{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "I'm currently following a class on signal processing applied to audio on Coursera. It's awesome and I learned quite a number of things in it. In particular, I realized how important analysis windows are when working with sounds. This post will detail the properties in terms of main lobe size and side lobe level for commonly used windows, such as the rectangular (boxcar), hanning, hamming or blackman windows.\n", "\n", "\n", "This post is organized as follows:\n", "\n", "- using a hamming window, we go through the details of computing mainlobe width and sidelobe levels\n", "- we then do this calculation and graphical representation common windows\n", "- finally, we try to gain intuition of mainlobe width versus sidelobe level using concrete examples of signal analysis: \n", " - a single sinuisoid (using different windows)\n", " - analyzing two sinusoids with close frequencies \n", " - analyzing two sinuisoids with different frequencies and very different amplitudes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Window properties with a hamming window " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's do some imports." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import seaborn as sns; sns.set() # styling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our first step in this post is to define a \"time\" vector, with which we will define the hamming window we want to analyze." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "m = 513\n", "t = np.arange(m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using this time vector, we can define our window signal `w` using SciPy's `get_window` function (found in the `scipy.signal` module)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy.signal import get_window\n", "\n", "w = get_window('hamming', m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot this window:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-0.025, 1.025)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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9vZIH7yyib4BW24vEse0p1zu2gSzvjcBc4FVjzM3A7k6PlQLJxpjBHSexTQV+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\nzftPsnJLOZXV/ovtx5lMFk0frF3kIiJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t, w)\n", "plt.xlabel(\"(time) sample #\")\n", "plt.ylabel(\"amplitude\")\n", "plt.title(\"hamming window\")\n", "plt.xlim(0, m-1)\n", "plt.ylim(-0.025, 1.025)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We recognize the typical hamming window characteristic: it's tapered on both sides by a nonzero value." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now perform the FFT of this window. The signal is real, so we use the Fourier transform tools for real valued signals in the following analysis (`rfft` instead of `fft` for instance)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "w_fft = np.fft.rfft(w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the spectrum of the window (we ignore the phase and just plot its magnitude)." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "freqs = np.fft.rfftfreq(w.size, d=1/m)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(freqs, np.abs(w_fft))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Actually, we need to zoom this representation to be able to make sense of it." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0, 20)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(freqs, np.abs(w_fft))\n", "plt.xlim(0, 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly, we don't see a lot of things here. Fortunately, we can interpolate the spectrum by doing zero padding. The idea here is that this doesn't change the spectrum itself, it just computes more points of it, which makes it appear very smooth." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0, 20)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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yJheWNlhY2aC50WFts8Nma+tl6yyXCtSqRSZq/fVN1MpMjJeZrPd/TtTKVEoF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\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 4096\n", "w_fft = np.fft.rfft(w, n=4096)\n", "freqs = np.fft.rfftfreq(n, d=1/m)\n", "plt.plot(freqs, np.abs(w_fft))\n", "plt.xlim(0, 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In fact, it's even better to represent the previous plot using decibels on the vertical axis, as this is the commonly used unit in signal processing." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0, 20)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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TA0YGu7ojgDMjc0vKY/OxFDwN1m/Jvr7IOrc4CtVb5PUoR+znXrwePRtJIBxN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\nWN3hx2Xr5H6W3cv4d33N5g7E05lstimLuroJfau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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(freqs, 20*np.log10(np.abs(w_fft) / np.abs(w_fft).max()))\n", "plt.xlim(0, 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using this figure, we can appreciate the two main properties of filtering windows:\n", "\n", "- the main lobe width, which is the location where the mainlobe ends and \"dives down the y-axis\" the first time when starting from 0\n", "- side lobe level, which is the height of the oscillations that appear at the right of the mainlobe (here around -40 dB)\n", "\n", "The main lobe width will allow us to determine the spectral resolution of the signal we are analyzing. The sidelobes are \"noise\" that gets added to all frequency components and can hide other spectral peaks present. They are important when analyzing a signal with lots of peaks with different magnitudes.\n", "\n", "Let's now write a little bit of code to computes these two properties from the Fourier spectrum." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def compute_mainlobe_width(spectrum):\n", " \"\"\"\n", " computes mainlobe width from spectrum\n", " \n", " assumes the mainlobe starts at 0, that spectrum size is odd, and that \n", " the spectrum is real-valued (half of the frequencies)\n", " \n", " returns the number of samples of full mainlobe (not just half)\n", " \"\"\"\n", " abs_spectrum = np.abs(spectrum)\n", " current_value = abs_spectrum[0]\n", " for ind, next_value in enumerate(abs_spectrum):\n", " if next_value > current_value:\n", " break\n", " else:\n", " current_value = next_value \n", " return 2 * ind - 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's test this on the previously computed spectrum." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "33" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "compute_mainlobe_width(w_fft)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at the first $(33 - 1) / 2 + 1= 17$ samples of the spectrum to see if they end on a local minimum:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 2.76560000e+02, 2.73145445e+02, 2.63112161e+02,\n", " 2.47073148e+02, 2.25991449e+02, 2.01098528e+02,\n", " 1.73791853e+02, 1.45521952e+02, 1.17680000e+02,\n", " 9.14966227e+01, 6.79610733e+01, 4.77674316e+01,\n", " 3.12913805e+01, 1.85977221e+01, 9.47556072e+00,\n", " 3.49534175e+00, 8.00000000e-02])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.abs(w_fft)[:17]" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.4184820846613027" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.abs(w_fft)[17]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So indeed, our mainlobe computation works.\n", "\n", "Let's now move on to sidelobes. Using the mainlobe computation, we can quite simply take the maximum value outside of the mainlobe as the sidelobe level." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def compute_sidelobe_level(spectrum):\n", " \"\"\"\n", " computes sidelobe level from spectrum\n", "\n", " assumes the mainlobe starts at 0, that spectrum size is odd, and that \n", " the spectrum is real-valued (half of the frequencies)\n", " \n", " returns the level of sidelobes in dB \n", " \"\"\"\n", " mainlobe_width = compute_mainlobe_width(spectrum)\n", " \n", " ind = (mainlobe_width - 1) / 2\n", " \n", " abs_spectrum = np.abs(spectrum)\n", " \n", " return 20 * np.log10(abs_spectrum[ind:].max() / abs_spectrum.max())\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use this function on the previous spectrum. From the above plot, we expect the result to be a bit below -40 dB. " ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-42.680923568006968" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "compute_sidelobe_level(w_fft)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now complete the previous plot with lines to outline mainlobe width and sidelobe level:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/kappamaki/anaconda/lib/python3.4/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors == str('face'):\n" ] }, { "data": { "image/png": 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n2DZ0+Pn9D1yLy+ngwReGqt7fbpomX3zgGHPhBO9743b+9Ndu5CNv38UnP7SP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\nC/Z2MK/PqlFVEnG7nNa+WTv6WO4R5oR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(freqs, 20*np.log10(np.abs(w_fft) / np.abs(w_fft).max()))\n", "plt.xlim(0, 20)\n", "width = compute_mainlobe_width(w_fft)\n", "level = compute_sidelobe_level(w_fft)\n", "\n", "ylim_range = plt.ylim()\n", "plt.vlines((width - 1) / 2 * m / n, ylim_range[0], ylim_range[1], lw=3)\n", "xlim_range = plt.xlim()\n", "plt.hlines(level, xlim_range[0], xlim_range[1], lw=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With these functions in place, we can now perform this analysis for several windows" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Properties of common windows " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below, we reuse the code we have just developed and appy it to several common windows." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/kappamaki/anaconda/lib/python3.4/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors == str('face'):\n" ] }, { "data": { "image/png": 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KSUu+z0kphn3psD3/d3/+Y+A/lFJ/jqkZ+57W+jtOWmwQeI1S6pMYV+s1TurtG5gvHBuV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\nrkJggg==\n", 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4vD4A5AJpgIHVUiaiaMvBGjp7Brj52imkpUjrmK+i3DTWLCqlrrmbvbox2uGI\nOFOU607IuqMciRAiEiKZkGUzvHCi0+7GdLsf2AccBv6mtZZVnKNoYNDFc6+dJyUpgVtWyMzKQN68\nZqiVTMbyiPGUn20VhG2Vav1CxKRINoO0M7xwokNr7QJQSk0D/gGYDnQDv1NKvUtr/adgB4yVQnET\n8Tqe23mWts5+3r5xNpXT8kNuPxGv4UqM9jqKirLYsLyCzfsvcr65hxXzSyIU2ehiigWxch2Rkp2R\nDEB7V3+UIxFCREIkE7LtwFuAx5VSq4Eqr9dSASfQp7V2KaUasbovg4qVQnET7TqcLhePvaRJTHCw\nflFJyPgm4jVciSu9jo1Ly9i8/yJ/fOE40wvTIxBZ+GL9ZyFJ2pAcSciEiGmRTMieBG5VSm23H39U\nKXUXkKm1fkgp9Wtgh1KqFzgF/CqCsYgg9hxrpKmtlxuXV8TlmpWjNa0ki0WV+Rw+08Lp2nZmlmdH\nOyQRByQhEyK2RSwh01qbwKd8nj7h9fr3ge9H6vwiPKZp8tzu8xgGvGHVtGiHM2ncsWoah8+08Nzu\nc3z67YujHY6IA0mJCaSlJHC5ayDaoQghIkAKw8a54+daOd/YybWq2DOLS4Q2b3oe00uy2HeiiQaZ\n9SbGSXZ6Mu3d0kImRCyShCzOPb/nAgC3XyczK0fDMAzuWD0N04QXXrsQ7XBEnMjOSKajux8M+egW\nItbIb3Ucq73URVV1M7On5DCrXOryjta1qojCnFS2HaqTcT1iXGRnJGOakJwqkx2EiDWSkMWxF/ac\nB+D2lTJ27EokOBzcft00BgZdbNp3MdrhiDjgLn2RkhFyUroQYpKRhCxOXe7qZ8fhBopz01g+pzDa\n4Uxa6xaXkZmWxCsHaugfcEY7HBHjctLthCxdWrSFiDWSkMWpV/ZfZNDp4taVU3E4jGiHM2mlJCdw\nw7JyOnsG2HW0IdrhiBg31EKWF+VIhBBjTRKyONQ/4OTl/TVkpCaybnFZtMOZ9G5cXoHDMHhx7wVZ\nTklElCchS5cuSyFijSRkcWjnkXo6ewbYuLyClOSEaIcz6eVnp7JiXhE1TV0cP98W7XBEDAuUkJ2r\n76ClvTcaIQkhxkgkK/WLCcg0TTbtu0iCw+Cma6ZEO5yYccuKqbx2rJGX9l5g/nTpThIj3XfffXzz\nm9+8qmOk55Rw0z0Pkuw1hmz5DW9l2Rs+S19XG9t+fy+9nc1XG6oQYgyMtsdEWsjizIkLbVxs6uJa\nVUReliyoJsnAAAAgAElEQVSTNFZmlWdTWZbFwZOXaGzriXY4IkYN9lvvrcSkVAAyC6ay7PZ/xOUc\nJDUznxVv/TIgY0KFmIwkIYsz7vIM0jo2tgzD4JYVUzGBl6UEhogQzx23YSVdhVMXYzgSOLzpQepO\n7iS3dA65ZXOiGKEQ4kpJl2UcaWnvZf+JS0wtzmTOFJk2P9ZWzivmsZdPsbWqlretqyQtRX69xJD7\n7ruPz3zmi1d1jM6eAT77g62ex9nFMwH4v8d+y6XLvTzwpyr+/fuP8t6bIpeUFRVl0dTUEbHjjye5\nlokplq5lNKSFLI5sPliDyzS5+dopGIZ0a4y1xAQHNy6voKfPyY7D9dEOR8SBnOKZJCU6KCtIZ+GM\nfFKTE9inm2S2rxCTkCRkcWJg0MWWg7VkpCayakFJtMOJWRuXV5CYYLBp30X5oygiynAkklUwlSlF\nmSQ4HCQlOlg2u5BLl3s539AZ7fCEEKMkCVmc2Hu8kY7uAdYvLSclSUpdREp2RjIr5xVT39LN8XOt\n0Q5HxCjDMMgqmIojIYnpJZme5xdW5gNQXXs5WqEJIa6QJGRx4qV9FzGwipiKyLpxuTVh4pUDNVGO\nRMSaoZEGBjklswCYVjq00Pi0EutraSETYvKRhCwOnK5t50xdO0tnF1KUmxbtcGLerIpsphRlcuDk\nJdo6+6IdjohRGbnWKhvlBRme58oK0klMMLjQGH8DooWY7CQhiwMv77fKMNx8rZS6GA+GYXDjNRU4\nXSavvl4b7XBEDPGeimM4rI/vpMShj/HEBAcVhZlcbOrC6XKNc3RCiKshCVmM6+wZ4LVjjZTkpzN/\nhlSQHy+rF5SQkpzAloO18odRjCEjwNdDppZkMjDoor5FChQLMZlIQhbjth+qY9Dp4sZl5Tik1MW4\nSUtJZM3CUlo7+nj9lCxlI8aYYRAoIZtWbA3yv9Ag3ZZCTCaSkMUw0zTZcrCWxAQHaxaXRTucuOOe\nQCGD+2ODUmqeUqpNKZVsP16tlNqllNqmlPr6eMTg757K9zn3wP4LjTKwX4jJRBKyGKbPt1Hf0s3K\neUVkpiVFO5y4M6U4k9lTcjhypoWG1u5ohyOuglIqG7gf6PV6+ifAXVrrdcAqpdSy8YrHwPCbnAEU\n5ljrXDa39/rfQAgxIUlCFsM2H7RaZm5YJqUuouUmu5VsywEZ3D9ZKaUM4EHgX4Ee+7lsIEVrfcbe\n7HnglnELyvD+cnhmlpOZjGFAW4fM8BViMpHF9mJUe3c/+3QT5YUZsm5lFF2risnadJJth+p4+4ZK\nkhKlKO9EppS6B/icz9PngD9orauUUmClQ9lAu9c2HcDMSMc3vFXMfxNZgsNBdkYybZ39kQ5HCDGG\nJCGLUdsP1eF0mdywtFzWrYyipEQH65aU8eyu8+w53siaRTKWbyLTWj8MPOz9nFLqJHCPnayVYrWG\nvQXI8tosG2gLdfyioqxQmwTV0zdof2V4srO8vPQRxy3KTeN8fQeFhZkR+f2/2uuYSORaJqZYupZw\nSUIWg1z2YP6kRAdrFpdGO5y4t3FZBc/tOs/mA7WSkE1CWus57q+VUmeA27TW/UqpfqXUTOAMcBtw\nX6hjNTVd3czHvn7niOfa2rppShne8pqZmkT/oIuzF1rHfPxoUVHWVV/HRCHXMjHFyrWMNqmUMWQx\n6Pi5Vhpbe1g5r5iMVBnMH21FuWksrMznVM1lappk5tsk571i/CeBR4DdwH6t9Z7xCsIwfEeODZeX\nlQKMHEf2l62n+dGThzh1Uda6FGKikRayGLT5oDWAfKMM5p8wNiwt5/CZFrZW1fG+m+eE3kFMSFrr\nmV5f7wauH9cAwux9zLUTstbOPqbYdcnO1LXz1+1nAdh/oomvf2Ql00vjr1tIiIlKWshizOWufg6c\naKKiKINZFdnRDkfYls0pJCs9iR2H6xkYlMr9YgwEGRuWm5kMDLWQmabJnzZXA3DbyqmYJry070Lk\nYxRChE0SshizraoWp8tk47IKGcw/gSQmOFi7qIzOngEOnGyKdjhikvL8RntV6vf3e57n1UIG0Hy5\nl2PnWlkwI4/33DSb4rw0XjvWSGfPwDhELYQIhyRkMcRlWotZJyc6uH5hSbTDET7WL7UG9MuC4+JK\nhXuPlZc5fAxZzaUuANS0PByGwY3LKxgYdLH7aENE4hRCjJ4kZDHk2NlWmtp6uW5+CekymH/CKSvI\nYO6UHI6ebaWxTRZ+FldjqFK/vxzNM4bMTshqm62ErLwgA7C60AFO1cjgfiEmCknIYsjWKqvlZcOy\n8ihHIgJZv9T62WyrklYycSX8LWY58qn0lESSEx2e4rC1dgtZeWE6AMW5aWSkJnKmtn3kzkKIqJCE\nLEZ09gyw/8QlygrSmVUug/knqhXziklLSWRbVR1OlwzuF1fGKnoRuP/SMAxSkhPoH7TqltVe6ibB\nYVCcl+Z5vbI8m8a2Hjq6paK/EBOBJGQxYvfRBgadLtYvkcr8E1lKUgKrF5bQ1tnPoeqWaIcjJhl/\nSyeF+m03TZO65i5K89NJcAx95M8ss27cztRN/gKcQsSCiNUhU0o5gB8DS4A+4GNa62qv11cC92N9\nntQAH9Zay63aFdpaVYvDMLh+kVTmn+huWFrOK/trePX1Ws9YHiFGJYx7LvcmrR199PY7KSvMGPZ6\npScha2fJrIIxDlAIMVqRbCG7E0jWWq8BvoyVfAGglDKAnwF3a63XA5uAygjGEtPO1XdwvqGTpbML\nyMlIjnY4IoRpJVlML83i9epLnkHXQoyOMZRxBWkRN03vAf3pw16rtIc2nK2TcWRCTASRTMjWAs+B\np6L1Cq/X5gLNwBeUUpuBXK21jmAsMW3boToA1i2RdRIniw1LyzFNaxF4IcLlL/cKmI4ZBiZw2R7Y\nX5CdOuzl7PRk0lISudTeO6YxCiGuTFgJmVJqnVLqk0qpVKXUhjCPnQ1433o57W5MgEJgDfBD4Bbg\nZqXUjeEGLYYMDDrZdaSe7IxkFs+UbofJYvWCEpKTHLz6ei0u0wy9gxBerLUsg/dbul91v78cjpHb\n52en0NIurbRCTAQhx5AppT6H1f1YDjwB/Ewp9bDW+jshdm0HvBdKc2it3dPKmoFT7lYxpdRzWC1o\nrwQ74GhXTp+oxvI6th6soat3kHdsnE1Zac6YHTcU+VlcvfXLKti05wL1bX0snVt0xceRn0X88JeE\nBZ3DEyLZz8tKoaapi56+QdJShv4c7D/RxKuv11KQncqd6yvJSpehEEJEWjiD+u8GVgG7tNZNSqkV\nwB4gVEK2HXgL8LhSajVQ5fXaaSBTKTXLHui/Hvh5qECamib/bKCioqwxvY5ntp0G4JrZBeP2/Rnr\na4iWaF/HKlXMpj0X+OurpyjPSw29gx/RvoaxEug6JEkLItRsavfLQXKyfLuAbFtnnychG3S6+N0L\n2lPDLDHBwV23zLnaaIUQIYTTZenUWnu3afcCg2Hs9yTQq5TajjWg//NKqbuUUh+3Z1PeA/xeKfUa\ncF5r/exog493Le29HDnTwqyKbMp9ZlCJiW9WRTZlBensP3FJ1hQU4Rk2kD/0VEvvXMxf/paXZd0I\ntHhNLnntWANtnf3cuLyC/OwUthysob1LJsALEWnhtJBtUUrdj9WidSfw98DLoXbSWpvAp3yePuH1\n+itYLW/iCm0/VIcJrF8ilfknI8MwWLe4jMc3V7P7aAM3Xzsl2iGJSShQ3UEDwAzaQOZpIWvxGtj/\n4t6LGAbcsXoa5YUZPPLiCTbtu8jbN8wcu6CFECOE00J2L3ASeB34MPAM8MVIBiVCc5km2w7VkZzk\nYOW84miHI67Q9YtKcRiGZ6asEMF4Gsi81rIMuK3PBv7Gn+VlD1/zsm/Aybn6DuZOyaUwJ411i8tI\ncBgcOStFjIWItIAtZEqpaV4Pn7X/uZUD5yMVlAjtxPk2mtp6WbuodNhgXDG55GamsHhmPq9XN3Oh\nsZOpxZnRDklMYP5aw4KO6fduHwvSZelOyBpaugE8RWRTkhOYVpLJufoO+gecJCclXFngQoiQgrWQ\nPQM8DWwBqoH/w5pleQL4W+RDE8FsrZLaY7Fi3RL3guPSSibCZHj+E5IZZKblUJellZDV2wlZaf5Q\nEdlZFTk4XSZn6yf/5BEhJrKACZnWepHWejGwH1ijtV6mtV6BVZ7i7DjFJ/zo7h1kn26kOC+NuVNz\nox2OuEpLZxeQmZbEziP1DDplwXERJndrWZC8zPQaQ+Zvs7SURNJSEmjtsMaQ+UvI5kyxPmOqay5f\nbcRCiCDCGUM2V2v9mvuB1voQMDtyIYlQXjveQP+gi3WLy2Qh8RiQmOBgzaJSOnsGeP3UpWiHIyYF\nw89XPluE+dGQl5Xq6bL0JGReyyzNspdYOiUJmRARFc7go3NKqf8EHsVK4O4GjkYyKBHctqo6DAPW\nyELiMWPd4jJe2HOBbVV1XKtkkoYIzPD6b+jtCN5EBmSmJVF7yVrvsr65m8QEB4VeyyzlZ6eSl5XC\nGVnzUoiICqeF7ENYyyA9CvwO69f7o5EMSgRW09TJ6dp2FlUWkJ99ZcVExcQzpTiTGaVZVJ1upq1T\nlrIRQfgmViEWFx/aLUh5DKyxZvUt3ZTkpY1YZqk4N43Lnf0jutSbL/fy6EsnefCvRzgnY8yEuCoh\nW8i01q3AP45DLCIM7vII62Uwf8xZt6SMsy90sPNwPXesnh7tcMQEZhiBEyyvrYDgdcjcxwJo6+yn\nt99Jidf4Mbf87BRMrNmYZV4N809sqWbX0QbA6u782kdW4JBhFEJckXDWsvQ3yrhWay1VLMfZoNPF\njsP1ZKYlsXR2YbTDEWNs1YIS/rDpFFur6njDqmkyPlD45UnEjHA6L01PM1mot5N7HFlhzsiWd3dr\nvHcB2fbufvbqRsoK0qkoymTv8Ub2Hm/kuvklYV2HEGK4kF2WWmuH+x+QArwXeDzikYkRqqqb6ege\nYPXCEpISw+ltFpNJRmoS18wtpL6lm+paGa8jgglvUH+o1jFvLjtx8+2uBK+EzGuJpe2H6hh0mmxc\nVsG7bphJgsPg+dekPKUQV2pUf9W11gNa68eBmyIUjwjCXadq3WLproxV7rpy26pqoxyJmKhG23Aa\ndlIWxiLk3i1k+3QTCQ6DNYtLKc5Lp7I8m7P1HfT0hbPUsRDCVzhdlh/xemgACwEZdTzO2jr7qKpu\nZnppFtNKsqIdjoiQBdPzyc9O4bVjjdx181xSkqUyuvDDOysLUYdsaJcAg/oN91gzM+Dhhros++zj\nmtQ1d1OSn05GahIAc6fkcuriZaprL7OosiDMCxFCuIXTQnYjsNH+twHrPuq9kQtJ+LPzcD0u05TB\n/DHO4TBYs6iM3n4ne3VjtMMRE5RB4ATLs439cpBC/cOYQcpjFGQPbyHr6Bmgp2+Qkrw0zzZzp+YA\ncOKC1CsT4kqEU4fs91rrF7yfUEq9AzgTmZCEL9M02VpVR2KCg1ULZMBsrFu3uJSndpxl+6E61kr3\ntPAxlIe5B/WH14d5NVNE0lISSUlO8Iwhc6956T0jc3ZFDgZw8kLbVZxJiPgVbHHx92EN4v+mUurr\nXi8lAV8B/hzh2IStuqad+pZurptf7OkeELGrOC8dNTWX4+fbaGzroTg3LfROImKUUgnA94BrgWTg\n61rr55RSq4H/BQaBF7TW3xq3oMIYSGZgYJqhl+Iaaklzd1n6WcDcMMjPSvG0kPlbYik9NYmKokxO\n17Uz6HSRmDC8A+ZCYyfHz7cyf1oeU4ozQ8YlRLwJ1mWZjdVd6f6/+99qrIRMjJOt9gDv9fYi1CL2\nuQf3b5cFxyeCDwGJWut1wJ3AfPv5nwJ32c+vUkotG59whq9hGTA380m0QnFvFuh4BdmpdPUO0ts3\nSGNrD8CwLkuAaSWZDAy6hs3GBDh0upn7fvEaj750kgeeqGJg0BlWTELEk4AtZFrrnwE/U0rdrLXe\nNI4xCS+9/YO8dryRguwU5k/Pi3Y4YpysUMU88uIJth+u423rKv2WIhDj5jbgsFLqKaw05x+VUtlA\nstbaPXTjeeAW4OD4hBTe+8HEa+WkALsYXtsGk2fPtGxu7/W0kPkWkfUM/r/cO6xld9O+i5jAosp8\nDp9p4YU9F3jT9TPCugYh4kWwLsuHtNYfB/5NKfVvPi+bWmspfTEO9h5voq/fye0rp8of5TiSkpzA\ndfOLefX1Oo6da2VhZX60Q4oLSql7gM/5PN0E9Git36yU2gD8Eng/4F0srgOYOR4xGp4GshCD+kd7\nwBAtaYl27cNBp4uGlh5SkhPIyUgeto1n8H/HUHmM1o4+Dp1uprIsm0++bSH/+rNdPLPrPG9YNY0E\nh9RTFMIt2KD+n9r//6af10ZTb1BcBXc9KhncHX/WLS7n1dfr2FpVKwnZONFaPww87P2cUupR4Gn7\n9VeVUnOxkjHv+jPZQMjR7EVFV1+yxpphOfS4sDCTgpyR4wwTEhw4Bl1kZlhJUk5Omt/zJycl2K9b\nrV3p6cl+t0uzx6+aJjS29TClOJPi4uxh28ycar1Pe52m5xibq+owTXjj2kqmT81n7dIKntt5lvY+\nF3On5Yzu4iNgLH4mE4Vcy+QWLCHLtO8G3a3ehs//RYTVt3Rz4uJl5k/Po0gGdsedWRXZlOans//E\nJbp6B2RCR/RsA94I/FkptRQ4p7XuUEr1K6VmYs04vw24L9SBmprGagFuw5OVNTd34eofWYzV6TJx\nukw67cXq29t7/Z5/YMAaz9XaZnVD9vT0+92ut3fA+n//IP0DTjJSEkds57AnEVyoa/e8duhkEwCz\ny7JoaupgWqGV+O2uqiUvLZyJ/pFTVJQ1hj+T6JJrmXhGm1QG+234JsETrxtHdSYxatvthcTXSe2x\nuGQYBuuWlPGnzdW8drSBG6+R5WOj5CHgJ0qpnfbjT3r9/xEgAXhea71nXKIJsy8y3LFhnsH/BClE\nxlAXqXvipr8xafle48zcGlp7SEtJJDvdLiA7NReAExfaeMOqaaGiEyJuBBvUv9H7sVKqAHBqraXI\nzDhwulxsP1RHWkoi184tinY4IkrWLCrlz1tOs7WqThKyKNFa9wP3+Hl+N3D9+EcEw9ayDJagmV6L\ni4c6ZLgFZINU9E9LSSQjNdFT0d9lmjS29jClKMNTyDY/O5Wi3FROXGjDZZo4fC6gvbuf/SeaKMpN\nY+EM6aoX8SPkiEql1DKl1OvACeCMUmq7Ump25EOLb0fOtNDW2c+qBSWeMR4i/uRmprBoZj5n6zu4\n2NgZ7XDEBDA0mD90pf5wciz38VzusheBNwRCV/7Pz06lub0X0zRpae9l0Omi2Kc8hpqaR3ffILVN\nXcOeb2nv5as/28VvntM88KcqGtt6wrgCIWJDOFNcfgF8VWtdoLXOA76LNctIRNBWu/6ULJUk3IvJ\nb5WaZMLNq1UpVMuXJ38aqyYyTwj+D1iQnUpfv5OeYfXKhpfHqCjKAKzuTG/bDtXR1TvIwhl5DAy6\n+P2LJ8KuoybEZBfWnGOt9VNeXz8JSJnlCGrv7ufgyUtUFGUwozT+ZpqI4ZbNKSQzLYmdR+oZdIau\nvC5inBHeWpbgs7h4oLFhPi1foeqVuUIkSPnZ7nFkfZ6EqyR/eAtZgWex8qGxZqZpsuNwPcmJDj79\n9sXMm5ZLVXUztc3dQc8nRKwIJyF7RSn1ZaVUjlIqUyn1CeCoUqpYKVUc6QDj0a7D9ThdJuuXlIf1\noStiW2KCgzWLSunsGeDgyUvRDkdMGMFL9bs/O8JeXDzM04Xa0F0ctrm9d2jNyzz/BWS9B/9X17bT\n2NrDNaqItJREVi8sBUCfbw0rfiEmu3ASsncCn8CqQH0I+DKwBtgN7IpcaPHJvZB4gsPg+oWykLiw\nuGfaSrelMGBUXZZhbzjaQf0Bjpdij3kdGHQNdVn6VPQvyBmZkB092wLAynnWff68adZszOPnZR6Z\niA8hi8BorWeMQxzCdqaug5pLXaxQRWSlJ4feQcSFKUWZVJZlc/hMMy3tvZ4WBhF/jPDG9FsFI8No\nHvM0fLlnYwZqcWOULW6mSUNrN+kpiWSmDa+hl5WeRGKCg+bLQwmZO3mrKLTGlxXlppGXlYI+34pp\nmiPiMk2TExfaGHSaUjhZxISQCZlSah7w94D3Qoqm1vrvIhZVHHNX5l8nC4kLH+uXlnGmrp3th+t5\ny5oZ0Q5HRJXh90t/mwQrU+EteBUyPxsGOq3XAfoGnKSnjvwz4zAM8rNTho0ha2ztIcFheFrPDMNg\n3rRcdh5poLa525OogTWO7ft/PMiRs1Z35pc/cI2nvpkQk1U4XZZPYi0JssXnnxhjfQNOdh9rIC8r\nhUVyxyd8XDevhOREB9uqakMOrBaxzLD/G2ZnZajB+mGONXPv7wrRkjbs1EGOWZCdSnv3AP32SgGN\nrd0U5KQOW99yjp1kVddcHrbvifNtHDnbytTiTAzgV88eZ2DQGTIeISaycNataNVafyvikQj26yZ6\n+pzcfO0UWUhcjJCemsiKecXsOFzPifNtzJueF3onEZMMrwUtQzSQjUKoQmTDtgpoqAvUfhzgeJ6Z\nlh195GQk0949wDSfWeWl9mSAJp96ZLuO1gPwvpvnsFc38sr+Gg6cvMR182XcrZi8wknIfqWU+k9g\nE+BZME1r/WrEoopTW2UhcRHC+iVl7Dhcz9aqOknI4pRvGhaspco0vROo4JlW2I2uIQvIhpcKDpXH\n6KWv32rdKsn1P/jfu2tzYNDJnuNN5GWloKblkpzk4JX9NRw/1yoJmZjUwknINgIrsWZWepO1LMdQ\nY2s3x8+3oabmjpgiLoTb3Km5FOelsU838oFb50Y7HBEF4VfCMcKr1O8Za+beK9R24WVuJqY1GD/A\nyBhPC9nlXrp6rIXLfSv652WlYMCwwf/6Qhs9fYNsWFqGwzCYUZpFanICx0LMxvS3TJMQE0k4CdkK\nYK7WWgatRNC2Q1YT/Pql0jomAjMMg/VLynhiy2leO9bA9KnSShaXwkgshgq+Bi9T4WaG6GMcMcsy\nRAHZUBlent1C1tbZ52nl803IEhMc5GalDCuPUW8Xip1ud28mOBzMnWoVkW3t6CPPXuDc7UxdO3/Y\ndJKapi6+/MFrmFIkdc3FxBTOoP5DwJLRHlgp5VBK/VQptUMp9YpSalaA7X6mlPr2aI8fS1wu015I\nPIFrpdauCGHNojIMY6iLW8Sn8IpGh9thGT4z1GLlXi8Eu4t3D953ukxPyQvfhAyslrTWjn6cLmuV\nCvf6lt49CfOmWTcmx88NLyLrcpk88EQVJy9eprtvkIefPiarXYgJK5yEbBawXylVo5Q6Y/87HcZ+\ndwLJWus1WMVk7/fdwK76v4jRLqIWY46cbaG1o49V80s8RRWFCCQvK4XFMws4U9fB2br2aIcjosYe\nTRaqpSrUUXxmWYZcXDzM45r2f8KJ43JXP8CI1i2wxpG5TJO2Dmsbf8mbsovInq4d/vtw7Hwrlzv7\nuWFZOWsWlXKuvoPth6S4spiYwknI3gfcCzwI3Af8O7A9jP3WAs8BaK13Y3V9eiil1gDX2ceN6459\nd/V1qT0mwrXefq+8+Nq5KEcixttollMzzdBdjJ5twy/V7w7E78sjng1jO3erm78xXgU+yyw1tvaQ\nkZpIRupQsVl3cnbp8vDZmLuPNgCwekEJb11XCcCh0y1+4xEi2sJJyL4HvAWrOOztwLeAcG7Ls322\ncyqlHABKqTLg68A/EOfJWEd3PwdONFFRmEFlmSwkLsKzdHYBWelJvLL3onTBxCHvGmTBWrTMYQ+D\nJ0ajXVw8nAKywVI830XNA527wGs2pstlculyD8U+E5/SUxJJSU6gub3P89zAoIt92pqNOWdqLsW5\naRTmpKLPt+Jy+Y/MZZpc8imxIcR4CWdQvwJmAw8AvwD+GatVK5R2wDvDcGit3X853gUUAs8ApUC6\nUuqY1vo3wQ5YVBQbCYv3dex8tRqny+QNayopLs6OYlSjE4s/i8nm5pXT+MuWak43dLF26eRvXZ3M\nP4txNyxzCTEIP+Sx7P+HWWAsdAFZ93nDTNxCnNqz7uXlXlo6ehl0miPGmhmGQWF26vDB/y3d9PQN\nct38Yk/L2/zpeWytquN8YwczSod/3l5o7OThp49yvqGTD942l5uumRJG5EKMnXASsgattamUOg4s\n0Vr/WilVGsZ+27Fa1h5XSq0GqtwvaK1/CPwQQCn1EWBeqGQMoKmpI4zTTmxFRVme6zBNk2d3nCHB\nYbB4Ru6kuT7va5jMJvt1XDunkL9sqeapbdXMLZ/cyUygn4UkaSMNrWUZRqpjEsbgMPemoytEFt6c\ngtDHNIdtF7jLsqW9d2j8WK6fwf85qdRc6qK7d5D01MShhc29WtPcCdmxc60jErJfP3ec8w2dJCc6\neOzlU8yfnkdZQQZCjJdwuiyPKKV+CLwCfE4p9a/AyJGXIz0J9CqltmMN6P+8UuoupdTH/Wwbl4P6\nz9Z3cLGpi2VzCsmWhcTFKFUUZqCm53HkdMuwwpkivgRMjMIcDDKyy3KsFhe3PthDLdk0bCaon20z\n7c/Grt7BkLMxwWusWZtVHqPEa1t3MeUTPjXLmtp6OF3bzoIZedzz5gX0D7r4246zQa9PiLEWTgvZ\np4DrtdZHlVLfAG4G3h9qJ7tu2ad8nj7hZ7tfhxNoLNpmD+Zfv0Rqj4krc+t109HnWtl+qI63rK2M\ndjhiHHgayMLIuEyvdq+Qi4uH15AW9tJJoxF0rJnXNpfsArFFAVrIwOranFqcSZOdvBV5JWS5mSmk\npyTSdHn4Dcye440AXDe/hBWqiJyMZI6ebbUK20oxWTFOQraQaa0HtdZb7a//qrX+J6314ciHFtv6\nB5zsOtpAbmYyC2UhcXGF1i8rJznJwbZDdbLgeBwxDCNk5mOA3WXp9dj/wbA2Df7+GVloNnS9jXDe\nksNmgoY4nnsCS3LSyD9dvi1kDe6EzCd5K8hJpfly71AhXOC1Yw0kOAyumVuEYRjMn55He1c/NZe6\n/OGIlZgAACAASURBVMRrcvDUJe7/wwGOnJEZm2LshNNlKSJgr26kp2+QtYvLPAUShRit9NQkVs4r\npqmtFx1i6RgRI3wSocBdgmEezv1FuOUxRtFlacURoAvUz9NBYw5xYu8WMrDKY+RmJo+o7ViQnUrf\ngJOuXmtp5oFBFxcaOplVnk1mmlVKY77dtXns7PBCswCvvl7LA3+q4sjZVh786xFaO/pGbCPElZBM\nIEo2H7SqrG+IgdlxIrrcNcm2SeX+OGIQTuegVwNZyAwt7PbVEC1uvl2p4W4XiHeX5VC3auDB/5fa\nexkYdNHS0Rtw8D8M1Sy7dLkHEyjOHxr8v2CG1Wtx7NzIhGzzgVoSHAZvWDWNzp4BHn1pxEgcIa6I\nJGRRUNPUyamLl1lYme93LIQQozFnSg4l+ens1U109Q5EOxwRYYbnP+7HVzeqf0RXZKAyGvbT4XaN\nuxcXD7mdGfzc4Y7hyslMJjHBoPlyr5VkmYyoVwZQ6KclDYbP3CzISaUwJ5XTtZeH7dvQ2s25hg7m\nz8jj3RtnUVaQTlV1MwODUgtQXD1JyKJgy+tWS8bGZdI6Jq6eYRhsWFrGwKCLHYfrox2OiDQ7Pwkn\nURme7ITYNswTm8MfjtzKd/JkiHxx2Ni1oF2Wwce5OQyD1ORE+gecNLWNHNDv5hlr5k7I2vzP3CzO\nS6O9e4D+AafnuT3H7MH/80owDIOFlfn0D7qorhmeuLnVNHXy478cluWaRFgkIRtnfQNOdh6uJzsj\nmaWzC6MdjogRaxeXkZhgsOVgbVitEmJyM4Y3kfnfxjOq3/txEGGXIQu/4Gswo93f9Pwn+LWYwOVO\ne23MTP9rY4LVtQlDLWQjBv/7TBIAeL36kj343/rsXjDd6to86qdr83RtO/f9cg97jzfyq2ePc0bW\nnRUhSEI2znZU1dLVO8j6JWUkJsi3X4yN7PRkrplbRO2lLk5e9H+3LmKDby5ylWXIvCrrux8HP95o\nysea4SwubhK05MZoq06Y5lA7mr/5Ur6D/5sCtJD5bgfQ0NJDYW4a6fY6mmpaLg7D4NjZkbMtX329\nBqfL5LaVU3G5TH7+1FG5WRJBSUYwzp7fZS0GvV4G84sxtnFZBQBbDtZEORIRcYYRVqYSsqSE78aj\n2izc2ZPBMzzviQfBumG9E61AfHf3NyYtKy2J5ERH0MXKYfgkAYDu3kE6ewaGjTVLS0mksjyL03Xt\n9PUPdW0OOq11NHMyk3nPTbO5VhVR19xNfUt30OsLtMamiA+SkI2j2ktdHDndzMIZeX5n/whxNdS0\nXEry09lzvInOHhncH6uspMVrcfExqtTvCtJK5X2eoTpkoY8dvLzY6GZZeh8w1Pi5YC1RhmF4apE5\nPYuVj/w89h3872lJ8/nsrijMxDSHEjeA4+da6eodZIWy1tFcNLMAgKN+ymgAVFVf4l9+soNvP7KP\ngUGn321E7JOEbBy9ag/mv8FuyRBiLBmGwQ1Lyxl0utghg4jHjFIqXSn1f0qpLUqpF5VSJfbzq5VS\nu5RS25RSXx//yMJLaEK2Po3oAw2V7ISKyr3EktX2FdbYtVF25QXLQd1LNgXbMDMtie7eQZov9zDo\nNENW/oehwf++EwX8dW0eOHUJgBWqCIAFdl2zo366Ni82dfKDx6tobu+juqadP758KsDViVgnCdk4\nGRh0sv1QHbmZKSybI4P5RWSsXVxKYoLBZhncP5Y+DBzTWt8A/BG4137+p8BdWut1wCql1LLxDGqo\nhSnw2pOm90j4EMJ/v4QY1D+i2zDAZl6zLM1gx/NaQzNkp6Vv0dwgRzSBVrtVKz8rdcQ2eVkpOAzD\na/C/1d3o20I21JLW43muvtnatrLMWsC8MDeN4tw0jp9vxekaXiJj99EGTODuO+ZRXpjBy/trPOcS\n8UUSsnGyTzfR1TvIzSunymB+ETFZ6cmsUMXUt3Rz4oJU7h8jPUCB/XUO0K+UygKStdZn7OefB24Z\nj2BGjJMa68XFA553lIuLj2LbYCf2vr5QLV+ebcIcbOa5Zj8fyQkOB3lZySO6LEe0kPmMNYOhVQKS\nvVYJWDAjj54+JxcaO4diNU32Hm8kOcnBqgUl3HyN1XtyJEDXpmma7DxczwuvnZcbrhgUzuLiYgxs\nsSvz37Z6+qib54UYjRuWlbPraANbDtaipuVFO5xJRSl1D/A5r6dM4B+ALyuljgB5wAasxMy7jkEH\nMHO84gxnLUtwF2d17xNq2/CErEPmu2EYSzGN9hMxaA7qPfg/7KTU/4YF2amcvHiZQadrqDxGzvDW\nNN+xZoNOa5WAORU5w7YrK8wArGRtRqnVcnahsZOG1h5WzCsmJSmBBfa6xkfPtHDj8uFDW0zT5Cd/\nOcxe3QRAQoKDm/9/e+8dLkd1Jui/dfvmrBuUsxAHkIgSScZgm2Qw2MZhxnjGOTDrWU/YnZ31zngd\nduYZ+zcePGPvOq3BZgaz44DBYxsDMhkESAIJJIR0EMpZV7o5h67fH1XVXV1dVefU1b231VfnfR64\n3dVfn9DVqvr6i6vm623QUBQYhWwKOHKyD3mgk3MXzWBuSy1tbT2FXpJhGnP2gkbmNFfzkjzO7f3L\nqasuL/SSigYp5d3A3f5jQoj/C3xTSvlDIcT5wC+Bq4A6n1g9oDRJtrbWqUSUpAIW9tbWulCre3lZ\nCguods9/Y2N16PyVbnZhTY1Ts6u2riJUznvds8xUVZaHytXXd7njVGJZUFqaCpXrGnSC16uqyikr\nTWFZVqhcv9t9oqw8lVnrjKaaUNlUyiKVKqHOrT/WUF8VKldennL34jyvrg7fy9xZdbxxsAurrJST\nPUM0N1Qyb25jjkxTcy2pEouu/hFaW+s41NaLbcOCOfU5Yy5d4Pw4GhqzM8ef2eoUcn776gW0ttbR\n0lLLzKZqdhzozIzr8ebBTl6SbZy1oJG2jn5+9sROrl61gLmttRmZifh+nS5Mp73oYhSyKcCzjl1j\nKvMbpgDLsrjmonn89PGdrNt6lHdevrDQSyp2ashaw9qAOilljxBiWAixFNgD3AB8RTXQRPwYS4+l\n8feybGvrCVXIRkbGsG3o73eKpHZ1DoTOPzTkNNnu7XUsPH29Q6Fy/f1OE21PiRkcHAmV6+5xLEk9\nPYOk0zA2mg6V6+x04qQGBoYZGRnDIvzzGRwezaxzwM0e7ujopzqVb9UaS9uMjqXp6XH20t09GDrm\nqFt932sDNTAwHH5uxpx4r8NHuznRMcDy+Q2hcjPqKjh6so+2th527DoJQH1laY5smWu323u4K3N8\n98HOPNlzFjTyzKuH2bj1EMvmZq1sj724F4AbV89nYGiMH/1uO4+9uJebrlgEOAqMf76OniEOHO/h\n/KXN2u2nTheCeylWkiqVJphpkhkaGeO5LUeor3EKdxoMU8GalbMpTZXw9KsmuH8C+BvgU0KIZ4AH\ngM+4x/8EuA9YD2ySUm6cmuU47krvJhuXPJkTx6XhOtRB7bLUjOr3zauuMKaH15xAVeQ2KcOjY9iQ\nKQgbpKWhkq7eYUZGo9s2BV2b4ItL87lBxULHArf3SFYhsW2bjTuOU1GW4vylzVywzAlpfG1PftYm\nwKY32vjiXS/yL7/YwmMvH0yyVUMBMRaySWb968foHxrlllWLTTC/YcqorSrj0nNaeWHbMXbsd9zl\nhvEhpdyHYwELHl8PXDnV69FWMjQFsxX4vfpiUVmbrpxu6yTb1lK0bOKDyHIUPMXciRMPlDU8fNVr\nY/BKX7R3D/malec2Nq+uLKOqojRHIQsL/veyOP1yh9r6ON4xwKXnzKS8LEV5WYoFM2vZebCLoZEx\nKnzvHx1L8+PfbWcsbVNbVcbPn3iTs+c3smj2mecCLDaMhjCJ2LbNEy8fpMSyTCNxw5TzNjco+IlN\n5hfydMOvpKgKrGYUrejBPEEtEukwMa2Tgk3Ik2SLxvey9PfvjOomEMiyPMV2US0NjhJ1omswa/Vq\nzC+l0dJQyYnuQWzbzgT/B8toZHpt+spo7DvmWMv8P6xWLGlidCzNzkA29Y79TlHaqy+YyyduPoex\ntM2zWw5Hrn1gaJRXdp5gdCwdKWOYGoxCNonsOtTN/uO9XLy8hab6/H+cBsNkcta8BhbOrGXzGydo\n96XkG6YZE5XtqJwnU6o/5+lEoKML6mZjJvHQ2xP04VRXOs6mgaFR2joHqKpIUVuV795srq9kaHiM\nvsFRTnYNYtv5Tc3ra8opTZXkNDUP67d53mJHOduxP1che2mHk4W5+pyZnL+0mYryFNsiXJv7j/Xw\n5R9t4Nu/3ML/e2xn/CYNk45RyCYRzzLxjktMZX7D1GNZFteumk/atnlys+lvOa3Q7GUJGiW5cirr\nT2BzcVeB0im34UytcJX6SnhEkdfeSWON8QM6f9Kanw1A/9AotVVlodY5fxxZVKxZidva6URYrJlP\neZvX4mRXeh0EANJpm80726ivKeeseQ2Upko4d+EMjnUMcMIn5/GTtW9wsmuQxtpyntp8iPWvHwvf\noGFKMArZJNHVN8zGHceZ01zNOSZ+x1AgLj9vFjWVpTz9ymHTI2+akN9AWyGXKfg6MSYtdXPxvF5M\n8XIqt2GoyzJeeVORVHFTj+cqte6YkXXNfO7I4yFKlkdLfQU9/SOZhuXHOwdIlVg01VdkZBpqyylN\nWTkdAo6099PTP8L5S5socUtmrHBrm20LtG3q6BnizUNdiIWN/PcPX4IFPP1K9A+33oERHnphb6hi\nZ5gYjEI2STzz6mHG0jbvuGR+0aUcG6YP5WUprr5wLr0DI2zYfrzQyzFMILoKlrrdkPNnopqL+w/H\nWaBy365hd9NsA5Wk0Kx2DFnSTOWI8fwWsmzwf1gfTTcmzXVbtnUM0FxfSaoke8susSya6itzszbd\nMWc3ZRMKPNdmsLH5pjcc1+YqMZNZTdUsnF3HzoNdmTIjfg619fLlH23gl0/v5p9/8SoDQ/kyhlPH\nKGSTwFg6zVObD1FRnmLNytmFXo7hDOftF8/DwgT3TxcsrJxK/aoffLpKh25Jf31lR6+5uOeKVPay\n9C8xVtZWW90yc8eTded646k+63j1t6rCiTUbHBnLuCRVjc0Hh0fp7h/Jc22Co+B1948w5NZVy8aa\nZRWy2U3VlJeVcKw9tz/my9L5geaVY1q5pImxtI3cn1/f+DfP76WjZ4hl8+o5crKffzfxZpOCUcgm\ngVd2nqSjZ4g1K2dn/gEaDIWipbGKC89qYc+RHnYf7la/wXB6o9sOaBy9J7XklEpRYB2KF5K2OYqT\nzdeX4gV1LV+q0P+ceWOVy6yMp0SF3SP8DcvbOqMVt2Bts+MhGZ6WZdHSUJWTJDCWTrPzYBeLZtUx\no85xg670XJuBBICR0TFe3XWSloZK/vuHL6G1sZKX5PHIrMwDx3v5+k9e5uH1+1SfgiGAUcgmgUww\n/8UmmN9wenDtaqfn3eMvHyjwSgwTQ7ZSvwqVyzI/1ixKLllYv6q5eECHiZbL+g31siwV4+XIqixf\nVkBQF1UtN8WYLZlYs2zwf5xr01O2omSb6yvpGxylf9BxNXZ0DzGWtpnTkrWkLZvXQEVZiu37cl2b\n2/Z2MDQ8xmoxk9JUCecvbWZweCz0x92+oz383b++xBsHu/jFk7t4aYcJk0iCUcgmmINtvWzf18E5\nCxuZ5+sxZjAUkvMWzWBOczUbdxynq2+40MsxnAK5MVoataMmurm4ogx+nt6mTHXEtSppuEo1rHO2\nTxPUiXOLI08F1dDbYj9H34LiPkbPatXRmy00G1XXDMi4P9s6B6ipLM3rKJCxpMUobqWpEua21HCs\noz+TVQqwSXqxZo5r00sSCOsS8MyrhxkdS/Oeq5ZQUZbi3x6VjKWjv6OH2npzskTPdIxCNsH8fqNj\ngbh+9YICr8RgyGJZFu+4ZD6jYzbPxGRSGYqJeLUiUDZMOY6t8EUGA9xVMV9K/JmJWn6+/PeqDqvc\npWnNLEvdGm1O1wFbo9xG/IheV5d02qaz1+khGlbLsrk+m7WZTtu0dQ7Guja9YrNRGZ4tDZWMjtl0\n9WZ/tL15qIvqilKWzK0H4JyFM0iVWGzbczLnvWnbZtMbbdRWlXHLmkVcuXI2vQMj7DkS3pPyoRf2\n8qUfbeDv7tnI8Y7+UJkzDaOQTSDdfcO8sO0YM92YHYPhdGLNytlUlqd4cvMhU5W7mPH3sNRwpWUr\n9ccrMcrYMG0Fz5sXN1hfr0SFOrtTv+eltoNRGRzmzZ2sPMapZqD68ZTGEkVds/buQUbH0rFJAllL\nWnhcWjAmLW3bnOgaYFZTVWb+qopSls6tZ++RnpyMzN2HuunqG+ai5S2kSkpYsdi1pO3OVdwAdh7s\n5JdP76a6opS+wVH+zwNbzTUJo5BNKE+5N7rrL12QqQFjMJwuVFWU8tYL5tLZO8yG7aYAZFHjsy5F\nirh/tV2RSeVUgfW60f8KP19uL8v4IS0sJ9NRoWgFi+EqUblpfXJa8XCqY95wdrxcY20FqRKLk12D\nHD3ZB+RW8/fwWjud7Mp1WQYVsmDbps6eIUbH7Dy5eS012OT229y003Vtulmb5y6aQYllhXYJ8LoJ\nfPbdK7hixSwOtvWx61BX/gaBvsERvv8fr/H1+zZlYuCmK0YhmyBGRtM8sfkQ1RWlvOV8U+rCcHpy\n/er5WBY8uuFA8tpKhtMCJ5xfP6hfswyZr75YlNKRq8QojEru1NGT++vC6lT0j5oj7gWVVVBZew21\n4usfQJXI4JGjaKmadcaMV1JiUVmeYmhkLOP286xcfsKyMctKS2ioLQ+VO6GtuGUVsoPHewE4e0Ej\n4LSTWjqvnt1HuukdGMlux7bZ9MZxqipKOXfRDC47dxYQHpM2lk7ztZ9sYsP247xxoJP/+5ttpNPT\n97plFLIJYv3rx+juG+bqi+ZSWW5KXRhOT1oaq1gtZnLgeG9eNpWhOMgtsRBnWspVJqa6PrUXhK8/\nbbyfT1XjK2debeIzHsZb0V9Zrww965xuxqiNYxQApxh0kLrqMspLSzIK1InOAVobq/LcoM2+JukQ\nF2uWKweO8lZbVZZTxkMsaMS24cCxbBzZvmM9nOwe4qKzmilNlXDOwkZSJRav7c5XyN7Y38nhE32s\nPmcmK5c0sWXXSbaEuEA9tu1p5/6ndjE8UpxdSYxCNgHYts3ajfspsSyuWzW/0MsxGGK54TIn4WTt\nRlMCo2ixUGpYQctXtGCyemXZQHi9FEYtj6VueQylKxLXbajnLtX2WGoX140fJ1RRizvkW2Cskqf6\nDDP9MQfoGxyhb3CU1jBLWn22/hkkiDVL25zoyk8o8J6f8NVA81yYFy13XJuV5aUsn9/AvmM9dAcy\nwF92uwm8/aK53LJmMQBbIxSytRsP8M2fvcLvXtzHPQ/vKEoPgFHIJoDt+zo42NbH6nNaQzNhDIbT\niWVzGzhrfgNbdp3k8Im+Qi/HME40nWnqhtyeHPFWoIRlyJQlIHLrmqkzE3PeqwpgU7ois2uMk/NQ\nVvT3ZVnaGlmW/hFDZXP9vppzx4wH1FSWMTA0xglXyWoJCf6vKE9RV12WY0mD/JIbwazNjh6nrlkw\nfi2ouEHWDTq/tSZzbOXSZgB27M9a7dO2zeadJ6ipLOXshY0snVtPVUWKbSGWtKGRMR54ehd11WUs\nml3Hi68fi22U3tM/zLqtR047S5pRyCYAz9Jw/aWm1IWhOLjx0oUArN24v8ArMYwPDatWwGyj7Kmb\nML5dFTCfPaCZZRmpY/n3qufm0yWjhCoTFBIMClqWOa1YM9SKsien1C4tZyzPtVlZnu/aBEeJOtk9\nSNq2s03N63IVsvqacsp8LtA2peKWVci8umr+WLcFM52ancc6sjXJ9h3toaNnKJO1WZoq4dxFTRzv\nHMgrk7FtTzvDo2muumAun731PCBrXQty4Hgv/+uejdz90Hbuemj7aWVJMwrZKXKwrZctu06ybF49\ny+Y2FHo5BoMWFy9vYWZjFc+/dswUii0yLMvrZalnU1Leb4LlLBRuOTutUBASxqrpNgP3x1PFug59\nsWZ6Sp7O3JrlNvS8w+6YuWvJkQsKKef1W9xiFGCN0iHN9dlaZG2dA7Q0VOZVDbAsi+b6yvxYs4Zc\nC1lTfSUWwVizQWbUVVBWmlUI/a2iPDJJAvMbM8dWRhSlzTZKb2V2UzUtDZW8vrcjtCjtT9ZKTnYP\nOS2gdhzn8Zeje/ym0zbb9rQzNDw1lrRJU8iEECVCiO8LIZ4XQjwphFgWeP12IcSLQojnhBDfE0IU\nZZ2Ih190LAw3X7GowCsxGPQpKbG4/tIFjI6ledI0HS9iYrIYA05NpftOUa9Mp9RG7sr0FDdNw5cW\nlhUMmFcE1ys0KN3m4sE4t1O9mfnn0S0zon1eFPFw1ZVOUH5P/zA9/SOhWZvgKFG9AyMMDo9GZmOW\npkporKvIKFqjY2naewbz4teyBW59iluX1yg9O+by+Y7R44CrrHljvvrmCWbUVbB4dh2WZbFySRMD\nQ6PsOZxblLarb5g3D3Zx9vwG/vYjq0mVWLywLdy12T84yr/c/yp3/uwVvv3LLVNSJ20yLWTvBcql\nlGuALwB3ei8IIaqAvwPeJqW8CmgAbpnEtUwKJ7oGWP/6Mea21JhCsIai46rz51BTWcrjLx/MKfBo\nOL2xQh6FygUyBFUkDXBXxvTrBsJ7z2Msfp7lK6nipvTSKhStPDn9mSOO+hQ8zSzLxPFwMZ+3nXck\nesSRseisTciND8u0YgqtgVZJe88Qo2NpTnYPYtv5ilt5WYr6mvI8SxrkyoZldx492U/f4CgrlzRl\nzqMXk/ZaoJvA5p1t2MAlZ7dSX1POWfMa2Hukm57+fC/Br9ft4bXd7dRWlbF9XwcPPL079HPweONA\nJ90h4yRhMhWytwCPAEgp1wOrfa8NAldKKb1PtRQouoZWj64/QNq2ufmKhaFVlA2G05mK8hTXrV5A\n3+AoT79yuNDLMejiXmoszwelQrNIaua5ymWpsqQFplUyLpdl9Nw6iqW2VUk7fTI7d6xkwGWpzkBN\noEwn8ZfqiCmGa/b1x2zrHKQ0ZdFYW5En19JQiW07gf9tXl/OCMXtZNdgJou3rXMgb8xg0oEnBzC7\nOdso/ZyFMwCn7ZMfry/nJW7x2pVLm7CB1/fmlgCybZuXpVMr7Wt3XEFDbTnPbT0SWgNtLJ3m3rWS\nr9+3ia/d+3JOzbWkTKZCVg/428GPCSFKAKSUtpTOJyOE+DxQI6V8bBLXMuF09w3zzJbDNNdXZgrb\nGQzFxrWr5lNRnuKRDfszwb6GIiCBn0rPeadvIVNn/XnjaZbbcDMT42X1lhaMDdNVeHStT8rK/17G\nqDJ/In6BoXVhYzIP7Jyn8W7VxHuOoNyNARsZdfptNtZWhHao8Vu1olybjlwlY+lsH822zgGaG6ry\nxnQUt4EcxQ1y49eqK0upry7LZJSCEw+2Y38n81trMhmmK5e4lrRAKQ2vVtqFZzVTU1nGBUub6R0Y\nYe/R/L6cz289ypObDlFTWcqxjgF++JvXIz8zFZNZwbQbqPM9L5FSZq74rnL2j8BZwPt1BmxtrVML\nTRGPvrSdkdE0H7h2OXNmJwvmP532MV6mwx5geuzjVPbQCrxrzRIeeOpNXt3bwU1XLp6wdSVeyzQ4\nF1OBtsvS/aur7OjKZeqQKYLDtOOuFK42R9bSKqaaN4Smy1IppyemnNa/54lK3AwmMmiPp6k0KrNz\nsUnbNuUl4fYdf4mMqLpmkNu2af7gCD39IyyanX9NaG6oYs+RHrp6h5lRVxFdK62xin1He0inbUpK\nLDp7HbfpvNbajMyCWbXUVpUhD3TmvNdLErjErZV2/tJmnt1yhNd2n2Sp22Td4yXX6vY/P7aau367\nna27T9LRM8SMunxroYrJVMjWAbcCvxBCXAFsCbz+AxzX5W1SSq3vUltbeNf4qWZgaJTfPLubuuoy\nLlralGhdra11p80+xst02ANMj31MxB6uWjmLXz+7m5//XnLx0hmkIi6sk0nUPoySFoXfIhOPysIS\n9FDpxnxpzzsJxNZI1VBOLF2/nKay6h9OrxSJI6tqvK7nivTJEqO4BbNpI8fTtDIG9hJFo6uYeFmb\nEGUhy1rSjrX3R8q1+mLXZtRVZIL/w4rX7j7cTWfvEE31laGlOUosiznN1ew61M1YOp259m3b005p\nyuJ8NxbtvMVOX87X9rTz7quWZN4/MDTK9n3tLJhZy8wZ1awWrbx5qIvX9pzkrRfMjf5QIpjMK++D\nwKAQYh1OQP9fupmVnxFCXAx8ElgJPOFmYb53EtcyoTy5+RD9Q6Nct2o+FREBjwZDsdBYW8FbL5zD\nia5BNrx+vNDLMSix0OllaQXcmkqFKmlQf+S8npyeNcvTOeLWZ+VHpCsGjY9z8456VRGi5fJSD2Kn\nz8S56VrcNLQdtWxuvTIV2uclQfyas+fwBZZkFDyb/iEneaimMt8W5K9Z5jVKD5bRyJXzugkMUFNZ\nmskO9Qj224wqzdHSUEnatmnvHsocO9Y+wMwZ1VS4tdqqK8tYMreOXYe7corJbt19ktEx2xeT5ihw\nYQ3VdZg0C5lr9fpPgcNv+B4XpSYzMDTKI+v3U1VRyrWmTZJhmnDTZQt5evNhHnpxH5evmGWSVE5j\ntHtZeiLKAZ0/aUWwvuW7seatI3849cRBi42y/6OtU/tUcSB/VB2S1g5VKni2vgKlnotE5khlYkTe\neYkVi3we90LY1P5aZEdPRlvI/P0207ZNW+dgTtX/7HhV7niDsCC6DZR/vNbGKvoGR+gfGs2U2PCY\n11LDrkPdnOweZE6zM5/Xxukit8rCnOZqmusr2LanfVxN0E1h2IQ8sekgvQMj3HjpAqorywq9HINh\nQmhprOLKFbM4fKIvk4lkOI2x0M6aUylQWUHf2BOA2gWabwXSRpFlqauEJrX2KSv6Q+zkSeVs29ZY\nY8ASGrlGyy+mRPV1yFHodBulx1guK8sd+9DwSDrTaqmpPjxrExwLWVfvMKNj6VjXpmdJOxHhEVL3\nEAAAIABJREFULg3KRblVPcWtzZcocKxjgBLLYp6rEFqWxYolTfQNjubUStPFKGQJ8Kxj1RWlXLfa\ntEkyTC9uWbOYEsviV8/tGdevO8PUYAX+RsrpKh0ku1GnM1YqlYUlPpsvixN4peOyVK/RSlS7K61Q\nYnwrVIyXtR7aKPyv+APm4+X8s8eW+sixtyksjdpZlnofjuemTWQxVbhfvQr7qZCsTb8rMi4mLeiy\nbHPbQAWD7YP9NtUN1bMVuto6B2iqr6A0lVWl5rrWM29tSTAKWQIef/kgfYOj3HjZgjx/tcFQ7Mxq\nqmbN+bM5fKKP9dujG/MaTgdy3YdxaMZw++Ku4uUmqvef37CjjrvyFC29NWbfpUJTaUzsslQMp5ll\nqanD5Cjdp2oJTaqgJ4kVTDpemBJaUZaisjxFb/9IRulpaczvJhCs/n88og1Uc2NusdkoJS/Yl3No\nZIyu3uHQ7E6/XBKMQqbJwNAoj27YT02lsY4Zpi/vXrOYVInFfzy3J7QP3JmAEOI2IcR9vudX+Nq8\nfcl3/MtCiPVCiHVCiEunbIEZE5mmb9FWW1hgPG7DqMPOCxkj62TEI8YOqRGdpdnL0lt6WjN4zW+d\nixsvO3dUvF5QTj2m/l7i5XQtnAk9ljlyYWPqunMdWUdBj2uUXl6WoqGmnBNdAwwMjdLTPxJqSWuq\nq8CywhSyYKN012Xpynny0Q3VjYVs0njspQP0DY5yw2ULqaow1jHD9KSlsYqrL5zL8Y4Bnt96tNDL\nmXKEEN8C/oHce8b3gNvdNm+XCyEuEkJcAlwtpbwc+BDwnalcp3bZBi0JV06hdGTdfAqrUsBHpWV9\n0siy1LEqWbhyCndbUrdc9n3x43luVV0dNFF8nTK4Xs8VmdQqqL+X+AA7leUrZGq1W1Wxphl1FXT0\nDPuUp3yFrDRVwoy6irwYspaAbENtOaUpK+Oy1LWkJcEoZBr0Dozw6IYDjnXMZFYapjm3rFlMaaqE\nX6/bcyZW71+Hkx1uAQgh6oEKKeUe9/VHgetwWsOtBZBSHgBKhRDNU7HA7M06/qamW/YiaGFRNRef\nuPIYWdeYja1VgFRZwiOhy1Kdx6BnSVMuJHPUP56GMu13RSrktIvcKiyXwfi6KHTtnrqGr4DnXDmJ\nv0Zb1Hc2lbKwbZsBr9xGVbgxpaW+kg6332Zb5wANNeV5Ja1KLIvm+sqMohWVJFBdWUZ1RalRyCaL\nh17YS//QKO+6crGxjhmmPTPqKnjHJfM42T3Es1umZ49LIcSnhBBbA/+tklL+PCAabAHXAzS4x7tC\njk8+7r1HVZsraNFSkTT7TmWx0VUQdAgOER/grjGedsKDN6a+yzKJ+06lWNpamQy5XwSVQq0uDJtZ\noWrizHh2TFKGdpkWn6BeIV478DxELi/WMlyw2e232d49SHv3UGhMGjjWr57+EQaHR2O7DrQ0VI7L\nZWm0CwUnugZ4/OWDNNdXcO2qeYVejsEwJdx8xSKefuUwv163lzUrZ2dS0qcLUsq7gbs1RIMt4OqB\nTmA4cLzOPR7LRHQeKCstyd5csSPHLHd/PJa7566puYbWlto8uepqJ+usssIp49NQXxU6Zl2dc5Py\nbm411RWhco3ujaqqqiwzf5hcibuuivJSSkpKSNnpyL1YJRap0lRmT83NtdTXlOfJlZWlsICqaue1\nxhnVoWN6e/X2UlsXvpdqd466WmfvVZVloXIN9Y5uXus2wi4vS4XKdQ85RUWrqsooLUthlVihckNu\n8dHy8lIqKrN7bm3Or7eVKi3JKY/R0BB+/ircz7veDXavrYnYc1W5K+coGpURe/a+D3V1TqB8aWlJ\nqNxRt+BqVXU5ZeWlWFb4v4PSSud7U15RmlG1mppqwr87JRapVAk17nmprwvfc1lZChtoaHQaj9fU\nlIfK1dY4562sspyxtE1LY/j3Zv7serbt7SCdStHtNhE/Z1lr3ndx7sxa9o+j7MX0uspOAg8+s4fR\nMZvbrl5KWWlR1rI1GBJTX1POOy9fyH88t4eHX9zPbVcvLfSSCoKUslsIMSyEWArsAW4AvgKMAf8o\nhPgnYAFOr15lee6JaNU1mnEjW7FjDg87bpoh113T0d5HWYjlYaDfaeY8MOj87e4ZCB2zt8d1wbhD\n9PcPh8p1dfZnXgcYGR4LlevsdW7Ug0MjjI2lnSKfEXuxbZuRkTEGB52b4MmTvQz159eBHB1NY9vQ\n1zecWUvYmINDI+64zvO+3qFQOe+z6Xb3Pjg4EirX3e287nxGNqOjEXv2fTYjI2PYEXv2qsEPD40y\nWOY4strb+0iFJNqk3c/OOzFd3eHnz/s+dLmWm/7+iD27ikan65IbHhoN/z6456+7Z4B02nbcfTHf\nh76+YWcNdvh3tts9Z0ODI+AqOB0d/VSn8q1a3nw97nmJ+s6OjDqfsbeGgYjvrPe9am93OgSMjISf\nv2o3eeDNve0cPN5DVUWKwb5BhvqHcuTqq8ZXo9S4LGPYf6yHF7cdZcHMWq5YMbvQyzEYppR3XraQ\nxtpyHt2wn/bu5PEQRUz27ubwJ8B9wHpgk5Ryo5RyE/As8AJwP/C5qVyg5XOmTcBgzkiarixlc/FA\nAVLd3pixQf2BV+PbCKmDxy2fhVEH3cKwui5LL4QsuitCrpx6ffEZjP4XlLFhgSxLnUC8OPer/xzE\nJJbqB5t5Y9qB5zFDameqhizFT3mpozKNpdP09I9QX10eOrdXAy0pxkIWgW3b/OKpXdjAB9+2zLSS\nMZxxVJSnuO3qpfz4dzt48NndfOpd5xV6SVOClPJp4Gnf8/XAlSFyXwW+OoVLA3xKgeKalBdDpnnT\nUt7ctFapL5gTkB6FIl7OL6ajxeju2UM/UzUwgQqN7ARlxmEwkUGZuTlBMYWJb4l2rBLqn1fnY0zy\nPVTLBmLNdLJB7OhElJb68SlkxkIWwStvnmDbnnZWLJ7BiiVNhV6OwVAQ3rJyDvNba3l+61H2Hzt1\nd5thgtD56Z/4R6SuBhX/snYyQY4lzUZ1F9TqZWklD6yPX2IwEF7vM1X1A3WUBE3Tl2Lq5IVcA2tR\nyanGy8ytOZ7KYppj+VLMrdF1ICdpM9JimrvGKPwqrR2zvrLS8alWRiELYWR0jJ8+vpNUicXt152t\nkY5tMExPSkos/vDas7CBf39s54RVaTecChZJzBO6riy1JUbTFRm02MRPG/m++DH0Ro12q3oPkmlu\nqj6RPtHYae2MtShqvOzqtFygtq3MJNStWpLfkSHeYqqqV5ZTQDZm9tzPUJ1lqXUt0tW0gm9TjDdZ\nl0GjkIXwyPr9tHUOcu2q+cxtyc9qMRjOJFYsbuKis1qQBzp58XXTUqnQePcYlesn5+ZPzE3GQ1s3\n0S+HoCuopSRMkNULfFa8tG/8GDndShHKXpaa7sVcvPMXvchcK5BiNKVVSVfx1gv6ylm3bnydgsTn\nJfA8Uk7Tve/IakycEKOQBWjvHuShF/ZRX1POe65aUujlGAynBR++bjnlpSX87Ik36XczkgyFJBDz\nEofSDeOMpV2vTNN9lw2Ej9d2kgTC6wXX+12bOg43Deuhpvsu8LbYWXU+bZ0eldm4uYQotBNtxdv9\nvJV7VljSsnK+86fZ9V23ObzKJJnWPs/x32319y4co5AF+OnjOxkeTfOBa5aZIrAGg0tLYxW3rFlM\nd98wDz67p9DLOaPJXOpVQf3BG6uui1FlLVL2ONSLaUristSP3dJ92+S4nlT5BH43n3YvS9WkATea\nygqkq3gH3zduwYziHW8JDTv/ca7D3G0oPkfN2DDdIDLdMICkGIXMx+Y32nhJtrFsXj1rzjdlLgwG\nPzdetpBZTdU8sekg+46aAP9CYvnv7AoSZwhOFNoTq0Us0OplSUZOHYME+hmoSjnfjT82PSHwfpXb\n0BtThWNxUyneuUFkqr6cyobq3tyK85Lv5tOwP6liyNC3MvrH07OXqn+U+MecSIxC5tI/OMK9ayWl\nKYuP33SuKXNhMAQoKy3hj284G9uGex7ZwejYGdfn8vTAyvxP72at6b5TBXETUGLUbiK9QHjPFanr\nXoydO2AROWUXo2Y/0Mj3RWD7B42T02jI7bgsfXLKbFUFASuQQkx7XmXwvydmhxyMHFP3u+iNp3Cf\nJ9WxNBS3JBiFzOXnT+6is3eYW9YsZp4J5DcYQlmxuIk1K2ez72gPD6/fX+jlnNGo4muCr+sUNY2V\nS+jmS2w/iNlOfuamZuxOkpt/DGqxhG5aN5FBnQWqnxU50UkZKktarrkoZpyc71eySPhYl6AvGUTp\nPtewuDmrU1lW/T8i1O7hpBiFDNi+r4NnXj3M/NYabr5iUaGXYzCc1tx+3XIaa8v59XN7ODiOfm2G\nU8PCysYNJbSyxAueyqqyJK00YGtkWUKC4H8d16ZufB2acgENTxE7riSpayzHfadSvJWWqsB3S8tl\nGa2dWD6NTCf437/GKDyXpS7aSRmayQRKa/I4OeMVsv7BUX78u+1YFnzi5nMpTZ3xH4nBEEtNZRkf\nv+kcxtI2dz30unFdTjVW3oNYMfX9PNe6o1ImVNmT2RuwQi5gYUl0a4sxTXg1vnLWEoHubTVJkVTQ\ndKElcDerxtRqnRRAfZ4VcoFXdJTQuBAy//crqwzGbdr3+WgojXHDZTONtYbzpo9mnCFPZ7z28ZPf\nS050DXLzFYtYMqe+0MsxGIqCC5a1cNX5c9h/rJffPr+30Ms54/C7vlRCWSVB91d/PBMVq5+nMMas\nz+tdqHQp5b0vSk7P/ZrUopWkQ4DjsoxSVvVcoH7Z4FqiSF7eRCHnU4CVclrjZVG5IrNy8Uq/cm5d\ni2nOcVsr+D8JZ7RC9sK2o7y47RhL59abmmMGQ0I+dO1ZNNdX8Jvn9yL3dxR6OWcMmgayLLrxM7rW\nhrRCTNPC4n9F12Wp5UXTUNyCN2B1L0vPFakICteMQUqCbjkL5XnWDRb0hlMmZWQE4+Ph/Muz1cpT\nRlZBzmetUow0ExSS/og4Vdd0kDNWITve0c9P1koqylN89tbzjKvSYEhIdWUZd7xnJSWWxfd/vY3u\nvuFCL+nMwbKU7jjtm0xgmFO2NmRIEOVj24msCnGWCd1YMxLIJd2yWvGy9SySmj7LnDg8rQxPfZfl\nqTpB81onJTjRcaI65U3yCr7qFppVjOfNP9GckVrI4PAo//uBrQwMjfGRG85m5ozqQi/JYChKzprX\nwPuuWUpX7zA//O3rpNOTcJUy5GABluVduvUCvnVIHPyvsEqkVXI5MUPxeoTXu1AdDmfFPc1bo65F\nS1WTS7fBd56FJW7PBIL1FYPqWtLU59nKkdPRYZIoJ6qYNJ2yF8HMUrWOF59skeeyVMYe2rHxcOPl\njFPIbNvmx7/bwaG2Pt5xyTzWrJxT6CUZDEXNjZct5IJlzWzb084vn95V6OVMfzLNLFV3g+Q3Vt/b\nQkbLVTpUN7fEtbt0mKDsNv3A9fjnwReUyk6eNVJDVtl7MvBcIag+zwG5qOGCe9GJ14sbNMdlOVGx\ngt54scPlB/XruEBj3a/j+36ecQrZw+v3s3HHcc6a38CHrl1e6OUYDEVPiWXxmVvPY1ZTNQ+v38+6\nrUcKvaQzhrgbV3IrwqnPmSOXIIg7cRFSzRuwdjFcnfgnDbT7NWqOmSMSM6aW+y4wqPL7oFRW/a/o\nn2udgsJZtTvOTZvAehh4Hr9C9XiRz0+RM0ohe3HbUe5/ahcz6ir40/euNHFjBsMEUVNZxp9/4AKq\nK0r510d28MaBzkIvadpihTyKQ23pyHXLqa1AmTdGiFl6cnkWlnifpc4NOK9/Z7Sk4vVcMe16Zbqz\nenuJyyzFysopRvUnPKjmVlqf8vasVmp16oupyrjmWJ8Ca4mS1nYxZr7b8d/FJOVN9GMp9TljNJJt\ne9q5+6HtVFWU8pcfvJCG2opCL8lgmFbMbqrmc7etxLbhW/dvMf0uC0yeu0bRr1FV+ikYdxVpOdF2\nBwbivSLk/MtLHOamiEHyYh7165WpbugqpVZ/z7oWTkfOp+4oNq2Uc1HW5NK0FuVkY8acv2Bduji8\nPYe+N2dJyUxYuu7crMsybn3JOSMUsp0HO/k/D27Fsiz+7P3nM39mbaGXZDBMS85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KKTfwA2A54Af+Umt9xPH4O4AvAFHg51rr+0bLFmF4mjv6eXnnaSaX57N2qSSt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TDSyfV0TJBJomYuGMfKYWZ7Gjopo7r19Ablaq2yGpOGGMuW2Yx7cCV45zOADM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\nUyqtKKBc6seGFWAXVLpV9ebWzkDVTBLwz51XLns4JbZPu8z33S2Lx6i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sLCEzlywUCrFx1ynS04Ks8rpQEtmapVP4zR8P8szWY5aQmQuo6r3AvdHLRaQK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\nHGPAtuDtOtTPYDjGkrnNyRX7Z9pVAPSe7qzjtx/o5TuPrOe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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for window in ['boxcar', 'hanning', 'hamming', 'blackman', 'blackmanharris']:\n", " m = 513\n", " w = get_window(window, m)\n", " n = 4096\n", " w_fft = np.fft.rfft(w, n)\n", " freqs = np.fft.rfftfreq(n, d=1/m)\n", " plt.figure(figsize=(10, 4))\n", " plt.subplot(121)\n", " plt.plot(t, w)\n", " plt.xlabel(\"sample #\")\n", " plt.ylabel(\"amplitude\")\n", " plt.title(\"{} window\".format(window))\n", " plt.xlim(0, t.size)\n", " plt.ylim(-0.025, 1.025)\n", " plt.subplot(122)\n", " plt.plot(freqs, 20*np.log10(np.abs(w_fft) / np.abs(w_fft).max()))\n", " plt.xlim(0, 25)\n", " plt.ylim(-120, 1)\n", " width = compute_mainlobe_width(w_fft)\n", " width_bins = width * m / n\n", " level = compute_sidelobe_level(w_fft)\n", " ylim_range = plt.ylim()\n", " plt.vlines((width - 1) / 2 * m / n, ylim_range[0], ylim_range[1], lw=3)\n", " xlim_range = plt.xlim()\n", " plt.hlines(level, xlim_range[0], xlim_range[1], lw=3)\n", " plt.title(\"{} window\\nmainlobe width = {:.0f} bins, sidelobe level = {:.0f} dB\".format(window,\n", " width_bins, \n", " level))\n", " plt.xlabel('frequency bin #')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can put this information within a dataframe to display it in a nicer way:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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mainlobe width (bins)sidelobe level (dB)
blackman6.136963-58.238288
blackmanharris8.140869-92.034821
boxcar2.129150-13.383597
hamming4.133057-42.680924
hanning4.133057-31.475492
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" ], "text/plain": [ " mainlobe width (bins) sidelobe level (dB)\n", "blackman 6.136963 -58.238288\n", "blackmanharris 8.140869 -92.034821\n", "boxcar 2.129150 -13.383597\n", "hamming 4.133057 -42.680924\n", "hanning 4.133057 -31.475492" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "props = {}\n", "for window in ['boxcar', 'hanning', 'hamming', 'blackman', 'blackmanharris']:\n", " m = 513\n", " w = get_window(window, m)\n", " n = 4096\n", " w_fft = np.fft.rfft(w, n)\n", " freqs = np.fft.rfftfreq(n, d=1/m)\n", " width = compute_mainlobe_width(w_fft)\n", " width_bins = width * m / n\n", " level = compute_sidelobe_level(w_fft)\n", " props[window] = {'mainlobe width (bins)': width_bins,\n", " 'sidelobe level (dB)': level}\n", "df = pd.DataFrame(props).transpose()\n", "df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can sort the windows by increasing mainlobe width:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/kappamaki/anaconda/lib/python3.4/site-packages/IPython/kernel/__main__.py:1: FutureWarning: sort(columns=....) is deprecated, use sort_values(by=.....)\n", " if __name__ == '__main__':\n" ] }, { "data": { "text/html": [ "
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mainlobe width (bins)sidelobe level (dB)
boxcar2.129150-13.383597
hamming4.133057-42.680924
hanning4.133057-31.475492
blackman6.136963-58.238288
blackmanharris8.140869-92.034821
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" ], "text/plain": [ " mainlobe width (bins) sidelobe level (dB)\n", "boxcar 2.129150 -13.383597\n", "hamming 4.133057 -42.680924\n", "hanning 4.133057 -31.475492\n", "blackman 6.136963 -58.238288\n", "blackmanharris 8.140869 -92.034821" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.sort(columns='mainlobe width (bins)', inplace=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or by increasing sidelobe level." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/kappamaki/anaconda/lib/python3.4/site-packages/IPython/kernel/__main__.py:1: FutureWarning: sort(columns=....) is deprecated, use sort_values(by=.....)\n", " if __name__ == '__main__':\n" ] }, { "data": { "text/html": [ "
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mainlobe width (bins)sidelobe level (dB)
blackmanharris8.140869-92.034821
blackman6.136963-58.238288
hamming4.133057-42.680924
hanning4.133057-31.475492
boxcar2.129150-13.383597
\n", "
" ], "text/plain": [ " mainlobe width (bins) sidelobe level (dB)\n", "blackmanharris 8.140869 -92.034821\n", "blackman 6.136963 -58.238288\n", "hamming 4.133057 -42.680924\n", "hanning 4.133057 -31.475492\n", "boxcar 2.129150 -13.383597" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.sort(columns='sidelobe level (dB)', inplace=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This makes it clearly apparent that mainlobe width and sidelobe levels are in fact a compromise. Either a window permits clear positioning of peaks, or it allows identification of peaks with large amplitude variations. In the next section, we apply this to spectral analysis problems." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Examples of signal analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A single sinusoid " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a first step, we'll look at the effect of different windows on the Fourier transform of a single sinusoid. Let's generate our sample data and look at it." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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KWkdU35lbt15EfNqhjd3j2lEeuvVqyfLNZLRbkbZ6lDJsKyZtBaJLGHPr3Vb0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1jOVXwnisy1WSOm6RwZjbME4BVZNfxOmOQonbY9+4kM1ZF7XKUkHsBRV9rsgg2eXtc2ZEYKAW62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\nU+eq+/W9RN2oO9Tv/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.arange(0, 2, step=1/500)\n", "m = t.size\n", "s = np.sin(2 * np.pi * 10.1 * t)\n", "plt.plot(t, s)\n", "plt.title(\"sinusoid, {} samples, sampling rate {} Hz\".format(m, 1/(t[1] - t[0])))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now perform the FFT with several windows and plot its magnitude." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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npbO/zs7emokZ6gLBdCPEWCA4isq68ID7xWVZE45JksTyuRaGvIGE45hjO2/5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e7rbedfwKbfezdWKsXZz99M4qy0TK0EavGM/wC42zCM64C3AV/Ivv6PwBsNw7gGuELX9creucKK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\n7viB6yGbqRSzTz6Jt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for window in ['boxcar', 'hamming', 'blackman']:\n", " n = 4096\n", " w = np.fft.rfft(s * get_window(window, m), n=n)\n", " freqs = np.fft.rfftfreq(n, d=t[1] - t[0])\n", " plt.plot(freqs, 20*np.log10(np.abs(w)), label=window)\n", "plt.ylim(-60, 60)\n", "plt.xlim(5, 15)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This plot illustrates the fact that the Fourier transform of a windowed sinusoid is obtained by shifting the Fourier transform of the window used in the time domain to the frequency of the sinusoid.\n", "\n", "Depending on the window used, we clearly see the compromise between narrow mainlobes and low sidelobes in this plot.\n", "\n", "The mainlobe widths computed in the previous section allow us to size the frequency bandwidth over which the Fourier transform of the sinusoid will stretch, using the following formula:\n", "\n", "$$\n", "\\Delta f = \\text{window_mainlobe_bins} \\frac{\\text{sampling_rate}}{\\text{original_signal_samples}}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In our case:\n", "\n", "- boxcar: 2 * 500 / 1000 = 1 Hz\n", "- hamming: 4 * 500 / 1000 = 2 Hz\n", "- blackman: 8 * 500 / 1000 = 4 Hz\n", "\n", "This formula allows for accurate sizing in case of interferences with two close frequencies as can be seen in the next paragraph." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two sinusoids with close frequencies" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this problem, we're looking at the problem of estimating the frequencies of two sinusoids that have close frequencies. \n", "\n", "First, let's generate our sample data and look at it." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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VD1wRy5UimktFVqcGAJAChuh0s5LqerAI2K8CuF/X9SUAffh0+K/N+qGtrS52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JAAAG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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.arange(0, 1, step=1/1000.)\n", "m = t.size\n", "s = np.sin(2 * np.pi * 10.1 * t) + np.sin(2 * np.pi * 12.3 * t)\n", "plt.plot(t, s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As the frequencies of the sinusoids are close, we observe a beating effect. Let's now perform the Fourier transform of this signal, using a blackman-harris window. We do zero padding to have a smooth spectrum representation. " ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0, 20)" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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WuKNTrERiIyXJR1qyT13cLqWAlrjTrFOsRGImLyuF1s4BrYV2IV+kf8E0zSzg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\ne87wlV8e4GfPnODRV6t56UA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 4096\n", "w = np.fft.rfft(s * get_window('blackmanharris', m), n=n)\n", "freqs = np.fft.rfftfreq(n, d=t[1] - t[0])\n", "plt.plot(freqs, 20*np.log10(np.abs(w)))\n", "plt.ylim(-60, 60)\n", "plt.xlim(0, 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The previous plot doesn't allow us to identify the two spectral peaks present in the original signal. This is expected, because we used a window with a very large mainlobe. What about using a window with a narrow mainlobe, like the boxcar window?" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0, 20)" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ppqljiEinnfv2FLNvSx5/8/13+OWb9WxenUHJDGUC5zxmbRdff+I0DoeN33to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\niXLy8zcuMzx6bfGq+Sx7QJv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QAlpERMSCFNAiIiIWpIAWERGxIAW0iIiIBSmgRURELEgB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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "w = np.fft.rfft(s * get_window('boxcar', m), n=n)\n", "freqs = np.fft.rfftfreq(n, d=t[1] - t[0])\n", "plt.plot(freqs, 20*np.log10(np.abs(w)))\n", "plt.ylim(-60, 60)\n", "plt.xlim(0, 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, we can clearly see our two peaks, at the expense of very high sidelobes. These sidelobes can hide other peaks, as we will see in the next example." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two sinusoids with different amplitudes " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's generate our sample data: two sinusoids with different frequencies and different amplitudes. One of them will have a low amplitude." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Jq6d4jAZkoj9KFp2AWQdjHkQzAdI4RCZkeEnXpnI6DaV1UrJEg7FvZHpYpx/t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\n94V0qDZpdVUZFbESjpzoY3IyPnVQH+YDokgkwu9+qIX2swNTk4HDrGV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.arange(0, 1, step=1/1000.)\n", "s = np.sin(2 * np.pi * 10.1 * t) + 0.025 * np.sin(2 * np.pi * 15.2 * t)\n", "plt.plot(t, s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can barely see the second sinusoid in the time domain plot. What about in the frequency domain?" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0, 20)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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iTnYR0xhMjQYDKsusGYrE4mug1eyMRdo4Ssy4cXUNhsaC+OneeCZMVLH+OZ0V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\nSEADQEMCGgAaEtAA0NACm1RCcZ8N99oAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 4096\n", "w = np.fft.rfft(s * get_window('boxcar', m), n=n)\n", "freqs = np.fft.rfftfreq(n, d=t[1] - t[0])\n", "plt.plot(freqs, 20*np.log10(np.abs(w)))\n", "plt.ylim(-60, 60)\n", "plt.xlim(0, 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The boxcar window sidelobes hide the second sinusoid at the 15 Hz frequency. Using a blackman window, we can make it appear!" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0, 20)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ahKwD+pm3e6AoiblnbgGbuTt2rYGCxPaolBkGNBFmArqWu4gVHUEQ4HKYs1oH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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 4096\n", "w = np.fft.rfft(s * get_window('blackman', m), n=n)\n", "freqs = np.fft.rfftfreq(n, d=t[1] - t[0])\n", "plt.plot(freqs, 20*np.log10(np.abs(w)))\n", "plt.ylim(-60, 60)\n", "plt.xlim(0, 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So again, it's all about making compromises. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conclusions " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We've reached the end of this blog post. I think there are a couple of nice takeaways from this exploration:\n", "\n", "- I realized that digital signal processing is far from easy. Even doing \"just a basic Fourier transform\" actually implicitly makes you use a boxcar window. This might or might not be a good thing depending on what you do. \n", "- The mainlobe / sidelobe plots I produced above can be used as references for practical applications. In particular mainlobe sizing is a great thing to do when working with your own data.\n", "- There's no one-size-fits-all best choice for digital signal processing windowed data. Carefully explore the different options you have before jumping to conclusions.\n", "\n", "I hope you've enjoyed this post. I've you like this topic and music in general, I highly recommend [Xavier Serra's class on Coursera](https://www.coursera.org/course/audio)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This post was entirely written using the IPython notebook. Its content is BSD-licensed. You can see a static view or download this notebook with the help of nbviewer at [20151028_FilteringWindowProperties.ipynb](http://nbviewer.ipython.org/urls/raw.github.com/flothesof/posts/master/20151028_FilteringWindowProperties.ipynb)." ] } ], "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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }