA7ydTVVmKrJm2PngL364IC9+oSdjbLpVVejci5F0/WfiEiEKciLiESYgryISIQpyIuIRFhJQZ7kzSTf9CZPeIhkv5R1U72JFd4ieVrpWRURkUKVWpN/EsBYM/ssgLcBTAUAkgcCOBvAQQAmAPgNyeoS0xIRkQKVFOTN7AkzSz5/PReJEfmAxIBOM8ys2czeR2Kcj3GlpCUiIoXzs03+mwAe837vbmIFEREpo5wPQ5GcA2CvDKuuSY67TfIaAC1IjLtdkNTZcwBsIflWN5sOBLCu0P2HSPkNVjH5De2R0QULFqwjubyb1XH424cpDvnttmznDPJmNj7bepL/CuBMACd7I/QBBUysYGbTAEzLlQ+S882sMdd2lUL5DZZr+TWzbqeGcu2zKL/B8ju/pfaumQDgSgBfNLNtKatmAjibZD3JkUjMbP9SKWmJiEjhSh275jYA9QCe9Mb2nmtmF5vZYpL3A1iCRDPOJWamWRBERMqspCBvZt0O/2hmNwK4sZT9p8nZpFNhlN9guZbfbFz7LMpvsHzNL00zboiIRJaGNRARiTAFeRGRCHMiyJOc4I2Bs4zkVWHnJxuSw0g+Q3IJycUkvxd2nvJBsprkqyQfCTsvuZDsR/IBb9ykpSSPDjtPxVC5Dp7KtQNt8t6YN28DOAWJJ2dfBnCOmS0JNWPdIDkYwGAze4VkHwALAEyu1Pwmkfw+gEYAu5vZmWHnJxuS0wE8b2a3k6wD0MvMNoSdr0KoXJeHyrUbNflxAJaZ2XtmthPADCTGxqlIZrbazF7xft8MYCkqfEgHkkMBTARwe9h5yYVkXwCfB3AHAJjZTtcCvEflOmAq1wkuBHlnx8EhOQLAYQDmhZuTnP4biYfa2sLOSB5GAmgC8EfvMvx2kruFnakiqFwHT+UabgR5J5HsDeBBAP9uZpvCzk93SJ4JYK2ZLQg7L3mqAXA4gN+a2WEAtgKo6PbsKFG5Dkxg5dqFIJ/3ODiVgmQtEifC3Wb217Dzk8MxAL5I8gMkmgxOInlXuFnKaiWAlWaWrEU+gMTJ4RqV62CpXHtcCPIvAxhNcqR3M+JsJMbGqUhMjO9wB4ClZnZL2PnJxcymmtlQMxuBxN/2aTM7N+RsdcvMPgawguQB3qKTkRg+wzUq1wFSue5Q6tg1gTOzFpKXApgNoBrAH8xsccjZyuYYAOcBeIPka96yq81sVoh5iprLANztBcf3AFwYcn4KpnItGQRSriu+C6WIiBTPheYaEREpkoK8iEiEKciLiESYgryISIQpyIuIRJiCvIhIhCnIi4hE2P8HL7ZGLsKBF0kAAAAASUVORK5CYII=\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ecglf = np.convolve(ecg, impulse_response)\n", + "quickplt(ecglf)\n", + "plt_polar(fft(ecglf))\n", + "plt_rect(fft(ecglf))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "EmUprtsbGVdT" + }, + "source": [ + "Just for fun, we add some high frequency noise to the signal (because heartbeats are repetitive and boring!):" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 513 + }, + "colab_type": "code", + "id": "UEQt8JUpGjdB", + "outputId": "8166fb68-294d-4e35-b2db-bcfeb1d3535f" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "real, imag = np.random.random((2, len(ecg)-len(high_pass)+1))\n", + "whitenoise = ifft(real + imag*1j)\n", + "noise_hf = abs(np.convolve(whitenoise, high_pass))\n", + "quickplt(noise_hf)\n", + "noisy_ecg = ecg + noise_hf\n", + "quickplt(noisy_ecg)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "1BHX-N2qG_Cx" + }, + "source": [ + "To smoothen the noisy signal back to normal, the low pass filter shoud be able to does the job:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "colab_type": "code", + "id": "7TpUggulHG0b", + "outputId": "bbdd7926-b39d-4344-fe4e-9af6531f9aa7" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "recovered_ecg = np.convolve(noisy_ecg, impulse_response)\n", + "quickplt(recovered_ecg)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "0G7413ANVjDq" + }, + "source": [ + "## Bonus" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "pwceV47wVoNB" + }, + "source": [ + "In this section, we'll try to have some fun playing the signals\n", + "using [palace](https://pypi.org/project/palace/). While the main purpose\n", + "of palace is positional audio rendering and environmental effect,\n", + "it also provide a handy decoder base class, which can be easily derived:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 124 + }, + "colab_type": "code", + "id": "Q5rVNQDeKMbQ", + "outputId": "b5f12c91-391b-427b-c73c-83cc2c3eea6a", + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Defaulting to user installation because normal site-packages is not writeable\n", + "Requirement already satisfied: palace in /home/cnx/.local/lib/python3.8/site-packages (0.2.0)\n" + ] + } + ], + "source": [ + "!pip install palace\n", + "from palace import BaseDecoder, Buffer, Context, Device\n", + "\n", + "\n", + "class Dec(BaseDecoder):\n", + " \"\"\"Generator of elementary signals.\"\"\"\n", + " def __init__(self, content):\n", + " self.content, self.size = content.copy(), len(content)\n", + "\n", + " @BaseDecoder.frequency.getter\n", + " def frequency(self) -> int: return int(sample_rate)\n", + "\n", + " @BaseDecoder.channel_config.getter\n", + " def channel_config(self) -> str:\n", + " return 'Mono'\n", + "\n", + " @BaseDecoder.sample_type.getter\n", + " def sample_type(self) -> str:\n", + " return '32-bit float'\n", + "\n", + " @BaseDecoder.length.getter\n", + " def length(self) -> int: return self.size\n", + "\n", + " def seek(self, pos: int) -> bool: return False\n", + "\n", + " @BaseDecoder.loop_points.getter\n", + " def loop_points(self): return 0, 0\n", + "\n", + " def read(self, count: int) -> bytes:\n", + " if count > len(self.content):\n", + " try:\n", + " return np.float32(self.content).tobytes()\n", + " finally:\n", + " self.content = []\n", + " data, self.content = self.content[:count], self.content[count:]\n", + " return np.float32(data).tobytes()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "cP3jOX1IlQvc" + }, + "source": [ + "The input and output signals can then be played by running:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 271 + }, + "colab_type": "code", + "id": "vbgVYiGelOft", + "outputId": "91bc61f4-baaf-4ecb-e4c2-315dc661e33a" + }, + "outputs": [], + "source": [ + "from time import sleep\n", + "\n", + "with Device() as d, Context(d) as c:\n", + " with Buffer.from_decoder(Dec(input_1kHz_15kHz), 'input') as b, b.play() as s:\n", + " sleep(1)\n", + " with Buffer.from_decoder(Dec(output), 'lf') as b, b.play() as s:\n", + " sleep(1)\n", + " with Buffer.from_decoder(Dec(outputhf), 'hf') as b, b.play() as s:\n", + " sleep(1)" + ] + } + ], + "metadata": { + "colab": { + "collapsed_sections": [], + "name": "dsp.ipynb", + "provenance": [], + "toc_visible": true + }, + "kernelspec": { + "display_name": "Python 3", + "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": "3.8.3rc1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/usth/ICT2.9/filters.ipynb b/usth/ICT2.9/filters.ipynb new file mode 100644 index 0000000..dd6e41a --- /dev/null +++ b/usth/ICT2.9/filters.ipynb @@ -0,0 +1,812 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "Untitled0.ipynb", + "provenance": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "RsxAag6zVgGa", + "colab_type": "text" + }, + "source": [ + "# Filter Design" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "S-FLJ4AAY14k", + "colab_type": "text" + }, + "source": [ + "## The preparation" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "mvme4rlMVkNV", + "colab_type": "text" + }, + "source": [ + "First, we load a sample sound as an example for later experiments:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "FT2qT4zdVMxC", + "colab_type": "code", + "colab": {} + }, + "source": [ + "import wave\n", + "\n", + "import numpy as np\n", + "\n", + "with wave.open('blue-ocean-floor.wav', 'r') as wav:\n", + " frame_rate, sample_width = wav.getframerate(), wav.getsampwidth()\n", + " ocean = (lambda a: a/ a.max())(np.frombuffer(\n", + " wav.readframes(wav.getnframes()), dtype=f'i{sample_width}'))" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "5_47f9h6WcCM", + "colab_type": "text" + }, + "source": [ + "Then for convenience purposes, we define a few `matplotlib` wrappers:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "0dkqk-_9WsOq", + "colab_type": "code", + "colab": {} + }, + "source": [ + "from math import pi\n", + "\n", + "import matplotlib.pyplot as plt\n", + "from numpy.fft import fft\n", + "\n", + "\n", + "def plt_time(sequence):\n", + " \"\"\"Plot the signal in time domain.\"\"\"\n", + " length = len(sequence)\n", + " plt.plot(np.linspace(0, length/frame_rate, length), sequence)\n", + " plt.show()\n", + "\n", + "\n", + "def plt_fft(sequence):\n", + " \"\"\"Plot the magnitude of the FT of the signal.\"\"\"\n", + " domain = np.linspace(0, pi*2, len(sequence))\n", + " plt.plot(domain, np.abs(fft(sequence)))\n", + " plt.show()\n", + "\n", + "\n", + "def plt_db(sequence):\n", + " \"\"\"Plot the FT of the signal in dB.\"\"\"\n", + " domain = np.linspace(0, pi*2, len(sequence))\n", + " FT = fft(sequence)\n", + " plt.plot(domain, 20 * np.log10(np.abs(FT/abs(FT).max())))\n", + " plt.show()" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "hzFZU7lxXlrk", + "colab_type": "text" + }, + "source": [ + "The sample audio's waveform can then be visualized using" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "-dMPhzl6Xw5R", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 513 + }, + "outputId": "593f98e0-f1d3-4c93-e385-aa8988020276" + }, + "source": [ + "plt_time(ocean)\n", + "plt_fft(ocean)" + ], + "execution_count": 61, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Euu6xt44YRG0", + "colab_type": "text" + }, + "source": [ + "It is completely normal that the audio is mainly low frequency, given the `frame_rate` of 44100 Hz, while vocal is around 300 to 1000 Hz and we can usually hear only up to around 10000 Hz." + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "g_psAgGiYuMN", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + }, + "outputId": "9cda3d29-6fa2-444c-e227-162ff6a0ea30" + }, + "source": [ + "print(frame_rate)" + ], + "execution_count": 9, + "outputs": [ + { + "output_type": "stream", + "text": [ + "44100\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "DiWkQgwXY-Am", + "colab_type": "text" + }, + "source": [ + "## The sinc function" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zO-UY4-6ZLAx", + "colab_type": "text" + }, + "source": [ + "The ideal low pass filter has the impulse response of `h[n] = sin(w*n) / (pi*n)` which pass frequencies from 0 to `limit = w/pi * frame_rate` hertz. For the ease of calculation, we define `r = w/pi` and get `h[n] = sin(pi*n*r) / (pi*n*r/r) = sinc(n*r) * r`. We then define our own `sinc` sampler as" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "JU9Ra87canaJ", + "colab_type": "code", + "colab": {} + }, + "source": [ + "def sinc(limit, length=101):\n", + " \"\"\"Return the impulse response of the low-pass filter passing\n", + " frequencies up to limit herts, sampled to the given length.\n", + " \"\"\"\n", + " absolute = length >> 1\n", + " n = np.arange(-absolute, absolute+1)\n", + " r = limit / frame_rate\n", + " return np.sinc(n*r) * r" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VGEAxTCxbOw1", + "colab_type": "text" + }, + "source": [ + "Just to be sure, we plot a filter passing up to 420 Hz:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "GiIuofwLbsHG", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 513 + }, + "outputId": "d0847d62-cc59-4004-d7bd-4bf3678d55ca" + }, + "source": [ + "plt_fft(sinc(3000))\n", + "plt_db(sinc(3000))" + ], + "execution_count": 85, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "WR0SOl2veOiO", + "colab_type": "text" + }, + "source": [ + "In order to have something for the later filters to compare with, we apply it to the input:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "yR-2V36OeXtU", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 513 + }, + "outputId": "dc55207b-2fb5-4ae7-fe4d-bd60a34512dd" + }, + "source": [ + "output_sinc = np.convolve(ocean, sinc(3000))\n", + "plt_time(output_sinc)\n", + "plt_fft(output_sinc)" + ], + "execution_count": 63, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Z7PKrdjdb9Xu", + "colab_type": "text" + }, + "source": [ + "## The FIR windows" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "brssPyVncKdx", + "colab_type": "text" + }, + "source": [ + "As seen from above, the low-pass filter sampled from `sinc` isn't ideal: there's quite some visible passband ripple and this could distort our output. Luckily we can improve this by multiply the impulse response with a window, whose functions are provided by `scipy`!" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "6nv8Ickhcwbt", + "colab_type": "code", + "colab": {} + }, + "source": [ + "from scipy.signal import windows\n", + "\n", + "\n", + "def fir(limit, window, length=101):\n", + " \"\"\"Return a low-pass filter using the specified windowing technique.\"\"\"\n", + " return getattr(windows, window)(length) * sinc(limit, length)" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "1poaLOrZdJUl", + "colab_type": "text" + }, + "source": [ + "We first try the Bartlett window:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab_type": "code", + "outputId": "ec91de0d-e007-4d83-84b4-50a63450d4ff", + "id": "Itc6VElKhW9g", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 513 + } + }, + "source": [ + "bartlett = fir(3000, 'bartlett')\n", + "plt_fft(bartlett)\n", + "plt_db(bartlett)" + ], + "execution_count": 89, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "A9qPm8wAiEDc", + "colab_type": "text" + }, + "source": [ + "Considering only the plot in dB, this seems to be worse than the vanila sinc samples. Next, we try the Hamming window:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab_type": "code", + "outputId": "8736f38d-4965-4f3c-ab02-1a36902cdd25", + "id": "R4Cp5Ya_iUyr", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 513 + } + }, + "source": [ + "hamming = fir(3000, 'hamming')\n", + "plt_fft(hamming)\n", + "plt_db(hamming)" + ], + "execution_count": 90, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "WuYjHCFOihPf", + "colab_type": "text" + }, + "source": [ + "The Hamming window seems to provide a smoother filter (i.e. almost no ramples); other than that it's quite equivalent to the original filter." + ] + }, + { + "cell_type": "code", + "metadata": { + "colab_type": "code", + "outputId": "b5f2cd8a-2055-4650-a08f-9c4917ed4133", + "id": "DflFR72-i582", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 513 + } + }, + "source": [ + "blackman = fir(3000, 'blackman')\n", + "plt_fft(blackman)\n", + "plt_db(blackman)" + ], + "execution_count": 91, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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thcSVmFmVnZ3rZoxH6DmaGB0G4IwD3cxydLrZBmDr2HCyGiof6P0fbv+HbWaWhzMO9Pw50M2sCB6hF2DLaB3JgW5m+TrdbDNUE+O9ebsUKh/otZrYMlJf+uuQmVkeTjfbTIzWkZSshsoHOsDE2LBH6GaWq9PNNhMJ2y2wQQJ9qwPdzHJ2utlO2j8HB7qZWSbOtBzohXCgm1ne3HIpyNaxYU+KmlmuzrjlUgyP0M0sTxExOD10SQckvSBpRtK9F3j/45KOSPqypL+Q9I7sS127ibFh5hYWvUCXmeWi2e7Q7kT5A13SEPAAcCuwD7hL0r7zDnsGmIqIHwQ+C/yHrAtdj/4P2W0XM8tDGe4ShZWN0G8EZiLiaETMAw8Bty8/ICIei4g3ek+fAHZlW+b6+PZ/M8vTIAX6TuDlZc+P9V67mI8A/+NCb0i6W9K0pOmTJ0+uvMp1mnCgm1mOTr/RzZb+6q6pZDopKunDwBTwaxd6PyIejIipiJianJzM8tRvyyN0M8tTWUboK1lF5jiwe9nzXb3X3kTSjwH/BnhfRMxlU142HOhmlqf+fgupA30lI/SngGslXSWpAdwJHFx+gKT9wG8Dt0XEiezLXB8HupnlqSwj9EsGekQsAPcAjwLPAw9HxHOS7pd0W++wXwPGgT+S9Kykgxf5uCQmRrt/EXGgm1keTjfbSN3lulNa0dkj4hBw6LzX7lv2+McyritT9aEa4yN1B7qZ5eJMs82WkTq1Wrqlc2GD3CkK/dv/va+omWXvdLPN1k1p2y2wgQLda6KbWV7KcNs/bKRAH/WuRWaWj+5uRQ70wniBLjPLi0foBXOgm1leyrB0LjjQzczWzSP0gm0dG6bZ7jC/sJi6FDOrkFa7w9zCYvLdimAjBfom3y1qZtk7U5K7RGEjBbpv/zezHJTltn/YQIHuJXTNLA8O9ASWdi1qOdDNLDsO9AT6F/375iIzy1I/0D0pWiD30M0sDx6hJ7AU6G840M0sO/1F/yYSL50LGyjQG/UaY8NDHqGbWaZON9uMj9SpD6WP0/QVFMh3i5pZ1spylyg40M3M1uV0s12KCVFwoJuZrUt3Ya70/XPYYIHuTS7MLGtuuSQyMeZNLswsW2XZ3AI2WKC75WJmWfMIPZGtY8O8Pt9hoeMldM1s/eYXFmm2Ow70FM6t57KQuBIzq4L+2lD95blT25CB7raLmWWhTLf9gwPdzGzNyrQwF2ywQN+xdQyAF759JnElZlYFL3x7FoDv62VLahsq0N+9Ywt7t23ikWdeSV2KmVXAI88c552Tm3nXleOpSwE2WKBL4o79O3niG6/yynebqcsxswF2/LtNnvzGd/jQ9TuRlLocYIMFOsAd1+8kAg5+yaN0M1u7zz97HIDbr9+ZuJJzNlyg792+mf17LuORZ46nLsXMBlRE8LkvHmfqHd/Dnm2bUpezZMMFOsCH9u/kq9+e5flveXLUzFbvyLfO8PUTZ7ljf3lG57DCQJd0QNILkmYk3XuB90ck/bfe+09K2pt1oVn64A/soF4TjzzrUbqZrd4jzxxneEh88Ad2pC7lTS4Z6JKGgAeAW4F9wF2S9p132EeA1yLiGuA3gF/NutAsbRsf4X3vmuTzz7zC4mKkLsfMBkhnMfj8s69wy3VX8D2bG6nLeZOVLOJ7IzATEUcBJD0E3A4cWXbM7cAv9x5/FvjPkhQRpU3LO/bv5C++eoIf/JU/Z/PIEJsbdWq1csxUZ6Va38YGTWn/41+jxcXg9fkFXp/rcHZugQ+VrN0CKwv0ncDLy54fA/7OxY6JiAVJp4FtwKnlB0m6G7gbYM+ePWssORsH3vO9/MKB6zg5O8cbcx1en1+gvL9+Vi8q95+TDSJVaFghweZGnU0jQ1yxZZQP7LsydUlvUeg2GxHxIPAgwNTUVNLEGR6q8TO3XJOyBDOzTK1kUvQ4sHvZ81291y54jKQ6sBV4NYsCzcxsZVYS6E8B10q6SlIDuBM4eN4xB4F/2nv894G/LHP/3Mysii7Zcun1xO8BHgWGgE9HxHOS7gemI+Ig8Cng9yXNAN+hG/pmZlagFfXQI+IQcOi81+5b9rgF/INsSzMzs9XYkHeKmplVkQPdzKwiHOhmZhXhQDczqwilurpQ0kngm2v8x7dz3l2oA2jQv8Og1w+D/x1cf3opvsM7ImLyQm8kC/T1kDQdEVOp61iPQf8Og14/DP53cP3ple07uOViZlYRDnQzs4oY1EB/MHUBGRj07zDo9cPgfwfXn16pvsNA9tDNzOytBnWEbmZm53Ggm5lVxMAF+qU2rC47SZ+WdELSV1LXshaSdkt6TNIRSc9J+ljqmlZD0qik/yvpS736fyV1TWshaUjSM5L+NHUtayHpJUl/I+lZSdOp61kLSZdJ+qykr0p6XtJ7k9c0SD303obVXwM+QHcrvKeAuyLiyNv+gyUi6UeAs8DvRcR7UtezWpJ2ADsi4ouStgBPA3cMyv8HkgRsjoizkoaBvwY+FhFPJC5tVSR9HJgCJiLiJ1LXs1qSXgKmImJgbyyS9LvA/4mIT/b2itgUEd9NWdOgjdCXNqyOiHmgv2H1wIiIv6K7ZvxAiohvRcQXe49ngefp7ik7EKLrbO/pcO/P4IxqAEm7gA8Cn0xdy0YlaSvwI3T3giAi5lOHOQxeoF9ow+qBCZOqkbQX2A88mbaS1em1K54FTgD/MyIGqn7gPwK/ACymLmQdAvhzSU/3No8fNFcBJ4H/0mt9fVLS5tRFDVqgW0lIGgf+GPiXEXEmdT2rERGdiLie7v64N0oamNaXpJ8ATkTE06lrWaebI+IG4FbgZ3utyEFSB24Afisi9gOvA8nn9AYt0FeyYbXlrNd7/mPgDyLiT1LXs1a9vyI/BhxIXcsq3ATc1utBPwS8X9J/TVvS6kXE8d7/ngA+R7edOkiOAceW/e3us3QDPqlBC/SVbFhtOepNKn4KeD4ifj11PaslaVLSZb3HY3Qn2L+atqqVi4hfjIhdEbGX7r//fxkRH05c1qpI2tybUKfXpvh7wEBd9RUR3wZelnRd76UfBZJfGLCiPUXL4mIbVicua1UkfQa4Bdgu6RjwbyPiU2mrWpWbgH8M/E2vDw3wr3v7zg6CHcDv9q6YqgEPR8RAXvo3wK4EPtcdG1AH/jAi/ixtSWvyc8Af9AaXR4F/nriewbps0czMLm7QWi5mZnYRDnQzs4pwoJuZVYQD3cysIhzoZmYV4UA3M6sIB7qZWUX8f2sHnegqciGyAAAAAElFTkSuQmCC\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "sNmW3UPVjMNV", + "colab_type": "text" + }, + "source": [ + "The Blackman seems to provide a slightly better result, with the gain dropping noticiably faster in the transition bandwidth." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "kal1ldxbpxSh", + "colab_type": "text" + }, + "source": [ + "There is very little point ploting the output signal however, since the original is already too complicated for human eyes. Pretty much all we will see is very similar to that of the vanila sinc samples. Instead, we write the output to files and listen to them instead:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "LuJy6wpdqUAi", + "colab_type": "code", + "colab": {} + }, + "source": [ + "def write(signal, filename):\n", + " \"\"\"Write the given signal to the corresponding filename.\"\"\"\n", + " with wave.open(f'{filename}.wav', 'w') as wav:\n", + " wav.setnchannels(1)\n", + " wav.setsampwidth(sample_width)\n", + " wav.setframerate(frame_rate)\n", + " width = sample_width << 3\n", + " wav.writeframesraw(getattr(np, f'int{width}')(signal * 2**(width - 1)))\n", + "\n", + "\n", + "write(np.convolve(ocean, sinc(3000)), 'output_sinc')\n", + "write(np.convolve(ocean, bartlett), 'output_bartlett')\n", + "write(np.convolve(ocean, hamming), 'output_hamming')\n", + "write(np.convolve(ocean, blackman), 'output_blackman')" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "wIlx2i3Mqy2p", + "colab_type": "text" + }, + "source": [ + "After a quick listen, `output_{sinc,bartlett}` seems to have better soundstage than the other two, which means Hamming and Blackman does better jobs filtering *away* high frequencies. `output_hamming` seems to be the most *dull* to me, which means it's the best filtered one.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "3k6HmI3XsTAK", + "colab_type": "text" + }, + "source": [ + "## The IIR filters" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "6tBjWTKNwBKq", + "colab_type": "text" + }, + "source": [ + "In this section, we are going to examine a few IIR filters. Before we start, let's define a thin wrapper for convenience:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "ez0jOaiawNfc", + "colab_type": "code", + "colab": {} + }, + "source": [ + "from scipy import signal\n", + "\n", + "\n", + "def iir(limit, design, order=4):\n", + " \"\"\"Return the specified IIR filter.\"\"\"\n", + " if design == 'cheby1': return signal.cheby1(order, 1, limit/frame_rate)\n", + " return getattr(signal, design)(order, limit/frame_rate)\n", + "\n", + "\n", + "def plt_iir(b, a):\n", + " \"\"\"Plot the given IIR filter in linear as well as log (dB) magnitude.\"\"\"\n", + " w, h = signal.freqz(b, a)\n", + " plt.plot(w, abs(h))\n", + " plt.show()\n", + " plt.plot(w, 20*np.log10(abs(h)))\n", + " plt.show()\n", + "\n", + "\n", + "def apply_iir(data, b, a):\n", + " \"\"\"Apply the given IIR filter to data.\"\"\"\n", + " return signal.lfilter(b, a, data)" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "iuTzduyKz7EG", + "colab_type": "text" + }, + "source": [ + "We can then respectively plot the Chebyshev, Butterworth and Bessel filters in frequency domain:\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "yYawU_7G0B_x", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "outputId": "29933810-3ae2-4ae2-87da-7a858784009e" + }, + "source": [ + "cheby1 = iir(3000, 'cheby1')\n", + "plt_iir(*cheby1)" + ], + "execution_count": 108, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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Ok6w/pXl/1zbvZdh7jLyyJul5NFvCf7SupEf+gxnWlTQw2JV0qpjMPADc7u2qP25mZaNMT2WTncdUdq23O/+UmV2S7GLG4x1KuJLYludQvlgO49QPKb4czCxoZtuBOuAZ59yYyyBZeTRbwn+u+DlQ4Zy7HHiGs1sOMjNeJdZXyhXAA8DPklzPmMwsC/gx8BnnXEuy6zlfE9Sf8svBOdfvnFtFrGfjNWZ2abJrGmm2hP9s6Ep6wnlwzp1yznV7L79D7D7IfjKZ5ZSynHMtg7vzzrkngbCZFSa5rHOYWZhYcD7snPvJKE1SejlMVL9flgOAc64JeA5YN2JS0vNotoT/bOhKesJ5GHFc9n3Ejof6ySbgTu9qk2uAZudcbbKLmiwzWzB4XNbM1hD7/5NKGxB49X0X2O2c+8cxmqXscphM/am+HMysyMzyvOF0Yvc03zOiWdLzKGXv5HU+XOx2kPcAT3O2K+mdNqQraWL/oH5oZlV4XUknr+JzTXIe7jWz9wF9xObhrqQVPAoz+xGxKzEKzawG+CKxk104574FPEnsSpMqoAP4WHIqHd0k6v8A8Ekz6wM6iXVHnkobEABvBT4CvOEdcwb4c6AcfLEcJlN/qi+HEuD7ZhYktmJ6zDn3RKrlkbp3EBGZg2bLYR8RETkPCn8RkTlI4S8iMgf54oRvYWGhq6ioSHYZIiK+sm3btgY3xj18kxb+ZrYO+BqxK1u+45z7ylhtKyoqqKysnLHaRERmAzM7Mta0pBz28S6B+ibwTmAlcIeZrUxGLSIic1GytvzPdGIGYGaDnZjtmo4v6+sfoLtvgK7efrr6Bujs6aert5/O3n46e/oByEwLkZkWJDMSIj0Se04LBejs7aelq5fG9h4a23vISguxYkEO6ZHgdJQqIjIjkhX+o3UstXZoAzPbCGwEKC8vn9KX1Ld2c83f/pr+gcT+liE3PcwfXr+EP7rxAsJBnTMXEf9J2RO+zrkH8W52vHr16imld1ZaiLtvXEpaKEg0HCAtFCQtFCA9EiQ9HCQjEiI9EsA5aOvuo727n46ePjp6+unw9g4yIkGyo2HyM8PkZ6bR1NHD49tq+Idf7ePXe+r42oeupLwgI6HzLiIy3ZIV/jPSsVR6JMifvmNFoj+Wt1+ygCd2HOf+n7zBu77+Il9+/6WsX5VyPeKKiIwpWccsJtMRW0p7z+ULeeq+61mxIJv7HtnOnzy6ncb2nmSXJSIyKUkJf+/mBYOdmO0m1vHRzmTUEo/SeRk8svEa7rtlGT9//Ti3/N/neXTrUQYSfI5BRCTRfNGx2+rVq12qX+e/90Qr/+tnb7D18GlWLMjmc29fzq0XF5Nad4oUkbnEzLY551aPNk2XqiTI8gXZPLrxWv75Q6vo6u3nD39Qye9987956o1a+voHkl2eiMgw2vKfBn39A/zk1WM88Nx+qhs7WZgb5SPXVrDhLWXMy4wkuzwRmSPG2/JX+E+j/gHHr3ef5Hu/PcxvD5wiEgzwthXFvP+qRdy8vJhISDteIjJ9xgv/lL3OfzYIBoy3X7KAt1+ygL0nWnl0azWbXj/GL3eeIC8jzLsvK2HdpQtYu6RAKwIRmVHa8p9hff0DvFjVwE9fPcavdp2gq3eA7GiIt60o5raV87nxoiKyo+Fklykis4C2/FNIKBjg5uXF3Ly8mM6efl6qauCZXSfYvLuO/9p+nFDAuLI8j7deWMj1ywq5ojSPkLqQEJEE05Z/iugfcGw7cprn99bxUlUDbxxrxjnITguxdmkBb72wgLdU5LNiQbZWBiIyKdry94FgwFizJJ81S/L5M+B0ew+/O3iKF/c38FJVPZt3nwQgIxLkyvI8Vi/OZ3XFPK4sn0dWmhajiJwfbfn7xLGmTioPN7LtyGm2Hj7NnhMtOAcBg2XF2VxWmssVpblcVprHigXZRMPqclpkrtOlnrNQS1cvrx1tYtvhRnYca2ZHTfOZvoVCAWP5gmwuL83lskV5rCjJZvn8bDK1hyAypyj85wDnHMebu3ijpokdNc284a0Qmjt7z7RZXJDB8vnZrCjJ4eIFsefy/AyCAXVBITIb6Zj/HGBmLMpLZ1FeOusuLQFiK4Sa053sOdHKntqW2POJFjbvPslg33PRcIDl87NZNj+bC4uzuKAoiwuKMinPz9CJZZFZTOE/i5kZZfkZlOVncNvK+WfGd/X2s/9kG3tOnF0hvLCvnse31ZxpEw4aFQWZsZVBcez5wuIslhZl6QSzyCyg/8VzUDQc5LLSXC4rzR02vqWrl4P17VTVtXGgvo0DdW3sq2vlmd0nh90Kc35OGhUFmVQUZLK4MIPF+ZksLsigojBTKwYRn9D/VDkjJxpmVVkeq8ryho3v6RvgaGPHmZXCwfp2jpxq59m9ddRXdg9rW5gVYXGBtzIY8lxRkEluhn65LJIqFP4yoUgowIXFscM+I7V193H0VAdHTrVz+MxzO787cIqfvDr8zpw50RCl8zIoy0+ndF4GpfPSh73WXoPIzNH/NolLVlqIlQtzWLkw55xpXb39VDd2cPhUB4cb2qk+3UHN6U4O1rfzwr4GOnv7h7XPywhTOi+dsiErhtJ56ZTlZ7AoL12XqookkP43ybSJhoMs864kGsk5R2N7D9WnO6nxVgrVjbHnfSdbeXZPHd19w2+Ck58ZoXReOgtz0ynJi7IoL52FeemU5MaGC7PSCOiyVZFJUfhLUpgZBVlpFGSlnXOOAWBgwNHQ3j1spVDjrSiq6tt4YX89HT3D9xzCQWNBbpSFuelnVwx5URZ6l8CW5EbVY6qIR+EvKSkQMIqzoxRnR7mqfN45051zNHf2crypi+NNnRxv7jwzXNvcyZZDjZxo6Rp2lRJAdjR0ZkWw0FtBLMyLrTAW5qWzIDdKWL9vkDlA4S++ZGbkZUTIy4iMer4BYvdOqG/r5nhTJ8eauqht6vRWFLGVxPbqJk539I74XCjKSjuzUijJHbGiyI3q8JLMCgp/mbVCwYAX3ulcvXj0Np09/d5ew+Cji9rmTmqbu9hzopXn9tSfc2I6HDTm50TPrAxKvOfY+YfYSiM3PYyZVhCSuuIKfzP7IPBXwMXAGudc5ZBp9wMfB/qBe51zT3vj1wFfA4LAd5xzX4mnBpF4pEeCXpcW517GCuceXqptju051Horisojpzmxo5a+EYeX0sPB2OEk7xDT4Eph6AoiI6JtL0meeP/1vQn8PvDtoSPNbCWwAbgEWAhsNrOLvMnfBG4DaoCtZrbJObcrzjpEpsVkDi8NDDga2ro51hTbYxi6B3G8uYu9J+qpb+tmZB+KuenhIXsPsRXE0PMR83OiurezTJu4wt85txsYbfd2PfCIc64bOGRmVcAab1qVc+6g975HvLYKf/GtQMAozolSnBPlyjHa9PQNcLJlcO+hy1tRdFLb1MXx5tgexNAeWOHs+YfBw0rD9x5iz0U6/yBTNF37nYuAl4e8rvHGAVSPGL92tA8ws43ARoDy8vJpKFFk5kRCgTOd7I2lo6fv7B7DiPMPe0+28vzec88/hAJnL289u/fgnaj2rmLKy9D5BznXhOFvZpuBBaNM+gvn3H8lvqQY59yDwIMQ689/ur5HJFVkREJjdqMBZ88/HGuK7TEMHlY67r3eduQ0J5pHP/8wuCIY3GMoy8+gPD/Wtcb87Kj2HuagCcPfOXfrFD73GFA25HWpN45xxovIOIaef7hkYe6obfq98w/Hxzj/sG9fPXWtwzvjiwQDLPK60Sg78xxbMZTnZ+jKpVlqug77bAL+w8z+kdgJ32XAK4ABy8xsCbHQ3wD8wTTVIDLnBAOxy1Dnj3P+obuvn2OnOzna2BHrXqOxg+rTHVQ3dvJ6ddM55x6y00KUDlkxlHuPxQWxw1j6UZw/xXup5/uBB4Ai4Bdmtt059w7n3E4ze4zYidw+4NPOuX7vPfcATxO71PMh59zOuOZARM5LWijI0qLYjXlG09LVS3VjbGVQc7qD6sYOjjZ2cLChnd/sqx/W51IwYJTOS2dJYazb7iWFmVQUZrK0MJOFeem6RWgK0z18RWTSnHPUt3VT3djBoYZYb62HTrVzqD7WlffQ/pYiwQBl+bEVw+BKYUlhJsuKsynMiuhQ0gzQPXxFJCHMzva5dPXi/GHTnHPUt3ZzqCG2IjjY0M7hhnYON3Tw4v6GYXsM8zLCLCvO5sL5WSwrzmJZcTbL5mdRnJ2mlcIMUfiLSEKYnf29w9qlBcOmDQw4TrR0caC+jaq6NvadbKOqrpVf7Kgddo4hOxoatjJYWZLDxSU5zMuMzPTszHoKfxGZdoGAnekc7/plRWfGO+doaOthf10rVXVt7D/Zxv66VjbvPsmjlWd/ErQwNxq7aVBJjvecS1l+uvYS4qDwF5GkMTOKstMoyk7jugsKh0071dbN7tpWdtU2s+t4C7tqW3h2Tx2DP2PITgtxcUkOlyzKYVVZHleWzdMK4TzohK+I+EZXbz/7Tray63gLO4+3sPN4M7tqW+jqjZ1PyM+MsKosjytK81hVnseq0jxyM+buDXx0wldEZoVoOMjlpXlcXnr27m99/QPsPdnK9uomth9tYnt1E8/trTvTkd5F87NYu6SAtUvzWbukgKLstCRVn1q05S8is05rVy87app57ehpXjl8mm2HG2n3LkNdWpTJ2iUFXLM0n+suKJzVK4PxtvwV/iIy6/X1D/Dm8Ra2HDzFlkONbD3USGt3HwCXLsrhpouKuWl5EavK8gjNol8sK/xFRIboH3DsOt7CC/vreX5vHa8ebaJ/wJETDXH9RUXcenExt1w8n5yov88XKPxFRMbR3NnLS/sbeH5vHb/xOr+LBANcv6yQd15Wwm0Xz/fliWOd8BURGUdueph3X17Cuy8vYWDA8Vp1E0+9UctTb57g13vqCAeNm5cX84GrS7l5RfGs6MxOW/4iImNwzrGjppkndhznp68dp6Gtm8KsCL+3ahEb1pSPee+FVKHDPiIicertH+CFffX8Z2UNv95zkt5+x40XFfGxt1Zww7KilLwhjsJfRCSBGtq6+dGWo/zw5SPUtXZzQVEmf/y2Zbz3ioUp1Y21wl9EZBr09A3w5Bu1fOs3B9hzopULijK579aLePdlJSmxEhgv/P1/1kJEJEkioQC/d+Uinrz3ev71w1cRDBj3/ug13vPAS2w93Jjs8sal8BcRiVMgYLzzshJ+ed8NfG3DKpo7evjgt37HZx/dTl1rV7LLG5XCX0QkQQIBY/2qRWz+3I18+uYLeGJHLW//pxd46o3aZJd2DoW/iEiCZURC/Ok7VvDkfddTnp/BJx9+lc899jqdQ25zmWwKfxGRaXJhcRY//uR13Pu2C/nJazV88Nu/pba5M9llAQp/EZFpFQ4G+Ozbl/Pdj67mcEMH733gv9lR05TsshT+IiIz4W0r5vPTT11HNBzgw/+2hW1HTie1nrjC38z+3sz2mNkOM/upmeUNmXa/mVWZ2V4ze8eQ8eu8cVVm9vl4vl9ExE+Wzc/msT+6loKsCHd+d0tS9wDi3fJ/BrjUOXc5sA+4H8DMVgIbgEuAdcC/mFnQzILAN4F3AiuBO7y2IiJzwsK8dB7ZeC15GRE+/v1KjjUl5xxAXOHvnPuVc67Pe/kyUOoNrwcecc51O+cOAVXAGu9R5Zw76JzrAR7x2oqIzBkLcqN872Nvoaunn49/b2tSrgJK5DH//wk85Q0vAqqHTKvxxo01/hxmttHMKs2ssr6+PoFliogk37L52Xzjw1ex92Qr/+cXu2b8+ycMfzPbbGZvjvJYP6TNXwB9wMOJKsw596BzbrVzbnVRUVGiPlZEJGXceFERG29YysNbjvL83roZ/e4Jb+binLt1vOlmdhfwHuAWd7aXuGNA2ZBmpd44xhkvIjLnfPa2i3hm10m+uGknT3+mgGg4OCPfG+/VPuuAPwPe55zrGDJpE7DBzNLMbAmwDHgF2AosM7MlZhYhdlJ4Uzw1iIj4WVooyF+vv5Qjpzr49/8+PGPfG+8x/28A2cAzZrbdzL4F4JzbCTwG7AJ+CXzaOdfvnRy+B3ga2A085rUVEZmz3nphITdeVMSDLxygvbtv4jckgPrzFxFJAa8ePc3v/8tvuf+dK/ijGy9IyGeqP38RkRR3Vfk81lzCb9AAAAbGSURBVC7J5+EtRxkYmP6NcoW/iEiK2LCmjKONHWw5NP03glH4i4ikiHdeWkJ2NMRjldUTN46Twl9EJEVEw0HefVkJz+w6SU/fwLR+l8JfRCSF3LZyPm3dfWw5dGpav0fhLyKSQq67oJBIMMBLVQ3T+j0KfxGRFJIeCXJFWS4vH5zek74KfxGRFLN2SQFvHmue1t4+Ff4iIinm0kW59A849pxombbvUPiLiKSYSxflAPDmcYW/iMicsSgvndz0MLtrFf4iInOGmVFRmMmRU+3T9h0KfxGRFLQ4P4MjpzombjhFCn8RkRS0uCCD402d0/ZLX4W/iEgKKs/PYMDBsabOafl8hb+ISAoqyU0HoL61e1o+X+EvIpKC5mWGAWhsV/iLiMwZ+ZkRABrbe6fl8xX+IiIpaF7GYPhry19EZM6IhoNkRoLa8hcRmWvysyLa8hcRmWvyMyI0dqTglr+Z/bWZ7TCz7Wb2KzNb6I03M/u6mVV5068a8p6Pmtl+7/HReGdARGS2ys+cvi1/c85N/c1mOc65Fm/4XmClc+5uM3sX8MfAu4C1wNecc2vNLB+oBFYDDtgGXO2cOz3e96xevdpVVlZOuU4RET9q6eolGgoSCU1tO93MtjnnVo82La4t/8Hg92QSC3SA9cAPXMzLQJ6ZlQDvAJ5xzjV6gf8MsC6eGkREZqucaHjKwT+RULwfYGZfBu4EmoGbvdGLgOohzWq8cWONH+1zNwIbAcrLy+MtU0REhphwlWJmm83szVEe6wGcc3/hnCsDHgbuSVRhzrkHnXOrnXOri4qKEvWxIiLCJLb8nXO3TvKzHgaeBL4IHAPKhkwr9cYdA24aMf75iT5427ZtDWZ2ZJJ1jKYQaIjj/cnm9/rB//Pg9/rB//Pg9/ph5udh8VgT4jrsY2bLnHP7vZfrgT3e8CbgHjN7hNgJ32bnXK2ZPQ38jZnN89q9Hbh/ou9xzsW16W9mlWOd9PADv9cP/p8Hv9cP/p8Hv9cPqTUP8R7z/4qZLQcGgCPA3d74J4ld6VMFdAAfA3DONZrZXwNbvXZfcs41xlmDiIicp7jC3zl3+xjjHfDpMaY9BDwUz/eKiEh85sovfB9MdgFx8nv94P958Hv94P958Hv9kELzENePvERExJ/mypa/iIgMofAXEZmDZk34m9k6M9vrdSb3+VGmp5nZo970LWZWMfNVjm8S83CXmdV7HeltN7NPJKPOsZjZQ2ZWZ2ZvjjF9zA7/UsEk6r/JzJqH/P2/MNM1TsTMyszsOTPbZWY7zey+Udqk7HKYZP0pvRzMLGpmr5jZ6948/O9R2iQ/j5xzvn8AQeAAsBSIAK8T62RuaJtPAd/yhjcAjya77inMw13AN5Jd6zjzcANwFfDmGNPfBTwFGHANsCXZNZ9n/TcBTyS7zgnmoQS4yhvOBvaN8u8oZZfDJOtP6eXg/V2zvOEwsAW4ZkSbpOfRbNnyXwNUOecOOud6gEeI/ehsqPXA973hx4FbzMxmsMaJTGYeUppz7gVgvN9tjNXhX0qYRP0pzzlX65x71RtuBXZzbv9ZKbscJll/SvP+rm3ey7D3GHllTdLzaLaE/2Q6jDvTxjnXR6wjuoIZqW5yJtvp3e3ervrjZlY2yvRUNumO/VLYtd7u/FNmdkmyixmPdyjhSmJbnkP5YjmMUz+k+HIws6CZbQfqiPVkPOYySFYezZbwnyt+DlQ45y4n1h329ydoL4n1KrDYOXcF8ADwsyTXMyYzywJ+DHzGDe963RcmqD/ll4Nzrt85t4pY/2VrzOzSZNc00mwJ/7E6khu1jZmFgFzg1IxUNzkTzoNz7pRzbvC2Pt8Brp6h2hJlMsspZTnnWgZ3551zTwJhMytMclnnMLMwseB82Dn3k1GapPRymKh+vywHAOdcE/Ac5963JOl5NFvCfyuwzMyWmFmE2AmUTSPabAIGbxv5AeBZ551tSRETzsOI47LvI3Y81E82AXd6V5tcg9fhX7KLmiwzWzB4XNbM1hD7/5NKGxB49X0X2O2c+8cxmqXscphM/am+HMysyMzyvOF04DbOdno5KOl5FPfNXFKBc67PzO4BniZ21cxDzrmdZvYloNI5t4nYP6gfmlkVsZN6G5JX8bkmOQ/3mtn7gD5i83BX0goehZn9iNiVGIVmVkOse+8wgHPuW4zR4V+qmET9HwA+aWZ9QCewIcU2IADeCnwEeMM75gzw50A5+GI5TKb+VF8OJcD3zSxIbMX0mHPuiVTLI3XvICIyB82Wwz4iInIeFP4iInOQwl9EZA5S+IuIzEEKfxGROUjhLyIyByn8RUTmoP8P3C/dVXI2ZQQAAAAASUVORK5CYII=\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "r2qImpDh1OIs", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "outputId": "17c3b88e-4e7a-432d-e6f2-8a3d0e7e0477" + }, + "source": [ + "butter = iir(3000, 'butter')\n", + "plt_iir(*butter)" + ], + "execution_count": 110, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "1ByMdegV1O9X", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "outputId": "523fc3e9-09b2-49ee-e626-e667fe3d7abf" + }, + "source": [ + "bessel = iir(3000, 'bessel')\n", + "plt_iir(*bessel)" + ], + "execution_count": 109, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zkPBz9lt1eTY", + "colab_type": "text" + }, + "source": [ + "We then apply these to the input a pay listen:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "YA0Z9AZP1kI8", + "colab_type": "code", + "colab": {} + }, + "source": [ + "write(apply_iir(ocean, *cheby1), 'output_chebyshev')\n", + "write(apply_iir(ocean, *butter), 'output_butterworth')\n", + "write(apply_iir(ocean, *bessel), 'output_bessel')" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "n5u3BNy-3Ys8", + "colab_type": "text" + }, + "source": [ + "As shown in the frequency domain, these filters are not as effective as the ones we discovered in FIR, at least using the configurations above. The outputs sound a lot clearer which indicates some higher frequency sounds excapes from the filters." + ] + } + ] +} \ No newline at end of file diff --git a/usth/ICT2.9/output_bartlett.wav b/usth/ICT2.9/output_bartlett.wav new file mode 100644 index 0000000..a3ae1ff --- /dev/null +++ b/usth/ICT2.9/output_bartlett.wav Binary files differdiff --git a/usth/ICT2.9/output_bessel.wav b/usth/ICT2.9/output_bessel.wav new file mode 100644 index 0000000..27f8e33 --- /dev/null +++ b/usth/ICT2.9/output_bessel.wav Binary files differdiff --git a/usth/ICT2.9/output_blackman.wav b/usth/ICT2.9/output_blackman.wav new file mode 100644 index 0000000..43cc293 --- /dev/null +++ b/usth/ICT2.9/output_blackman.wav Binary files differdiff --git a/usth/ICT2.9/output_butterworth.wav b/usth/ICT2.9/output_butterworth.wav new file mode 100644 index 0000000..7880779 --- /dev/null +++ b/usth/ICT2.9/output_butterworth.wav Binary files differdiff --git a/usth/ICT2.9/output_chebyshev.wav b/usth/ICT2.9/output_chebyshev.wav new file mode 100644 index 0000000..db55a6e --- /dev/null +++ b/usth/ICT2.9/output_chebyshev.wav Binary files differdiff --git a/usth/ICT2.9/output_hamming.wav b/usth/ICT2.9/output_hamming.wav new file mode 100644 index 0000000..0596d61 --- /dev/null +++ b/usth/ICT2.9/output_hamming.wav Binary files differdiff --git a/usth/ICT2.9/output_sinc.wav b/usth/ICT2.9/output_sinc.wav new file mode 100644 index 0000000..ee7a28e --- /dev/null +++ b/usth/ICT2.9/output_sinc.wav Binary files differ |