{ "cells": [ { "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", "from numpy import sin, pi, linspace\n", "from scipy.io import wavfile\n", "import IPython.display as ipd\n", "\n", "# Stdlib imports\n", "import os\n", "import sys" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Lab 8\n", "\n", "## Set your names on git!\n", "To make it easier for me to grade, make sure you set your username to your **full name** as it appears on bcourses and set your email to be your Berkeley email account. Make sure to ssh onto the SCF cluster and do the same there.\n", "\n", "Git configuration:\n", "- Who are you? `git config --global user.name \"Eli Ben-Michael\"`\n", "- How can I reach you? `git config --global user.email ebenmichael@berkeley.edu`\n", "\n", "## Numpy and Matplotlib: A Basic Fourier Analysis Example\n", "\n", "\n", "### Creating a Square Wave\n", "\n", "We're going to look at reconstructing a square wave:\n", "\n", "$$ y(t) = \\text{sgn}(\\sin(t))$$\n", "\n", "First, create a function which returns a square wave" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def square(npts=2000):\n", " \"\"\"Create a real square wave.\n", " \n", " Parameters\n", " ----------\n", " npts : int, optional\n", " Number of points at which to sample the function. \n", "\n", " Returns\n", " -------\n", " t : array\n", " The t values where the wave was sampled.\n", " y : array\n", " The square wave approximation (the final sum of all terms).\n", " \"\"\"\n", " \n", " # get time points\n", " t = linspace(-pi, 2*pi, npts)\n", " \n", " # create the square wave\n", " y = np.sign(sin(t))\n", "\n", " return t, y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's plot it." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_square(npts=2000):\n", " \"\"\"Plot a real sqaure wave\n", "\n", " Parameters\n", " ----------\n", " npts : int, optional\n", " Number of points at which to sample the function.\n", " \"\"\"\n", " # create the square wave\n", " t, y = square(npts)\n", " # use the basic plt api\n", " plt.plot(t, y, label=\"True Wave\")\n", " plt.grid()\n", " plt.legend()\n", " \n", " plt.xlabel(\"t\")\n", " plt.ylabel(\"y\")\n", " plt.title('True Square Wave')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_square()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reconstructing a Square Wave with a Fourier Series\n", "We can represent a square wave $y(t)$ as an infinite series:\n", "\n", "$$ y(t) = \\frac{4}{\\pi}\\sum_{i=0}^{\\infty} \\frac{1}{2i + 1} \\sin((2i + 1) * t)$$\n", "\n", "So, we can approximate a square wave with just a few terms of this sum." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def square_approx(nterms=5, npts=2000):\n", " \"\"\"Add nterms to construct a square wave.\n", "\n", " Computes an approximation to a square wave using a total of nterms.\n", " \n", " Parameters\n", " ----------\n", " nterms : int, optional\n", " Number of terms to use in the sum.\n", " npts : int, optional\n", " Number of points at which to sample the function.\n", "\n", " Returns\n", " -------\n", " t : array\n", " The t values where the wave was sampled.\n", " y : array\n", " The square wave approximation (the final sum of all terms).\n", " \"\"\"\n", " # create equally spaced time\n", " t = linspace(-pi, 2*pi, npts)\n", " # initialize the wave\n", " y = np.zeros_like(t)\n", "\n", " # add nterms terms in the infinite series\n", " for i in range(nterms):\n", " y += (1.0/(2*i+1))*sin((2*i+1)* t)\n", " y *= 4 / pi\n", "\n", " return t, y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, let's plot it" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_square_approx(terms, npts=2000):\n", " \"\"\"Plot the square wave construction for a list of total number of terms.\n", "\n", " Parameters\n", " ----------\n", " terms : int or list of ints\n", " If a list is given, the plot will be constructed for all terms in it.\n", " npts : int, optional\n", " Number of points at which to sample the function.\n", " \"\"\"\n", " \n", " if isinstance(terms, int):\n", " # Single term, just put it in a list since the code below expects a list\n", " terms = [terms]\n", " \n", " for nterms in terms:\n", " t, y = square_approx(nterms, npts)\n", " plt.plot(t, y, label='n=%s' % nterms)\n", "\n", " plt.grid()\n", " plt.legend()\n", " plt.xlabel(\"t\")\n", " plt.ylabel(\"y\")\n", " plt.title('Square wave with n terms')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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s4EszsyLGxpNykzEbBVuOHCNEpcJTIaexsZFzzz2XhIQEfvrTn/od27p1K3Pm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\nCW7y2JhgH1K7hPPvrRlNLwR4gQq7k2e+2EdCuB/3jIhvSdY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_square_approx([2, 10, 100])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And let's overlay the true square wave on top" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_both(terms, npts=2000):\n", " \"\"\"Plot a true square wave and construction for a list of total number of terms.\n", "\n", " Parameters\n", " ----------\n", " terms : int or list of ints\n", " If a list is given, the plot will be constructed for all terms in it.\n", " npts : int, optional\n", " Number of points at which to sample the function.\n", " \"\"\"\n", " \n", " # use our previous functions!\n", " \n", " plot_square(npts)\n", " plot_square_approx(terms, npts)\n", " plt.grid()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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paWm11vT+3//93yatS3HnnXdSVlbG6tWrff/am8IAozQMkY6fpVFWXRZQaZyS\ndgpxjjjWFqzlzMFnkpj9i94xIIRKwxED57+qH6RvXx60xEhA8jbCR3/Sa5GfdGebiRiQAVOhZC/H\nJ6aRmpDK2oK1TO49mV4J9eMzcY44SmP9rAtjaXRIjNIwRDRilRHpfe+9lFWXkVjHPQXQLbYbj5/4\nOH8Y+wduPupm2LUEOveBbmmhFbb7IDjnGdi7Ct65Qq/j0RgH9sAb5+py5+e9rNfuCCX99apxUVkr\neGrGU1wx+grum3ZfwKbxUfFsGdUZ16ChAKh2amkYGsYoDcNhgX3SEbiVO2gweWrqVOYcOYdOUYmw\n60c9gpZA03zamJFnwhmPQubn8PZl4CwN3jY/A145HarK4NJ3oXNq6OT00nMkxHSB3UsY0m0If574\nZ9/yrnWJd8RT7q7AOcMKkrfjlFtDcIzSMEQ03phGhbsCIKClUYvCbVCaF1rXVF2O/h84/RHI+Axe\nnAG7fqq9310Ny1+CF04CVwVc/iH0Gh0eWW126DcJdi9ttGm8I55yVzm+ObdGaXRIIn2ehqGjYz2X\nyl1aaQSKadRit/WADqfSAJj0B+2uWjgHXjkNeo+D1Al6JvbOH3SWVNpxcM7TLVuCtjUZMAW+/hLK\niyC+e9Bm8VHx5Ffk19RpMEqjQ2KUhiGysR5MeoTbBKWRtRxiu0DSkLaWrHGGzIDrf4ZVb8DGD2HL\nIrDH6BX4jrhUpwQ3sKhSyLDiGuxeCiNOD9os3hFPhauixu1nAuEdkgj4xRoMDaEfTBXuSqAJE+Sy\nV+qHciQ8jEGvy33MtXDlIrhlK9y8AS76LwyfFTkyph4JtijY07CLKj4qnvLqclQ4YkWHAYWFhZx4\n4okkJiZyww21qw2sXLmSsWPHMmTIEObMmRO05P/hQIT8ag2GwIjVt6o8en5ArL2BSW9VZbBvI/Rp\ntLqzwZ+oWOg9BrypykHwxjRETEwjELGxsdx333088kj9xbmuu+46nn/+eTIzM8nMzOSzzz4Lg4St\ng1EahghHP5icVvpqrKMBpbF3tZ4n0dcojWbT5yh9/zzB02jjouJwup14vIGmdqo0du7cyciRI/nD\nH/7A6NGjOeWUU6ioqGj0ewkJCRx77LHExtb+jebk5FBcXMyUKVMQES677DI++OCDthK/zTExDUNk\nYz2YnB69bkS0PTp422xr8a0+R7W1VO2P1CNh+YtQmAk9Atfkindo16BLaQUeinkaDy17iM1Fm3G7\n3djt9lY55ojuI7ht0m0NtsnMzOStt97ihRde4IILLuDdd99tVml0f7Kzs+nbt6/vc9++fVt1caZQ\nY5SG4bCgymNZGg25p7JW6AnabbiiAAAgAElEQVR9Ca23hkGHwatos1cGVRreJASv0qi/sk374VBK\no9clUPxCDuO4kFEahsjGa2m4taURY29gFbTslTWZQIbmkTwUojvpezjhtwGb1FgaLr0hBO4pr0UQ\n6uVeW1oaPRB9+/YlKyvL9zkrK4vU1DBM5GwljNIwRDj6wVRtWRpBlUZxDhRnm3hGS7HZ9TySBoLh\n3sy1aq+l0Z5NjQA0Vho9GCkpKXTq1ImlS5cyefJkXn/9df74xz+2gYShwSgNQ0TjzZ6q9FoajiBK\nI3ulfjXxjJbT50j46WlwOXUBxjrEOfQa2dW+mEbHUhpNIS0tjeLiYqqqqvjggw/44osvGDVqFM88\n8wxXXHEFFRUVzJo1i1mzZjV+sAjFKA1DRKN8gfAq7GL3rSZXj9y1IDboNSbwfkPjpB4JnmrIWx9Q\n+Xoz19whdE+Fg0Cl0ZvKzp07A26fOHFirWMezpiUW0NE412EqcpT1XDmVM5aSB4G0Y1M/jMEJ/UI\n/bp3VcDd3iQEF16lEQqhDJGGURqGwwKnp6rhzKnctbq+k6HldO2vS7DkBh4Rey0Nl3JbW4zW6IgY\npWGIbCxLo9LtDG5plBXqIHjvsSEUrB0iohVv7tqAu71JCD73lKk91SExSsNwWFDlqQ4+Gzx3jX5N\nMZbGIdN7HORtALer3i5vILxmnoZRGh0RozQMEU7NPI2g6ba56/SrcU8dOr3HgqsSirbV2+W9/y7c\n9fYZOg5GaRgiG7+ChUGVRs5a6NKvwbUgDE3E6+LzKmI/fEqjnWdPGRrGKA1DRCPUxDSCWxprTTyj\ntUgeBvbogHENESHWHtvuU25bSktKoxcVFTFz5kyGDh3KzJkz2b9/fzhEbxZGaRgiGuXxuqeqAk/s\nqyqDgkzjmmotHNHQY4S23gIQ44ih2lIairYvWHg40ZLS6A8++CAzZswgMzOTGTNm8OCDD4Za7GZj\nlIYhovGWdXMqJzG2AEojbwOgTBC8NUkZp91TASyJWHssbtp3wcJQlkb/8MMPufzyywG4/PLLD4uS\n6WZGuCGyUY1YGl43irE0Wo/e4/QStSW50Dml1q5YR6zP0giFeyr3//4P56bNuNxuilqpNHrMyBH0\nvv32BtuEqjR6Xl4eKSn6HqekpLBv376WXFJIMUrDEOHULPcacHJf7jqI7Qpd+tbfZ2gZ/sHwukrD\nHtshAuGmNHpwjNIwRDQ1y71WB57cl7dR15s6jDthxOGt35W7FoadUmtXjCMGlyrWH0KgNLwWQXst\njd6rVy9ycnJISUkhJyeHnj17tuJVtA1GaRgiGuWdp+Fx1rc0lIJ9m2D8RWGQrB0T2xm69Nf3tu4u\neywuVag/tF9DIyBtURr9V7/6Fa+99hpz587ltdde4+yzz25tsVsdozQMEY34Te6rZ2kczIKqEug5\nMgyStXN6jgysNByxVHtrT7Vj91RLaW5p9Llz53LBBRfw0ksv0b9/f955550wX0HjGKVhiGys55Jb\neeqXEfE+1HqOCq1MHYGeI2HbN+CuBntNOfoYe0xNGZF2amqEsjR6UlISX3/9dbNlDCcm5dYQ4VgP\nJgmwat++jfq154jQitQR6DlKr61RWLucSJwjztSe6uCEVWmIyGkiskVEtorI3AD7rxCRfBFZbf27\nKhxyGsKI9WBSBFIam6BTKsR1C71c7R2vy8+rmC1i7DF+KbchlskQEYTNPSUiduApYCaQBSwXkYVK\nqY11ms5XSt1Q7wCGjoH1YFLBLA0Tz2gbkofplRDrxDV0TKOqzU+vlDqs01IjmUNdpjeclsYkYKtS\nartSqgqYB0R+6oAhpIjfcLZWTMPjhvwtRmm0FVGx0H1wPUsj1h6L2+Mtm942pkZsbCyFhYVmDfI2\nQClFYWFhvVnrzSGcgfA+wB6/z1nA5ADtzhWR44EM4Cal1J66DUTkauBq0HnP6enprS9tGCktLW13\n19RUig8eBLSlkbEpg7hdek2HuPJsJrudbC6ykdsB7k04fgOjJZmEXb+wzO+8ew/sxSO65tSWzVuo\njHa2+nlFhISEBPbsqenqxvJovXvgdrspKytj165dLfp+OJVGoKuvO7T4CHhLKeUUkWuB14CT6n1J\nqeeB5wEmTpyopk+f3sqihpf09HTa2zU1lX3vpQP6hzFx/ESm9Zmmd2xcCMtgxPG/ZkSfI8MmX6gI\ny29A/QTf/4Pp0yZDlFbWuzbsIm/5RwAMGzqUKdOnhUSUjtwHvETKPQineyoL6Of3uS+w17+BUqpQ\nKeUdyrwAHBUi2QyRgt8wotY8jX2bAIEew0MuUoeh50hQHijI8G2KtceiOvaAv8MTTqWxHBgqIgNF\nJBq4CFjo30BE/Avf/AqoP9vI0K4Rv5TbWjPC922EbmkQnRAWuToE3vkvfsHwWnElE3PokITNPaWU\nconIDcDngB14WSm1QUTuBVYopRYCc0TkV4ALKAKuCJe8hjDhn3LrX+V23yYzqa+t6T5IL8jkFwyP\nccTUGH/KrKfREQnrjHCl1KfAp3W2/c3v/V+Av4RaLkMEIlKTcutyQuFWGHlWeGVq79gdkDy8lqUR\nY4vxc08ZS6MjYmaEGyIbv9GsT2kUZIJym3TbUNBzpK4kbFFrrozRGR0SozQMEY0ofIuK+mIavppT\nRmm0OT2GQXEWOEsBnYzgszRMTKNDYpSGIcJRvoeUL3uqIEPPVk4aEj6xOgrJVnaalUEVY/eLaRhT\no0NilIYhslEK75SeGvfUFug2EAIt/2poXXrUVhrR9mjfDCvlMUqjI2KUhiHiUQIOmwO7zVojuiBT\n10YytD3dB4HNoUu2oFNua7KnwiaVIYwYpWE4LPDFM9wunTmVPDS8AnUU7FFacfi7p0z2VIfGKA1D\nRCNWsNXnmjqwC9xVZiZ4KEke5rM0/GfliwmEd0iM0jBEOKr2WhoFmfrVuKdCR4/hULQdXFW1LA1T\nhbZjYpSGIbJR1loaDr8gOBj3VChJHq7nxRRt1ym34ZbHEFaM0jBENtZo1hfTKMiAhJ5mtb5Q4lXQ\nBVtwiAMR67FhLI0OiVEahghHz9Pw+dLzM4xrKtR473d+BiKC3WZVHzJKo0NilIYhohGlc3Ri7bH6\nIVWQoWcpG0JHTCJ07uvLoLLbogAT0+ioGKVhiGyUAq+lUVYAlQeMpREOegzzxZO8SsNkT3VMjNIw\nRDwKax0HXxDcKI2QkzxcZ655PMY91cExSsMQ4fjN0/CuIGeURujpMQyqy6E4y2dpmMl9HROjNAyR\njVIoUVpp5GdAVAJ07hNuqToe3sKF+Rk4fDGNMMpjCBtGaRgiGm/FCp+lkTwEbOZnG3J8hQu31Fga\nRmt0SEzvM0Q2StVM7jOFCsNHQjLEdYf8LTjsxj3VkTFKwxDZeJUGNji4u8ZNYgg9PYZDQYaxNDo4\nRmkYIhql3ADEOEv0BlM+JHxYhQujvErD03BzQ/vEKA1DRKNw65Tb8oN6g6luGz6Sh0FFEVbCLWLc\nUx0SozQMEY1SHl1GpLxQL/HafVC4Req4WAo72u3Un417qkNilIYholFo91Rsab5Z4jXcWEkIMS6j\nNDoyRmkYIhsrphFdkmsyp8JNl37giCPaVR5uSQxhxCgNQ0SjcKMEYktyTRA83NhskDyE2KpSAJTH\nHWaBDOHAKA1DRKOUDoTHuMwSrxFB8jBiqnRSgkeZ9KmOiFEahohGKQ8IxCiMeyoSSB5GbFUZAG5V\nHWZhDOHAKA1DZOO1NJTHuKcigeRhRFsTNNweozQ6IkZpGCIapayYRmx3s8RrJJA8jCgra8rlNkqj\nI2KUhiHC0aPa6G4DwyyHAYCkIXgrT3mUK6yiGMKDURqGiMZnaSQNDrcoBoCoWCSmKwBuj1EaHRGj\nNAwRjagqAKKTTDwjUrDHJQMmptFRCavSEJHTRGSLiGwVkbkB9seIyHxr/88ikhZ6KQ3hxOGp0LWn\neowItygGC4nvBYDLXRVmSQzhIGxKQ0TswFPALGAUcLGIjKrT7H+A/UqpIcA/gYdCK6Uh3Ng9ThCI\n7lH3p2EIFyo+BQCbc3+YJTGEg0aVhojcICJtkbYyCdiqlNqulKoC5gFn12lzNvCa9X4BMENEhDbg\nwO71fHLOeH5+6da2OLyhhdg8us6RdOkXZkkMPjr1BcDmLAizIAZ/Fs2ZwSdXH9fm53E03oTewHIR\n+QV4GfhcqVapVNYH2OP3OQuYHKyNUsolIgeBJKDWr1VErgauBujVqxfp6enNFsZZtIdBm6vY1G9p\ni77flpSWlkacTKFCLBdI+vffh1mS8BJJv4Ed+dWkAhX7s0ImUyRdf7ho7B6oLTlEV9Hm96lRpaGU\nulNE/gqcAvweeFJE3gZeUkptO4RzB7IY6iqjprRBKfU88DzAxIkT1fTp05stTOm+vezh/4ixu2nJ\n99uS9PT0iJMpVHz8uAsldNjr9xJRvwFPNfA6iY6qkMkUUdcfJhq8B0rx6QMebLboNr9PTYppWJZF\nrvXPBXQDFojIPw7h3FmAv8+hL7A3WBsRcQBdgKJDOGdQoq2S226rGJshAqiutKrctolH0tBCHPZo\n/aaqOLyCGGooycGjQOz2Nj9VU2Iac0RkJfAP4EdgrFLqOuAo4NxDOPdyYKiIDBSRaOAiYGGdNguB\ny6335wHftJJrrB420bfCVVUOHlOILSIo2oYHUEZpRBRRXqVRXRJeQQw1FGSgALG1vdJoSkwjGfiN\nUmqX/0allEdEzmzpia0YxQ3A54AdeFkptUFE7gVWKKUWAi8B/xGRrWgL46KWnq8xvPF1l/JAcRZ0\n7d9WpzI0lYIM3IhRGhGG19LweKqgrBASksIskYGCTDyA2KMabXqoNCWm8bcG9m06lJMrpT4FPg12\nPqVUJXD+oZyjyXiVhgD5GUZpRAJWRzBKI7Jw2PSDyYVAwRZImBpmiQza0hBstqbYAYeGmRHuxVIa\nbgQKMsIsjAGwLA2bURoRht16MJm+EkFYSkOk7R/pRml48SoNm8N0hEihIAO32FBtMzXH0FKsv0e1\n2KEgM8zCGAAoyNQxDaM0QojXPWWPMR0hElAKCrbixobJnoowrD+H0xEL+VvCK4sBnCWo4myUArEZ\npRFCLEvDHqX9tIbwUrwXqstMTCMSsQZYVfZYY5VHAoVb0fWGlS8LtC0xSsPC6wFxiQPK8qG8TaaD\nGJqK9TBSUPPHMUQIlnvKFg0HdkN1RZjl6eAUZFIlgiiwGUsjhPhiGtYtKdwaRmEMXhehQhlLI8IQ\nm5/SQJm+Em4KMnDaHAgmphFa/LOnwPhqw01BBsR0NkojEvEGwr0TyYyLKrwUZFDVtR8osIVgcp9R\nGl58SkOBPdp0hHBTkIE7eYgOiBulEZG4sAOi5zUZwkdBJs7uacbSCDlepeF2QdIQk0EVbgoycXYf\nbKkLozQiCquveJQbug0wA6xw4nFD4TacXfuZmEbI8SoNjxuSh5mOEE6cJVCyF2f3NFAmeyri8CkN\nFyQPN30lnBzYDW4nVV2sNU7EuKdChvex5Pa4tNLYvwNczrDK1GGxAqvObgOMpRGBeF0geoA1VP+9\nPO4wS9VBsTwizs4piJmnEWJ8BQvdqKShoDxQtD3MQnVQvB2hS19EYWaERyja0hgGrko4uKfxLxha\nH8vKcyb2BEwgPDwohStpkH5vzO7wUJABYqcysQdg3FMRh9c95XFBj+F6mwmGh4eCDIhPxumIRgBb\nCAZYRml4sW62KHB2syrcmo4QHgoyoFsaVShEgfmZRhhWX1HKiv+BGWCFi4JMSB6G0+PUKbcmphFC\n/DS002aHLv1MRwgXBZmQPJRKdyWCsTQiDe/kPrfHBfHdIT7Z9JVwUZAByUOpcldpS8O4p0KIn6VR\n5a7SAT7TEUKPx60Dq1ZHsOqIhFsqQy1qLA2llMk2DBflRVBeoC0Nt9NyT5lAeOjwKg0Ule5KK5Uw\n05pcZggZB3aBuwqSh/ksDU8IOoKhGfjp8GpPtRlghQvvXDK/AZaxNEKId7lX/C2N6jIozg6vYB2N\nAquOUfIwnC6niWlEIv7xP7dTB8PLC/XSr4bQ4VXUyUNrLA2jNEKPgGVpmABfWPCWpU+yOoKZ3Bd5\nSM3sGafbafpKuCjI0CWPug7w9RUTCA8xyiovXGW5RwBTTiTU5G/RgdWEJP1AAszPNMLwSxqp3VeM\n0ggpBZm65JHNbgXCxUzuCzneFcncTkjsCbFdTLXbUJO/BXqMADCWRqRi/TlEWVZ5l37giDNKI9Tk\nb/LNk3G6ndiQkOSMGKXhh4hok9vl1KMpkxUSWpSylEZNRxBAmUB4ZOHvnnI5wWaD5CGmr4SSqnLY\nvwt6jNQf3VXYkJrYbBtiemMtpCa4B5bSMO6pkFGSA86DPkuj0lVpak9FIOJ9bNTtK8YqDx2FmYCq\nM8ASQtFXjNLwx9LSNR1hKJTmQuXBMArVgcjfrF97aqVR5a5ClFEYEYefpVHprtTbkoeZpV9DiVdB\ne125Lq97yiiN0CJ1LQ2rro6xNkJDnY6g52nYTMHCSMM/5dblZ2mgoHBb+OTqSOzbBDYHdNd18mpi\nGkZphBZvTMPf5Abjqw0V+Zshrhsk6EKFOhAuJhAeafj9OWpZGlCTMm1oW/K36MwpRzQATo/lnjJK\nI7SISG0/bbc0sEUZX22o8GZO+bkJbUZhRBz+zyVfX0kaAoixykNF/uaaCsPUBMJN9lSoEUGQmo5g\nd+jOYJRG26OUNrn9OoKeEW7cU5FHjXuq0mVZGlGxeulX01fanupKvUic5caFmkC4yZ4KNSI4RE+U\n8dFzJOzbGD6ZOgql+6DygC+FEGpMbuOeijDqzgj34q3XZmhbCjP1InH+SsMbCDfZUyHGUhq+0RNA\nz1G6iJ6zNHxydQS8mVN1LA2bEkwCVYThV6etttIYqh9oHk945Ooo1EkYgZo5TSamEWIEcGCnylPH\n0gAT4GtrAnQEPU8jNKMnQzOwHkw2qD3A8i39ujs8cnUU9m0CsUPSYN+mSnclNmUC4aFHBLvNXnv0\n5FUa+zaFR6aOQv5miOkCnXr7NlW6K3X2lNEZEYX3z2GjjlXew6Soh4T8zVphOGJ8m3wDrPaqNESk\nu4h8KSKZ1mu3IO3cIrLa+rcwBILhwF6Tew46g8oRa5RGW+MtH+K/gmIIZ7kamoH1N7LjqEm5hZq0\nWxMMb1v8Su146Qi1p+YCXyulhgJfW58DUaGUmmD9+1WbSyWCXWy1LQ2bXf+BTDC8bcnf5JsJ7qXS\nZVkaYRLJEARLaTikjlXuW/rVKI02w+WEou213LhKKV/JnfacPXU28Jr1/jXgnDDJURsRHOKonT0F\nOhhuLI22o6xAL+LTo47ScGuT26TcRhi+mEYdqxysbEPTV9qMwq2g3LX6SrWnGoUKmVXuaPMzBKaX\nUioHQCmVIyI9g7SLFZEVgAt4UCn1QaBGInI1cDVAr169SE9Pb5FQPVwuXM5q9u3fV+sY/UqiGVyS\nw+IvP8IV1alFxz4USktLW3xNhwNd969jArAmx8l+v+usqKpAuaNRNtr19TeFSPoN7C31cASg3Iqs\nvKxacg2p7kJKznJ++PYbaMXqxJF0/eGitLSUDd/9wGhg+a5SygrTASj3lAPgrnaRm5dHRhvfpzZT\nGiLyFdA7wK47mnGY/kqpvSIyCPhGRNYppeoVt1FKPQ88DzBx4kQ1ffr0lohMRlQU8bHxxCbEUusY\nmdWw/TWOHZYEA6a26NiHQnp6Oi29psOCn7fAGhg/87e+QLjb48b1Hxd2Wxwg7fv6m0Ak/Qa27iuh\nGohxxNCpW6facnXeDQs/Zvr4gdB9YKudM5KuP1ykp6czOl5A7Bx96kV6QiWwr3wf7IEoRxQ9UlI4\nso3vU5spDaXUycH2iUieiKRYVkYKsC/IMfZar9tFJB04Ami7imgiOMRWO7gHfhlUG8OiNNo9eesh\nPgkSe/k2eX3locoIMTQPD4K9bvYUQM/R+jVvQ6sqDYNF3gadcGApDKgpGtne52ksBC633l8OfFi3\ngYh0E5EY630yMA1o22i0CPa6M8IBOveBmM6wb3Obnr7DkrdBx43qZE4BJhAeoSjATp1AOFjJDGIS\nR9qKvPXQa3StTd5BrrTz7KkHgZkikgnMtD4jIhNF5EWrzUhghYisAb5FxzTa/JdYL3tKC6YDTybA\n1/p43Pq+9hpTa3MtS8Ok3EYY4htg1esr0QnawshbHx7R2jF2V5les6SO0qjpK6EhLIFwpVQhMCPA\n9hXAVdb7JcDYkArm7Qh1M0JAu6g2faQL6xl3SeuxfydUl9frCBUuvZiPKPCY+x1xKAJM7vPSa7S2\nHg2tSkKZNdO+zgDL+zdo7+6pyEQEOwEsDdDuk4oiXVjP0Hp4Hy7BRk8KY2hEIIqG+spoPZegqjz0\ngrVjEkt36je9RtXa7nNPqfY9TyMy8cY0PFUoVceT7guGmxFUq5K3Qadm1p2j4arx05oqtxGIWJZG\n3aQR0AMA5akpQmloFRLKdkJsFx1j9aMmEG6q3IYeAbt1S+qNoHr5ZYUYWo+89dB9METH19pcM3oy\nMY1IQ69VprOnArpyvX3FBMNblcTSndo1Vcea8CluhXFPhRpBWxoQQGkkJEOnVMhdFwbJ2jF5G+qZ\n21A7jdAULIw8FGATG1WeKjyqTin0bmkQFW8GWK2Jx0NC2a56blyoEwg3SiPEWDENIHCAr/dYyFkb\nYqHaMc5SHQivE9iD2paGcU9FHkq0pQEBBlg2u3Y3GqXRehzcjcNdEVBp+Fy5SrXrlNvIxFqECQjs\nq00ZBwUZUF0RYsHaKfmbAdVwRwixSIam43PlBnNRGaXRevgSRuoPsGopbWNphBipcU95Uz5r0Xus\nLhZmfLWtgzeXvwGTGzAFCyMMQcc0bDQwwOo1GsoLTLZha5G3QVvcdRJGwN/SMNlToccqIwLB3FPj\n9KtxUbUOuesguhN06V9vV01HMAojElEi2ILF/6BmRJxr+kqrkLuOytheEJNYb1elu5IoW5SeQ2ay\np0KM4LM0yl0Bcsy7DtDlREwwvHXIWQMp48FW/2fon3tuLI3IxK4aGGClWAOsvatDKFE7JmcNJZ0G\nB9zldDuJdcTqcjvG0ggtgl65D4K4p2w27aIyo6dDx+2C3PVaaQSg0lWJTWyWK8QQaWj3VJD0dNDz\nCboPghyjNA6Ziv1wYBeliYMC7q50VRJrjw1ZtQqjNPxpLKYBWmnkbdA1kwwtp2ALuCogdULA3U63\nkxh7DFbyeUhFMzSOTrltwD0FekCQsyZ0QrVXrHtY0mlIwN2+vmKURhiwlnuFICY36LhGdTkUtl2F\n9g6B92HSgKUR54gz7qkIRESvpmhrKD0dIGWCLrBXXhRC6dohlouvpFMDlobDa2m0vThGafjjN0+j\nQUsDjIvqUNm7GqISICnw6KnSXWmNnjxmnkaEErR6ghevFWlcVIdGzmro2h9XVOeAuyvdNe4pkz0V\naprinuoxAmxRRmkcKjlrtAK22QPurnRppaFnuYZUMkMT8I9pBB9gmWB4q7B3dVCLHKC8upz4qHiT\nPRUWBGwIDnEE7wiOaF32Yu+q0MrWnvC4tdINEs8A/SDydgRjaUQeyipYCA0ojfjuOuPQxDVaTsUB\n2L9Du/qCNXFVEOeIM9lT4UAQUIpYR2xwPy1An4mQvQo8nuBtDMEp3KrjQg2NnlzlxDvigdD4aQ1N\nR6z/7Y0pDdADA+Oeajlej0ZjAyxHvAmEhwXRCZ5xjriGO0Kfo6CqRJcUMTQfr7uigdGT1+QWhbE0\nIhC9CJN+fJRXN7BuRsoEXV+sYn9I5Gp3NKOvGKURDkRQSiuNgJP7vPSdqF+zV4RGrvbG3l/AEQfJ\nw4I28Y2ezCyNiESJXr2h0b7itSaNi6pl5KyGzn11le0geN1TJnsqHOiFAhq3NJKG6pnh2StDJ1t7\nYs8y6HMk2IOvNlzuKrdSbpVJuY1AFE3sK6lH6NcsM8BqEXuWQ9+jgu5WSvn6ismeCgfSxJiGzaY7\ng+kIzae6Qvtp+x7dYLOKaisQjrE1Ig3fc8lrlTfknorvri3KrOUhka1dUZILB3dD30lBm1R5qnAr\nt3FPhQ3B1xEaHD2BjmvkbTBl0ptLzhrwuKBf8I7gHT3FO+KtNQKMpRFpKCv+Fx8V37B7CvRDb88y\nKyXU0GT2LNOvDfSVCuv548ueMim3oUUsS6NJSqPvRF0m3fhqm4d3xNmApVFr9IRJuY1EvI//eEd8\nw5YGQL+joaLIVFFoLlnLwB7daJYhENLsqeBO5Q6JN3sqvmH3FGhLA3Rco/8xbS5ZkygrhDVvwq6f\noPIAdOoNQ06G0b+BqNhwS6fZs0zn7if2DNrE+xDSflrjnopYlNJKoymWBuiHYHLgCgAhp3gvrH5T\n/x6rSqFLPxh2Kow8C+xR4ZZOs2e5VhiOmKBNfH0lKs64p8KCX/ZUo5ZGp976h7bn59DI1hAeD/z8\nHPxrHHxxp5UKLFp5fHAd/PtIyPwy3FLqH3XW8gbNbag9ehKMeyrS0HlTOhDeJPdUjxE6ccTrbgkn\nbhd89w/41wT45j44uEdv3/Y1LPg9PH2M7jfhxlWlJxA3EM+AmjkyNZZG24tmLA1/rIdTk5QGwICp\nsO2bkGn4gLic8MFsWL9AWxWn3A89R+p9SsH2dPhsLvz3PDjpr3Dcn8Mna3E2lOQ0KQgOevRksqci\nE702ljXAaiyuZ7Npd264g+GVxVoxbP1KW98z/gbdB+p9Hg9kLNJ95dUz4MzH4Kgrwidr7jpwO7Vr\nrwFquafAWBphwS+NUDUWuBswFcry9QzncOCuhvm/0wrj5LvhkgU1CgP0D2jwiXDN9zD2fD2y+vbv\n4ZEVYPdS/dqI0qjrpzXuqchDIUhT3VOgR8x5G/SDOxxUleuB07Zv4ax/wfmv1CgM0IptxBlw3RIY\nfBJ89CdY9kJ4ZAXtyoMmWxo+91QIMErDHysQHh8Vj1u5A1bvVErx2c7P2FS4CQZM0xt3/RhiQdE/\nkI9uhMzP4YzH4NibgmdKMpEAACAASURBVI8yHDHwmxfgiN/B9w+HrzPsXKyXd+09jsXZi1meG3jk\nWW/0ZALhEYdC94X4qPigVrnL4+KjbR+x4+AO6D9ZfyscLiqPW1sYe5bBeS83bEHEdIKL58HwM+DT\nW2DDByETsxY7F0OX/qjOqXy560vW5gcukOqNaXgHWGaeRqjxeCj95hv6Lt0JQGl1ab0m72W+xy3f\n3cKln15KXlwnSOgJO8OgNJa/CKvfgBNug6P/p/H2InDm4zDsNG2Ch6Pz7lwMA6aydN8KrvvqOq78\n/ErWF6yv18zXEd7+griKUswy4ZFHN2cp3X74kh7ZZVS4KnAHWJTs5fUvc/vi27l80eWU9R6rq0Pv\n/D70wn73D8j4DE5/GEaf03h7uwPOe0nH3j6YDflb2l5GfzwePRAdeDyf7viUm9Nv5rJFl5FfnV+v\nqXeA5bn3n9YWozRCiquwEIC+L34GQElVSb0287fMp1NUJ6o8Vbyb+Z52Ue36MbQ56Dlr4PPbYegp\ncMLcpn/P7oBfPwdd+sI7V4R2cZziHCjMhLRj+e/G/xJrj8UmNt7LfK9eU29HkKf/Y20xWiOSEIFo\njwuAwe//AtSs6e5FKcWCjAXEOeLY79zPJ1nfarfkjhArje3fwXcPwfiLYdIfmv69qDg4/1X9+vZl\n2r0VKvLW61pdA4/j9Y2v0ym6E27lZllZ/YGe18qr+sRKdDGWRmhxF1v+1jidnlpaVdvSKKgoYFPR\nJq4adxVH9z6ar3Z/pV1Uxdl6hbKQCFkN710N8UlwzrPaF9sc4rrC+a9BaR4suq1tZAyE5cIr63sU\ni7MXc/GIi5nRfwbfZ9V/iNTN+zfzNCKXKKe2MOr+zTL2Z5BTlsPcSXMZ0HkAX+36CgYepwc8lQdD\nI1xlMbx/DSQPhdMfaf73O6fCuS9A/mb45v7Wly8YO38AYH/KODYWbuT3o3/PkT2PZEPFhnpN63lD\njNIIMW7dAey5hYhSlFTXtjQy92cCMDppNNNSp5G5P5P83lbgeefiWm0POg9yz0/38Pelf2988lNz\nWPa8/hGf8RgkJLXsGKkT4PhbYN3bsPnTVhNtb+lebv3+Vp745Qk8qk7Z+B3fQ0xnfrG5cCkXU1Kn\ncETPI8grz2Nf+b5aTcuqy+hd5Ge5GZ0RsXRatZUol6r38NpQqB9wR/c+mpP6ncTy3OWU95sEygO7\nltRqm1+ez+0/3M7jKx+n2l3desJ9/w9diuOcZyEmsWXHGHwSTPwfWPo07G699PptB7Zxc/rNvLr+\n1foJNzt+gO6DWF6eBcCklEkc2etIsquy68VZS6pKSHbF1WwwBQtDjN/6GFd+7qHUWVtpbD+4HYBB\nXQYxNXUqAD9VFUFCD51668c9P93DgowFzNsyj7//HDxjye1x817me7yy/pV6lk098YpzqPz2ARgy\nE4bPatal1ePYm6HXWMo/vhFVcaDBpntL9/LM6mcCWgVeqj3V/OnbP7FoxyJeWPcCr214rXYDK56x\nPG8lDpuDCT0nMDZZL527Ln9draYlVSU88VyNj9xYGpHNFV956rlytx/YTow9htSEVI7ufTQu5WJt\nTDQ4Ymu5qJRS3PbDbXy0/SNeWv8ST65+Muh5qt3VvLnpTd7Y+EbwJWYt3Ps24lz6DBz5uwYL/jWJ\nmfeguvSj4sPZOsW9AbYf2M6Tq55kRW7wunTl1eVc//X1fLnrSx5d+SgLty2s2elxa6WadhzLcpeR\nEJXA6KTRjEkagwcPm4s21zpWaWUJTzzmd+/bq6UhIueLyAYR8YjIxAbanSYiW0Rkq4g0w3l/6Jy6\nStH5gZdxl5b5tu04uINOUZ1IjktmePfhdIvpxs95y2DwDK00rGDglqItfLnrS2aPn82VY65k4baF\nbDsQuITCg8se5K4ld/HYyse45qtrqHJXBWyXsT+D0z84i8mpXflH/+F4giSiFlcVc3P6zUyfP51H\nVzwaMEAJUOqp4vr+aUzuEcMV75/NQWdgl8G+8n1c8uklPL3maa7/+no+3PphwHaf7fiMzUWbefSE\nRzmuz3G8tP6lGgtr/04o2gYDT2B57nLGJY8jzhHHyKSR2MTG5v01HcFVVMTIxz4OeA5DZDJzlaL6\nlXkod81vbUfxDgZ0HoDdZueInkdgExsrC9fp4PL273ztVuStYHnucu6cfCe/Gvwr3tj4BrllufXO\n4VUuDyx7gIeWP8SN395Y35q1WJX3CzMX/ZZj+qfwfOrgoKnz+eX5XPvVtZz09kk8v/b5oO2KVDWX\nDxjIpM5V/PH9Xwf1HGw7sI1LPr2E59Y+x5WfXxl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_both([2, 10, 100])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also plot the individual components of the sum to get some intuition" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def square_terms(nterms=5, npts=500):\n", " \"\"\"Compute all nterms to construct a square wave.\n", "\n", " Computes an approximation to a square wave using a total of nterms, and\n", " returns the individual terms as well as the final sum.\n", " \n", " Parameters\n", " ----------\n", " nterms : int, optional\n", " Number of terms to use in the sum.\n", " npts : int, optional\n", " Number of points at which to sample the function.\n", "\n", " Returns\n", " -------\n", " t : array\n", " The t values where the wave was sampled.\n", " y : array\n", " The square wave approximation (the final sum of all terms).\n", " terms : array of shape (nterms, npts)\n", " Array with each term of the sum as one row.\n", " \"\"\"\n", " t = linspace(-pi, 2*pi, npts)\n", " terms = np.zeros((nterms, npts))\n", " for i in range(nterms):\n", " terms[i] = 4 / pi * (1.0/(2*i+1))*sin( (2*i+1)* t)\n", " y = terms.sum(axis=0)\n", " return t, y, terms" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_square_terms(nterms, npts=2000):\n", " \"\"\"Plot individual terms of square wave construction.\n", " Parameters\n", " ----------\n", " nterms : int, optional\n", " Number of terms to use in the sum.\n", " npts : int, optional\n", " Number of points at which to sample the function.\n", " \"\"\"\n", " # first plot the true wave\n", " plot_square(npts)\n", " \n", " # plot individual terms\n", " t, y, terms = square_terms(nterms)\n", " for i,term in enumerate(terms):\n", " plt.plot(t, term, label='freq=%i' % (2*i+1))\n", " \n", " # plot the reconstruction\n", " plt.plot(t, y, color='k', linewidth=2, label='sum')\n", " plt.legend()\n", " plt.grid()\n", " plt.title('Individual components of a square wave')" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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rr71GYGAgdHoOHOrBvi/K3a8xSkPl/kZVGirVmzLs5pcvXyY7O5vGjRuXP0Tx\n2BLIToZebwJKeo9169bh7e3N/v37ad26NR9//DHvv/8+bdu2Zc+ePTRs2JA///wTLy+v8vVpBMOG\nDeOnn35Co9Ewe/ZsunTpwn/+8x/eeOMNevXqRVxcHEOGDGHu3LlKBRsH6DERInbArbBy9WmK0lBd\nGvcnqtJQqdGEhSkPR39///I1kJcNB/8HTR+CRn+bt5o3b87evXvp1q0bsbGxzJgxgzlz5nDnzh16\n9+7NsWPHaNmypTkOoVTGjx/P9u3badiwISdPnmTq1KnMmzePnJwcJk2axNq1a7GyKjLdqsuLYGUP\nh+aXq782bdqg1Wq5dOkSmZmZZjqKmse8efNo06YNzzzzjMX7Wr9+Pe3bt6djx4506dKlMIdadaW6\nT+5TUSnVhn7u3DkA2rZtW77GT6+CtFgYvbDYrqZNm3Lw4EE2bNjAnj17sLKyYujQoTz00EOWT59R\nhAEDBhAVFcWqVas4evQoderUYeTIkXTpYmASo4MbdHwKTvyiZOd1Mi50uAA7OztatWpFWFgYYWFh\ndO5cfKKiKNPLVPOZP38+W7ZsoWnTpoXb8vLy7lbQZmLAgAGMGDECIQSnT5/miSee4MKF8kfBWRpV\naajUaCqkNKRUHOAN2ynpxg2g0WgYNWpUieuNVxZ2dnaMHz+e8ePHl124xyQI/QlCf4R+puc28vf3\nJywsjPPnzxtUGrWdoqnRr127xtixY4mKiqJevXosX76cd999l927d5Odnc1rr73Gq6++ipSSf/7z\nn/z11180bdoUKSUvvPCCUWG3Tk5Ohd/T09Mr9YWkPKhKQ6VaU5bdvEJK4+oBuHUWRnxTu0KC6rWA\nFoPh6A+Kn8batPkjbdq0ASjzbbcy5ml8fuRzLiSY9627tVtrpnWbVuL+qkiNvnbtWt577z1u377N\n5s2bzXq85kZVGio1lry8PC5evAiU06dxeBHY14UA43JM1SgenATLRioLSXUybX2M1q1bA2UrjfuF\ne1Ojnz59unCBpeTkZKNSo5fF6NGjGT16NHv37mX69Ons2LHDMgdjBlSloVLtKcmGHhkZSU5ODo0b\nN75riG8USdFwYRP0nAzW5Us9Uq1p+pBidjs0Hx4YZ9JIqiylUZmDstJGBJVFZaZG79u3L5cvXyYu\nLu7vBcGqGWr0lEqN5dIlJWV6q1atTK8cql+zoqvxq9vVKISA7q/C7TC4Ztpkv4KosPDwcPLy7r9M\ntqVRkBo9NzcXUK7B9PR0+vbty2+//YZOp+PmzZt3KYmyFmGKiIgonPV//PhxcnJycHd3r/yDMxJ1\npKFSrSkthUZ4eDgALVq0MK2AhV/VAAAgAElEQVTR3ExlbkbroVDHpwLSVXPaPQrb/gVHf4QmPY2u\n5uTkhI+PD9HR0URFRZW4EuL9mNTQEqnRf//9d5YtW4a1tTX29vasXLmyWjvDVaWhUmOJiIgAMGl5\nVwDOrIHMROg+seyyNRkbRyX89uiPkPaZSeG3rVu3Jjo6mgsXLph+fmsBUVFRAMUyFxdMtJw9e3ax\nOt9++23h9wkTJhjd17Rp05g2rerNcMaimqdUqj0lvXSVe6RxbDHUbw1NjFsdr0bT5QXIz4UTy02q\nVppfo/q+A6tUBupIQ6XGUi6lEXsWrh+DwM9qV5htSdRvBb59FEXZ603QGPeeWDC6uHz5siWlq7Us\nWbKkqkWwGOpIQ6VaU5LZPDs7m2vXrqHRaO6atVsmx5eC1hbajzWPgDWBLi9A0jW4vNPoKn5+fkDp\nSuP+82iogKo0VGooV65cIT8/nyZNmmBjY2NcpZwMOLVSyWbr4GZZAasTrYeBYwPFt2EkxigNlfsT\nVWmoVHsMGZHKZZoKW69ks+30nHkEqylY2SgT/MK3QfJ1o6o0bdoUIQRXr14tDC8t5D6w6qmUjKo0\nVGokBUrDpMie40vBzQ98e1tIqmrMA+NA5sOpFUYVt7W1xdvbG51Ox7Vr1ywsnEpNQlUaKtWakuzm\nJo80bl9QJrl1fu7+cIDfi1szaNIbTv5idNKoskxUtXmaRmWmRt+9ezeurq507NiRjh078tFHH1m8\nz4qgRk+pVHsMTXQqmKNhtNI4vgw01tDhaXOKVrN4YBysm6goTyMm+/n5+bF79+5iSkNNjW5++vTp\nw6ZNmyzStrlRRxoqNRKTRhp52YpZpnWQyetL1Cr8R4CNs7LWhhHcr87woqnRXV1deeWVVxg0aBDj\nx49Hp9MxZcoUunbtSvv27Vm0aBGgzI5//fXX8ff3Z+jQoQQFBRUmNaxtqCMNlRpHTk5OYbitr69v\n2RUuboHMBOhkxFoUtRkbR2g3Gs78DkM+A1vnUotXB6URO3s22efNm23Xtk1rPN5/v8T9VZEa/eDB\ng3To0AEvLy+++OKL8i8qVgmoSkOlWmPIbn7t2jWklPj4+BgXbntqBTh7QrOHzS9gTeOBZxVT3bl1\nZaZML9OncZ/M1LB0avROnTpx9epVnJycCA4OZtSoUYUj6eqIqjRUqj33WtAL8gIZNcpIuwPhf0LP\n10GjNbdoNQ/vruDeQnGIG6k0IiMjkVIW+pYqM46gtBFBZWHp1OguLi6F24KCgpg0aZKaGl1FxZyY\npDTOrAapu78d4EURQnGIXzsIcRGlFq1Tpw5ubm6kp6dz69atShKwemOJ1OixsbGFGYOPHDlCfn6+\nmhpdRcWcmKQ0Tq0ArwegQWuLylSj6PAk7PwITv4Mj8wqtaifnx8JCQlcvnwZDw+PShGvOmOJ1Ohr\n1qxhwYIFWFlZYW9vz2+//aamRldRKS+G7OYFSqPMnFO3zkHsaRjybwtIVoNx9oDmA+D0aug/o9Qk\nhs2aNePo0aNERUXRq9c9WYFrsUujMlOjv/7667z++uvlEbNKUM1TKtWfe166rly5Ahgx0ji1AjRW\n0O4xy8hVk2k/FlJi4FpIqcWaNGkC/P0QBTWLyP2OOtJQqXEYZZ7S5cHpVdBiMDhWX/twldEqCGyc\n4PTKUtOqFCiNq1evVpZktQI1NbqKSjUhOzubGzduoNVq8fb2Lrlg5C5Iu6WsXKdSHBsHaDMczq2H\n3KwSi6lKQ+VeqlRpCCEChRAXhRARQoh3DeyfIIS4I4Q4qf+8VBVyqlQfCpLneXt7l57S4dQKsK+r\njDRUDBPwuJL1N3x7iUVKUxq12KWhUgpVpjSEEFrgf8AQwB94Sgjhb6DoSillR/3nh0oVUqXKkfJu\nG7pRTvDsNLgQDG3HKGnBVQzT9CFwaqiYqEqgQGkUTKgEw7nAVO4fqnKk0Q2IkFJGSilzgN+AkVUo\nj0oNwCgn+MVgyMtU3qRVSkZrBe0eVUYamYkGizg7O1O3bl0yMzO5c+dOJQuoUh2pSqXRCIgu8jtG\nv+1eHhVCnBZCrBFC+BhqSAjxihAiVAgRql7YtRujnOBn1oCrD/h0rxSZajTtnwBdjrJAVQkUnOui\nEVQq9y9VqTQMjXHvNZNuBHyllO2BHcBSQw1JKb+TUnaRUnapX/8+zmJ6H1Cm0shIUNbCbjem1PkH\nKno8O0K9lsqcjRIoya9Rm9fTUCmZqryrYoCiIwdv4EbRAlLKeClltv7n90DnSpJNpRpR1IZeptII\nWwf5eercDGMRAgKegKv7ISnaYJF7lUZtd2mkp6czdOhQOnToQLt27Vi5ciW+vr7ExcUBEBoaSr9+\n/QBl8t9zzz3HoEGD8PX15Y8//mDq1KkEBAQQGBhYfKncWkBVKo2jQAshRFMhhA3wJLChaAEhhGeR\nnyOA85Uon0o1pCB6quBBVowzvytvzh4BlShVDSdAr2DPGB5tVGXYrRDCIp/S2Lp1K15eXpw6dYqz\nZ88SGBhYavnLly+zefNm1q9fz7hx43j44Yc5c+YM9vb2bN682Zyno1pQZUpDSpkHvA5sQ1EGq6SU\n54QQHwkhRuiLTRZCnBNCnAImAxOqRlqV6kBeXh43b95ECIGXl1fxAik34OoBZZRR21+HzYlbU/Dp\nUS2VRlUQEBDAjh07mDZtGvv27cPV1bXU8kOGDMHa2pqAgAB0Ol2hkgkICKiVfqAqnREupQwGgu/Z\nNqPI9/eA9ypbrppMRGIEu2N2E5seSxOXJgQ1DcLdvnbMiL558yb5+fl4eHgYXkfj7B+ALHxzzsvP\nI+RGCEduHiGffDo37EyfRn2w0d6fYbgJWQlsj9pOVEoUzjbOPNL4EVq5tVJ2BjwGwe/A7fPQoM1d\n9Ur0aVTCTA1pQcdJZl4mqTmp6KQOW40tLrYuWGmsaNmyJceOHSM4OJj33nuPQYMGYWVlRX5+PgBZ\nWXdPhrS1tQWUvFTW1taFIxmNRkNeXp7F5K8q1DQitYRcXS6fH/2cVRdXIZE4WTuRlpvGvOPzeLPz\nmzzd+ukaGV+vrOOgfI+OVmzuJc4EP7NayWjr7kdkUiTv7nuX8wnnsdXaIhAsD1uOn6sfs/vMxt/d\n0JSg2sva8LV8fvRz0nPTcbJ2IjMvk4WnFjLSbyTvdX8PR/+RsGWqonj7f3BX3WI+jUqX3rzo8nXc\nTL9JcnYyABqhIV/mcyvjFp6OnmQkZODm5sa4ceNwcnJiyZIl+Pr6cuzYMYYMGcLvv/9exUdQtahK\noxaQmZfJP3f+k8OxhxnXZhwvBbyEu707V5Kv8GXol3x25DNiUmOY2nVqjVQcBcTExADg42Mg8jr+\nMtw8CYM+JSw+jJe2v4S1xprP+3zOwCYDEUKwJ3oPs4/MZsLWCSx8ZCGdGnaq5COoGhacWsD8k/Pp\n5tGNad2m0bJuS5KyklgatpSfzv5EVEoUiwYuwtG3D5z7Ax5+/y7znru7O46OjiQnJ5OUlFSFR1Jx\ndPk6rqZcJSsvi/oO9XGzc8NKY0VmXiax6bFcT7vO2aNn+XT6p4UjhwULFpCZmcmLL77I7Nmz6d79\nPg/lllLWqk/nzp3l/UR+fr58Z/c7MmBJgFwfsb7Yfl2+Tn52+DPZbkk7ufjM4soXsILMWHdGdvhw\nm5RSyi+++EICcvLkycUL7vpMypmu8sbNE7LPij5y4OqB8nrq9WLFbqfflsP+GCa7/9JdXkm6YmHp\nq57VF1fLdkvayff3vS/zdHnF9u+I2iE7LO0gX9n+itQd/UnKmS5S3jhVrFybNm0kIE+fPi2PXomX\nTaZtknsu3raIzGFhYRZpNz8/X15JuiLPxZ2TKdkpBvdHp0TLs3fOysTMRIvIUF0wdI6BUGnEM1YN\nZK/hrLiwgq1RW5ncaTIj/EYU268RGqZ0ncLAJgP56vhXnL5zugqkNA8FI41i5ikp4cxq8pr0ZNqJ\n/5Kty+a7gd/h5VTcWV7foT7fD/oea4017+x5h2xddrEytYWLCReZc3gOPb168lHPj9AaWO52QJMB\nfNDjA0JuhPCjSFFSyZ8tbn4pGN0VmAhrIrczb5Oem46noyfONs7F9gsh8HLywtHakZvpN8nOq73X\nRkVQlUYNJiY1hrnH59LLqxcvtnuxxHIaoeGjnh/R0KEhH+z/gKy8krOaVjckf9vQCx5YxcxTsach\nPpxfPJty4vYJpj84HV9X3xLb9HD04NPen3Ix8SI/nKmd6cx0+TpmhMzAxdaF2b1nG1QYBTzW4jEC\nfQOZf24JEU0fVExU9zigCxR1TExMjQxMy8zLJC4jjjq2dahrV7fEchqhoZFTI4QQXE+7blFHfE1F\nVRo1mM+PfI5GaJj54MwyfRVONk7M6jmLqJQofj7/cyVJaF5KHGmcWcMtaxvmxx+lr3dfhjYdWmZb\nfb37EtQ0iB/P/EhUcpQFpK1aVl5cSVh8GNO6Tiszek4IwXvd38PB2oFP7fORSdfg+vG7ylT2SMOc\nD2spJTfTbqLVaGno2LDM8tZaazwcPMjMyyQpu2b7cAxR0XOrKo0aytHYo+yO2c1LAS/h6eRZdgWg\np1dP+vv05/vT3xOXGWdhCc2PwZGGlHBuHfN9WpGXr+Pdbu8a7eyf0nUKNlob5p2YZwlxq4z03HQW\nnFpAd8/uDPY1LjW8m50bb3R6g9D0aP5yclZGG0UoUNRFlYal3sHt7OyIj483m+JIyUkhMy+Thg4N\nsdIYF/vjauuKg7UDtzJuocvXmUWO6oCUkvj4eOzs7Mrdhho9VQORUjL32FwaOjRkXJtxJtV9u8vb\njFg3gp/O/sTUrlMtJKH5yc3NNTyx78ZxotOvs8FNw9jWT+HjbDCnpUHq2dfjOf/nmH9qPufiz9HW\nva0FJK98VlxYQVJ2Em888IZJ0XJjWoxhedhyvsWWfufWoh34cWH+rgJFXTDasyTe3t7ExMSYJauu\nlJI7mUo7wl4QK2KNrpujyyEuM45Um1ScbJwqLEt1wc7OrvQFzMpAVRo1kNBboZyOO830HtOxszLt\njaGxS2OGNhvKmktreDng5VLtu9UBKRXzyc2bN5FS4unpibW19d8Fzq3jhzp10WiseKHdCya3/6z/\ns/x64VcWnFzAtwO+NaPkVUNaThqLzy6mT6M+BNQ3LZWKlcaK1zq+xpS9U/hTl0hgzBFo3AO4d6Rh\nWaeGtbV16eulmMCWK1uYenQq/+n7H/ybmj43Z9KOSZy6c4rtj23H0drRLDLVdFTzVA3kxzM/4m7n\nzsjm5Vt+5MV2L5KVl8Uv538xs2SWw+AcDSmJubCODc4OPN7qcRo4NDC5XScbJ55u8zR7YvYQmRxp\nLnGrjBUXVpCSk8JrHV8rV/1BvoPwdW7MkjquyDN/R1EVHWnUFOdwvsxn4amFNK/TnEG+g8rVxsQO\nE0nJSWFdxDozS1dzUZVGDeN8/HkO3DjAOP9x2Gpty9VGszrNGNB4AL9e+JW0nDQzS2gZDM4Gv3GC\nX0kBNDzf9vlytz221VhstbYsD1teQSmrllxdLisurKCnV0/a1iufqU0jNDzb9jnO2VhzInwD6O35\nLi4uuLi4kJGRQUqy4hyu7srj0I1DRCZH8kK7F9CI8j3q2tdvT8f6Hfk57Oda5duoCKrSqGEsDVuK\no7UjT7R6okLtvNDuBVJzUtkYudFMklkWQ07wjLO/s87ZiYE+/YyKiikJNzs3hvsNZ+PljSRkJVRY\n1qpix7Ud3Mm8wzNtnqlQO8P9huOqtWeZTR5cDSncXqCwb924XqH2K4tfLvyCu5270cEAJfGs/7PE\npMWwO3q3eQSr4ahKo4rRpaWTvGkzSWvWkHvrdqllE7MS2R61nRF+I3CxcalQvwH1A/B391dyVZXx\nxpgdHk7ib7+RumsXspITsEkkAgPhtlKyKXIjqRoNT7UaR+rOnST+tpLsyPKZmJ71f5ZsXTarL5a8\nGFFFyL1xg8TVq0kJDiY/I8Miffx6/ld8nH3o3ai3yXVlfj7phw6R8OuvEBbOE62e4C8He6JP/x2e\nXaCwb8feKKkZi5KXmEjSunUkrV1HXkLpyv1qylX2xuzl8VaPVzhBZf/G/fFy9GJZ2LIyy2aeOUvi\nihWkHTiA1Cc4rG2ojvAqJPPkSaJf/yc6/eIuwsYGj5kzqfPoGIPlN1zeQG5+Lo+3NM/a12NbjWVm\nyExO3D5hMA+TzM/n9uf/JmHp3wsm2rZpg8//vsXaUGpyC3LvSEPeOMkKq2wezPTA5ZUPibl8WSko\nBO6vvkL9N0yLHGrm2owenj34I/wPXm7/crnNGYZIWrOG2A8/QuoX5LHy8MD7m3nYB5hvzY+w+DBO\n3jnJlC5TTJZdl5xMzOQ3yDh8uHDb0MABLA2AtTF7mJyvA43275HGzetAK7PJbgzpBw8S88ab5Kek\nAKBxdMTr889wfuQRg+V/u/AbVsKKJ1pWbEQOSoDAk62f5L/H/ktkUiTN6jQrVkbm5HBzxkyS1/3t\n+7Dv0hnvb77Bqm71DjYxFXWkUUVkR0Rw7dWJaBwcaPLLzzTbuAGHLp25+cEHpGzbXqy8lJLVl1bT\nsX5HWtRtYRYZAn0DcbZ2ZuXFlQb33/7ySxKWLqXu00/RfOcOGv33S3JjYrj2yivkp6ebRQZjuXek\ncerkT9zKs2bSqjzy4uLw/vYb/Hb8ievo0cQvXET8okUm9/Foi0e5kX6DQzcPmU3upHXruPmv6Th0\n7Uqz4GAaL1mC0GqJfvkVcq+bz8zzR/gf2GptGdVilEn1ZF4e0f+YRObx43jMmknzXX9R7/XXydm6\nk+l/OrHeVpAXtQ8oMtK4qYw0KsujkXHsGNH/mIR1w4b4rl6N7+9rsPHzI+at/yPj+Ili5XN0OWyM\n3MiAJgOo72Ce5Z9H+I3ASljxR/gfBvffnDmL5HXrcJ/4Ks13/YXnJx+TdfoM0a9ORObkmEWG6oKq\nNKoAmZvL9bf+D2FtTeOffsShc2dsW7TAe+FC7Nq35+aMGeTG3h1PfiT2CFdTrvJ4K/OMMgAcrB0Y\n7jecP6/+SVLW3TNf0w8fIeHHn6jz5FgaTp+OdaNGuAQF4T3va3Iir3Dzww/NJocx3DXSkJL11/fw\njy352Mal4bNgPs6PPIKNtzeen36Cy9Ch3PnmWzJOFH+glEb/xv1xtXUt8cFgKjkxMcR+9DEO3bvj\nvWA+ts2a4tijOz4/fI/MyyPmjTeRuoo7V7N12QRfCWZA4wEmmy3j5s8n8/hxPOfMoe6TT2Lt6Un9\n11+j3uR/0upkMm3Oazhw6ifgb4Ude7PyfBr56encmDIVq4YNaLx0CfYB7bBv25bG33+HtacnMW9M\nRpecfFedvTF7Sc5OZlRz0xRoabjbu9PPpx8bIzeSq7t7CdfkzZtJXruWepP+QYM338Ta05M6jz2G\n178/J+v0aW5//bXZ5KgOqEqjCkhYtozs8HA8Z83Epkg0kMbGhkb//hyZk8Ot2XPuqrMpchOO1o4M\nalK+0MGSGNV8FLn5uWyL2la4LT8nh5v/+hfWTRrTcNq0u8w8jg8+SL2Jr5KyYSMZoaFmlcUQUgL5\necTGxqLRaPD09CTreig3r+bR5ZKk/muv4dDpb9OaEAKPWTOxbtiQ2BkzTXoo22htGN5sODuv7TSL\nQzx25ixlMuKc2Whs/450s23aFI8PZ5F19ixJayq+NsPu6N2k5qQy0s+0EOzsyCvELfoO15EjcR12\nd+qVeq++il2Xzjy/M5+N0UchX1c40qhMR/idefPIvXkTrzlzsHJzK9yudXXFe+5X6OITiJs//646\n6yPWU9++Pg96PmhWWca0GENCVgK7Y3YXbtOlpXHr40+w69CeepMm3VXeJTCQOo8/TsLiJWSHh5tV\nlqpEVRqVjC45mbj5C3Dq18+gPdbG1xf3F14gdft2Ms+cBZRQyp3XdtLfp7/Jk/nKorVba5rXaX5X\nFFXy77+TGx2Nx7+mo7G3L1bH/eWXsfLw4NZnn1dK2GVOqpJSwsPDA2tra3aFLuTR3RKddwPcn59Q\nrLzW2ZkGU94hOzycFBPXaB7TYgx5+XkERwaXXbgU0g8fIf3AAer983WD/h+XoCDsu3Tmztdfo0ur\nmKlvw+UNNHBoQHdP09Z5uDNvHhpbWxpMnVJsn9Bq8fzXv7DPhnrHBXGX/6x0R3juzZsk/LqCOo89\ndteLQQF2/v7UeewxEn75lewrVwCIy4xj3/V9DPMbVmqSxvLQ06snDR0asjZ8beG2hJ8Wo0tKwmP6\nDIRVcRdx/f97C42DA7f/+5VZZalKVKVRyST88gv56enUf/ONEsu4PT8BbZ063Jmn5EQKuRFCak4q\ngU1LX+C+PAghGNZsGKfunOJayjXys7OJW7gI+06dcOzdy2Adjb099SdPJuvsWdL37TO7TPeSm6wE\nChSYps6FHMY7HrzfnIIwtOwr4Dx4MHb+/tyZ941JEV8t6ragtVtrtlzZUm55pZTEffMNVvXrU/fJ\nJw2WEULQcOpUdAkJJK0uf8RWXGYcB64fYHiz4SY9JLMuXCB161bcnn8eK3fDCQ3tWrdG80gvAkMl\nOw9+f1fIrZTS4k6NuO++A6DePyaWWKb+5H8itFrif/wRgODIYHRSZ/Koyxi0Gi3Dmg0j5EYICVkJ\n6JKSSFiyBOfBg7FvZ3hejFXduri/9BJpu3aReeaM2WWqClSlUYnkZ2aSuHQZTg8/jF3r1iWW0zo5\n4TbhOdL37SM7IoKtUVtxsXEx+3C7gKHNhiIQbIrcRMqWLeTdukW91yaVGn3kOmwoVg0bEr94sUVk\nKkpOshKK7O3tza0re2hzWEd6PTtchwwpsY7QaHCf+Cq5MTGk/vWXSf0FNQ3idNxprqVcK5e8WWfO\nkBEaivvLL6EpJTGcffv2OHTrRsKyZYWRVaayOXIzOqljRPPia6mURsLSZQgHB9yeG19quaZvvodt\nHsTvPY+zoyOurq5kZ2eRn5VaLnmNJS8xkeQ1v1Nn9OhSI/Ws6tXDdcxoUtZvIPf2bdZfXk9AvQD8\n6vhZRK6gZkHopI7tUdtJWrOG/IwM6k36R6l16o57Bo2jIwlLyw7ZrQmoSqMSSdmyFV1yMm4GTCr3\nUueJJxA2NsQtX8au6F0MaDwAa611mfXKg4ejB908urEpchNJv63EpmlTHHv2LLWOsLHB7dlxZBw8\nRNb58xaRC5SX2ZyUeEAZaezdNJdmt8D12acQ2tLfrJ0HDMDay4vEZabN9B7SdAgCQfCV8pmoEleu\nRDg44DrGcOh0UdxeeJ68mzdJ2V48Ys4YNlzeQPt67WnmWjwMtCTy4uJI2bSJOqNGonUp3XFu6+dH\nYht3OpyUXDu/sXC0oUuxbJbk5D/WInNzcXu27ISc7hMmIPPyiPjpWy4lXjK4GJm5aFm3Jc3rNGdL\nxGYSfvkVh27dsGtVevix1smJOo89SsrWreTeumUx2SoLVWlUIkmrV2PTtCkOXbuWWdbKzQ2X4cNI\nWree/LS0Cs9qLYthfsPQRFwj8+RJ6j451qg5DnUefxxhY2MWZ25p5BaMNBo1Inv/JXKsodkzk8qo\npdjl6z7zDBmhoWRdumR0fx6OHnRu2JnNkZtN9tnoUlJI2RyM69ChaJ3Kzozq1Lcv1t7eJP9u+jmM\nTIrkUuIlgpoFmVQvaa3yQK47zrgMyY1enIRbGoSu/l+hXyMvteIZaEtCSknSqlXY66MKy8KmSRMc\ne/cma0MwWinKnWfKWIY2G4rm4HHybt6krhFKDVDOtU5H0uo1FpWtMlCVRiWRHR5O5okT1HnsMaMn\nndV9/HE02Tk8fNmebp7dLCrfwCYDGXxKoLPW4jrSOHuw1tUV50cGkLJpE/kWjEXP0b/V2hNH2/OS\npAc8jHogA7iOHgVWViSvW29Sn0HNgohKieJ8gmmjqOT1G5BZWdQZO9ao8kKjwXX0KNIPHjJ53sa2\nqG0IBAObDDSpXsrmYOw7dsS2mXGjk8ZDxpLiLOBINI0aNQJAlxqPtJBTI+PwYXKuXqXuWOMn5rmO\nGY1dQjqPJbfEzc6t7AoVINA3kF5hklxne5z79TOqjo2PDw7du5O8fn21z9lVFqrSqCSS1qwBa2vl\nIWYksm1LYt0EQRcdsNZYxjRVgH2uoO85ydG2NghX42P9XUePQZecTJqJfgNTyElW3mrTz+zCLhd8\nnzM+g6uVmxtOffuSvHGDSQ7xQU0GYaWxMimKquAN2a5duxIdo4aoM0q5JpLWGZ9JVUrJ1qitdG7Y\n2aTsvtmRkWRfuIBLkPGjE6HVktWjGS2vgL1QQpHzUiw30khcuVJ5IRls/Oj6xgPepNrBI2csvxat\nl9aNrpcFx9vaIqyNvy/rjB5FbnQ0mceOWVA6y6MqjUpA5uaSvGEjzv373xVrXhb7ru9jVztBgwu3\nyYmxbGx82p492GTp2OqfzYnbxk+Kc+z5IFYeHiT9YZ4JcfciJeTqlYZnRAK36wka93/UpDZcR41E\ndyeO9JCQsgsX1LF1pXej3myJ2kK+NC6HUPalS2SHh+M6ZrRJ8lk3aoTjgz1IXrvO6HxFEUkRRCZH\nmmy2TAneAkLgHGhaPf8Xp6KVIK+eA0CXahmfhi4tjbSdf+EybNhdc1vK4s8bu9jfTovr4Yvokiy7\nRGva7t3Y5OQT7JdKeKLx8y+cBw5E4+Bg0stBdURVGpVA+uEj6BITcR0x3KR626K2caazkrcmZeMG\nS4hWSPLmzWgb1CfS147tUcY7ZYVWMWel7z9A7u3SEy6WB11uLrnpiWg0gg5xWrK6+5qUUwrAqV8/\ntK6uJpuoAn0DuZ1x22glmrI5GLRaXEx4Qy7AdfQYcmNijH4L3Ra1DY3Q8EgTw7mXDCGlJCU4GIeu\nXbFuYNraI/U79iXWU4PPjUwA8iykNNL++guZk4PL0LLXeS9ASsm2qG3E928PubmkbCl/uLQxJAcH\no6nnziUfzV2TYstC4+CAc2AgqVu2kp+ZaUEJLYuqNCqBlC3BaBwdcextfPbRjNwM9sXso3OHQBy6\ndSN5neVsobrUVNL37EhHdfkAACAASURBVMV1yBB6+fThz6t/Gv12DUr4Lfn5pP75p9llS028DVJS\n18EGKyHwf+ZNk9vQ2NjgMnQoqTt3okszfv2Qh30exk5rx9YrW8ssW/BAduzRo8R5D6XhPKA/ws6O\nlC3G9bUtahtdG3alnn09o/vIvniRnMhIk0xTRRF9/GmXrkxg06XEYYnLMWVzMFZenth37GB0nQsJ\nF7iWeo1OvcZg06wZKVuNf5CbSuG9EhREF89ubIvaZtJ96TpyJPnp6aTt3m0xGS2NqjQsjMzJIXXH\nTpwG9DdpuL07ejdZuiwCfQNxGTaUnKtXybZQaGvqjp3I3FxcgoIY1GQQdzLvmGSism3RAtsWzUk1\n4oFnsmzxSohiA42GGx4afDqVLzLGZdhQZHa2Sb4XB2sH+nj3YfvV7eTll+4PyTpzhtyYmHI/kDUO\nDjj160fK9u1lpj65lHiJqJQoBjc10TSlHwk5Dy7fOezw3Ac0sFFs+HmpcWZ/idElJZF24AAugUMQ\nGuMfTduitqEVWgY0eQSXwEAyjh4lzwzrixsidadyr7gGBTHIdxBRKVFcTLxodH2HLp3R1qtnUcVm\naVSlYWHSDx0iPzkZl1Imohlia9RWGtg3oFPDTjgPHAhWVqQEVyy1RUmkBAdj3agRdu3b85DPQ9ho\nbEwyUQE4BwaSceyY2U1UqXFK4kaffCvyuviWux37jh2x8vRUbPomEOgbSEJWAqG3Ss+zlbI5GKyt\ncR5ovLnoXlwCB6OLiyMjtHQT1daorWiFlkcam26acuzZs9ypuuv6dSSpiTVOWg3ocklOjC9XOyWR\numMH5OWZpHgLRl3dPbtTx64OLkMCIT+fFAuMekF/r3h5YdehAwObDEQrtEaNRAsQWi0ugwaStmeP\nxdZVsTSq0rAwKcFb0Dg749jLcEoOQ6TlpLH/+n4G+Q5CIzRY1a2LY88HSQneYva3u7zERNJDQnAJ\nCkIIgaO1I70b9WbH1R0mmahcAgNBSlK3m/dmLRhpeFpblcs0VYDQaHAJDCTtwIFiWVFLo493H+yt\n7Et9MMj8fFK2bMGpT58yJ8uVhlPfvgh7e1K2lqzYij4k69oZ//DPOn2a3OvXyz0SKsCmRxs89ZNM\n75g5B1VKcDDWTRpj19bf6DrnE84TkxZTGBBg26IFNs39LDLqVe6Vg7gEDUEIQV27unT37G6yicp5\ncCAyK4u0vXvNLmNlUKVKQwgRKIS4KISIEEK8a2C/rRBipX7/YSGEb+VLWX7yc3JI3bkT5wED0JSQ\nI8kQu6J3kZufe1dkjEtQELk3bpB16pRZZUz9f/bOMzyqamvA75lk0jPptISQ0EvoTYpIEQggHcWC\nYG+oqPeqn1evCgpWVOxeBRtKryK9iEqT3kKHkEp6MumZsr8fh4kpM5lzJgWC8z5PHkhmt2Rmn7XX\n2qts2gwmE7pRfz9MhkcMJ7UwlSOpRxSP496iBe6tWlX5wHMEfYasaXgEutG0q7p4hIroRo4Eg0E+\n0SrE09WTQU0HsTVuKwaz9VQfhQcPYkxNrfYDWTZR3ULu5i023YNPZ54mPjdedbZj/fr1SFotvrcO\nqdYau0x9iUZa+V4jNTm5WmOVxZieTv7efehGjFDl6LApdhOukiuDmw4u/ZkuegQFBw7UvNa7eUsl\nTWh4xHAS8hKIyYhRPE59N1FdM6EhSZIL8BkwAmgP3CVJUsUjxoNAlhCiJfAh8E5tr6smT/L5u3Zh\nzs2VVWYVbIzdSCPvRnQK6VT6M98hQ5Dc3MipYROVfuNG3CIjcS+TCqHURHVZpYlqRDSFBw/ZLVur\nhuIEOdNvUIfqVwr0iOqAtmlT2ZSkguiIaHKKc9iXvM/q6/oNG5Hc3fEdNLDaa9RFj8CUkWEz7fzm\ny5txkVwYHD7Y6uvWkDWhjXjfMgAXX99qrc+vZTd0/rKmkXoloVpjlSV3yxYwm9GNcMA01UQ2TVnQ\nRQ+vFa1Xv2EDbhERuLdrV/qzIeFDcJVc2RirzkTlO/RW2URVg15UdRU0aFdoSJL0pCRJtVGvsBdw\nXghxUQhRAiwGKoYijwUstUaXA0Mktf6WCvnmw1n4u2uZMLh7jY2Zu3EjGj8/vPsoTzSYU5zD7qTd\nDG82vFzZThdfX7wH3Ezuho01UrgHwJiRQcFff+EbPbx8zYyrJqotseq8qEpNVJtq7gSVnySnvO41\nYVq1x5IkCd3IkeTv3YsxQ7k9vl9oP3y1vlYz3wqTCf2WzfgMGIDG27vaa/QZcLNsorJy9yKEYHPs\nZno26qnKNGXRhPyqqQlZCIxsBEDCUeUamz30Gzfh1rw57q2VV6WMyYghMS+R4c3KOwS4t2wpa701\n6HprSE2lYN++UjOuBT93P/o06aPaRKUbHo0oLCRvZ82ZqEJ8PWjg60GGis+2IyjRNBoB+yVJWnrV\nnFRTD+1QIL7M9wlXf2a1jRDCCOQAlfwZJUl6RJKkA5IkHUhz0GsisElzckqMxJ2+4FD/ipiLi8nd\ntr1UQ1DK9rjtGM1Gq2nQ/UaOxJiWRkENRZSWnu6iK881LGKYehNV8+a4t2mDfmPN2ZNzcuSTWPch\n6gL6bKEbOVJ2D1aRINDNxY1B4YPYEbeDElP5dCmFhw5hSktXHSxnC42nJ76DBpK7pbKJ6mzWWeJy\n41TnVspZvx7J0xMfhSkv7NFigHy2Sz9dM6m+jenpFOzfj67C4cUemy5fNU1Z0bp8R0RTeOhQjSUI\nzN20GYRAN7KyQ0t0ZDTJ+ckcSz+meDyvnj1wCQpCv6lm9kp+rp6M/BIy84vx9/e336Ea2BUaQohX\ngFbAfOA+4JwkSXMkSapu7mFrn46KolpJG4QQ/xNC9BBC9AgJcawmcIu2HQHIyirCUFD9tM/5f/6J\nOS9PtdfUpthNhPmE0SGochoKn4EDr55Ca8ZEpd+4SVa3W7eu9NrApgMdMlHpRoyQN2sN2LvP7VxE\nlsGERoLGjRtXezwA99atcGvRQrWJakTkCHINuexK3FXu5/qNm2TTVA09kAF8R4zAlJVF/r7y5jBL\nQN+QcOX3EsJoJHfjJnwHDUTj5VUj62sSJWvOuan5mMzV13othxff4crNuBat66YmN+Hn7lfpdV30\niBrVevXr1+PeujXuLVtWem1Q00FoNVrVXlS+Q28l77eaMVHt+HYWAMF+3rjYyf5cXRTdaQhZ77py\n9csIBADLJUl6txpzJwBNy3wfBlR0xyhtI0mSK+AHVL8OpxVKq5IZjBxePLva4+k3bMTF3x/vm5RX\nU8sqymJv8l6GR1g/cWm8vORT6KbNqvIoWcOWacqCt9ZbjlGI3azORHX1/kZfA5t113efIQB3H78a\n2wiyiWqE7B6s4hTau3Fv/N39y9muxVWNxWfAzTVimrLgM2AAGi+vcuYVIQRbLm+hZ8OeqhLy5e/d\nhykrq9qX9GVp2EQ2CGQVGjm87X/VHk+/cZN8r+aAacqWQ4B780jc27ZVFCxpD0NSEoWHD9v8G/q6\n+dIvtB+bL6vcK9E1Z6I6efUgGdGq6jTtNYGSO42nJUk6CLwL7AI6CiEeB7oD1bEZ7AdaSZIUKUmS\nG3AnUDFXxlrAYsyeBGwXtXTbExAQgKenJ/lmM3G/Vu+BZy4qIm/7dnyHDlWV0Gxr3FZMwlRlPiHd\nyJHyKXSv9UtZpeRu2WrTNGVheMRw1YF+bs2a4dG+fY3Yk/UH5YtWl4CKVsvqoRsxUj6FqjCjaTVa\nhoQPYUf8DgqN8smw8NAhjGlpqk7IStC4u+MzZAi5W7aWFmc6l32OWH2satOUfv16ND4+eN98c42t\nr9HVokhXjEYurPq5WmMZMzJk09SIaMe8pqpwCNCNGEHh4cPV1notgseaacqCJeWMGnOuV8+eshdV\nNS0HJkMJxWdlN/JmkZU1oZpGiaYRDEwQQgwXQiwTQhgAhBBm4DZHJ756R/EksAk4BSwVQpyUJGmW\nJEmWKirzgSBJks4DzwGV3HJrCkmSSrUN84kcSgr0Do+V98cfmAsKVHtNbYrdRDNdM9oG2q7q533z\nzWh8fKr9QdNv2ohbs2blvKYqckvYLbi7uKvKrwOyPbno6LFqJVm8/OdyitPl+wM3nfJUGUpwbx6J\ne7t2qj3RoiOjKTQW8keCXOJWv3ETkptbjd0VlEU3YgTmnBzy9+wBYHPsZjSSRpXXlLmkhNwtW/C9\n9VZV2Qjs4eXljcbDB4MQuBy4gsHkWNVBqIZp6rJt05QF3dV7pupqG/r16/GIisItPNxmm4FNB+Lu\n4q7ai0oXHU3ezp2q0ttU5PiqD9Dnye+BpUhWbaLkTuNVIcRlG69VK6+FEGK9EKK1EKKFEGJ2mfnW\nXv1/kRDidiFESyFELyHExerMZw+L0MgpMHDkJ8dNVLkbNuISEIBXL+U1MNIL09l/Zb9N05QFjbs7\nvkOGkLtli8M1LIyZmRTs+wvf6KpPd15aLwaEDWDL5S2qbNeWe5zcalzynV76FVcMsgnOzU9dcj0l\n6EaOuCrYlLuN9mzYkyCPIDbGbvzbNHXLAFx8as40ZcG7fz80vr6lXlRbLm+he8PuqnJN5f/5p+zy\nParmTFMWXHyvriPVyKEtjpuo9Bs21rhpykKp1lsNx4ySy5cpOnnSrnnPW+vNzaE3q98rI0fK6W22\nbXN4jYm/riHJJO8VS72T2sQZEV4Gi5SOxUj6FsfeRHNhIbm//YbvsGFIrq6K+1kisKMj7J+4dKNG\nYs7NJf/PXXbbWqPUNKVAExoWMYz0wnQOpR5SPL5bWBgenTqpTtlRFvdDiZzzsAgNx5wbqsIi2NSY\n0Vw0LgxtNpTfE34nc/8ejKmpNW6asqBxc5MPB9u2cS7lFBdzLqoP6Fu37uq92k01vj7Xq0IjyWgg\nYeUih8aolmlKU7VpyoJu5AiKjqk7HJQl59df5XEU7JXhkcNV7xXPrl3QNmnicPyVyVBC0IlsYt1k\nQWU5+NYmTqFRBssf/IJO0Oh0PsX5ytNNWMjb+TvCAdPUxtiNtPBrQasA+ycu7z59cPHzc9hElbN2\nbaWAPlsMCB2Ah4uHahOVLjqaopMnKblsVUmtkkt/LqdhuiDdU3ZVdq8FoeEWFoZH506q716iI6Mp\nNhVzfvE3SB4etWKasqAbEY05N5dD6xYgIalKg27S68ndug3dqFGq7tWU4nLVZHjWz0SDIxmUGItV\nj6Ffv0E2TVVxr1aRUtNU46pNUxYsY6u5vyo7V86aNXj17o1WgffegNABdlPOVMTimJG/azfGrCzV\nazy+/H388iHr6nt8XZin/klY/uD5/oF4lsDRH99UPUbOqlW4NmyoqA64hZT8FA6lHFJcUEfSavEd\nNozc7dtVu+uVXL5M4cGD+I0fr+h057iJ6qoXlQMX4ud//ByjBvK1ch4nN/+aFxogaxvFMacovnhJ\ncZ+uDboSqg3B/bcD+A4bWiumKQveffqg8fPDvOV3ujXspso0pd+0CVFSgt/YMfYbO4DFPJUT5E+w\nHg6u/UT1GNmrVuLRvj0eVly+baHUNGXBovXmqHSxBig8cgTD5TjF5Y8te2Vr3Fa7WZHLohs5EoxG\nhyLYU1evId8dsorlR7lT06hjLH/wQvcGZHuDfr06E5UhJYW8P/7Ab/w4JBUuohtjNyIQjGyu3Pas\nGzUSUVCg2l0vZ80akCRVBaGGRwwnsyiTgynKgwq1jRvj1aMH2StXKa5GB3KVQ//9yVxooSElQ3ZG\ncNfVntBAktBvUP5A0UgapqS3xr3QiPa2mgnos4Xk5gZD+tH+hJ7oIOW1WEB+n90iI/Ho2LFW1ubq\nK78nhsDmFLtC6qoVqvoXnT5Nccwp/CZMUNVPjWnKgt/YMRSfOkXhiZOq5spZvQbJwwPfYcrNgpas\nyH9d+UtxH/d27XCLjCRnrbpCa4acbBqe1HOujSupaem4uLjUWDxTVTiFRhksQiPpSirxnb1ofK6Q\ngnjl5pWc1WvAbMZ/vLpyn+svradDUAea6Zop7uOIu54wm8lZvQbvvn3RNmqkuJ8l06taE5X/5Dsw\nxMVRsE+5e/CFlV/jUwCmm1qQkpKCpHFB61sbWWxA27AhXt27q84e3PVANmk62N1IvflSLbt7eOFm\nhH7HlZ9cSxISKDxwEL+xY1RXOVSKxTyVlJlLYhtXmh7NpihXeZnVnFWrQatVdUmv1jRlwW/0aCQP\nD7KXLVPcx1xcjH7DBnyHqtMm+4f2x8vVS131S0nCf9JECg8epOjsWcX9Yr57CzcjGLt1QAhB48aN\naz2wD5xCoxwW81R8fDyNbxsKAmK+eF1RXyEE2StX4NWzJ27NlD/8Y3NiicmIYWSkOg+XUne9337D\nmKks3rHgr78wJCXhN26cqrk8XT25JewW1Wq377BhuPj5kbV0qeI+yUsWkukDYQPuBcAnIASNpvY2\ngu62UZRcuEDRMWUpIAxXrqA5cJxD3f3YGKcuWl4tQgiWiP2khPtiWLVesWDLXrZc1iZHqysvrBRJ\n+vsiPCEhgcBbe+FZAke+e1tRf1FSQs4vv+A7aJCq2h7H0o/JuaZU1kV30enQDR+Oft06zPn5ivrk\nbt6CWa9XbJqy4OHqwcCmA6vMimwNvwkTkNzcyF6ifK/of91MQhA06CSHy9WFaQqcQqMc/v7+eHt7\nk5eXR7s+j3EyEti6X1H0dcG+fbL9U6W6veHSBiQkq7mm7BFw52RESQnZS5WdoDJ/XIiLv79DhYIs\nJqr9V/Yr7qNxd8dv3Dhyt25TlCCwJCmJgFNZnOvgQrFoCIBvcEPVa1WD7rbRaLy9yVz4k6L2WT8v\nAiFwHxPNvqR9ZBcpP12r5UjaERLzEpHGDqP43DkKj9gPHDMXF5O9dCk+gwahrUX3SxdfOQVcQkIC\nXSe+SFIQGFYrS9qn37QJU2Ym/pPUxQb/cuEXPFw8GNpMfYp8/8l3YM7PV3zHlrVwIW7NmuHdV3my\nUQuWrMh7k/Yq7uMaEIBv9HBy1qxRJNhyjx8lOK6IpM4eZGTLwskpNK4BkiSVahtXMvLI6abDW28i\nfeOvdvtmzF+AS1BQlVGjFRFCsP7Seno26kkDL/WxCO4tW+Ldty9ZixaVRg7bouTyZfK2b8f/zslo\nPDxUz9U/tD8+Wh/WXVynqp//HbeDwUDWkiV22575VI6NCR7Sjfh4OZelb2DtCg0XH2/8JkxAv3Gj\n3RKh5oICspcswffWWxnYazJGYWRrXM1leq3Irxd/xcPFg273PI3Gy4usH3+020e/fgOmrCwC751S\na+sC0Gg98PULwGAwkG3WkdTNjeDEInL27a6ynxCCjG+/xa1FC7z7K7+nKTGVsOHSBgaHD8Zbq975\nwLNrV9xbtSTzhx/t3rEVHjtG4dGjBEyZoqrsrIV+of3w0fqoCvQDCLjzTsx5eeSss/+8OTvvDQrd\noMXIoaV7xSk0rhGWP3x8fDw9hk8kKQASPn63yg9a0Zkz5P/xB4H33qsq8jYmM4ZYfaxq01RZAqdN\nxZiSQvbq1VW2y/j2W3B1JeDuux2ax8PVg+jIaLZc3kK+QZmKD3JxJp9Bg8j8/gdMebb7mXJyEOt+\nY287GHjrs38LjWDldy+OEjjlHjCZyPhmfpXtslesxJSTQ+B902gb2JZmumaq3CvVYDAZ2BS7iUFN\nB+Hr34CAe+5Gv2FjlZ5ewmgk46uvcG/dGq9aiM2oSEgjOZ1IQkICLaKHkOMFl+ZVbaIq2LOH4phT\nBE6bquqB/EfCH+hL9Ixu4ZjJTZIkgh56iOKzZ8n77bcq26Z/+RUaX1/8xqsz41pwc3FjcPhgq1mR\nq8Kza1c8oqLI+PrrKg+BhsRE3HefZHdHuGnA33ulLtxtwSk0KmERGgkJCXTp+Qg7bwKPuExyq4jY\nTPvgQzTe3gTcdaequdaeX4tWo1Xlf18R7wED8OjcifTPv8BcbN1XvvjiJbKXLSfg9kloGzgeXT22\nxVgKjYWq64cHP/E45pwcshbaPimnfvkl2hIz6T21+DTp+rfQCGpUa5e5FtyaNcNv3DiyFi3CcOWK\n1TamvDzSv/gCr5498ezWDUmSGB4xnP0p+0kvTK/xNe1K2kV2cTa3tZAz9QTedx+Suzvpn39us0/O\nmrWUxMYS8vRTtfo3k64mnw6+KjTi4+PpddN0dnQHj8PnKdhv3YQpzGZS35+La5PGqu8K1l5YS7Bn\nMDc1dlwY6kaNQhsWRvqnn9msSVN45Ah527cT9OADuPj4ODzX8Ijh5Bpy2Z1UteZVFkmSCHnqSQwJ\nCWSvWmWzXeLc9zBpQPTyw1XXmISrgYtOTeMaUfYyXPL0J6xLYxKCIGn2m1ZtjXm//07ezp0ET5+O\ni59yj45iUzHrLq5jSPgQVZ4gFZEkiQbPPIMxOZmMb76p9LoQgtT33kPj7k7wE084PA9A55DOROgi\nWH2+aq2mIp4dO+Jz6xDSv/yKkvj4Sq8XX7pE1o8/sqOTxIDOtwDUqaYBEPzEEwghSHnHenHIjK++\nwpSZSYMXXih9II+IGIFZmNlyuWYrxIH8kAxwD6BPE9mm7hoUROC0aejXrSN/b2VbuSk7m7R58/CI\nisJnSPVKuioluKHs3pmQkIBrUAvMPbzJ0EHSm29afSjnrF1LUUwMDZ55RpVGnl2Uze+JvzMyciSu\nGuVZFioiuboSMuNpimJirJpLhdHIlbfewiUwkMB773V4HoA+jfugc9NZLdxVFd4DBuDZpQtp8z62\nGuxXePQohes38WtPiVu7yFqX0zx1jSmraQCMaTeZ/43QYE5JJeXtt8td9BlSUkl++RXcIiJkE4cK\ntsdtR1+iZ3wrde651vDu0wfdbbeR/vkXFFbwAspevJi8HTsIfvJJXIOrl/hPkiTGthzLodRDxOnj\nVPVt9PLLSBoNyf95uVzOLHNhIUn/fp4SF8HmfoLe3R4BygiNoNq907DgFhZKyPQnyN2wkZxfyt/b\n5O/ZQ8Y38/GbOAHPjlGlP28Z0JKW/i1r3ESVXpjOjrgdjG4xGq3m72ju4McfQxseTvKrr5V7oAgh\nuDJrFsbMTBq9/nqta2YWQspoGgC3tRzO94M1GM6cJe2jeeXalsTGkvLGm3h26YLuNnV5TjfEbsBo\nNjKmRfUDFXW33YZXn5tIm/sBxefPl3st/auvKDp6jIYv/6faqe61LlqiI6LZenkrOcXKXbMlSaLR\nzJmY9HquvPZ6ueeNKSeHxH8/j16n4Vh3E2273A/gNE9da8pqGgCNOk4mINjAtj5uZC9bTurbb2Mu\nKaEkIZH4xx7DlJ9P6Lx5qqrzAaw8t5Im3k2qpW6XpdF/X8G1QQPin5hOwaFDCLOZ7NWruTLnLbwH\n3EzgfdUvlwowuvloNJJGtbahbdyYhq/+l4L9+0l89jlMubmYsrNJfOZZimJimDcaBni649JQfiiX\nNU/VFUEPPYRn164kv/IK+o0bEUKQv3cfic88i1vz5jR6+eVKfUY1H8Wh1ENczKm5XJprzq/BKIxM\nbF3eu0jj4UGTt9/CmJJC/EMPY0hOxlxURMqct9Cv30DIk9PxjKpcvKu2KKtpAHTq+hAZzY3s7+FJ\nxtdfk/HNNwijkeJz54h/9DEkrZbQD+aqussQQrDs7DLaBbajTWD1a0VIkkTjN95E8vQk7sGHKDp9\nGmEykfnDD6R/+hm60aPxGzWq2vMA3N7mdkrMJfxy4RdV/TzatKbBjKfJ3byZKzNnYi4sxJCSSsL0\nJzEkJfHOWImRXkFIfk0oKioiLS0NV1dXGjasmwOW47reDUrZi3AAPP0Z5x3JiwMS6R8iX+hmLV6C\nKClB8vQk7KMP8WijPA0CQGJeIvuS9/F4l8fL1QGvDi5+foR/8zXxDz/C5bvvQfL0RBQW4tmjO6Hv\nv++QF4g1Gno3pG+Tvqw5v4bHuzxe7iRsD/9x4zDn5pEyZw5n+/YDIcBs5vS0PhxstI9ZjYeDJFFQ\nUEBGRgZubm546QIgQ31OHkeQXF0J+/wz4h95lMRnnkXy8kIUFKBtFk7TL7+wWvluXMtxfHbkM5ae\nWcr/9ap+5n6zMLPi3Ap6NOxBc7/mlV736taN0HkfkTjjGc4PuRXJ1RVRUkLA1HsJevTRas+vBIsi\nU1HTkAIjmaTx593B+fzs3ZvU9+eS9ulniKIiXPz9Cfv8c7RXa3Eo5XDqYc5lneP1Pq/X2PrdwkIJ\nn/8Ncfc/wKVx45E8PBBFRfgMHEjjN9+osXnaBralY3BHlp1dxj3t7lGlAQY++CDGrCwy5y8gZ8VK\nhNmM5OLC3mkdiQs5xtjWdwCQmCiXHwgNDa2TwD5wCo1KlDVPCSGQJImh7e/hvSNv8/XNObw3bgF5\nO39Ho/PFf/x4RYnMKrLo1CI0kobxLatvmiqLe4sWRK5dQ86q1ZTExeHZqSO6kSNVpTRRwp1t7uTJ\n7U+y9fJWRkSqK2cbeO8UvLp3k2scSBJeo4bzxIEH6K8vomkn2cRXTt2uIaGqFNeAACJ+WkjO+vUU\nnYzBLTIC/3HjbJZKDfYMZmizoaw5v4anuz6Nl7Z6JVX/uvIX8bnxTO8y3WYb34EDaf7rOnJWyz79\nvoMHqcp1VlNUFBoAt7WawIcXf2DZnUE8N/kzCvbtwzUkBL/x43ENClI9x5IzS/DV+qr+nNnDo00b\n+W+4chXG1BQ8e/TAd8iQGjtcWbi99e28uvtVDqUeonvD7or7SZJEw+eflzMdb92GxtMT7chb+WLX\nXYzQF+DXcTJQ96YpcAqNSuh0Onx8fMjLyyM7O5uAgAC07Udzx5//5XPXY6QPaEKzPi86PH6+IZ8V\n51YwrNkwGnnXvOnFxcen1n30bw67mXDfcBaeWujQZvZo3x6P9u0BOe9WujGfO4U3NJLzJNX1xV5F\nJDc3/MeNA4WR83e1vYsNlzaw/tJ6JrWeVK25f4z5kQD3ALsedW5hYYQ8aVuw1AWBIfLnNzExEbPZ\njEajQddpMtHHv+TX+O3MuOO/NBysPEdURTIKM9h8eTOT20yutjC2hmtAAEEPPlDj45ZleMRw3tv/\nHj+f+lmV0LDgHfmT9gAAIABJREFU1a0bXt26AbDo9CIKhZHJ3s1BJx9Wr8Vecd5pVKBsBT+LrRbP\nAG4P7IKrgEWnqlfecvX51eQZ8pjSvnYf7LWJRtJwd7u7OZZ2jONpxx0eRwjBTye+I8xgpH/riaV2\nj2stNNTSJaQLrQNaszBmoaoa0RW5kH2B3xN+5652d+HuUnOV9moLdw9PgoODMRqNpFjqrQdEMM2t\nCYXCyKIzjtXZsLDkzBKMZiN3tLmjBlZ7bfDSenFHmzvYGrdVtfNIWYxmIz8en09UcTFRHf527XcK\njeuEipfhAMEdJhGdn8+qcysdTh1hMpv46dRPdA7pTKeQTjWy1mvF2BZj8dZ6833M9w6Psf/Kfo5k\nnGRajh5Nx78vfStuhDpyBnIYSZK4P+p+LuRcYEfcDofH+e7kd3i6enJXm7tqcHU1T9n3w7JXEsoU\nOWrZfhK3FBSyKGZhaT11teSV5LHw1EKGhA+xerdTn5jSfgoukgvfnfzO4TE2xW4iviCFh3Jyof3f\nMS6Wv3tdmqecQsMKlTQNgLajeFCfT6GpiG9PfuvQuBtiNxCfG8+0DjXjyXQt8XHz4a62d7EpdhNn\nMs84NMaXx74kRGgY7xEKDdqX/rys0BAozz57LYmOiCbcN5yvjn2lKmOuhZT8FNZdXMf4luPx9/Cv\nhRXWDpUcRwDaj+P+bD1ZJXrVXnYWFp9ZTG5JLg93ergmlnlNCfYMZkyLMaw5v8ahQFCzMPPN8a9p\naZIY1KA7+PwdoOvUNK4TrG4Er0BahvVlRAksOv2z6jffaDby5dEvaR3QmiHhdRN8Vdvc1+E+fLQ+\nfH7EdpSyLQ6mHGT/lf08kJmBe4eJ5Y6v9c08BeCqceWhjg9xKvMUfyT+obr/V8e+AmBqh6k1vbRa\nQ2BdKycwkm6BbeliduWbY9+o1jYKDAX8GPMj/UP70yGo7lyIa5P7o+7HKIzMP151qhpr7Ijbwfns\nCzyYkYamQ3k3bKfQuE6wuhEAOozn8ZQkio3Fqt/8ledWcll/meldpteYm+21xs/dj6kdprI9fjsn\n0k8o7ieE4KODHxHk4snE3DyIKp8ZuD4KDYDbWtxGqE8oHx36SFUK+Us5l1h5biV3tL6DUJ/ay0xb\nG1jVygGpw3hmpCSSWpjKT6eUZRC28O3Jb8ksyuTRTnXjQlwXNNM1Y3zL8Sw+s5j43MpZEWxhMBn4\n6NBHRLj6EF1QDO3KBzg6hcZ1gq2NQLvRRJglxns2ZfHpxZzNUlYwJbsom48Pf0zPRj0Z1HRQTS/3\nmnJvu3sJ9AjkrX1vKS4Hu+7iOo6kHWFGsRbPhlEQ/HdddCEEcXHyhWF9udOwoNVo+XePf3Mu6xzL\nzipLVy+E4K19b+Hh6sEjnR6p5RXWDJbcU2BDKwdoP44eRcUM9Arn62NfcyXfek6viiTlJfHtiW8Z\nETmCLg261Niarwemd5mOVqPl3f3vKjZh/nz6Z2L1sTyflYdr84Hg/bfbckFBAZmZmWi1WkJCaqe6\npTWcQsMKNjUNzwBoNZRnEi7g6+bLzD0zFZ0o39n/DnklebzU66U6S/FQV/i4+fB8z+c5ln6MxWcW\n222fXpjO+wfep6N/a8bGn4AO5bWMnJwc8vLy8PLyIiAggHpypVHKkPAh3NT4JuYdmkdiXqLd9r9c\n/IU9yXuY0W0GQZ7q4xiuNdYuwgEIjITGXXghKweB4M29b9p9UJqFmVd3v4pG0vBc9+dqa8nXjBCv\nEJ7o/AS/xf+mqArmZf1lPj38KTcHdWJAehx0KB/XVfYSXFPD8SVV4RQaVqgY4FeOqIn465N5MXIc\nx9KO8enhT6sc65cLv7Du4joe7fQorQJaVdm2vjIqchT9Q/vzwYEPOJlhuw6zyWzilT9fId+Qzxu+\nUfKHr8JGKKtu10cBK0kSr/d9HQmJl/54CYPJdorri9kXmb13Nl1CujC5zeQ6XGXNIEQVmgZAx0k0\nTTrOk63vYmfCTrtmqh9O/sC+5H280POFWolhuh6Y0n4KUUFRzNo7q0oX3CJjES/98RJuLm685tII\nNFpoVz5n17Uy4zqFhhV0Oh06nY6CggKyKmaabDMCtF6MSo1jUutJzD8xn+Vnl1sdZ0/SHl7b/Rrd\nG3a/IbxAbCFJErP7zybQM5AZ22dY3QxCCN7Y+wa7knbxQs8XaHF2O4R2l0+kZaiv9xllCfUJ5dU+\nr3I49TD/+fM/Vs12V/Kv8NT2p/Bw9eC9W96rt/dcoVerAyYmJmKqmNm2wwRAYkpeMYObDub9A++z\nLc56iYFNsZv44OAHDG02lImt1FX0q0+4alx595Z30Ugantz+JGkFlQt/GcwG/vPnfziRfoJZfWfS\n8PQmaDFYtnSU4VpEg4NTaNjEponKzVsWHDFreKn7v+kf2p+Ze2by4cEPKTIWAfKb/tOpn3hy25NE\n+kUyb9C8aqV0rg8EegTy6eBPKTGVMG3jNHbG7yzV0tIK0pixYwYrzq3g4Y4Pc0dwd7hyrJJpCqwL\njbI29PrCiMgRPNPtGTbGbuTxrY+TnJdc+tre5L1M3TCVjKIM5g2aV+9O1WUVQA8PD0JCQjCZTH8H\n+FnwC4Vm/dCcWM6c/rNpH9Se5357jm+Of1OqgRUaC/ny6Jc8v/N5ujTowpz+c+qlhqmGpr5N+XDg\nh1zJv8K9G+4tV0I5Pjeex7Y8xpbLW/h3j38zRKODnPhKziJAndfRsHBjP8mqQdOmTYmJiSE+Pp7O\nnTuXfzFqEpxYgVvsLuYNmsfsfbNZcGIBi04vopV/KxLyEsgsyuTm0JuZ3X92tepl1CfaBLbh2+hv\n+ddv/+LJ7U8S6hOKn7sfZzNlh4EXer7AlHZT4Pf35Q4dKufeqig06tmVRjke7Pgg/u7+zNk3h+iV\n0bQJaEO+IZ+43DjCfMKYP3z+DeFS2rRpU9LS0oiPj6dJxYSEHSfBumfwzrjAN8O+4T9//od5h+ax\n4MQCInWRxOpj0ZfoGRE5gtf7vI6Hq/pSxPWRno16smD4Ap797Vke2PQAEboIPFw9OJt1Fq1Gy+z+\ns+VU8Bv+D1zc5INqBa6VpuEUGjYIDw8HKPXkKUfLIeDhJwuO1sOY2XcmY1uM5deLvxKfG0+fJn0Y\nGTmSm0NvvuFPTRVp4d+CZaOXsfbCWv5M/JMiUxFT2k/h9ta3E66T/6acWAHhfeSTaAVuBPNUWSa2\nnkjfJn1ZenYpZzLP0Mi7EVPaT2FCqwn1IlVIVVgCL8PCwjh06BAJCQn07t27fKP2Y2H983B8GV7D\n3uSjQR+xO3E3my9vJiEvgcHhgxnTYgw9Gvb4x+2VqOAofhn3CyvOrWBf8j4MZgM3h97MnW3vpIFX\nAzCb4ORKaDVMft5U4PLlywA0a9asTtftFBo2sLwRljemHK7usr/0yVVgKAStJ90adqNbw251vMrr\nE62LlomtJ1aqBwFASgyknYIR71nte6MJDYDGPo2Z0W3GtV5GrWF5r6wesLwC5UPWiZVw6yzQaOgb\n2pe+oX3reJXXJx6uHtzT7h7uaWeliNulnZCXAh1vt9r3WgkN552GDSIiIgCIjY213iBqIpTkwVn7\nrnNOynBihZzuvL31GtGWv7fl7w/1J07jn0LFt6PKAxbIDz19IsTtqd2F3WgcWwbuOmgdXeklIcQ/\nS2hIkhQoSdIWSZLOXf03wEY7kyRJR65+ra3LNdrdCJEDwLsBnLDuOeXECmYzHF8KzQeCb+UqYyaT\nqVTTsJgHHcnj5KRusXvAuupxyHFlAY9OkC0Yp36RLRrayvc8aWlpFBYW4u/vj59f3d6ZXitN4/+A\nbUKIVsC2q99bo1AI0eXqV/ULBKvA7kbQuMgXuWc3Q5HyGsD/aOL3QXYcdLrT6stJSUkYjUYaNWqE\np6dnHS/OiVos8tyyV2wesNy8oc1IiFkNxhLrbZyU58wGKMmFTtZNU9Y08rriWgmNsYAlp/b3gLJq\nN3VI48aNcXV1JSUlhcJCGwnXOk4CUzGcXl+3i6uvHFsinzjbWq/BfC03ghPHsXvAAtlEVZgFFx1P\nHf+P4vgy8GkEETdbfflamabg2gmNhkKIZICr/zaw0c5DkqQDkiTtlSTJpmCRJOmRq+0OpKVVDpZx\nBBcXl6o9qADCeoJfuFPtVoKxWHYcaHsbuPtYbWJLaDivNK4vKt4xBQcH4+XlRXZ2NtnZNmrNWILT\nnHvFPgWZcG6LfCjVWC/VfENqGpIkbZUk6YSVL+s3oNYJF0L0AO4GPpIkqYW1RkKI/wkhegghetRk\n4i679xqSJL+xF3dAbor1Nk5kzm2GomzoZDtdhmUjlD09OW80rn8kSbK/V1zdZOeH079CSX4drq4e\ncnIVmA3QyXbFwhtS0xBC3CqEiLLytQZIkSSpMcDVf1NtjJF09d+LwG9A19parzUUqd2d7wRhdp6g\n7HFsCXiHyJfgNnCap+oXZQW6YhOVoUC21zuxzfFlENwGGtmu7nlDahp2WAtYytdNA9ZUbCBJUoAk\nSe5X/x8M9ANi6myFKNA0AELaQJNucNR+htd/LIVZsmty1CRwsR0a5BQa9RdFQiO8L+hC5QOEE+tk\nx8muyZ1ur9LX/IbUNOzwNjBUkqRzwNCr3yNJUg9Jkr652qYdcECSpKPADuBtIUSdCg1FGwGg812Q\nchyuHK/1NdVLYtaAqaRKdRv+3giV7jScgRrXGZXfD7seVAAajWyePL/Nac61hcViYSOgD2Q39H+c\npiGEyBBCDBFCtLr6b+bVnx8QQjx09f+7hRAdhRCdr/6rvk5iNVGkaYAc6KdxdWobtji2FIJaQRPb\n1kWTyVTqcFDuTsN5qVEvUHzA6nI3CJMcr+OkPELIAX1Ne0NAhM1mWVlZ5OXl4ePjI9ecqWOcEeFV\noHgjeAdBq+HyKcGkvMznP4LsOLi8CzpPrlLdTk5OxmAw0LBhQ2eMRj2hbOCl4r0S3ApCe8CRn50n\ngookH5FT7NjRyMtqGddCC3cKjSoIDQ1Fo9GQlJRESYmdoKTOd8p5Yi7+VidrqzcoULfBuueUk/qD\n5X2zKzQAutwFqTGQfLR2F1XfOPwTuLjLlosquJb3GeAUGlWi1WoJCwsrV7faJq2Hy37oRxfVzeLq\nA0LIJ8rwPlWq21D1JbjzRuP6wtrhtkGDBnh4eJCVlUVOjp0MCVET5XTfzr3yN4Yi+YDV7rZKxZYq\ncq0PWE6hYYfmzZsDcPHixaobul49IZxeB0X6OlhZPSB+H2Sch65T7Da1JTScBoz6gSRJyi7DQX4o\nthkpPySdaUVkzqyX45i6WMl2W4ELFy4A0KKF1bC1WscpNOzQsmVL4O83qko63wXGIjnHjhM49CO4\n+UB7+1liLl26BDjdbeszkZFy6V67ByyQL8QLMuD8llpeVT3hyE+yO3LzgXabWp5FlmdTXeMUGnaw\nSPPz58/bbxzaHYJbw+GFtbyqekBxrhzZ2mG8zbQhZbH8fVu1alX5Rad96rrC1tuh6oDVYoicJfrI\nzzW3sPqKPgkubJcPnTbShpTFslecmsZ1iqqNIEnQbapslkk9Xcsru845uQoM+dD1XkXNLRvhWp2e\nnFQfy3un6IDl4ip7CZ3dBPkZtbyy65yji+SsEl3uttvUaDSWmnItpvO6xik07KBK0wA57bdGC4d+\nqMVV1QMOL5S1rqa97DbNz88nKSkJrVZbqWKfs55G/cEiNM6dO6esQ5d75BxLx/7B8U2lziJ9Ici+\n5hAXF4fRaCQ0NPSauaY7hYYdLELj4sWLmM1m+x18QqDtSPn0YCyu5dVdp6SdkbWtrlMUld2z2MCb\nN2+Oi4t99dzJ9UFFea5K0wBo2B7CesHB7/65MRvxf111FrF/AQ7X/j4DnELDLjqdjpCQEAoLC0lO\nTlbWqds0KMyUPan+iRxeCJKLbKNVgD3TlPNK4/rCVkBZREQEGo2GuLg4iosVHpi63wfpZ+Hy7ppb\nYH3i8I+g9VbkLALX/j4DnEJDEapPUM0HyXU2/okmKpNB1rJaR4OPrTIp5XHeZ9wYuLm50axZM4QQ\npd5wdukwHtz9ZG3jn0ZRDpxYAR0nKnIWgetjrziFhgIsUl3RZTjIidm6TpGjw7Nia21d1yVnN0F+\nGnRTdgEOf9vArW2Ef6jRot6i+oDl5iWnmIlZIxcf+idxbKmcKr7HA4q7XOsYDXAKDUWo3ggg2ygl\njRyr8E/iwHzwbQIthyrucj2cnpyoR1gR6Q7tle73yWWT/0kJP4WAAwugcZcqE3lW5HrYK06hoQDV\nmgaAXxi0vFUO2vmnJDHMuCD7m3e/r8q6GRWpMkYDZ2r0642q3g3Le6hKaDTsIJdO/iddiMf/Jeff\nUqFlmM3mUqcRp6ZxnePQ6QnkC/HcZDj7D6lUdmCBnCK+21TFXQoLC4mPj8fV1dWZrPAGQLXbrYXu\n90H6GYjbW/OLuh45sADcdXaTE5YlOTmZwsJCgoOD8fPzq8XFVY1TaCigrNBQFTfQOhp0YfDX/2pp\nZdcRhkLZa6rtbaBrrLhb2fQhrq5WtJN/yMHzRsHhA1aH8fJD9OC3tbCq64yCTDn4tdMdii/A4fpw\ntwWn0FBEUFAQ/v7+6PV6UlJUVBxzcYWeD8Kl32/8CPGTq+SEaz0fUtXterDROnEMa+enyMhIJEki\nNjbWfjmBsrh5y1X9Tq6CvLSaW+T1yJGf5Tuc7ver6nb6tPwMsWXGrSucQkMBkiTRrl07AE6dOqWu\nc7dpco78G13b2P8NBLeBiP6qup09exaoeiM4bzSuL6q6YvLw8CA8PLyc/V0xvR6RywLfyNqG2STv\nlaa9oVGUqq6WZ4/lWXStcAoNhTgsNLyDoOMk2TOkyE6dgfpK0hFIPChrGSovrWNi5LLv7du3r42V\nObkGWN5L1XslpLWcyHD//Bs3ZfrZTZB1CW56XHVXp9CoZzgsNAB6PSwn77tRM3ru/UJOgd55suqu\nFqFhayNYc+t0cn1jeS8t760qbnoc8q7IcRs3Ins/l+85245W3dUpNOoZljfKYldURZOuco6dv74G\nJfmr6hP6JDixXM5m66HOo0MI4dQ06jG2fEIs76VDQqPFEAhqCfu+qMbKrlOuHIfYP6D3I6pc0kFO\n6hkXF4dWq72m7rbgFBqKadu2LeCgpgGyvTbzwo1XdGbfV3Ja55seU901MTGR3NxcgoODCQkJsdnO\nGaZxfSHZuWVy2DwFcjaF3o/J5s74/Y4s7/pl75eg9VLlkm7hzJkzgHz3Z9XLsA65trPXIyIiInB3\ndycxMRG9Xo9Op1M3QIdxsPV12PWxXE/cCkVFRWzevJnY2FgiIyOJjo5Gq9VWf/EqycvLY/369aSm\nphIVFcWAAQPQaKycL4rz5EvLdqPt1gC3hlPLuDEpa8o1mUzqMxd3vhO2zZK1jaY9rTYpLi5m/fr1\nJCQkEBUVxS233GL9M1rLpKWlsXHjRnJzc+nWrRu9e/e2HoyalwrHl8oCw04NcGtcL6YpcGoainFx\ncametuGihT7T4fKfkHCg0svbtm2jVatWjB07lhkzZjBmzBhat27NL7/8Ut2lK0YIwccff0yjRo2Y\nPHkyTz31FIMGDaJ///7Wf+cjP8mX+32ecmg+JULjnxIgfCPh7+9PkyZNKCoqsl8v3BruvvLD9eRq\nyKrcf+XKlYSHhzNhwgSefvppBg8eTJs2bdi1a1cNrF4ZJpOJ1157jYiICKZOncr06dPp06cPQ4cO\nJSEhoXKHAwtkz7De6jVysH/3V5c4hYYKOnbsCMDRo0cdG6DbVPDwh10flfvxkiVLSj9sUVFRPPbY\nY7Rp04bY2FjGjh3LBx98UN2l28VkMjF16lRmzJhBfn4+/fr14+GHH6ZRo0bs2bOH/v37l/+9zSb5\nUq9pb5unQXtcTxvBiXqqkueWg8DJkycdG/ymJ+Tcbbs/KffjefPmMXHiRFJTU+nUqROPPPIIERER\nnD9/ngEDBrBwYe2XWi4sLGTMmDHMmjWLgoIChg4dyoMPPkhgYCDbtm2jV69e5bP8lhTILvethkOw\nYzEWlr3XqVOnmvgVqocQ4ob66t69u6gt3nvvPQGIJ554wvFBts4S4jU/IdLOCSGE+P3334VWqxWA\nePHFF4XBYBBCCGE0GsWcOXOEJEkCEPPnz6+JX8Emjz76qACEj4+PWLlyZenPs7OzxejRowUgGjRo\nIJKTk+UXTq4W4jWd/K+D9OzZUwBix44dNts89uMBMeyDnQ7P4aTmicvIF81eXCeWHYi32ebZZ58V\ngHjjjTccn2j1E0K80UCI3BQhhBBr164t3Q/vvfeeMJvNQgghiouLxb/+9S8BCI1GU+7zW9MYjUYx\nYcIEAYigoCCxffv20teuXLkibr75ZgGIli1biuzsbPmFPV/IeyV2t8PzhoWFCUCcOXOmur+CTYAD\nQsEz9po/5Gv6qzaFxubNmwUg+vXr5/ggualCzAoRYu3TIicnRzRr1kwAYsaMGaWboCyff/65AISL\ni4vYu3dvNVZvmxUrVghAeHh4iN9//73S60VFRWLgwIECEMOGDRMmo1GIL/oLMa+LECajQ3MaDAbh\n4eEhAJGVlWWznVNoXH8oERo//PCDAMTEiRMdnyjtrHzA2vK6SExMFH5+fgIQb775ptXmr732WunB\nJyYmxvF5q+DNN98UgPDz8xPHjx+v9HpOTo7o3LmzAMS0adOEMBQLMbedEPOjHZ4zIyNDAMLLy0sY\njY7tNyU4hUYtkJKSIgDh6+srTCaT4wP98owQs0LEow9MFYDo0aOHKCkpsdl8xowZAhCRkZEiJyfH\n8XmtkJqaKkJCQgQgPv74Y5vtEhMTRVBQkADEgjnPySenQz86PO+JEycEICIiIqps9+gPTqFxvWER\nGkv3x9lsc+zYMQGI5s2bV2+yJfcKMSdMTBgra7sjR460ergSQgiz2SzuuusuAYioqChRVFRUvbkr\ncOzYsVKrwKZNm2y2O3XqVOmBaN28f8l75exmh+fdvn27AETv3r0dHkMJTqFRSzRq1EgA4sKFC44P\nknFBHH7UV0gSwtXVVZw8ebLK5kVFRaJr164CEFOmTHF83gqYzWYxadIkAYhBgwbZFYQLFy4UgGio\ncxPZc9oJYbQt6OxhGWvcuHFVtnMKjesPJUKjpKREuLu7C+BvM40jJB4Wm6Z4lWoQcXG25xRCiLy8\nPNGqVSsBiJdeesnxeStQUlIiunXrJgDx6KOP2m0/d+5cAYjWDdxF8Sd9hLAh6JTw4YcfCkA88sgj\nDo+hBKVCw3kRrpLOnTsDcOTIEccHCWzOv/foEAKmP3yfXZdTd3d3Fi1ahJeXFwsXLmTVqlWOz12G\nJUuWsHz5cnx8fFiwYIFdl8W7776bvt06kKIv4d1zzWWPMAc5fPgwAF272i9A44zTqH9otVqiouTc\nSg47jgDmRp148Xf5c/bfl16kadOmVbb39vbmu+++Q6PR8M4777Bv3z6H5y7Lu+++y6FDhwgPD+e9\n996z2/6pp56idbPGnE0t5ouEttX6EFueNZZnz7XmmggNSZJulyTppCRJZkmSelTRLlqSpDOSJJ2X\nJOn/6nKNtrA85A4ePOjwGHv27GHbsUR07vDqQE9Ffdq0acPbb78NwGOPPUZ6errD8wNcuXKF6dOn\nAzB37lwiIiLs9pGAudG+AHy8bCcZGRkOz2/ZCF26dHF4DCfXN5a9YjkgOMKyZcs4EpdDmE7iqV7K\nDil9+/blX//6F2azmfvvv5/i4mKH5wc4fvw4M2fOBGD+/Pn4+vra7aPVSLw71AOAt7/fQGFhocPz\nW541Sg5YdcG1Cu47AUwAvrLVQJIkF+AzYCiQAOyXJGmtEMKB3AT2EUJQaDDZbde1u+xe+ufu3RSU\nOFaR783ZcwB4/LZuBJxZTGH6vxC6ULv97n/4UZYtX84fv//O49Of5PsfHXMvFELw4EMPk5mZya1D\nh3HPtPsV/S6aC1u5SRvD0N7t2bIvhnfee5/XZ72hen6z2cz+/XK0b7uoTlXObTQ7AzWuV4qN5irf\nu6hO8sl4z759POzAXhFCMHuOvFdentgVjwOfUdDrIUXpav7vlVdZvXoNp06d4rWZs3j19Zmq5wcw\nGAxMnTYNg8HAgw89TN8BAxXtFZcjCxnTJJ0u7Zpz5NRFPv/yKx6f/qTq+XNycjh58iRarZY2HTra\nnVsjSXhoVQZTquSaCA0hxCmwW8azF3BeCHHxatvFwFigVoRGZn4J3d/caredKb8AgD927aXdK+uR\nNOreoJK0WJJ/XYfk6sb2JtMwGl9nxUfP8orxQUX9De2mIu3Zx/KlS9hZ0gKvNn1VzQ+Qd3wbGevX\nIbl7c6rl3XR4bbPdPhJmfnV7GW8aENNqKuz7P97/cB6LCjvh4qkuOr4kLRa9Xo+LbwhD/3cSqNqX\nv0MTldH3TmoVrYtsoHhl9QleWX3CZruSVFngr1i/nb2vblI9T+HFg6QeO4aLTyCrgu7lsaLXmP/u\nc8w13qGof1GvB+Hci7zzzjv8cKURbg2aq15Dzu4lZB8+jIsuhM0+Q2mv4Pdww8B29zdIFy1JbDsC\nTs3hxVff5OPECCRXdSbdwtgjCCGQgpvTbc5Ou+27NPVn9fR+quZQy/WcRiQUiC/zfQLQ21pDSZIe\nAR4BCA8Pd2gyLzdXXhrRVlHbV1Y0JT05nqltXQhroayPhQVv/o9kYMBtd3DXxFGcPXuMu5NWou37\nBNnekQpGaMsO9xdZ8vEsinZ+xYv3jcPHP1Dx/Fmpycz69BsApj77Gn2ildW/aHllPe1PXWZr+zn8\nd0g0H59ZR8z+P+mcs4fRE2Yonh/gj1+O8BPQtUcvHlLwN+/eTH3aBSe1R0OdO3Nv70x6XtVmH7Op\nFc8u9qY4J4UnegXiF9RA1TxzZ8wiFRg75WGG3Taa8yd38VjGJnS3PEmRm5LPfFsW5R9n5+qFaHf9\njxc+X46LirxNiRfPMGfuYgCefPV92vXopqhfh4TFhJ1L50iXWcwc1IvZx1aSeOE0/c3HGTDibsXz\nA6z/YRsSS8H7AAAQAUlEQVRrgf59+3CHgr3SQOeuanyHUHJb7sgXsBXZDFXxa2yZNr8BPWz0vx34\npsz39wKf2Ju3tr2nhBClbn1ffvmlqn4XL14ULi4uwsXFRVy6dEn+YW6qELNDhfhpsuJxTCZTadzE\n5Mnq+g0bNkwAYvTo0TZdFythKBbiw45ybMZVD6udO3cKQAQEBIjc3FzFaxBCiGnTptl18XVyY3Dr\nrbcKQCxfvlxVv927d5fGQ5S6maedE+L1ACF+eVbxOHq9XoSHhwtAvP3224r7FRcXl3osKvGWKqUg\nU4i3I4T4dlSpx9TSpUtLXeYtwbtKGTlypADEokWLVPVzBOqDy60dodEH2FTm+5eAl+yNWRdC4+OP\nPxaAuPfee1X1e/zxx633+32u7Mt9Ublr6YULF4S3t7eqDWmJaA8MDPw7slsJuz6R13duS+mPzGaz\n6NOnjwDE3LlzlY8lRKlL5IEDB1T1c1L/ePXVVwUgnnvuOVX9xo4dKwDxn//8p/wLvz4vxOv+Qlw5\noXisjRs3CkC4u7vbdW+3YIkwj4iIUBcbteH/5IDE5GOlPzIajaJ169YCEAsXLlQ8lNFoFIGBgQL4\n+5BZi9wIQsMVuAhEAm7AUaCDvTHrQmhYApcaN26s+LSenJxc6rd+4kSFD3xJgRAfdCh3klfCp59+\nKgAREhIiUlJSqmy7Z88e4erqKgCxdu1axXMIfbKsCS2cVMnXfO3atQIQTZo0URxIlZSUVBrdWlVA\no5MbA8sDW82+PHnyZGmGgitXrpR/MT9DiLebCfHdbapiH+677z4BiHbt2tnVjDds2FCahWHPnj2K\n5xCpZ4SYGSjEmqcqvTR//nwBiA4dOigODN6/f3+p4FJsFagG17XQAMYj31EUAykWjQJoAqwv024k\ncBa4ALysZOy6EBpms1k0btxYAFZTCVjjxRdfFIAYO3as9QZHl8qn+b++UbwOk8kkBg0aJABx0003\nifz8fKvtLl68WLreZ59VrtoLIYRY8YgQs4KFSD9vdf6oqCgBiK+//lrRcAsWLBCAGDVqlLp1OKmX\n5Ofnlx6WKgkAG1jMlzZzvO37n7xXYn5RvI7c3FzRrl270s+erQPL0aNHhU6nE4CYM2eO4vGFEEIs\nvF0+YOWmVnqpuLi4NH/UmjVrFA03e/bsOgnqs3BdC43a/KoLoSHE3x/s999/327brKws4evrKwDb\n+aPMZtkOOqepEHplm0sIOb2HxWY7YMAAkZ6eXu7148ePi4iICAGIW265RRQXFyseW8Tuljfn1pk2\nm1giu1u1aqUoL44lAv2zzz5Tvg4n9Zrhw4cLQHz//fd228bGxgpXV1fh4uIiLl68aL2R0SDEp72F\n+DBKiOI8xes4ffp0aSqcMWPGCL1eX+71PXv2lKbUmTRpkrpUQSfXyHvlz49sNvnoo48EIHr16qVI\ncxgwYIAAxIoVK5Svoxo4hUYt89NPPwlADB061G5bSyK1wYMHV90w7Zx8ql92v6q1xMTEiCZNmgiu\nZqKdPXu2WL58uXj22WeFp6enAETPnj3V2WYNRUJ8dpMQc9tXuTENBoOIjIwUgFi6dGnVQxoMpUnn\nbD4QnNxwzJs3TwDizjvvtNv2scceU5Yux3KgWf+iqrX89ddfpZ/BZs2aiblz54ply5aJRx99tNR8\nO3z4cFFYWKh80IJMId5rJcQX/apMrZOXlyeCg4MFILZt21blkHq9Xri6ugqNRlNlQs+axCk0apnU\n1FTh4uIiXF1dRWpqZXXUQlZWVumHdOdOBRfdO952KMFZQkKC6NevnwAqfU2dOtWm6comW2fJ6zi9\nwW5TSyberl27VnmCsiRea9Omjbq1OKnXnD17ttTTripNNy4uTmi1WiFJkjh16pT9gdf9S750vqwu\n+/OZM2dEp06dKu0TjUYjZsyYof6ubfV0+XI+8ZDdppYsuUOGDKmynSVLcP/+/dWtpRo4hUYdYHGH\n++STT2y2mTlzZmlCQEUYioT4tJcQ77eRL/1UYDabxZo1a8QjjzwiRo0aJZ5++mlx8OBBVWMIIYRI\nOCC7Nq5SVjekoKBANGjQQABiwwbbQubee+8VgHj55ZfVr8lJvcbykF62bJnNNk8++aQ6N/IivexA\n8kkPIUpUaAZC9kxasmSJuP/++8WoUaPECy+8UNlBRQkXdsiHq02vKGpe1lS9b98+m+2GDh3qkFt/\ndXAKjTpg8eLFpaYfa6SkpJRqGb/99pvygZOOCjEzSIhFd1crO6ZDlBQK8UlPuQZAgXK1+O233xaA\n6NKli9W7jezs7FJTWbUyBDupl1js+dHR1utKnDlzplTLOHbsmNU2Vjm3VX5o//rvGlqpCvLS5cPd\nx92EKFauyVucYoYNG2ZVM09ISBCSJAk3NzeRmZlZkyuuEqfQqAMKCgpKPS3++uuvSq9b3PxsbZQq\n2fWxvBkOfFv9haphzVOVYjKUkJ+fL5o2bSoA8dVXX1V6/ZNPPlGncTm5oUhPTxdubm5CkqRK91lm\ns1mMGjVKAOKBBx5QP/iGl+TP7IlVNbRaBZjNckDurGAhko6o6pqamir8/f0FYLXK4H//+18B1Sxg\n5QBOoVFHPP/881ZPDevWrROAcHNzE2fPnlU/sMkkxPdjhHijoeoPpcMc/knefFted6i7RfPy9fUt\n9zvn5eWJ0NBQu+YJJzc2U6dOLb1jK8vXX39d+rlRFXRqwVAsxP8GCTEnTIiMOtJi//xI3iu7HfMC\ntMRYNWnSpNzvXNY68ccff9TUahXhFBp1REpKSump4YsvvhBClPf1fuuttxwfPDdFNhPNbV9aJ7nW\niD8gC6hvR8kujQ5QtqhTx44dRVpamjCbzeKBBx4QgOjWrVv1Kh46qdecP39euLm5lTth//HHH6VV\n7pS45NokM1aIt5oK8XlfIQprtrplJc5ski/gl0x12HxsNBpF//79Bcjlo/V6vTAYDGL06NGOWyeq\niVNo1CHff/99qQdG//79SzfBhAkTqh/JmXhYfph/PUSIInU5nhSTcVGId5oL8VEnq4FJasjOzi5N\nmRASEiK6dOlSGt176JB97xInNzbvvvtuabR1//79S91cH3rooeoPfm6r7MDxw7hqVZWskuRjskbz\nRT9VMSJWh0pOLtXAw8LCRPv27QUg/P39r8m9n1No1DFz584t3QAgF5VX5etdFTFrZZe+70ar9hKx\nS3aCEPO6yKkZ0hwwo1khMTGxnPtvYGBglV5VTv45mM1m8fLLLwtJkgQgJEkSM2bMUBQYqoiDP8hm\no+UPOqwx2yTtrHy4mttOiKyqy84q5dy5c6Jz586le6Vx48Zi9+7dNTK2WpQKDUlue+PQo0cPceDA\ngWsyd1JSEocOHaJ169a0bt26Zgc/8jOsfhxaDIE7fgB3n+qPmZMA390G+elw70po2qv6Y15FCMGB\nAwfIyMigb9++6HTOmhhO/iY2NpYTJ07QsWNHmjVrVrOD//EBbJsJHSbAhK/BpQYqQKTEwMKJYDbA\n/RshuGX1x7yKyWRi37595Ofn079/fzw9lVXzrGkkSToohLBZSbW0nVNo1CMO/QC/zIDGneHupeCj\nrj5BORIPwuJ7oCQf7l0FYXY/K06c1B/+/Ai2vgbNB8GkBeClvOZMJWL/hMV3g6unfLhq2KHm1nkd\noVRoXJMa4U4cpNtUmPwTpJ6GL/vDhe3qxzCb4cACWDACNFq4f4NTYDi58ej/DIz9TH7gfzMEEhw4\nSJpN8Pt78P0Y8GkID225YQWGGpxCo77RdiQ8tBU8A+DH8bDqcchJVNY3+Sj8MAbWPQvN+sAjO6BR\nVO2u14mTa0XXKXDfOjAWwze3wob/g7w0ZX0v75b7bH8TOoyX95y/Y1VBbzSc5qn6SkkB7Hwb9n4B\nSNB+DHSaDGE9wdNfbiOEfF9xfiscX8b/t3dvIVaVYRjH/0/jqTxGGZljaQdSsUQhSYRurLAyvenC\noJCiIDpgEFTWXd0EQieKICxvFILMIKSTHSg6GFmKadPBDA+VpJEHakwH3y7WDocQ+0hdr3vW84OB\n2Ws2zPOtYa1nf9/aaw8/vAsDh8PVj1azlqP/j3azvmH/3mqpas0S6DcIJs+DCdfDudNhwGnVcyJg\nzzb48UNYuxS2fgpDz4GrHoFLbmjEseJrGk3x+xb45GlY/zL8tafaNvgs6H8qdO8+vG3oKLjsNph2\nOwwanpfXLMuu7+GjJ2DDCujprrYNORs6BlTHyf7WsXLGhTB1fnW8/FMqDeDSaJqD3bB1Nfy0BnZv\ng579MHAonD6uWooaNQVO8WqkGQe7YfMHsGN99aIrDlXlMHJ8NVMfNbkRM4t/c2mYmVkxv3vKzMyO\nO5eGmZkVc2mYmVkxl4aZmRVzaZiZWTGXhpmZFXNpmJlZMZeGmZkV63M390naCWzJznGcnQnsyg6R\nqOnjB++Dpo8fTvw+OC8iRv7Xk/pcafRFktaU3KnZVzV9/OB90PTxw8mzD7w8ZWZmxVwaZmZWzKXR\nHp7PDpCs6eMH74Omjx9Okn3gaxpmZlbMMw0zMyvm0jAzs2IujTYgaZGkbyStl/SqpBHZmeoiaZak\nbyVtkvRgdp46SRoj6X1JXZI2SlqQnSmLpA5JayWtzM5SN0kjJC1vnQO6JE3PzOPSaA+rgEkRcSnw\nHbAwOU8tJHUAzwLXABOBGyVNzE1Vqx7gvoiYAFwO3NWw8fe2AOjKDpHkKeDNiBgPTCZ5P7g02kBE\nvB0RPa2Hq4HOzDw1mgZsiojNEXEAeAmYm5ypNhHxS0R82fp+H9XJYnRuqvpJ6gSuAxZnZ6mbpGHA\nFcALABFxICJ2Z2ZyabSfW4E3skPUZDSwrdfj7TTwpAkgaSwwBfgsN0mKJ4H7gUPZQRKcD+wElrSW\n5xZLGpwZyKVxkpD0jqQNR/ia2+s5D1MtWSzLS1orHWFb494jLmkI8Apwb0Tszc5TJ0mzgV8j4ovs\nLEn6AVOB5yJiCvAHkHptr1/mL7fDIuLKo/1c0nxgNjAzmnNzzXZgTK/HncDPSVlSSOpPVRjLImJF\ndp4EM4A5kq4FBgHDJC2NiJuSc9VlO7A9Iv6ZYS4nuTQ802gDkmYBDwBzIuLP7Dw1+hy4SNI4SQOA\necBryZlqI0lUa9ldEfF4dp4MEbEwIjojYizV3/+9BhUGEbED2Cbp4tammcDXiZE802gTzwADgVXV\neYTVEXFHbqQTLyJ6JN0NvAV0AC9GxMbkWHWaAdwMfCVpXWvbQxHxemImq989wLLWC6fNwC2ZYfwx\nImZmVszLU2ZmVsylYWZmxVwaZmZWzKVhZmbFXBpmZlbMpWFWg9Ynld6ZncPsWLk0zOoxAnBpWNtz\naZjV4zHgAknrJC3KDmP2f/nmPrMatD6ldmVETEqOYnZMPNMwM7NiLg0zMyvm0jCrxz5gaHYIs2Pl\n0jCrQUT8Bnzc+sdavhBubcsXws3MrJhnGmZmVsylYWZmxVwaZmZWzKVhZmbFXBpmZlbMpWFmZsVc\nGmZmVuxvMrXzlQwAbAEAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_square_terms(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Gibbs Phenomenon\n", "Notice the weird jump we get even with a lot of terms. It's almost perfect except for at the discontinuity." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_both(100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is called the Gibbs Phenomenon, and shows a fundamental difficulty of approximating a discontinuous wave with a sum of continuous waves." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Audio compression with the Fast Fourier Transform\n", "\n", "Just like we can represent the square wave as an infinite sum, we can represent a discretely sampled wave as a finite sum over frequencies. We can compute the coefficients of these frequencies with the *Discrete Fourier Transform* (DFT). If we bin up the frequencies into $k=1,2,\\ldots$, the coeffient for frequency bin $k$ for wave $y$ is \n", "\n", "$$ c_k = \\sum_{n=0}^{N-1} y_n e^\\frac{-j2\\pi kn}{N}$$\n", "\n", "Essentially, the DFT computes the correlation of the signal with each frequency.\n", "\n", "On a computer we can get samples from a wave. If the sampling rate is $r$ Hz, and the number of samples is $N$, the frequency corresponding to bin $k$ is \n", "\n", "$$f = \\frac{kr}{N}$$\n", "\n", "We can compute the coefficients explicitly by computing these sums directly. This is an $O(N^2)$ operation since we compute $N$ sums over $N$ variables. In practice engineers and researchers use the *Fast Fourier Transform* (FFT) to compute the DFT. The FFT uses symmetry of periodic functions to divide and conquer the sum and compute it with $O(N \\log N)$ runtime.\n", "\n", "Numpy has an FFT inplementation that we will use to reconstruct sound waves.\n", "\n", "First, read in some data." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "infile = 'data/CallRingingIn.wav'\n", "rate, y = wavfile.read(infile)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What is this?" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ipd.Audio(infile)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Exercise: create a function to plot the wave." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_wave(y, rate):\n", " \"\"\"P\n", " Parameters\n", " ----------\n", " y : ndarray\n", " Audio signal as a numpy array\n", " rate : float\n", " Sampling rate of signal in Hz\n", " \"\"\"\n", " \n", " ## Your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similar to the square wave, we can approximate the signal by only keeping the frequencies with the highest magnitude. Let's compute the FFT and plot the magnitudes. We'll show a straightforward implementation of a `plot_dft` function to illustrate how the data is structured, but in practice we'll use the matplotlib [`plt.psd`](https://matplotlib.org/api/mlab_api.html#matplotlib.mlab.psd) function which uses a windowed approach to better extract the peaks in the data:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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Zby4pY8L8Us7YQ11XOcUjmrLUey7laGCxPWDFokS0B2CMGemjfCYwM4J+pwPT\nCwsLR4fbh5UpvqAlT91wAbf4CU19Vfd88vwonbkPX+YxESnxY8nO2qf+CfO3UtS1hdd6j0+zPfv8\n3+xN/N/NvVwCAr6x+Ct+cXVXMtKjvxCP5ACjkjrEYhNYCUBamnDH4AK/dSbeUehyfffFHdi0+xh3\nDG4fQ8mUYJm4xvV8wIsfe18FOPOLd9e4XFdWG95Y/BVjLo2+i2+g+b8mWJzaFFMaS/rjxyIhTF2n\nSU4mE+8oJK9BZqJFUbzwyebwTgxPXbqDjbuPcsRLcptICHQQrHaTWDVAKmNJBRBNLyBdCCtWZtv+\n4xS/sJCbX7aFojgTZFpMbywp3U/JDpsiqasH2JT4YkkFoCsAJdXYsreCXk/M5rxff8jab8K77297\n7XMmr7N5KQUbCiJWJqATZ6pYv/NobDpXooYlFYCVzgEoSrw4esq2sbzi69DTUIZKrPcAHvzXSq4Z\nvzBlEvDUVSypABQllXl82jq27Iksnn/p3gq/78faQrSszBYiLBKTlhJ7LKkAomkCUm84pS5y5Z8X\n1LwOZ4N5s5MCKRg7I+IzB6FO5A431FitMPYcPcW+GEVqTSUsqQDUBKQotdw5aSl3TlrKkROVGGM4\nVek/mvqpymqPBx9fCiCYnMGLS/dz3q8/ZHmZe+Bf39TmJI4NA3/3ERc+Oy9GvacOllQAiqK48snm\nfdz88hJeXbiNbr+ZxcXjPubwCc+wFADdfjOL383c6FG+79hpZqyxxcFxTNDBRIJYVGoLTuhIlhMM\nuvAOjqrqs2zb599cF0tUASgujBp4bkzyJSuRs2VvRc3E/s3hk1zy+/ksKzvIweNn+ObwSb9t15Qf\n4cJn5/Gjf33BkZO1Zw7+80U5S7bu99MyPA7ZzzUkS47lWPGH2Zu4/E+fsOPgiYSMb8mTwCIyAhjR\nuXPniPq5rlcrfnZV1+gIZWGyM9JcYtg7ePDyzvw1iBOqzozo3ZpPvQQxU6zHsdNVfOflT0Nu1/vJ\nOS7nBG579XMAysZd67X+gYrwbe06/fvHsaraX3Gadk0bxH18S64AorUH8NeRfenQPPmfZn2F/g1X\n+enyPfk562Vm7vPUHHYdOcmo1z7jgt/OYuX2Q3y0YQ/vLC8HCGuloAsAa2NJBaBEzsNXnhd2Ww0k\nlpocPlHJ4Oc+ZnHpAY6fqebGl5Yw7sPavYTFpQfYcfAE33l5iYsZKRLe+uzrGpdRq1B91nD76597\nDeedbCS1AkiViaxVXnaiRVCSlC1u5wkeeXcNy8oO8cbir4JqH8jL6DfvrQ3LjBWIjbuP8uaSsrDa\n7q84zcIt+3lwysroCmVBklq5AXLdAAAdYUlEQVQBpApTRg/yKAtX9Qkw7qaeEcmjJC+O/aEX5m2h\ndG/gw2oVp4I7CTx99U6OnYrOqmLRlv0Uv7CwJhS3L6q92cGoNVvF6vGxsvqsZVY9llQAGgsoNPIb\nZdOuaX2XsvqZ6WH3V1jQlNWPXxWpWEqSM+x522G1bw6fpOJ0Fb+ftZHFpa77BO+tcs0G+83hkywp\n3c/8TXtdyh+cspJbXvnM56QcLB9t2MP3Xv88qLonfZyncKxaYmVA+P2HG/nOy5+GHfMpmljSCyjZ\nE8LEgg8euIRxszZwQ582rNx+mDsvKgiqXfOGmeyv8PQn95bQ3BdP33ABv3m/ziZ9UyLAPSnR30q2\nsvV3vnNaXzzu45rXDwx19fLbsOsof5qziUeKuwE276OmOZlUnzUcP1Md1D2568ipoGX35aJauwKI\njQbYZD+lfcBLetF4Y8kVgBI6jRtk8NxNvRjUsRn3F3Xym2XqtoHnkml/P1BiGn9c1KkZBc0acHsE\nfSjJR6df1SYDHP/RFvYe8z4pv+glleZLJVt5Yto6Nu4+Sv9n5tHh0Zl0fuxDej85hy/Lj7C/4jQf\nbdjjc+xJbnsTz85YT5WP026+1hqO8qqzru3KD52g+IUFSRWCQhVAHadnm+BcZd+9b3DN66dv6EFG\nuu3p5vsXF7D818Nq3gtl43z0JR0p+cXQoOsrqcn4j7aEVH/ykjKKX1joUT7ixUUUPjOPe95cXlP2\n3spvXALnbdt33KXNqwu/Yu567wqj1xNzKNlRyZSl2/n6QG07x8rAfWX8xuIyNu4+xoXPzqP8UHQO\nbh1K8CrAkiYgJTiWPnYFuVnBmWoKC5oCcHm3FqQ7nQISEZo3zAqqj9zsehwLclNPURz847PIAtH5\n46G3V9W8/laf1l7r/GTqKlo0yqLfuU08HnAmrzsD674E4IMHh3BB60YuZqTjp6vIybJNk68vql1d\nPPz2at5xeqgCeH/VN7RqXJ8BHZr6lXnhFts+ybqdR9huPwGcqFWFrgDqMC1ys0Pa7N3y7HBec8s1\n7KBxVuAn//uLQstd2yzHf/rKFPHSVeKE+4azgzPVZ/n23z7luQ83+g25cN1fF/HXj0td3FIv+78S\n7n1rOZVuZqSlZQdZud01b8NPpq7illeCd2l1TphzJpigTDEgbgpARDqKyOsi8m68xlRcyUhPI83+\n9P/L4baNtux6tlugZYPAs7HHppifJt1a5rLiN1eGJ2iIPFKc/OE+lMiZuGAbl/xhvt86z8/d7HK9\nv+I0s9ftYeMuT5fXG19awjvLd1AwdoaLglj7zRHOVJ3l+bmbuXb8Qkb/fTmbdvt3mU3UiemgTEAi\nMgm4DthrjOnhVF4M/AVIB14zxozz1YcxZhtwjyoAa3DH4AKXDeAxvbL4sjKf/u2bRKX/F2/rF7BO\nmgjVQd75Xz13DR0enen1vUbZwXssKUo4jHhxkdfyR95dA8AHa2pXH9f91bXuup1Hmbt+D51bNKR3\n2zyv/ZxNkAYIdg9gMvAi8HdHgYikAxOAK4FyYJmITMOmDJ5za3+3MWYvimVpVj+NJ4Zf4PP97q0a\neZT5WzN0btEw4JihWID8bU43b+jf1KQoseanb68OWKd0b0XATG3xJigFYIxZICIFbsUDgFL7kz0i\nMhW4wRjzHLbVQliIyBhgDEB+fj4lJSXhdhVR21hRUVGRELkCjelPrleubEC6VDFr21aX8jVr1sAu\n77dQMJ8xlFDBvvq7s3smWfs28qfL6vOzT/yHRFYUK7Fj115yMuB4JRz8eiMlh2u9peI1T0TiBdQG\n2OF0XQ4M9FVZRJoBzwJ9ReRRu6LwwBgzEZgIUFhYaIqKikKXbJbtcEpYbWNMSUlJfOUK8rvwKpe9\n7dVX2Fw9N5eUwuZNNW/37t2by847x6Wug5q+3MqdSU9Po9pHqsFnvtWDDs1zGPXa57X9ufUlAk/e\nUbvP8LNPfI+lKFZj9b5qurdqxPpdR+nfvz+9nMxD8ZonItkE9rYm9/lIZ4w5YIy5zxjTydfkX9Ox\nhoKwJO4P7C0bBR+Ezt/pUG9c07MVF3du7rdO+wTET1eUaLJ+l80TyOEaGm8iUQDlQDun67aAdz8s\nJam499KOzHv4Urq2zK0pu6hTs5rXr9ze36ON89kDB+oFqig2docQwiKaRKIAlgFdRKSDiGQCtwLT\noiGUJoW3NmlpQucWuS5l/xo9iIJmtify8/JzvTXzwLGv2yavvv+KXrj0vHP40y19vL53S2Fblj02\nzOt7imJFAoXNjhXBuoFOAYqA5iJSDjxujHldRB4AZmPz/JlkjIlKRLBopYRUIqdRdmSHxec9fGnN\nSUp3HOcKurXM9chpG2h18Pe7B/h87w839wZg0zPFbNt3nOF/8QwroChWwtLnAIwxI32UzwS8O2dH\ngEYDtQbTHriYlo097fy+JueBHZpRduAEuU5Kw32l4IzDKvS9we0ZfWlHbp34mV95Op2Tw1a3WC/+\nyKqXTlY9PeyuWJ9EhYa2ZCwgXQFYg14+Dq344ulv9WD0pR2Dji3k8O1PE2FQx2YBakPTnEy/CmD0\nJR1omuM6dofmOYwd3o0Tp6sY/7Fn9ElvFDRrQNmB6AT7UpRgWF2eGAVgyccj3QOwJoH89jPrpQV1\nACzUfoPlsWu7e8QrEhHuu6wTLRsHv8/QraXnoTdFSUYsqQAUaxOtIG7qBaQotby9LHZRU31hSQWg\n5wCihxfvy4Qx7+FLmffwZfRpZzMtNbOHcMiqF376ymBxV1reXFUdZGVY8s9CSXKemLY+7mNacg9A\nN4Gjx2e/uoKjJ6MTw//2QQWs2nGYuy/uEFZ79w3hp27oQdmB4wzqaIufflX3fOb4SN4Rba6+oKXX\n8mdv7MGpyrO87yO0sKIkE/qok+S0yM0Oyy7vjcYNMnjtzgtpFuQmry8cwduaNczkjsEFNZvBL40K\nHEE0XOoFuRQaNbB9zaE2R9Y0B5q/QIklJyur434gzJIKIFITULBpEpXE8Mfv9OZ3N/bkgtauv1M9\nP3mMI+VbfdvQ99zgvJrOb9WIsnHXclPfti7lOv8rsWbQcx/FdTxLKoBIvYDyG2XRvpElP5oC5DXI\n5LaB54bcziMhTQhkpKfxy+JuIbXp195VYZyrsYeUJCMpZ8lEnapTokfj+tFP8hLovph0l2u6zFsK\n27Hwkdqk95n2Q2UTnJLdzP95UdTkU5R4Y0kFEKkJSOf/uk9aDN2XBvpI2n15t3yXaxGhnZen/k4t\ncmped2ie4/G+okSCe/7hWGJJBRCNg2Bqr1WijcME5b6S+OcPfKbBUJSQ+ePsTXFLEWlJBRAp0TpZ\nqliMBGt1hxeQ++2lewNKNHllwTYmrDodl7GSUwGQ8LlCiSG924UWo8hBokLuKkqorNhTHZdxklIB\nAKoBkpixIXrzuBOpP78qEiVZSEoFoBag5OT5W3ozauC5XFjQJCHjSxxOgtXkWFaUOGBJBRANLyBd\nACQfbZs04Nkbe0b9wFioOQNi+YChp42VeGJJBaDhoJVYkJNpC33lnsx+9eNXsfHp4oDtg5mbO4bh\nFjp2eK1JK001gBJHLKkAImVscTdu756ZaDEUi9G7XR5/ubUPz97Y06U8OyOd7Az/EUnzGwUZ/yiE\n+Xv6A0Po2aaxz8B0rbxkY1OUaJKUCqB760Z0aBz7EMNK3eOGPm185ij2xZKxlzPnp5f5NM+EEz56\nzRNX0bNtY6Y/OIScrNp7tdM5tSsIPWWsxJqkVACKEgy/u7En7943OGC91nn1aVw/oyZFZqPsDJ66\nKJtZD10C2CKuBkubvPoMKGhKo+zaUBdNGtSuVh0pLe+9rGPAVUm8cXzeaEWXVRKPJfMBKEo8CDUg\n3RPXd2fkgHac26wB5zZK95o60nmRkNcgg8MnKl3eXzz2co82Gd42td02mn9xdVdOnKliwvytXmVr\n2Sib3UdjG0rYoehG9GrNn+dtjulYSnyI2wpARL4lIq+KyPsiclW8xlWUaJFVL71mFRCIAQVNeevu\n0ENE+DIzDezQlF9c3Y2Fjwxl+gNDQu43GjTNyWTdk1fz4OWdEzK+En2CUgAiMklE9orIWrfyYhHZ\nJCKlIjLWXx/GmPeMMaOBu4Dvhi2xotQFouzM0721bbXRrmkDerb17x037HxbULs7BrePrhBATla9\nmAbqU+JLsCuAyYCLn5yIpAMTgOFAd2CkiHQXkZ4i8oHbvxZOTX9tb6coHgzp3DzRIoSFw5XznFyb\nDb9Puzwy6kVvomyQGby19s6LbBP/A0P1Sb0uc6Yq9lFBg7qrjDELRKTArXgAUGqM2QYgIlOBG4wx\nzwHXufchtmOU44APjTFf+BpLRMYAYwDy8/MpKSkJRkQPKioqwm4bS1Qu/9zRwXBz2/oeslhBNmfc\nv69vttts/fUrj/L0xfVpnb2bXRt2e7QL9Dm2bbXZ+Lfv2EFJSW1+5EDtGqadqXld/c06JhfnsP6L\nzwJ8iloy0qDSy3zzYN8sGmYIDTMlrN+gYQZUVAaup3gyefp8zmsSW0eASDaB2wA7nK7LAX9GzweB\nYUBjEelsjHnZWyVjzERgIkBhYaEpKioKS7iSkhLCbRtLVK4QmTUDwHKyuX9fOz4tg/XraNOmNbeP\ncDpnMHuGSzufn8P+OTt26gSbN9KuXTuKis73/flnufbbrEkepYcPetZ1q+eLtLQ0OOupAX5001Cv\n3kif9T0VVPrCHu2a8tk2m1xvfP9Cvv/Gspr3po4ZxOi/L+fYqaqgZIwnjbLrcTTBcp3foxeXdIlt\naJBINoG9rW99HpI3xow3xvQ3xtzna/Kv6TjCUBCKEm8ijQ4x+6FLeWlUv7iGMBnU0XtinGBoGeQh\ntfPyc2teD+3awuW9Vo2zw/q8H//ssjBahcbfvtc/5mMEYlccEsRHogDKgXZO122BnZGJoyiuPDYw\nmzfuujDRYgRNuHmLu7bM5Zqerci1nw9olB3a4jwcBXRVd+8nkKPF727syY8C7ENcHMaeT8dzfJ9D\nGNyxWcj9pTKRmICWAV1EpAPwDXArcFs0hDLGTAemFxYWjo5Gf0rdpUuTdIq6tQhcMcE43EOHdIls\nE/u7F7ajsvosIweEdkbBSqz49TBEhKY5mew75juxSV79TH5zXXc+XOu5VxIOn//qCvIbZVMwNjiz\nl9WJx2owWDfQKcCnQFcRKReRe4wxVcADwGxgA/COMWZdNIRSE5BS1+jTLo91T17tM65PsKSnCXde\nVFCTgD5Ynrz+goB1Ql1VQHjRSZs1zKJpTuBYXI0bZFAvPfgBvnzCf9C+/EYaOylUgrrLjDEjjTGt\njDEZxpi2xpjX7eUzjTHnGWM6GWOejZZQGg1UqYuEGmMoGF4a1Y+/3z0gYL3zW3meSnYnnNhCsY5O\nGorJLCM9LW7hMSIJ+T0qxBPmvohH/glLhoIQkRHAiM6d1Y9ZSW2u6dkqan1l+FlV9D03r8ZbB+CD\nB4dQfdZ4D1ORIOpKpGzn2E6REI/zdtb5dZ3QFYCiRJd37h3sEoBuSOfmLsrl1TsKXer3aNM47NzL\nVqN/e88McsV2U13bhv5n2QaZoa84oqWo0uOgASypAHQPQFGiy4AOri6fIjZXzg7Nc/hhUSdyszNo\nXD/DR2vvXNA6sNkpEM0bZnLvZR158+4BvPy9fjXl3xvk34wSbH6GxWMv5+0xgzzK+55rU249mnsa\nQepnpNfkfXbU80fbJvVdruvIQgWwqAlIvYCUZCE7I42zJj7H+kOheUPbBOq8L2BCNHxPe2AIZ42h\ny2MfAjDv4cuCTq8548e2gHYiwqPDz/d4/5lv9eSZb/Vk5+GTDPn9x5w1rvsFn/9qWI23zy+Lu3F+\nq1yPPkZf0oE2efU9ygEu63oOz324kcKW6cwqcz2q3DqvdjM5mD0Kjyf+KC0B4rEHYMkVgKIkC6sf\nv4ovn7BO8FvH4a+b+rWJuK/0NHHZI+jcoiHtmjYIqu0FrYMz77bOqx9wI7pPuzyKunq6Cj92bXef\nbbq1bETZuGvpnBf5pnK4Zz8CEY89AEuuAHQTWEkWsupZK6mLw67sbdIa2LEZc9fv8SgPRPEFLWmQ\nFfvPGewD8e9u7FkTPTUY/nP/YLIz0rl2/CIAHr6ya03e6H7n5rGodH9IcjpndYuEeOSHtuQKQDeB\nFSX+jL+1b1jtXr69P8/f0ifK0tQSyDDlPk/eNvBc+oSwgd2/fVOXFcm1vVrRJT+XeQ9fyk+GnRew\nvfP47/3oYq7v3Trosf32G5Ve/GPJFYCiKPGnfhgeL6Gy7LFhfk0bSx+7gnpp3p9L47252rmF575C\nIEJRPIHQPQBFUbzSrWXok5MVOCc3i2YNfXvwtMjN9jhFHGhzOhreSJEQq2k6Zc8BqBuokmy8c+9g\n/nP/RVHr71fXeHrOJDvuT8Rd7ZFGc7NDc1+NNv6e1G8fFH5WNt0D0D0AJUkY0KGp1wNJ4eKYG4Z0\nbk7ZuGuj1m+saBTB4dhHim3Z1tyfiN+9fzALfjE0Aqlix90XdwCgVV748YnCOYQWKpZUAIqiBIcJ\nsEV6S2FbHrWnq4TIYtwkivsu60TZuGs9nrRzszM4t1lwbqfOhJsH4Y7B7Zn540s8ynu28XxQdaQD\njZWLaLTQTWBFqYN4m1he/l5/Nqxf61L2h5t7e29v7XkpZiweezlNw4zVc2mXczzcS5+7qSc39m3D\ntNV1MxWKKgBFqYM0ybHZvTs5JUcp7tGS7P0bEyVSncDXyeBg8LZ46t02L24RSmOBKgBFqYNc0Lox\n/xo9MKr7CqnO63cWcuhE4Az2Dw3rwgvztgDRX0kVNGtA2YET0e3UD5bcA1AvIEUJzEWdmod80rgu\n7gHEiyvOz+fm/m19vu9wR31o2Hkxc8Md67RfEw8sqQDUC0hRYkuKbgFEhDfd6VOheil/aVQ/urXM\n5Q839/I5RkFzpzASqXoOQFEUxSpE8rTvbCK6pmcrZj10KbcUtnOpkxMHd09fqAJQFCXpuaZnSx4f\n4Ts6qD+evbEHmelpFIa539IyQK7i6/u05rx822Z+vN1GdRNYUZSk56VR/cNu2799UzY/Ozzs9v/9\n4UWsKfe9n5nIfRlVAIqSQgQ6OKYExwu39mH8R1tqntzB5h3kjdZ59WkdwP00UUogbgpARM4HfgI0\nBz4yxvwtXmMriuJGnCwNTRpk0K1lLsWtz8RnwDjRrWUjl1VFJOE4nCd/EXjhu3146O1V9G4b+5zM\nQe0BiMgkEdkrImvdyotFZJOIlIrIWH99GGM2GGPuA24BCv3VVRQlOaiXnsashy6lT4vUMjZE8kD/\nrb5tmFycQ05W7L+zYEeYDLwI/N1RICLpwATgSqAcWCYi04B04Dm39ncbY/aKyPXAWHtfiqJYjOt7\nt6ZjlDJaKcEvtBJlmJNgE0GLSAHwgTGmh/16MPCEMeZq+/WjAMYY98nfW18zjDFe10wiMgYYA5Cf\nn99/6tSpQcnnTkVFBQ0bNgxcMc6oXKGhcoVGILleXn2Kz3ZV89tB2XSMQj7caMmVKGIl19SNZ5hV\nVsktXTO4poNn7KG7Zh2vef3ogGzeXHeanccNzw6pT5uGaRHLNXTo0BXGmICWlkjWGG2AHU7X5cBA\nX5VFpAi4CcgCZvqqZ4yZKCK7gBG5ubn9i4qKwhKupKSEcNvGEpUrNFSu0AgkV+HgKuas281N/Xyf\neI0FdfX7CpclJzZA2TY6dexE0WWdPN6fc/4xrvrzAgDuvekKvjz1BTvX7GLokMG0zqsft+8rEgXg\nbXXjczlhjCkBSoLp2BgzHZheWFg4OizJFEXxSsOsenGf/BVPzst3PVz2fzf35o7BBQG9haJNJAfB\nygHnI21tgajERNVYQIqipBL1M9MZ0CG8PAWREIkCWAZ0EZEOIpIJ3ApMi4ZQGgtIUZS6THY929Sa\nWc/awRaCMgGJyBSgCGguIuXA48aY10XkAWA2Ns+fScaYddEQSkRGACM6d+4cje4URVHiyv1FnTHA\nqIHh5wSOB0EpAGPMSB/lM/GzoRsuugegKEpdpn5mOj+7qmuixQiIJdcnugegKIoSeyypAHQPQFEU\nJfZYUgHoCkBRFCX2WDJAh+4BKIqS7Ey4rR85WYlNKG9JBaAoipLsXNurVaJFUBOQoihKqmJJBaCb\nwIqiKLHHkgpAURRFiT2qABRFUVIUSyoA3QNQFEWJPZZUALoHoCiKEnssqQAURVGU2KMKQFEUJUUJ\nOidwIhCRfcDXYTZvDuyPojjRQuUKDZUrNFSu0EhWudobY84JVMnSCiASRGR5MEmR443KFRoqV2io\nXKGR6nKpCUhRFCVFUQWgKIqSoiSzApiYaAF8oHKFhsoVGipXaKS0XEm7B6AoiqL4J5lXAIqiKIof\nVAEoiqKkKEmpAESkWEQ2iUipiIyNw3i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drjJe+3JHt1131qLtJESFc964AUfsy0qJA2Db/sC3U6gqH67dy5hBnl5YW0ss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\nRBFhLi4cP4gLcgdSUVNPQnREq8epKmX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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_dft(y, rate, ax=None):\n", " \"\"\"Plot a signal in the frequency domain\n", " Parameters\n", " ----------\n", " y : ndarray\n", " Audio signal as a numpy array\n", " rate : float\n", " Sampling rate of signal in Hz \n", " \"\"\"\n", " \n", " n = len(y)\n", " \n", " # compute the real FFT\n", " out = np.fft.rfft(y) * 2 / n\n", " \n", " # Note that nf may be off by one from n, see rfft docs for details\n", " \n", " # get the frequencies\n", " freqs = np.linspace(0, rate/2, len(out))\n", " # Typically power information is plotted on a log scale, as it often decays (for real-\n", " # world signals) as a power law\n", " if ax is None:\n", " f, ax = plt.subplots()\n", " \n", " ax.semilogy(freqs, np.abs(out))\n", " ax.set_title('Simple DFT plot')\n", " ax.grid()\n", " return ax\n", " \n", " \n", "plot_dft(y, rate)\n", "\n", "# In practice, we use the psd function:\n", "f, ax = plt.subplots()\n", "ax.psd(y, Fs=rate)\n", "ax.set_title('Power Spectral Density');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise\n", "\n", "Given a function which computes the FFT, write a function which zeros out all coefficients except for the top frequencies and then inverts the DFT to get a reconstructed signal." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def fourier_approx(y, rate, frac=0.5):\n", " \"\"\" Approximate a signal with the top frac frequencies\n", " Parameters\n", " ----------\n", " y : ndarray\n", " Audio signal as a numpy array\n", " rate : float\n", " Sampling rate of signal in Hz \n", " frac : float, optional\n", " Fraction of frequencies to keep, defaults to 0.5\n", " \n", " Returns\n", " -------\n", " y_approx : array\n", " Approximated signal.\n", " \"\"\"\n", " \n", " # compute (real) fourier transform\n", " n = len(y)\n", " out = np.fft.rfft(y)\n", " \n", " # compute the magnitudes of the coefficients and keep the top frac\n", " # zeroing out everything else\n", " \n", " ## Your code here\n", " ## Hint: after you get the magnitudes, you may want to look up how argsort works\n", " ## to find which frequency components you need to zero out\n", " \n", " y_approx = np.fft.irfft(out)\n", " \n", " return(y_approx)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's plot the signal and the approximated signal side by side." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_approx(y, y_approx, rate, frac=0.5):\n", " \"\"\"Plot an audio signal and its approximation.\n", " Parameters\n", " ----------\n", " y : ndarray\n", " Audio signal as a numpy array\n", " y_approx: ndarray\n", " Approximated audo signal\n", " rate : float\n", " Sampling rate of signal in Hz \n", " frac : float, optional\n", " Fraction of frequencies to keep, defaults to 0.5\n", " \"\"\"\n", " shorter_y = y[:-1]\n", " # get the time points\n", " t = np.arange(len(shorter_y), dtype=float)/rate\n", "\n", " # Make a figure with two axes, one for time-domain and one for frequency-domain plots\n", " f, (at, af) = plt.subplots(2, 1, figsize=(14,10))\n", "\n", " # Plots in the time domain\n", " # Original and approximate signal\n", " at.plot(t, shorter_y, label='original', lw=1)\n", " at.plot(t, y_approx, label='approx', lw=1)\n", " at.set_xlabel('time (s)')\n", " at.set_ylabel('Signal amplitude')\n", " at.grid()\n", " at.legend()\n", " at.set_title(f'Approx signal {frac * 100:2g}% of the total frequencies')\n", " \n", " # Plots in the frequency domain\n", " af.psd(y, label='original')\n", " af.psd(y_approx, label='approx')\n", " af.legend()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "frac = .01\n", "y_approx = fourier_approx(y, rate, frac)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": 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Pf/Ba99133w3AZZddxsSJEwEoKSmhd+/ebN++HaUUtbW1TT4vQRAEQRCEloqOtgBC1BFl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\nTEVuBEDXrl11enp6E8QNPRkZGTRVlo3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T6vPEw9ZfvOYVlieGl5iQEqcKRHSQa+VIoir9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Zbk59C7dTl5Oap7l6nEs1TRX4F+39FLee40AOptVOgT48v7tH1MggXRmN2w1Gf/Cfs41squALx6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\nkiRJkqQusNiSJEmSpC6w2JIkSZKkLvgJk7qdh/07y78AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_approx(y, y_approx, rate, frac=frac)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case it can be illustrative to look at the raw (unwindowed) frequencies visualized with our basic `plot_dft` routine:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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C/JU3+6/yVS3aECqE9kpKChHh/EH5yc5GWBZeNTTgPjugL3kZF3bPGIibXMu+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\nLyBEY7BKARPmxr8vfv028T0eVFybR7g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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = plot_dft(y, rate)\n", "plot_dft(y_approx, rate, ax=ax);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's convert into a wav file and take a listen." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "# linearly rescale raw data to wav range and convert to integers\n", "sound = y_approx.astype(np.int16)\n", "basename, ext = os.path.splitext(infile)\n", "new_filename = f'{basename}_frac{100*frac:2g}.wav'\n", "wavfile.write(new_filename, rate, sound)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now compatre the two signals, the original and the compressed one:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Original:\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Compressed:\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(\"Original:\")\n", "ipd.display(ipd.Audio(infile))\n", "print(\"Compressed:\")\n", "ipd.display(ipd.Audio(new_filename))" ] } ], "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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }