{ "cells": [ { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import scipy\n", "\n", "# Graphing helper function\n", "def setup_graph(title='', x_label='', y_label='', fig_size=None):\n", " fig = plt.figure()\n", " if fig_size != None:\n", " fig.set_size_inches(fig_size[0], fig_size[1])\n", " ax = fig.add_subplot(111)\n", " ax.set_title(title)\n", " ax.set_xlabel(x_label)\n", " ax.set_ylabel(y_label)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Wave Deconvolution - Multiplication and Addition\n", "\n", "* So a complex wave is made of simple waves.\n", "* How can you break a complex wave into it's simple component waves?\n", "\n", "### Answer: Multiplying a wave by another wave of frequency 100Hz cancels out all of the other component waves and leaves only the 100Hz component (kind of)." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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BublA+/a2IxE33QT8+9/+JqRvvQVcfbV/46WiUSNZJ+LnZBpFjyOXQnNcSriB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\nR8pKwpJw//WvwJYtwOefy6NBz+jRMsN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JNRSTJslFtlYt/8dOVvv2spbDRCtSLpikRGVn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\nHRJdAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, 3, 200)\n", "freq_1hz_amp_10 = 10 * np.sin(1 * 2*np.pi*t)\n", "freq_3hz_amp_5 = 5 * np.sin(3 * 2*np.pi*t)\n", "complex_wave = freq_1hz_amp_10 + freq_3hz_amp_5\n", "\n", "setup_graph(x_label='time (in seconds)', y_label='amplitude', title='original wave', fig_size=(12,6))\n", "_ = plt.plot(t, complex_wave)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Multiply complex wave by 1Hz wave" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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GdXfrb5NObIrmNwP4usXzPc/Ro+lFs0tfc5oazQDfNOWUbU7raT7nHPaEjY/r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\nUn3lmLZMU875MXQocORIaa1te/e6G0J1laf6FJrTTaFZodmbUkNzezt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "freq_1hz = np.sin(1 * 2*np.pi*t)\n", "setup_graph(x_label='time (in seconds)', y_label='amplitude', title='original wave * 1Hz wave', fig_size=(12,6))\n", "_ = plt.plot(t, complex_wave * freq_1hz)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "994.99999999999977" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum(complex_wave*freq_1hz)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Amplitude of 1hz component: 9.95\n" ] } ], "source": [ "print(\"Amplitude of 1hz component: \", sum(complex_wave*freq_1hz) * 2.0 * 1.0/len(complex_wave))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Multiply complex wave by 3Hz wave\n", "\n", "Notice that more of the graph is above the x-axis then below it." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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lq1aJ2JycrLdNIXDyJAwNZXNbQMS3D1GdNQ8PvSWqY3CqDx2S+8NilVsSeiVX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\nra+3As+tsiHW2i9Za38k7+9duCAXUF3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a4hHVrmfYYT4CcuWVMDo6yujoaOljZhXVbwP+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\nI1PNSabuhK6r5nKI7sSxLBsz1e6EfkPLSYrutGxp68SHHH+NfTdFgEG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4n+/fb294jx61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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "freq_3hz = np.sin(3 * 2*np.pi*t)\n", "setup_graph(x_label='time (in seconds)', y_label='amplitude', title='complex wave * 3Hz wave', fig_size=(12,6))\n", "_ = plt.plot(t, complex_wave * freq_3hz)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "497.5" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum(complex_wave*freq_3hz)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Amplitude of 3hz component: 4.975\n" ] } ], "source": [ "print(\"Amplitude of 3hz component: \", sum(complex_wave*freq_3hz) * 2.0/len(complex_wave))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Multiply complex wave by 2Hz wave\n", "\n", "Notice that an equal amount of the graph is above the x-axis as below it." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ZXFz0g3acNn8udiqhMGxs6Z6JGe6I7d4dTZaNbzyUrygC7sGDoy+9iOK1x5td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\no0ebHlF4YTPcDLgpCiYy3L4ZN06m269cyf25LCehqEycKO1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "freq_2hz = np.sin(2 * 2*np.pi*t) \n", "setup_graph(x_label='time (in seconds)', y_label='amplitude', title='complex wave * 2Hz wave', fig_size=(12,6))\n", "_ = plt.plot(t, complex_wave * freq_2hz)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.4549472737712679e-13" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum(complex_wave*freq_2hz)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Amplitude of 3hz component: 1.45494727377e-15\n" ] } ], "source": [ "# Very close to 0\n", "print(\"Amplitude of 3hz component: \", sum(complex_wave*freq_2hz) * 2.0/len(complex_wave))" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-5.0848214527832113e-14" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Same with 4Hz - close to 0\n", "freq_4hz = np.sin(4 * 2*np.pi*t) \n", "sum(complex_wave*freq_4hz)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# So how does this work?\n", "\n", "The summation of complex wave multiplied by simple wave of a given frequency leaves us with the \"power\" of that simple wave." ] } ], "metadata": { "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": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }