{ "cells": [ { "cell_type": "markdown", "id": "e05c5d3c", "metadata": {}, "source": [ "Title: The Fourier Transform\n", "Author: Thomas Breuel\n", "Institution: UniKL" ] }, { "cell_type": "code", "execution_count": 2, "id": "e24e1a7f", "metadata": { "collapsed": true }, "outputs": [], "source": [ "from pylab import *" ] }, { "cell_type": "code", "execution_count": 3, "id": "c063c50d", "metadata": { "collapsed": true }, "outputs": [], "source": [ "import os\n", "def play(data,r=1,pad=8000):\n", " data = array(data*16000.0/amax(abs(data)),'int16')\n", " if r>1: data = array(list(data)*r)\n", " data = r_[zeros(pad,data.dtype),data,zeros(pad,data.dtype)]\n", " data.tofile(\"_out.raw\")\n", " os.system(\"play -s2L -r 8000 _out.raw\")" ] }, { "cell_type": "markdown", "id": "e3be6c2d", "metadata": {}, "source": [ "Simple Sine Waves, Frequencies and Phase\n", "========================================" ] }, { "cell_type": "markdown", "id": "073a19fd", "metadata": {}, "source": [ "Sine waves complete one full wave over the interval $[0,2\\pi]$.\n", "We define a range of $x$ values covering this interval over\n", "1024 sample points." ] }, { "cell_type": "code", "execution_count": 4, "id": "1db5af9d", "metadata": { "collapsed": true }, "outputs": [], "source": [ "x = 2*pi*arange(1024,dtype='d')/1024.0" ] }, { "cell_type": "markdown", "id": "1f9d2092", "metadata": {}, "source": [ "Now let's plot the sine and cosine.\n", "Remember how these relate to rotation and polar coordinates.\n", "\n", "These functions also frequently come up in differential equations\n", "because $\\sin'(x) = \\cos(x)$ and $\\cos'(x) = -\\sin(x)$,\n", "so \n", "\n", "$$\\frac{d^2 f(x)}{dx} = -f(x)$$\n", "\n", "has the solution \n", "\n", "$$f(x) = \\sin(x)$$" ] }, { "cell_type": "code", "execution_count": 5, "id": "1cbbcb3d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { 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V6Zv580UnkbRg8YnFeJTxkEU+h1jciH7jRrXdgaHWdh+MO8jQnUO5OOoiuaxyZf8NzVhM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\nsfhjoqNoXvPmanfL9esN+76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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(x,sin(x))\n", "plot(x,cos(x))" ] }, { "cell_type": "markdown", "id": "95d4ba26", "metadata": {}, "source": [ "We can now generate sounds with these.\n", "\n", "Pure sounds (and many other oscillations) are sine waves because they are generated by\n", "harmonic oscillators.\n", "Harmonic oscillators are oscillators in which the restoring force of a motion is\n", "proportional to the deviation from equillibrium.\n", "By Newton's second law, $F = ma$, this gives rise to the second order differential\n", "equation above, and hence sine waves.\n", "\n", "Most oscillators are harmonic at least for small oscillations\n", "due to the Taylor series expansion." ] }, { "cell_type": "markdown", "id": "60809a76", "metadata": {}, "source": [ "The _frequency_ of an oscillation is how many waves occur per time period (i.e., how \"frequently\" the wave occurs in one time period).\n", "\n", "Since we defined a time period as 1024 samples, we can generate sine waves as above.\n", "\n", "Note that usually frequency is expressed in Hertz, that is vibrations per second.\n", "Since we have a sampling rate of 8000/sec in the player, this means that the\n", "frequency of this tone in Hertz is $128*8000/1024$ or 1000 Hz." ] }, { "cell_type": "code", "execution_count": 6, "id": "51bde4a6", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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30piqeZYWU9rapsnrpzAmD1ROEG9y6djxBuOUNWZwXFVzEvXeKK0jZpp+R41f\nmWLWGlfdOU8TM7jmpY6lLTHT5kdlbavGDL6e6KEwJh+mpRyJ2aoB/0gv6Q6fx7j2aGlHt/yIJp+c\nS8knTT4bCm/ygPmFZKtOM/Y0efu0lBzGMXnmvFg59+oO0UehTZ67/XSLP+3Y0+Tt0lJyyJxnrwGZ\nOffaRvRRCpNnIShXwQfMj5+NWkoOafLZ67R1lSZvD4U3eRaCchV8b2Nnevxs0oDdOTc9frbpAwf0\n1VWavHysMXnHqZwIYVql+HvxVHS9BVPkmKoLMm1OsogJxM+5apG0IWacPAdfb2vOGxvV+prHWNoQ\n08SaVI1J9GOFyQOVO7wwrVIIgkW1no67Qy5aTNW7ZZX8xDFnnTGljKWJmCpxVE1eNSdx8qM7ZvA1\nJsbSprkT9466no5j7HFyTvRghckn2SnySC+ZBuw+umXO42kpuUqrAea8CDn3ahDRR6lMHjC/wKRr\nXeMtQZseSxu0lFwx58w5TT4bSmPyDQ1uLNMLTLI+cEDveJvWUsZVspaSK+Y8ew3Iz7nXTqKPQpm8\n49TWgHoh8F7vXT9Kx1ls0mPGGcukCzjvmIB6AdSdH1Mxk5q8rpyYjBnX9HSNpWqeTcYMzjWpa5sm\nr5/CmDxQOUHCdJJC4E3SMJ1mdy0xZpKxjLNo846ZpKjqzo/UmEClVhnLLPKjO2ZR8qM7pndKV2/8\nkuRHZ8zg64keCmPycbTpYzOpWsJxnW4NMOe17upM5yeLtQ3IGGNJWkp+aPL5Q5OnBmBXIWDO0xf8\nLNaVFA2YH2Np2nROaPLmKK3JA+YXnhSdxRhL06bHWJKWkpMsTZ45tzPnXj0i+iilyXuFwPTCk6CL\nfldHk7e34DPn6TVgV869NhN9WGPyjlM5EcK06iQKmrynvetUX7PWQqr1Xlti6hjLtHHyillrLFWL\nZ5z8mIqpMl8k5kdizlVyEhxXqTGl5qdaE/2kNvm+vj5MmzYNHR0dWLFiRehrrrjiCnR0dGDWrFnY\nsmVLrPd6BHd4YVplcoW9N7iQ4iyqsEJdT0uNqWsso7Tq4s8yZrW2KT9JYtaLE2csVXMiLWZeYyl5\n7lSPZRwTVs1PFjGJPlKZ/OjoKC677DL09fVh69atuPvuu7Ft27aK1/T29uLJJ5/EwMAAbrvtNlxy\nySXK7/VIslPkkZ6alnBEl5cGzI+3SQ2UK+emx9u0PnAg+/qpW9Pk9ZPK5Ddt2oT29nZMnjwZzc3N\nWLhwIdZbMuoxAAAgAElEQVSsWVPxmrVr12Lx4sUAgHnz5mHfvn3YvXu30ns9WAho8rpMvsw5z3ot\nSdONr1c3CWPPtU2TN0VTmjcPDw9j0qRJY1+3tbVh48aNdV8zPDyMnTt31n2vx1//ej36+4FnngFe\neaUTBw500uQ1FHxbC4HOnI8bJycnuvXoaGXBB8yNPWDuuqbzYDLnEtYbTV6N/v5+9Pf3a4+byuQb\nvFVUBydl5iZMuB6nnAL86U/A1q21J0g9Xf3epiavjZULJti1WjrOIpQSc/9+//ujo/rGUmUBS4jZ\n1BS+6dGdH1Mxw967f3/ysUxbtIPt0hmzXju9O/k0Ode9DrOOuX9//ZxLWYdRccpKZ2cnOjs7x75e\ntmyZlripTL61tRVDQ0NjXw8NDaGtra3ma3bs2IG2tja89tprdd/roTJBgMoJEqbrvbfWYgvTaXbd\nJmPWu6tLM5a1Fq3JmOPGVRb/OOOXJj9SYgbHL7ixUx3LpIXaZMyy5hyIvpNXWTNx86MzZvD1RA+N\nad48d+5cDAwMYHBwECMjI1i9ejV6enoqXtPT04O77roLALBhwwYcddRRaGlpUXqvR5KdZZKjRClH\nbllrCcdyJrV3h2c6D8x5vjmXkIc8dB41MytNk9dPqjv5pqYmrFy5EvPnz8fo6CiWLFmC6dOn49Zb\nbwUALF26FAsWLEBvby/a29tx2GGH4Y477qj53jBYCFjws9jYmc5DXgW/Vs6jPq7JaiOd9bWCd+9l\nXdt51kzdmiavn1QmDwDd3d3o7u6u+N7SpUsrvl65cqXye8PQZeAqr5GwUGnyenRTU33TkZKTLE3e\ndB6C422qDY2Nbhsk5MT02s5rY5dE0+T102i6ASp4yQ9OhDCtOolq6epr1lpU1a9X0RJi5jWWSRd5\n3jEB9UIaJz+mYgbzXC/nNuRHV8w0Y6ljHeYR0+b8BPtO9GGFyQOVO7wwrTK56sWJs6jCCnU9bTqm\nN055jGX1uEqNKSk/OmOq5Fl1LFXj2BIz6VhKzHPcnMcxYdX8ZBGT6MMKk0+yU+SR3sE6z7G0RZvO\nSZZayhhL0QBzLl3T5PVDkw8pBKYXalaLP++xtEFLyQ8LPnOeRgPFyDlNXj80+SoNFLMQSFjAEnXj\n6yvAdH6Y83xzLiE/uk3e9Ljq0DR5/dDkS1IIJCxgqRownx/dBZ85L9faNlUndWuavH5o8jW0t5BU\ntMqCNBlTwgKWqoFi5dzkmrFBB09vbM5zEdc2TV4/hTF5oHKChOkkhcB7X5hOsus2FTPJna2usawV\nR1LMqPFLmp9acbKKmeSurt5YJina0mN6762XH53rMKuYutd20rHUEZMmr5/CmLw3QerpOCYf12wl\naiDZ0a2usVSJIyWm6Vzp0hLGUnpMQEaumHOafNYUyuSzOtIzvYDTaFPjZ6M2nSsdWspY2qKl5I05\nd/+jyeuHJl9DA+YXcNrFb3L8bNNS8saCz5yraKB4OafJ68cak3ecyokQplUnkaoGahcC7zVeG1V0\nvQWsM2bSfuscyySL3FRMldObOPlRLdo6Y0oZS1tiqp6E6VjbumN6r5EyljpiEv1YYfJA5Q4vTKtM\nLpU4YTFVC3U9HXfHnjZm2n7rGkvVxS8hpqdtyzlQqXWOZZFj2pbn4NoG4vc7jgmbjEn0YYXJJ9kp\n8khPxvGbbRqwM+cS1omNWuX0RqKWMn66NU1ePzR5xUIgYWHHKfhFLgTM+cEFX8I6sVUD5nNIk3f/\no8nrhyavWPAB8ws7jsmbHjPbtekcsuDna/LMuQxNk9cPTT5GITC9sFUXv5Qxs1lLyWeZCz5zfrAG\nip1zmrx+aPKKGrCjEJgep6Jom05vpIyZ7VpKPuuZvOlxylLT5PVTKJN3nPo6yaSr1sF2xVmo1e+N\n0mliZtnvssVMm596edYVM01fVcayTDGr86N7baeJGcy/1DWTNiZNXj+FMXmgcoKE6biTNyxOnIJc\nbwGHaR0xs+h30pj14tgQM01+ovKsI6bXv7D26h7LMsTUnZ+scp6m3/XGz3RMmrx+CmPyeWnTx3X1\ntJRxKoIGZOdc2tqwXUv/iEbKOGWpafL6ocknKAQSFnxYwS9LIWDO3XZJWxtF0ID53NLkiU6sMXnH\nqZwIYVp1EsXRtXb7XlHw2qii6y3mpDE9nVW/k8ZMssilxcz7s1eVmLaOpfSYQGXOda7ttDFtG8sk\nMYl+rDB5oHKHF6ZVJpdKHJWY3mvy+hyuXsx6d3W6+p00purilxrTxGevKjmPKp6qeVYdyzLGlJJn\nr726ch7HhE3GJPqwwuST7BSzPtKrVfx5jFcsLfGzWiljU1QtJc9xjdR2TZPXD02+AIVAyngUWQPm\n86xyV0ddvLUtuQbq1jR5/dDkC1IIJIxHkTUgI+eS10ORtJTTGynjkZemyeuHJp+yENDky6VN51ny\neiiaBri289Y0ef3Q5C0t+N5iKGMhKGvOpYxBWTTAnOetafL6KZTJO059nWTS1dKA+qL1Xu/1KUrH\nMXlT/S5zzLj50ZVzlTamLbCMeXBMnWs7br0oypqJE4fopTAmD1ROkDAdd/LWixl30YYt4LjGESz4\ntfqaZb/jxKwXx7aYuvKcJOeqbUxaVBlTTs6BbHJeL47pmDR5/RTG5E1pQH23z2M8+3Xj6ysmrzwz\n5+a1qY/iTPfbhKbJ64cmb2khkNLvMmog/4LPnJdrbdtS93Rrmrx+rDH54FFPlFadRHF0nJjB9kbp\neos8Thwp/U4bx7aYgFquVAu7as5N97vMMXWsbdVnNST1O++YRD9WmDxQucML03GKcxYxg4s8Suv+\nbE9Cv1ViximkNsXMK+dx2hgnz4ypbkbB10ta23H7bUtMog8rTD7JTjFvzaPb8mke3ZZHA9mv7WDO\npfQ7b02T1w9NXpPO64EsW8ajDJoFvzwaYM7z0DR5/dDkNRcC3tWVR7Pgl0/zlC5bTZPXD01eoway\nLQSm+0ddqfM4vZHSV+p8TN50/0xrmrx+aPIWFQIp/aP2NcC7ujJpntJlq2ny+qHJW1YIJPSPutLk\ns8i5jfO+DDqr0xsp/TOtafL6KZTJO059nWTSxY0ZtZgbGir7FKXj3tVJ6XeZY9Yy6rg5P3Cg/rzX\n1VfGjB8TSL62w97LtV35eqKXwpg8UDlBwnTcyZs0pspu35vQ1TruXZ2kftdbtEWOGTfPtXKeto1J\niypjqsUE8sl5vXYl6bf0mDR5/RTG5KVpoLbJ87O6Ymke3ZZP89kL/Zomrx9rTD64C4zSqpMojk4a\nE6jUwX7UWvxhr7ep30niFCVmMG9e/lUKvmrOpfa7zDHjrO1aH+PY1u+sYhL9NJlugCr1joNUJpdK\nHN0x4yz+sOJva7+rx6DoMYPfzzLnKsVTpa95xwTsaGecmBLWdtx+2xKT6MOaO3kJR0lJNI9uy6OB\n5Hn2ihtzbo/mR3H6NU1ePzR5CwqBhH5Qq5l8mpzbPtfLptP+OJ2UfkjSNHn90ORzKAS8qyuX5l1d\neTRAk9epafL6oclnrJPu9m3vd5k1C355NMCc69Q0ef3Q5HMqBLyrK49mwS+f5imdHk2T1w9NPgcN\nxCsEpttLnU4nOb2R0nbqfEzedHulapq8fgpl8o5TXyeZdDpjBvsUpU23kTHTxwT81+eZ87QFljGz\nX9tFq2k6Y9Lk9VMYkwcqJ0iYTrJodcYM+znZah33rk56v+vFKWpM7/VReQ5eUzXnqm1MWlQZM3lM\nlbUd1/TqtStJv6XHpMnrpzAmb4Pm0W35NI9uy6FVP6KR0l6pmiavH2tMXudxUBytO6ZKwTfdRp0x\nkyzyIsVUfcCyaP0uY0wgnskXpd86YxL9WGHyQP3jIJXJpRIny5j1dvveNU22MYuYqou/iDFVCr7O\nNsbJM2Pqj1lvY6d7HWZRLyTEJPqwwuST7BSlaqD+XZ3pNlLr0zy6LZ/mj80l1zR5/aQy+b1796Kr\nqwtTp07FmWeeiX379oW+rq+vD9OmTUNHRwdWrFgx9v1rrrkG06dPx6xZs3DOOefgueeeC32/lAmo\ny+TDCoHpdlFno2ud3khpI3U+Jm+6XTZomrx+Upn88uXL0dXVhSeeeAJnnHEGli9fftBrRkdHcdll\nl6Gvrw9bt27F3XffjW3btgEAzjzzTDz++OP47W9/i6lTp+Kmm24KvY6UCZhlIZDSLmr9GuBdXZk0\nT+mSa5q8flKZ/Nq1a7F48WIAwOLFi3Hvvfce9JpNmzahvb0dkydPRnNzMxYuXIg1a9YAALq6utD4\n+q3OvHnzsGPHjtDrSJmANHnqJBqozHlR5zS1n2eAazuJpsnrJ9Xfk9+zZw9aWloAAC0tLdizZ89B\nrxkeHsakSZPGvm5ra8PGjRsPet3tt9+ORYsWhV7nkUeux+go8NOfAk1NnThwoNP4ZNRl8oBfCMaN\nM98u6mxzfuCAm3Pve2XJOWC+DXno0VG/vzR5mnwc+vv70d/frz1uXZPv6urC7t27D/r+DTfcUPF1\nQ0MDGrzZXfX9etxwww045JBDcOGFF4b++7x51+ORR4DubmDr1toTpJ5OMumyiNkYOEOR2kYdMVXi\nlCGmZ/KS25hlTMCOduqK6fXXy3ljo7w2SoxZZpPv7OxEZ2fn2NfLli3TEreuya9bty7y31paWrB7\n925MmDABu3btwvjx4w96TWtrK4aGhsa+HhoaQltb29jXd955J3p7e/Gzn/0s8jreovEmQlF00ftH\nXam9jZ2Etpic6xLak4cObuZNt8UWXWaTz4pUn8n39PRg1apVAIBVq1bh7LPPPug1c+fOxcDAAAYH\nBzEyMoLVq1ejp6cHgPvU/c0334w1a9bg0EMPjbyOlAmoWxe9f9ThOZfSFmrmXJqmyesnlclfd911\nWLduHaZOnYoHHngA1113HQBg586d+MhHPgIAaGpqwsqVKzF//nzMmDEDF1xwAaZPnw4AuPzyy/Hi\niy+iq6sLc+bMwaWXXhp6HdWFVI8kizPvmDa0MW5MVYoeM+o6utsYt8Aypp6YpuIVKSZNXj+pHrw7\n+uijsX79+oO+P3HiRPz4xz8e+7q7uxvd3d0HvW5gYEDpOnFNyhZd9P5Rh+dcSltMzXUJ7cmzv6bb\nYpsmekll8pKIs/CkxKz1PSlt1BEzbmEscszg97NqY1zyiBn2fYntTBOzXp7TxMuijRJj8k5eP1aY\nvIndZB666P2jji5uEtplaq5LaE+e/TXdFps0TV4/NHkWAuqc8hxEQrtMzXUJ7WHOZWqavH5o8lz8\n1Mx5bmMgpT3MuUxNk9cPTV7A4i9qX6mjcy6hXSbGQEp7mHOZmiavH5q8gMVf1L5SR+dcQrtMjIGU\n9uSV5yAS2ihd0+T1Q5NnIaBmznMbAyntYZ5lapq8fmjyLATUBvIcREJ78xoPKe0xkXMJbZSuafL6\nocmzEFAbyHMQCe3NazyktIc5l6lp8vpJ9Wtt80LXAsti0cYtcFLbmGVMVYoU02Qb4xZYxtQTMw5Z\nxCtCTJq8fqy4k1dB92TMKqZubOh3UQpQkpi60WVceccM+77EduqIqQvdmxWbYhJ9WGHycSaRZF2m\nvpZdx0FCe/MaDyntYc5lat7J64cmL2zxF6nfZdZxkNDevMZDSnuYc5maJq8fmrywxV+kfpdZx0FC\ne/MaDyntMZHnIBLaLlHT5PVDk2choGbOcxsPKe1hnmVqmrx+aPIsBNSG8xxEQj+yHBsp7TGdcwlt\nl6hp8vqhybMQUBvOcxAJ/chybKS0hzmXqWny+qHJc/FTM+e5jY2U9jDnMjVNXj80ecGLP4iEPlFn\nn3MJ/chybKS0hzmXqWny+qHJC178QST0iTr7nEvoR5ZjI6U9pvMcREKfpGiavH5o8iwE1Mx5bmMj\npT3Ms1xN9GLF764nhBBSfHgnrx/eyXO3Ty0oz0Ek9E/3OElpj6ScS+iTFE2T1w9NnoWAWlCeg0jo\nn+5xktIe5lympsnrhybPxU/NnOc2TlLaw5zL1DR5/dDkLVn8QST0lTr7nEvon+5xktIe5lympsnr\nhyZvyeIPIqGv1NnnXEL/dI+TlPZIynMQCX01qWny+qHJsxBQM+e5jZOU9jDPMjVNXj80eRYCaqF5\nDiKh3zrGTEp7pOZcQl9Napq8fmjyLATUQvMcREK/dYyZlPYw5zI1TV4/VvwyHCkTMEybQEK/y6xN\nIKHfZdYmkNDvvDVNXj80eQsXfxAJY1A2bQIJ/S6zNoGEfuetf/ADYHAw9lCRGtDkBS3+4C5WVUsY\ng7LptCTJcxAJY1AGrROubTX99NM0ed1Y8Zn8uHH+/yXoxte3Ro2at0jBwqKqJYxHGbTO4p8kz8Hr\nSxiPuNozMCntUdE6SZLzYJ2RMB5x9YEDyd6ru66WHStMPjjZJeisdvtJCLZFwtgUVUtCwnjE1Z7J\nS2mPDWs7iISxKet6sx2afIEmoISxKZKWWvBt3NjR5NMhYWzy1EQfNPmMFn+tz1Szer+EcSqSTpPz\nJBQ557aYvApp13ZUrFrYuLHLOg9EDStMPvhZjTcBxo0L17UmTjBO3JhSd/hBogpBmn7rGEvVhS0t\npg2YHkvVuRNl8mliqrSzKGs7iK5+ZzGWumISfVhh8sHkRxUvlQc7oiaUSsy4RD1Qk9f7dfVbx1iq\nPngjIWYak09rEklyHvVAXl5jqTp3oh68SxNTpZ0qczyuyaddm1GxVAkbJ51rW1fMqAfvVGISfVhl\n8qo7RV3ath1+kLId7+nSNiNh/KK05ON62yjD2ib6oMkXdKKVoRAw55VIzrk0k7d5Ax9EwlhyHcqG\nJp/RRDPx4F0UEhatZK2r4Jt48C4ITd6OtR0VKwmSc24qP6QSK0xe18MfUZ//BON4i6ZIEy1qDLIe\ny7gL21TMIpLXWKrOHWkP3hWFsGcy0q7tLOpFWfMjAStMPpj8NA+URE2oYBxdx3emH7wLixXc7ecx\nljoe7Mojpi5MPHhXL1Z1IdU9lqpzR8KDd973JeZJB7rWtspYqsTkg3cysMrkVXeKaXTRyXMsJeui\nfCYbhbRjXAnH9UVHWs6ZKxnQ5EtQ8IMUqRCwiKghYbxp8tlTpLVN9EGTb9T7IE1YHNMP3gXjBDcy\nEhazadPRiekH76JiSij+pkzeo6FBztqOiqULx5GxxpJqfiavFytMXtfDH2FxgoWgbOgay3r5UV3k\nWccs04lNkLCNna78qM4dUw/elZWoZzLSjGWaehEnZpnzlgVWmHxwIuh6WCzsbxp7X+tA0oN3UTG9\n8ah+MlfyQ3JpYkaNhS4kPdAVFbMMD94FDU7i2o6KpYvqmsYH78qNVSavulNU0aSSLMZYgi7r3XsU\npo7u8zyuZ84rkbAOWZ/NUUqTr178ZfpMPiqmhIWdZ8Ev02fyUTGLavKq/U+KDZ/JB5HwTAZN3hxW\nmLyuz4WijujTkMVxYN7XC46H6iK05TN56ce1ca+nM6aO/Ej5TD6LtR3E5rUd1Glynqb2xo1J9GGF\nyXN3mC8SdvJpNI9r1cjzDi/rO3nmXA0J65O1Ol8Kb/LBxS/96M7U9apjSljkzHm218j76D5rk6/V\nNx0UZW3bcnRP9GGVySd5wlNlhy/xSNdkm8J+H7ZNT9erIPFI12TOgwXWlqfrVUxB4tqOiqUL1Zh8\nur4cWGXyWe0IJd7tSWmThF193Lt3FSTe7ZnMedZ3eFncyevsfxxse/AuCsl39UQfVph83Ic/ogq+\n9F29qevVihlVCKQ9eJekb0kpyoN3UcTJj8kH75L0LSllWttR+VGpvXHXeVRMog8rTJ67QHNI3u0z\n59mQRc513cnzAbtskLCGuZ6zIfFw7t27F11dXZg6dSrOPPNM7Nu3L/R1fX19mDZtGjo6OrBixYqD\n/v3rX/86GhsbsXfv3uhGapog0o/uTF1PNaaExR+34Bct53nElLyxS9u3pBR9bUvLOdFH4uFcvnw5\nurq68MQTT+CMM87A8uXLD3rN6OgoLrvsMvT19WHr1q24++67sW3btrF/Hxoawrp163DsscfWbuTr\nraz1oEaaHb7EI12JbQpbkCYfvEuDxCNdiTnX9ZBcmof50hR/iWMaFUsXaepN9cO2KrU3Tc754F32\nJB7OtWvXYvHixQCAxYsX49577z3oNZs2bUJ7ezsmT56M5uZmLFy4EGvWrBn79y9+8Yv4z//8z/qN\nzHjnJ/FuT2Kbgki+e1dB4t2exJxLuMNLk3OJYxoVSxe2rm3eyWdD4s/k9+zZg5aWFgBAS0sL9uzZ\nc9BrhoeHMWnSpLGv29rasHHjRgDAmjVr0NbWhhNPPLHutf7nf64HAKxYAUya1AmgE+PGVf6WNhWk\n7+pNXS9JTFMP3sUt+FLGS9f1TMY09eBdXKSMV5prmJyrYXf1tU7v0qzzsLVdVpPv7+9Hf3+/9rg1\nTb6rqwu7d+8+6Ps33HBDxdcNDQ1oCJlBYd8DgFdeeQU33ngj1q1bN/Y9p8b289JLr8ettwL//u/A\n1q3u93Te1ZH4mLrDI+ZIk7e4D95xbcv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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "data128 = sin(128*x)\n", "data128 /= norm(data128)\n", "figsize(8,6); plot(data128)\n", "play(data128,r=10)" ] }, { "cell_type": "markdown", "id": "fc0bd210", "metadata": {}, "source": [ "Here is a tone with half that frequency, 500 Hz. This is _one octave below_ the other sounds.\n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "bb55e9c5", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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RdsrwU9WcRc3lam5qJ07zJJok1TyvsaPrsbGx9hL24UyS5xNBtko7is+701pS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\nLbbq3Z3U6AAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data64 = sin(64*x)\n", "data64 /= norm(data64)\n", "plot(data64)\n", "play(data64,r=10)" ] }, { "cell_type": "markdown", "id": "4486c59c", "metadata": {}, "source": [ "And here is a 250 Hz tone, another octave below.\n", "\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "070c123c", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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PzainqGmu5NPQpaR1DXALlUHe52KBSj49+ZIqeeiyWHMTlfxU+ZLWNcAtVAT5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\nUckDU6E2yHMXdmT4xak+XS7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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "data32 = sin(32*x)\n", "data32 /= norm(data32)\n", "plot(data32)\n", "play(data32,r=10)" ] }, { "cell_type": "markdown", "id": "c5dbba61", "metadata": {}, "source": [ "We cannot perceive _phase_, so $\\sin$ and $\\cos$ sound the same.\n", "\n" ] }, { "cell_type": "code", "execution_count": 9, "id": "f916e9af", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ymuGnw+e2WSSdb1PT+YuqqlHvKEZ1yZNfND/XSl7hAmKCvGb46fC5bRY+56u6\nLNbalKZLreQVLiAmyGuGnw6f22bhc76qy/yuTeqLojjqUit5hQuICfKuFmAt5290yx3HDJ9ztZS1\nfK3kdW0C9BdFcdSlVvIKFxAT5F0twFrnsI3kc8zwuVRLHOVrJa9rs57sRtdncNSlVvIKFxAT5F0t\nwHoZI2WzyDrD51ItcZSvlbyuzXqyG8nnqEut5BUuICbI+8zwG8nnmOFzqZa4ya91FNOIr7rM79rM\ng59rJa9wATFBXjP8dPjcNgvqUUz1OWwjfi3Zja7P4DTXNORz4xfNz7WSV7iAmCCvGX46fG6bRdIz\ndt/8vOqSI79ofq6VvMIFxAR5zfDT4XPbLJKesfvm51WX3PjUo5g8+LlW8goXEBPk45zDusrwq/mN\nXozBrfqJ48y2uuQmn2MlL1WX3Pjmrpjqoxiffs5Rl0VaOwo3EBPkG53D1rolrl7WGyfDr8d30fbj\nxq81X9cVhC/5HCt5qbrkxnfhh1T5Lm+5c8Uv0tpRuIGYIE/JwA3fV4ZPlS+lWgJkV59ayfOrxlzx\ns/DzUomfn+dx7dTrxircQEyQ51S9UflSqiVu/HrOr7YtHl/9PL/8enfFKNxATJDnVL1R+VKqJW58\n6tMJs7Bto5YuJ11K56uf55ev5/F+ISbIc8rYqXwpGTU3vgTbUvlSdM+Nr7bNL7+e7hVuICbIc8rY\nqXwpGTU3vgTbUvlSdO+b7+LphNz4UnTPja+VvF+ICfKcMnYq3+VT1IrEl2BbKl+K7n3zXTydkBtf\niu658bWS9wsxQZ5Txu6bLyUD982XYCsqX4ruffMl2IrK1+sz4vG1kvcLUUHeVQZez5mzkl/LGRpl\nyL751Izdl3wXusyaz0WXceX74nP0Q25+Xj0eKX5uEp1qPlWXCjcQE+RbWtxl4PWcOSv5tZytUYbs\nm0/N2H3Jd6HLrPlcdBlXvi8+Rz/k5ue1gqSEtVMu1z6KoepS4QZigrxm+OnxfWX4jZ5OKKUyT7p2\nop6ixsVWvvkc/ZCbn0ut5OvpRiv5bCAmyNdbINQMnOrMvuXHcTaffGqGT5GfhS6z5Neab6OnqHGy\nlW8+Nz/k6OeUSp7T2qmnG2qCpXADMUFeijNLvzjL52aRhS6z5LuYb1a28s3n5occ/ZxSyXNaO/V0\nQz0qUbiBmCAvxZldZPhZvhhDK3le1aeUSj7OUQwnP9RKXiv5vEJMkG/kbJSzsTjO7FM+taWbRiVP\nOdujVvKe9IIgAAAgAElEQVRp6zJLvov5ZmUrKl+CLrOUX4vf1BQmR0Fgx3ddyfuS72otKNxATJBv\nlIHXy6hdZfg+5adREVAz/Fp8V5U8d1265LuYb1a2ovIl6DJL+bX4ca7PcFnJ28rP6kVRCjcQE+SL\nlOFT+VrJ8+RrJc9Ll1nKd+XnWVTyWb0oSuEGYoK8lOpNeiXP6RxW+dlen8Gpkld+8WyrcAMxQV5K\n9Sa9kudUvSk/2+szdC3w4hfNtgo3EBPkuWWZnPhFy/CVX5/vyrZZncMqvz6/aH6ucAMxQZ5blsmJ\nn9WLMSTopmh8V7bN6hxW+fX5Wskr4kBMkOeWZUrmS8/wlV+fr7bNL7/RLXd5XAsKNxAT5LllmZL5\n0jN85dfnq23zy8/q+gyt5GVDTJDnlmVK5kvP8JVfn6+2VX4UV8pdMQo3SBzkBwcHsWjRInR3d2PT\npk01Offeey+6u7uxbNky7N27l/S3BtyyTMn8RuewQaDnsJL5cZ6ixmXsynfL5zSWOHyFGyQK8uVy\nGevXr8fg4CD27duHrVu3Yv/+/VM4AwMDeO211zA8PIwnnngC99xzj/XfVoJblimZz2ksynfLd/WW\nOwlzVX5jPqexxOEr3CBRkN+9eze6urowf/58tLa2YvXq1di+ffsUzo4dO7BmzRoAwMqVK3H8+HEc\nPXrU6m8rwS3LlMznNBblZ8vnNBblu+VzGkscvsINEuVPo6OjmDdv3uT3nZ2d2LVrVyRndHQUhw8f\njvxbgw0bNmD/fuC//xsYGupBT0/P5O/K5doLpKWl9oJS/tRb7ipb8xLGHpd/6hSv8aTNN7dX1jqH\n5T525cfjcxpLHH7RMDQ0hKGhIedyEwX5UqlkxQtqHRASsGHDBjz3HHD6NFAR3wGEi6ZWq6dey1L5\nU1u6lZu+hLErPx6f01iUnw7fJPNBEPq8pLEXET09UwvYBx54wIncRKrt6OjAyMjI5PcjIyPo7Oxs\nyDl06BA6Oztx9uzZyL+dMtAUzovGx/3Jb3ROWi/rTUN+a2u0bG5ndVx1aSs/C34RdTljhl/5XPRZ\n7+mElcl8pSwpc1W4QaIz+RUrVmB4eBgHDx7E+Pg4tm3bhv7+/imc/v5+PPPMMwCAnTt3Yvbs2Whv\nb7f620pwOy+i8uu1qhplvWnLV12mIz8LvuoyHX4W+qx3S1w9+VLmqnCDRPlTS0sLNm/ejFWrVqFc\nLmPt2rVYvHgxHn/8cQDAunXrcNNNN2FgYABdXV2YNWsWnnrqqYZ/Ww/UrFH59c9h6/E5jV35bvn1\nuPVaupzG7pp/+jSv8fiyLZXPba4KN0jcJOnr60NfX9+Un61bt27K95s3b7b+23qgZo2NLvKg8Kny\nG/GpbcKk8hu1wWrJdznXvOnStfy0+fW4cVq60nVZazyS1mY1P0s/9zlXhRuIeeKdq6yxUavKdxZL\nbRMmld+oDSY5w89Cl67lc6v2KC1d6bqsl/xLnW+Wfu5zrgo3EBPkJVzcxI0fleHb8pubaz9FjdNc\ni8av93TCenxXa0GCborGz6ttFW4gJsjHyRqLzo/K8G355qIe2wpCgm6k8031U+suVp9rQYJuisZ3\nadty+cJkPqu5KtxATJDnlmVK4LvK8Kl8CbqRzlfbKj+KS+WbZN5csJvG2KPGr0gOMUFeQkbNje8q\nw6fyJehGOl9tm19+o6OYIq0FhRuICfISMmrf/KzOYal8CbqUzs/Ktnp9hn9+Vral8rWSlwExQV5C\nBu6bn9U5LJUvQZfS+VnZVq/P8M/PyrZUvlbyMiAmyEvIwH3zNcNXfhSXG1+CLrnx1bYKlxAT5CVk\n4L75UjJ8c/EOl6t0JfClnMNS+RJ0z42vtlW4hJggLyED982XkuFXPkXNhi9B9775UmxL5UvQPTe+\nFNv6vj5D4QZigryEDNw3X0qGT+VL0L1vvhRbUfkSdM+NL8W2vq/PULiBmCAvIQNvxK9V2Rp+rQVO\nzcDrVc71nIdTRZCFLrOUz0n3gN+1k4Uus+TXmm+jF0VxspXv8Wglnw3EBHkJGXgjfkuL33PYWvIn\nJho7J5eKwIUuDb/exstJPifdA37XTr2Wrk9dZsn37Yfc/JwyHq3ks4GYIM8tY3eR4ZuMt9YtcdIz\nfK3ktZIH6rd0i1TJu/RDbn6ulTx/iAnyrjLwegswjQyf6jzUjNqnfG6VPHXj5SSfk+4BXmszjcq8\nlm0l+Xk1P0s/92lbhRuICfKuMvB6raQ0MnypG69vfr2WrpSgXUu+lKcTArzWZhqVeb3kX4qfV/Oz\n9HOftlW4gZggr5V8fit56lW6Eir5RkcxnHQP8FqbWsnnu5Ivl+2fn6FwAzFBXiv5/FbyVL6ESl6K\nLgFea1Mr+fxW8tS33CncQEyQd/UUNa3k48nnxJdQyUvRJcBrbUqo5F0exRSpko8jX5EcYoK8q6eo\n+azkXd8Sx2Xj5cbXSj6/lXxzs/+33CWt5LPWpdRKPo58RXKICfIAfbNIu5JvdA7LzXm4VZNayWsl\nD6TzlruklXzWutRKXkGBqCBPWVBZVPKSgja3alIrea3k48jXSl4reUVjiAry3Ct5KRtjHPmc+NSW\nrougnde3xAGy16ZW8lrJKxpDXJCvtaBcOXO9isCWX49r+FRn4yafCz9OS5dqW8pRDCfdxOVLXZsu\nbEuVn7UuKZW89LWjSA5RQb5WFtuo/U5ty9WrCGz59biGT22bcZPPjU9p6VJtq7qUId+Fbanys9Yl\npZKXvnYUySEqyFMzfOotd1rJy+JTWrpJqz3VJU/5LmwbBI2PYrjMtR4/67WplTxviArylKyR+uCF\nWrKDIPz7WguQ28VTyqfZlsqXMtei8U3QSHLLnQkyLu6KUb5bviI5RAX5OFljkgt4yuUwUZDwaFLl\nu704i8vYld+Yb/yzOplX2+aDr0gOUUE+7WrPZUZKbVNxk8+NT5kvtZJXXeZ3baouZc1XkRyigryL\nrLHeAvSdkcZxHk7yufGTtnTNUUwWjyblxi/S2oxzps1prrUuXMtybfqeryI5RAV5F1lpvSs508h4\nOTkPt2rS53xrXZ/R6BxWdZnftUkNktzmSk1SpK8dRXKICvJaycuoltLgJ52v6vI8irQ2tZKXNV9F\ncogK8j4r+ebmC2+5k5TxcqqW0uAnna/q8jzytjaj3hKnlbyc+SqSQ1SQT5qVNjqHrfUUNUkZL6dq\nKQ2+VvJ8dJm1/Gp+1FFMuTw1mZemS63kFRSICvJJs9JGzl+PLyXj1epTK/m4/LytzUbcetdnSNKl\nVvIKCkQFeVcZvq18SRmvVp9aycfl521tRlWG1YFSmi61kldQICrIJ81K653H1+NLyniLXn02Ooqp\nJd+mWrJt6XLTDbe1w6mSN/zq5F+SLrWSV1AgKshrJc+nWsqaTz2KodiW2tLlphtua0crea3k48pX\nJIeoIK+VPJ9qKWs+dWOnVns+2/vc+Hlbm1rJx5fPbb6K5BAV5LlV8j5butw2Xm58n0GbKp+bbrit\nHd9HMVrJayWvqA9RQb56QTV6S1wtvstK3ndLl9vGy42vlbycasz3UYzPSr5WMp+1LrWSV1AgKsjX\nqszrvSWuHt9VJU/lc3MebtWkVvJ8dAnwWpsu/dDwbSv5Wm+5y1qXWskrKBAV5ONk7L4qeSqfm/Nw\nqya1kuejS4DX2nTph4ZvW8lT5WslTxtPo6cTKtxAlGqTZvhZVvK1nLPReOJk4L7lp8m3OYet1dKt\nh6TVXpQuq1u6nHRpw+e8NrOs5Knys/DDrP08yXyjjmIUySEqyKeR4fvic6veuPN9nMP64vt+ilrR\n+ern+eVH6V6RHKKCfBoZvs9Knlv1xpkvybZUPnfdc+OrbfPL1/N4/xAX5KktWi78Wi1d6tlbI/ku\nzvZsxp8WP0r3cc7Yucjnpnvfa6daftRdMZz8lspPW5eu5ac9nijdK5JDVJCvvmDG5kI6Lvw4V+nW\nypBdXgBDkZ82P0r31IqAk3xuuve9dmqdwza6K4aT31L5aevStfy0xxOle0VyiArynDL2OHxKdSg9\nw9dKno8uo/hpV5+ubcWJXyuZz7OfayXPH6KCfNILZmwy9iTybTYv2+owjvNQM2qKfG4X5MSptLnI\n56Z732vHt63i8Ks7C5L8vJqfpZ9Xz9Xli6IUbiAqyFM3i1ptQgrf9QU81Eo+zY03Sn5SfhBEVxBS\ngzZVftq6j+KnnRS4tlUcfnXyL8nPq/lZ+nmtuTY3u3lRlMINRAV5reTlVvImu3d1SxynoE2VT23p\naiWvlXylbM6VvGvbKpJDVJDXSl5uJZ+lLjnK51T5ayUvy8+5V/IubatIDlFBvkiVvNmIuLwYw/cZ\nu/Sg7XO+3Ct5m1viuOjS8LWSdzcereR5Q1SQL1Ilz+3FGFrJayVfT365nO1RjFbyWskr6kNUkC9S\nJU+Vr5W8rKQgT5W8JF0aPpdK3sUtd1rJKxpBVJAvUiVPla+VvKykIE+VvCRdGj6XSp4qP+1K3vUt\ncVrJpw9RQV4reT6VfNQ5rGRdpiGfatty2f76DK3k5VTyVPlpV/KmMHJ1S5xW8ukjUZB/++230dvb\ni4ULF+LGG2/E8ePHa/IGBwexaNEidHd3Y9OmTZM/v++++7B48WIsW7YMt956K06cONHw86RX8tUO\n6nI8tZy/kfykGX7UOaxkXaYlP0lL13Xln2TtSNJlrfFIWpu1bOvTz7O2rSI5EgX5jRs3ore3F6++\n+ipuuOEGbNy48QJOuVzG+vXrMTg4iH379mHr1q3Yv38/AODGG2/EK6+8gl/+8pdYuHAhHn744Yaf\nl0aGL5Uv/Yxd+boWlB/NL5ptFcmRKMjv2LEDa9asAQCsWbMGzz333AWc3bt3o6urC/Pnz0draytW\nr16N7du3AwB6e3vR9NvDnpUrV+LQoUMNPy+NDF8q3/e5Lae5Kt+vbV0/nVD5fGxL5WetG0VyJMqh\njh07hvb2dgBAe3s7jh07dgFndHQU8+bNm/y+s7MTu3btuoD35JNP4s4776z5ORs2bAAA/OxnQEtL\nD4AeANlnmZz4lS1dc5FMnjP8lhbg5Ele4+HCT2pb108nVD4f21L5WeumSBgaGsLQ0JBzuZHq7e3t\nxdGjRy/4+YMPPjjl+1KphFKNXaHWz2rJmjZtGu66666avzdB/vHHgZ///PzPs84yufKnTYvmS8/w\nla+2LSK/qenCK97zvBaKhJ6eHvT09Ex+/8ADDziRGxnkX3jhhbq/a29vx9GjRzF37lwcOXIEc+bM\nuYDT0dGBkZGRye9HRkbQ2dk5+f3TTz+NgYEB/OAHP4gebIys8fRpGp9TFsu5IpA016Lx1bZ0/vTp\nvMZjw4/Tscv6rhit5NNHojP5/v5+bNmyBQCwZcsW3HLLLRdwVqxYgeHhYRw8eBDj4+PYtm0b+vv7\nAYRX3T/yyCPYvn07ZsyYEfl53LJMyXw9h80vX3r1pnx/a8EkB1neFaOVfLpIFOTvv/9+vPDCC1i4\ncCFeeukl3H///QCAw4cP49Of/jQAoKWlBZs3b8aqVauwZMkS3HHHHVi8eDEA4Etf+hLGxsbQ29uL\n5cuX44tf/GLDz+OWZUrm6zlsfvlJ33Inaa7Kz7dtFcmRSL2XXnopXnzxxQt+fsUVV+B73/ve5Pd9\nfX3o6+u7gDc8PEz6PG5ZpmQ+p7Eo3x8/zvUZXMau/OR8TmOJw1ckR6GeeKf882huDn9vnqImaezK\np/GlncMqXyt5hTuICvLcskzJ/OqWrqSxK5/Gl3YOq3yt5BXuICrIc8sy88TnNBblu+VzGovy0+VX\nJ/OSxq5wA1FBnluWmSc+p7Eo3y2f01iU75YfdVdMNZ/T2G34iuQQF+Srs8CoBcWJT81ik8i3df7K\nak91mZ78NPlZzzVPurThp6nPqLtiquVLm6siOUQF+ZaWC7PAqNYQJz41i00i/9y50PHrvQe6Wn7W\nuuGsSx/y0+RHcSufomb4qsv4/DTXpk0l7NPPfc9VkRyigjy3jJ0z3yZDllzJK1/XgvLzb1tFcogK\n8kkv8rDJYpPIt+FTK4i48m0yZOkXZ6WlS1/y4/JtjmIotjV8SrUnXZeV45G4Ng2fg5/7nKsiOUQF\neWprqJpvk2X6vuiEmvXGlW+b4du2/agt3Tzp0pf8uHyboxhqS5da7UnXZXXyL3W+rv2c21wVySEq\nyNfKwCnnP0Xi2zi/Tz5n3Ujnq22V78u21cl81nNVJIfoIH/2LNDaqvxa/Ciubz5n3Ujnq23zyzdH\nMbYtcte2LZV4rQVFcogK8q2t4aIwiFogeeKfO9f40aTVfBvn8cnnrEvp/Kxta85VzSOROelGOv/s\n2VC/jW6J47QWfOtGkRzignz1eU7UgsoL33CjnL+a3wg++Zx1KZ2ftW2rqz1OupHOz9q2VL5v3SiS\nQ1SQb2m5MAuMamvlhR/F5cY3QaCy2uOiS25826vludiWyuese278rG1F5fvWjSI5RAV5zm023/ys\n23JUfqk09UpaTrrkxpfWoqXyOeueGz9rW1H5pjL3dXSjSA5xQZ5rm803P+u2nG8+Z9375mete998\nzrr3zQ+C8P+NqlVOtqLyTTJfed++tut5QVSQ59xmo/JtnJ9TW843n7OtfPOz1r1vvuEW8eimXA5v\nS4t6vDQXW/nma7s+fYgK8pzbbFT+xESYAee1RUvlc7aVb37WuvfNN0HOVHucdO+bn7XuufG1XZ8+\nxAV5atuM6pyV8ql8ynhsnYfaZktLPrXt51OX3OTbtmh96bKaz23t+LYVp7WTtS7jyudiW0VyiAry\ncdpm1QuK0kqi8injiZJdLd+2bZaWfGobL2o8pp1ZWe35tK1P+bYtWl+6rOZzWzu+bcVp7WSty7jy\nfdvW9uhGkRyigjznthyVn3XbTDpfbZtfPmfbBoGuhSR86tGNIjlEBXlzH3HlS1K4tOupLVqpbTwu\nLWbO7XppuqweT9byObfrz52L7tJw0mVc+ZzGo0gGUUEeoF/JmVa7ntqildrG49Ji5tyul6bL6vFk\nLT/p0Q0n22aty7jyOY1HkQzigjzXtl/WbbCi8Tm3dLPWTdH4att88xXJIC7IU7LGWs5MrQgoLdqo\njJS6uKkZcprybTN2SouZMp7m5vMv7bGRT63eKudqKkrbV2hK02X1eDjKp7brqV0d27WTd10a+Zzm\nq0gGcUGesqBqbey+NguOzuxTPjVjdz2eWi9JoSZ8XDb2rHVZPR6O8n0l5zbjKZIujXxO81UkQ+6D\nfFqvxOTQ1lK+HZfKz3rsyvdnW2mvcC4iX5EM4oI8JWs01V6cisCmRcutrVWkdn31eHy261WX2ctv\nxK8+uonTgWv05Mki6dLI5zRfRTKIC/JxssY4Z3u2zuBrLNzlx2kxZznfONWe6lKG/FKJpk/Jc01L\nPqfxKJJBZJCnLCjK+VL1RkG9dYQ6FpsMmat8akWQ9Xwrj25sWrSqS17yKefIlISP41w56JLTfBXJ\nIK5REmdBUQJBkozXR1uLs3wfF/D4mm/l++2DIJTt8uVARdJlFvJd+qLqkiY/6/kqkkFkJe+zpWuC\ngNQ2m7aYo+WrLhuPR7L8IAg7NlHXW+Rhrj7lcxqPIhlEBvk4rSTj/I1atKbaK5e1XR8lX3KLWXXZ\neDwc5dt2OgzX5kI68xx6bnPloEtO81Ukg7ggH7e1ZbiNnL9SvsS2lraY7eSrLqPHw00+pUsTNZbK\noxuOc+Wiy7TGo+16vxAX5OO2kmwzRiNfaputiC1mmxZtpXzbjSitoxtOupQu37b9S9kXuM7Vp3xO\n41Ekg7gcKm5ri+r82q5vLJ9Ti3liIqzMoro0lUlBlOzKV2IWSZdc5VPa9ZRknuNcOeiS03wVySCu\nkk/arreVL7GtVdQWs20CR2nXU+XnRZfc5Nu8v71Svg8/z4subfnc9jVFMogL8mZBUdqovtr1TU1h\n9WiqvazbWkVt18ep3ji1dDnpkpt8c7GsbZfGp20pCQdHXVLkcxqPIhnE5VBmQdk6v892vZHP8Yrt\nIrWYKZW5bbueKj8vuuQm36a9XCnfR7veHN2cO5eOLqdN8ytf2/XFgrhKPknL1XUbjyqfexuPS4uZ\ncmuTtuv9jIeLfB9+GEc+NeHjqEtbflrtevN+kCZxUUgWxKnXZ8u1Ur6PFnAe2nhptJjL5fPVk814\nOLTrzfMX4hzdaLu+vvw4HTif+4JkXVLkc7KtIhnEtuttnVPb9X7k+2wxx7Ft1u166virdRnVotV2\nvZ18H+366vFI1aWRz6Vdr636dCCukpfcrq98JSbHNh6XFrOPdjo3+UVt19u8wrlSvrbr3cvn0q63\ntZUiGcQFecnt+spXYkpt46XRYubQcvUtv6jtet+24mBbk8DYXqjH0Vbars8PRAZ5qe366vFwa+MV\npV3PQX5Rr66Po0tp7frK8XC0la92velSur6WRpEM4oK85HZ9NZ9bG89XizlOizbrdrpv+dVHN0Vp\n18fRpbR2ffV4uNnKV7veyKbc1qztev8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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "data32c = cos(32*x)\n", "data32c /= norm(data32c)\n", "plot(data32c)\n", "play(data32c,r=10)" ] }, { "cell_type": "markdown", "id": "c88a2901", "metadata": {}, "source": [ "Note that we often work with _periodic signals_. That is, we repeat a waveform\n", "indefinitely. The simple audio player above already does this.\n", "\n", "When working with periodic signals, it is important to pay attention to _boundary conditions_." ] }, { "cell_type": "markdown", "id": "781797ae", "metadata": {}, "source": [ "Here is an abrupt jump at the end of the signal when wrapping around back to the beginning.\n", "\n" ] }, { "cell_type": "code", "execution_count": 10, "id": "bca02c22", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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LlZkjdTxt+lK7dMEJeEIyMLcm1BYkgUdbp/VncClkSdtBg0LrJS2fOaHfcxZZ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\nVY+TmWvUzN3NfVo0OyeL5LJayOe7EpsGCxaqI7REpa1TxBY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PuTPdrqhWNA4cOEDrKp58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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dataodd = sin(31.3*x)\n", "plot(dataodd)\n", "play(dataodd,r=10)" ] }, { "cell_type": "markdown", "id": "63b78905", "metadata": {}, "source": [ "Orthogonality Relationships\n", "==============================" ] }, { "cell_type": "markdown", "id": "074f3f86", "metadata": {}, "source": [ "Although we thought of our data as audio signals with a given frequency,\n", "we can also view them as vectors.\n", "\n", "When we do so, there are some interesting relationships.\n", "\n", "Since we normalized our signals, the dot product of a signal with itself (as a vector) is 1.\n", "\n" ] }, { "cell_type": "code", "execution_count": 11, "id": "4b984a01", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.99999999999999978" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32,data32)" ] }, { "cell_type": "markdown", "id": "f870da5d", "metadata": {}, "source": [ "The dot product of a sine signal and a cosine signal is 0; the two signals are _orthogonal_ as vectors.\n", "\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "3a022de0", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-3.6591823321385775e-17" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32,data32c)" ] }, { "cell_type": "markdown", "id": "3bb402a9", "metadata": {}, "source": [ "Likewise, the dot product of a signal and a signal of a different frequency is 0,\n", "provided both signals actually correspond to periodic signals.\n", "\n", "(Actually, it also works for half frequencies; this gives rise to the _cosine transform_).\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "a8202d73", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.698077442546797e-15" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32,data64)\n", "\n" ] }, { "cell_type": "code", "execution_count": 14, "id": "6933f68f", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-4.9462849353357941" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32,dataodd)" ] }, { "cell_type": "markdown", "id": "91222ca2", "metadata": {}, "source": [ "Quadrature\n", "============" ] }, { "cell_type": "markdown", "id": "c6d20613", "metadata": {}, "source": [ "A general pure sine wave is parameterized by _frequency_ and _phase_:\n", "\n", "$$f(x) = \\sin(2\\pi f x + \\phi)$$\n", "\n", "Although there are many different sine waves of different frequencies,\n", "for any given frequency, there are really \"only two\" sine waves of\n", "different phase. " ] }, { "cell_type": "markdown", "id": "120a425f", "metadata": {}, "source": [ "That is, any sine wave of a given frequency and an arbitrary phase \n", "can be represented as a linear combination of two sine waves of that\n", "frequency, one with a phase of $0$ and another one with a phase of\n", "$\\frac{\\pi}{2}$ (recall that $\\cos x = \\sin(x+\\frac{\\pi}{2})$).\n", "\n", "The reason is this simple trigonometric identity:\n", "\n", "$$\\sin(u+v) = \\sin u \\cos v + \\cos u \\sin v$$\n", "\n", "This means that for a given $v$, we can write any $\\sin(u+v)$ as a linear\n", "combination of $\\sin v$ and $\\cos v$." ] }, { "cell_type": "code", "execution_count": 15, "id": "9896867a", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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t7y3miVrMukTjVyqyvoCmS/UdhSRgk3m1GmbvDc3pffHR9t5iTeYx6xK1PZJx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\nQqFQRA5N5gqFQqFQRI7/B2BzLltCIsVRAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data32p = sin(32*x+0.3)\n", "plot(data32p)\n", "play(data32p,r=10)" ] }, { "cell_type": "code", "execution_count": 16, "id": "35db23a1", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "21.616797112821246" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32,data32p)\n", "\n" ] }, { "cell_type": "code", "execution_count": 17, "id": "1ba24e9a", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "6.6868589474523308" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32c,data32p)\n", "\n" ] }, { "cell_type": "code", "execution_count": 18, "id": "d3e284f6", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.698077442546797e-15" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32,data64)\n", "\n" ] }, { "cell_type": "code", "execution_count": 19, "id": "301008b6", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.48469348354e-13\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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oX+bukKojD3ztAO86AJlLFsxBPmTsKNSnHZ025uwTw4F/PMAzF+QmpH04wJHp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84TOwGNEcWQPVOdviIGkbh6CJp14eKcsy0Z50LfOFUwJ9mWGji0JM5jfEGyLVXoqjFw88RO0NiJ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\nkPlqhV9+72tYP/heExq7jbfis++9j9vtu/TNAG5vP4D/6T1/i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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "rec = dot(data32,data32p)*data32 + dot(data32c,data32p)*data32c\n", "print norm(rec-data32p)\n", "plot(rec)\n", "plot(0.9*data32p)" ] }, { "cell_type": "markdown", "id": "cf32a2c1", "metadata": {}, "source": [ "A Complete Basis\n", "===============" ] }, { "cell_type": "markdown", "id": "cb0ea800", "metadata": {}, "source": [ "For periodic signals of length $N$ (here, $N=1024$), we have made the following observations:\n", "\n", "- periodic signals of different frequencies are orthogonal to one another as vectors\n", "- periodic signals of the same frequency at phase 0 and $\\frac{\\pi}{2}$ are orthogonal to one another as vectors\n", "\n", "This suggests constructing a complete basis in the following way:\n", "\n", "- take all sine and cosine functions for frequencies between 0 and 512 (inclusive) as a basis\n", "- remove the sine function with frequency 0 (since it is just 0)\n", "- remove the cosine function with frequency 512 (since it is just 0)\n", "\n", "This way, we end up with 1024 orthogonal functions, and since our space only is 1024 dimensional, this\n", "must be a complete basis for our linear space." ] }, { "cell_type": "code", "execution_count": 20, "id": "27ab6149", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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9Q3neecfCEo+UFDb7pVTx8XQwSyuyrIIphKOdI2b3no31WevFHTg1lbUWNafO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RTIJD6ePliSsER9ddIJCWyVoAtTHk89BaxfzyY8lDJqGMXe2r1YMX2F9QPb2tjfqWMHsYISaSIt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\nWJWySuqhVCksOQwfd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EC/b/ohNj0WRaVFTz1PCIGzeWcxLWEa7L60Q3uj9jj74Vk4GjtW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\nRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# first three elements of sine basis\n", "sins = [sin(i*x) for i in range(1,513)]\n", "figsize(12,8)\n", "plot(sins[0])\n", "plot(sins[1])\n", "plot(sins[2])" ] }, { "cell_type": "code", "execution_count": 21, "id": "0980ba84", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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3AufOSSe5qeJR6Tc3vYncglzpOGR2RUXAr78CPXpIJ9E3Dc+Ekbkcyj6Er7Z/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vAAAC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\niIioAP4fXtb+OZkKAGkAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# first three elements of cosine basis\n", "coss = [cos(2.0*pi*arange(1024)*i/1024.0) for i in range(0,512)]\n", "figsize(12,8)\n", "plot(coss[0])\n", "plot(coss[1])\n", "plot(coss[2])" ] }, { "cell_type": "code", "execution_count": 22, "id": "bfca63c3", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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2RmNjYzQ0NERtbW3Mnz8/1q5du9+as846K8aOHRsREbNnz46enp7DGBsAAEZXzVALent7\no76+fuC4XC7Hpk2bDrn+9ttvjwsuuOCg7y1btmzg162trdHa2jr8SQEA4CA6Ojqio6PjXX1myAgu\nlUrD/rI//vGP8fOf/zweffTRg77/9ggGAICR8M6Lq8uXLx/yM0NGcF1dXXR3dw8cd3d3R7lcPmDd\nU089FUuWLIn29vY47rjjhjkyAAAceUPeEzxz5szo6uqKbdu2RV9fX6xZsyba2tr2W/PCCy/ExRdf\nHHfffXc0NjaO2rAAADAShrwSXFNTEytXrow5c+ZEf39/LF68OFpaWmLVqlUREbF06dK44YYb4t//\n/ndcffXVERFRW1sbnZ2dozs5AAC8R0M+Im3ETuQRaQAAHAEj8og0AAD4XyOCAQBIRwQDAJCOCAYA\nIB0RDABAOiIYAIB0RDAAAOmIYAAA0hHBAACkI4IBAEhHBAMAkI4IBgAgHREMAEA6IhgAgHREMAAA\n6YhgAADSEcEAAKQjggEASEcEAwCQjggGACAdEQwAQDoiGACAdEQwAADpiGAAANIRwQAApCOCAQBI\nRwQDAJCOCAYAIB0RDABAOiIYAIB0RDAAAOmIYAAA0hHBAACkI4IBAEhHBAMAkI4IBgAgHREMAEA6\nIhgAgHREMAAA6YhgAADSEcEAAKQjggEASEcEAwCQjggGACAdEQwAQDoiGACAdEQwAADpiGAAANIR\nwQAApCOCAQBIRwQDAJCOCAYAIB0RDABAOiIYAIB0RDAAAOmIYAAA0hHBAACkI4IBAEhHBAMAkI4I\nBgAgHREMAEA6IhgAgHREMAAA6YhgAADSEcEAAKQzZAS3t7dHc3NzNDU1xYoVKw665tprr42mpqaY\nNm1abNmyZcSHBACAkTRoBPf398c111wT7e3t8fTTT8fq1avjmWee2W/NunXr4rnnnouurq647bbb\n4uqrrx7VgQEA4HANGsGdnZ3R2NgYDQ0NUVtbG/Pnz4+1a9fut+b++++Pq666KiIiZs+eHTt37ozt\n27eP3sQAAHCYBo3g3t7eqK+vHzgul8vR29s75Jqenp4RHhMAAEZOzWBvlkqlYX1JURTD+lyptOxt\nR61vvQAA4HB0vPUavkEjuK6uLrq7uweOu7u7o1wuD7qmp6cn6urqDvp9RbHsXQ0HAABDa423X1wt\nlZYP+YlBb4eYOXNmdHV1xbZt26Kvry/WrFkTbW1t+61pa2uLu+66KyIiNm7cGOPGjYsJEya869EB\nAOBIGfRKcE1NTaxcuTLmzJkT/f39sXjx4mhpaYlVq1ZFRMTSpUvjggsuiHXr1kVjY2McffTRcccd\ndxyRwQEA4L0qFe+8oXe0TlQqHXDvMAAAjLThdKefGAcAQDoiGACAdEQwAADpiGAAANIRwQAApCOC\nAQBIRwQDAJCOCAYAIB0RDABAOiIYAIB0RDAAAOmIYAAA0hHBAACkI4IBAEhHBAMAkI4IBgAgHREM\nAEA6IhgAgHREMAAA6YhgAADSEcEAAKQjggEASEcEAwCQjggGACAdEQwAQDoiGACAdEQwAADpiGAA\nANIRwVWmo6Oj0iO8b9ir4bFPw2evhsc+DY99Gj57NTz2aWSJ4CrjD/jw2avhsU/DZ6+Gxz4Nj30a\nPns1PPZpZIlgAADSEcEAAKRTKoqiOCInKpWOxGkAACCGStyaIzTHkIMAAMCR4nYIAADSEcEAAKQj\nggEASGfUI7i9vT2am5ujqakpVqxYMdqne99atGhRTJgwIaZOnVrpUapad3d3nHvuuXHaaafFlClT\n4sc//nGlR6pab7zxRsyePTumT58ekydPju985zuVHqmq9ff3x4wZM+LCCy+s9ChVraGhIU4//fSY\nMWNGnHnmmZUep2rt3Lkz5s2bFy0tLTF58uTYuHFjpUeqOs8++2zMmDFj4DV27Fh/pw/ipptuitNO\nOy2mTp0al112Wbz55puVHqkq3XLLLTF16tSYMmVK3HLLLYMvLkbR3r17i4kTJxZbt24t+vr6imnT\nphVPP/30aJ7yfeuRRx4pNm/eXEyZMqXSo1S1l156qdiyZUtRFEWxa9eu4uMf/7g/U4N47bXXiqIo\nij179hSzZ88uNmzYUOGJqtcPf/jD4rLLLisuvPDCSo9S1RoaGoqXX3650mNUvSuvvLK4/fbbi6L4\n739/O3furPBE1a2/v7846aSTihdeeKHSo1SlrVu3FqeeemrxxhtvFEVRFF/5yleKO++8s8JTVZ+/\n/e1vxZQpU4rXX3+92Lt3b3HeeecVzz333CHXj+qV4M7OzmhsbIyGhoaora2N+fPnx9q1a0fzlO9b\n55xzThx33HGVHqPqnXTSSTF9+vSIiDjmmGOipaUlXnzxxQpPVb0+9KEPRUREX19f9Pf3x/HHH1/h\niapTT09PrFu3Lr72ta95ks0w2KPB/ec//4kNGzbEokWLIiKipqYmxo4dW+Gpqtv69etj4sSJUV9f\nX+lRqtKxxx4btbW1sXv37ti7d2/s3r076urqKj1W1fn73/8es2fPjg9+8IPxgQ98ID7zmc/Efffd\nd8j1oxrBvb29+/2BLpfL0dvbO5qnJJFt27bFli1bYvbs2ZUepWrt27cvpk+fHhMmTIhzzz03Jk+e\nXOmRqtK3vvWt+MEPfhBjxvhnEkMplUpx3nnnxcyZM+NnP/tZpcepSlu3bo3x48fHwoUL44wzzogl\nS5bE7t27Kz1WVbv33nvjsssuq/QYVev444+Pb3/72/HRj340TjnllBg3blycd955lR6r6kyZMiU2\nbNgQ//rXv2L37t3x29/+Nnp6eg65flT/xvcDMhgtr776asybNy9uueWWOOaYYyo9TtUaM2ZM/PWv\nf42enp545JFH/Nz5g/jNb34TH/nIR2LGjBmucA7Do48+Glu2bIkHHnggfvKTn8SGDRsqPVLV2bt3\nb2zevDm+8Y1vxObNm+Poo4+Om2++udJjVa2+vr749a9/HZdeemmlR6lazz//fPzoRz+Kbdu2xYsv\nvhivvvpq3HPPPZUeq+o0NzfH9ddfH+eff3584QtfiBkzZgx6cWNUI7iuri66u7sHjru7u6NcLo/m\nKUlgz549cckll8RXv/rV+PKXv1zpcd4Xxo4dG1/84hfjiSeeqPQoVeexxx6L+++/P0499dRYsGBB\nPPTQQ3HllVdWeqyqdfLJJ0dExPjx4+Oiiy6Kzs7OCk9UfcrlcpTL5Zg1a1ZERMybNy82b95c4amq\n1wMPPBCf+MQnYvz48ZUepWo98cQT8alPfSpOOOGEqKmpiYsvvjgee+yxSo9VlRYtWhRPPPFEPPzw\nwzFu3LiYNGnSIdeOagTPnDkzurq6Ytu2bdHX1xdr1qyJtra20Twl/+OKoojFixfH5MmT47rrrqv0\nOFVtx44dsXPnzoiIeP311+MPf/hDzJgxo8JTVZ8bb7wxuru7Y+vWrXHvvffGZz/72bjrrrsqPVZV\n2r17d+zatSsiIl577bX4/e9/74k2B3HSSSdFfX19/OMf/4iI/97vetppp1V4quq1evXqWLBgQaXH\nqGrNzc2xcePGeP3116Moili/fr3b2w7hn//8Z0REvPDCC/GrX/1q0NtsRvXHJtfU1MTKlStjzpw5\n0d/fH4sXL46WlpbRPOX71oIFC+Lhhx+Ol19+Oerr6+OGG26IhQsXVnqsqvPoo4/G3XffPfCIpoj/\nPjZm7ty5FZ6s+rz00ktx1VVXxb59+2Lfvn1xxRVXxOc+97lKj1X13MZ1aNu3b4+LLrooIv77v/wv\nv/zyOP/88ys8VXW69dZb4/LLL4++vr6YOHFi3HHHHZUeqSq99tprsX79eveXD2HatGlx5ZVXxsyZ\nM2PMmDFxxhlnxNe//vVKj1WV5s2bFy+//HLU1tbGT3/60zj22GMPubZUuAkOAIBk/FNoAADSEcEA\nAKQjggEASEcEAwCQjggGACCd/wOyHYfgvpUnNwAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# there is only one zero frequency\n", "ylim(-0.1,1.1)\n", "plot(sin(0*x)[-10:])\n", "plot(cos(0*x)[-10:])" ] }, { "cell_type": "code", "execution_count": 23, "id": "29209798", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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MTdPbmBJbmTlpumzh8DmVjzY+oyhcDBflkEzhIi+tvPXjTXI2mi5bOGxl5qPpsoXD7kQ+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\n/n+EEwyAKfUv0wAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# there is only one frequency 512\n", "plot(sin(512*x)[-10:])\n", "plot(cos(512*x)[-10:])" ] }, { "cell_type": "markdown", "id": "71e54af7", "metadata": {}, "source": [ "Let's construct matrices out of these basis functions.\n", "\n" ] }, { "cell_type": "code", "execution_count": 24, "id": "0d34d2d4", "metadata": { "collapsed": false }, "outputs": [], "source": [ "sins = array(sins)\n", "coss = array(coss)" ] }, { "cell_type": "markdown", "id": "2cd22b08", "metadata": {}, "source": [ "Now let's verify the orthogonality conditions.\n", "\n" ] }, { "cell_type": "code", "execution_count": 25, "id": "59c89b6d", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-2.03463569425e-11 512.0\n", "-2.88650492397e-11 1024.0\n", "-2.1462665846e-11 2.21026530411e-11\n" ] }, { "data": { "image/png": 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MHz8+9SgAu8yTyPJobO/QWCBPNLZ0+gpAMdYO1IF169bF+PHj4957741Ro0alHgcAckNj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\ndXHHHXfExz72sdh9991TjwM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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(24,12)\n", "gray()\n", "subplot(131); imshow(dot(sins,sins.T),vmax=1); print amin(dot(sins,sins.T)),amax(dot(sins,sins.T))\n", "subplot(132); imshow(dot(coss,coss.T),vmax=1); print amin(dot(coss,coss.T)),amax(dot(coss,coss.T))\n", "subplot(133); imshow(dot(sins,coss.T),vmax=1); print amin(dot(sins,coss.T)),amax(dot(sins,coss.T))" ] }, { "cell_type": "markdown", "id": "4b123da1", "metadata": {}, "source": [ "We can also look at these matrices themselves\n", "\n" ] }, { "cell_type": "code", "execution_count": 26, "id": "6534734b", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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aimbD8Aw0swGh2Kyq24x2if0C7102vMqEs7QywyorttmNSlRfVTqly37PTq6d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\n2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JoeOWKXkh4oihuphVKv7RlNDmvW/TMxMTHYy9LSUksDZ0cS5YLaWhNXvWQQdemcWSSJ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\nL9HJNglYEcsOdqZt8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773vThy5Ehs27ZtRYm60d7zK6+8Eo8++mjMzMzEv/71rzhz5kw8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\nBJyjNVqjNVpDrhFwjtZojdZoDbn+H9fMiznKr6CVAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12,12)\n", "subplot(121); imshow(sins[:100,:100])" ] }, { "cell_type": "markdown", "id": "4266b093", "metadata": {}, "source": [ "Now we can perform transforms with this matrix.\n", "\n" ] }, { "cell_type": "code", "execution_count": 27, "id": "40d9bf26", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,5)\n", "plot(dot(sins,data32))\n", "plot(dot(coss,data32))" ] }, { "cell_type": "markdown", "id": "47634631", "metadata": {}, "source": [ "When there is a phase shift, we get both sine and cosine components.\n", "Note that we deleted the 0 frequency vector in the sines, so the non-zero components\n", "actually differ by 1.\n", "\n" ] }, { "cell_type": "code", "execution_count": 28, "id": "e3ea8776", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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AQAZK+p6vvr4++Xy+6Pc+n0+9vb03Pe71etXb25vsHw8AAJDWchZ6MhQKaWBg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\ngg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,5)\n", "plot(dot(sins,data32p)[:50])\n", "plot(dot(coss,data32p)[:50])" ] }, { "cell_type": "markdown", "id": "68c293ed", "metadata": {}, "source": [ "It's useful to combine these two signals in a way in which each component\n", "is independent of phase.\n", "This is the _spectrum_.\n", "\n" ] }, { "cell_type": "code", "execution_count": 29, "id": "129b0e70", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,5)\n", "plot(dot(sins,data64)[:-1]**2+dot(coss,data64)[1:]**2)" ] }, { "cell_type": "markdown", "id": "60b9312a", "metadata": {}, "source": [ "Invertible Transform\n", "=======================" ] }, { "cell_type": "markdown", "id": "d29ccad9", "metadata": {}, "source": [ "We can combine the sine and cosine tranforms into a single matrix and then invert that in order to get an inverse transform.\n", "\n" ] }, { "cell_type": "code", "execution_count": 30, "id": "348222e1", "metadata": { "collapsed": true }, "outputs": [], "source": [ "ft = r_[sins,coss]\n", "ift = inv(ft)\n", "def transform(signal):\n", " return dot(ft,signal)\n", "def itransform(signal):\n", " return dot(ift,signal)" ] }, { "cell_type": "code", "execution_count": 31, "id": "eb77879a", "metadata": { "collapsed": true }, "outputs": [], "source": [ "# computing a spectrum using the sins/coss matrices\n", "def spectrum(signal):\n", " return dot(sins,signal)[:-1]**2+dot(coss,signal)[1:]**2" ] }, { "cell_type": "code", "execution_count": 32, "id": "811bc3a8", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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BsVCaOl9PeRH1MkestJTG9+ijwOWXkxA+dCh5PpLXyPLDgNjFxEj+Y1AxIpiN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\noMtIiSKliIISkehGF4pMIImuREULZazeXZQOx57knBOd6aDnuXbzZia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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# generating a random signal\n", "from scipy.ndimage import filters\n", "wave = filters.gaussian_filter(randn(1024),5.0)\n", "plot(wave)" ] }, { "cell_type": "code", "execution_count": 33, "id": "c9cdc21f", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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iTz4xP6+vz1yPbGAgdImKSEErlkrYt74lvfyytGBB9P0AAEBqKi0tVWlpqf/3\nXbt2jenzxtSOnDVrliTpxhtv1Nq1a3X8+HG53W6dPXtWktTZ2ans7GxJksfjUVtbm/+97e3t8ljr\nUdgdWFg7MjyETZ1qPo5kJsyqhFkhLNYV82OphPl83PYIAADEbtQhrKenRxcuXJAkXbp0SUeOHFFh\nYaHKy8tVU1MjSaqpqdGaNWskSeXl5aqtrZXP51Nra6taWlr8V1TaHtjnS1REmgmzQtiUKbHNhGVl\nST09gRA2eXLoTFi0wfxYQ5h1Q3EAAIDhjLod2dXVpbVr10qS+vv79fWvf10rV67U0qVLVVFRoerq\nauXm5mr//v2SpIKCAlVUVKigoECZmZmqqqqK2qq0lqiwbtIdXgmbNs18tFuiIvh5cCWsr88MUz09\nI6uExdKOJIQBAICRGHUImzNnjk6ePDlk+/XXX69XX33V9j07duzQjh07Yvr84HZk8Ar4Y21HStJn\nn5khzKqEZWTEpxJGOxIAAMTKcbctslgLqfb3mz+RQtiCBWagkuwH88MrYZLU3S194Qsjq4T194eu\n3G+3D5UwAAAQK0eHMOuqR2noTJjVjvzSl6SKisB7wvcPvjrSqoR98onk9ca+WKu13ecLBL5gAwNm\nQCOEAQCAWDnu3pGW8BAWqRI2YUJgn+EqYdYC/d3dI786Uoq+hIVECAMAALFLuRBmhSqrEha8eOtw\nM2EWK4SNZMX84MdIrzMTBgAAYpVyISy8EhYcwoarhFm6uwO3OwpeooJKGAAASBTHhrAJE6LPhNm1\nI+1mwoarhAW3I4erhBHCAABAvKTMYH5wJSwjIzAgH2s7Mviejp98EpgJG0klzK4duW+fZC38TzsS\nAADEyrGVsGghbNKkQKgarh0ZfHWk5eLFwIr5sVTCorUjf/xj6a23zOdUwgAAQKxSLoRNny79wz/Y\nh7CMDDOgSUPbkdZ2S/hgfrQlKqK1I3t7pU8/NZ8TwgAAQKxSJoQFz4Tt2BEIX+FzYFOmhG6fMMHc\nHtyOlEa3RIVdO5IQBgAARsPxIcyqYIWvVJ+VFVoFs/aZPHno/tdeO3SR1ZHewFuyr4T19QVCGDNh\nAAAgVo4PYTNmBH4PZhfC7CphkvT++4HtVqgb6Q28gx+DUQkDAACj4dgQNmGCOUA/c6b5e/DQvWQG\nsODlKSQzVFlhK3j/668PhDIr1I30Bt5S5Jmwzz4znxPCAABArBwbwjIypJ6ekVXCgpeuCN/fCmzW\n51mLtcbLe/1YAAANFklEQVRaCZs4kXYkAACIH0eHsNG0I63t4ftHq4QFL1GxYYP0hz+EvvfKFfM2\nSdHakVOnUgkDAACxS+kQZteOzMw0XxuuEjZpUmglzFqs9e23pba20PdaISy80jUwYL722Wfm5xLC\nAABArFImhNnNhEWqhGVlDd0/OIRZAcxusdZLl0KXxpDMCti0adLhw9J3vxvYboWuTz8lhAEAgJFJ\nmRAW60yYFcKitSOD58bCK2E9PeZPMKsSdvy49Oqrge29vYHXp09nJgwAAMTO0feONAzphhsCvweL\nNhMWrR05c2YghNnNhPX02FfCZsyQOjtDK2xWCJPM18PbmAAAAJE4thJmhaZbbjEfxzoTFnzbo+AF\nXS9fDlTCLl82W4rhIcyqhA0OSh0dgYpXcPuRdiQAABgJx4awixfNx8JC8zGWmbDgdmS0mTCrEnb9\n9WZwsiph1ndGakdKZnXu//7PfB5eCaMdCQAAYuXYEPbOO+ZjpHW/RtqOtJsJmzXLfLQqYZZIg/mS\n+djaaj4PD2FUwgAAQKwcG8Lefdd8tG68HR6qpkwZej/IaIP5djNhN90UeC34Bt+R2pGSVFISCGF9\nfYELBwhhAABgJBwbwn7yE+nAAXOlemloqFq8WPrFL0K3uVyBNmWkdmRxsXTffebz4BCWkRF4T0+P\n9IMfBFbQDw5hy5ZJH3xgPu/tla67znw+bZq53+Dg6P9mAABw9XBsCNu8WfrqVwMVqvBQ5XJJXm/o\ntliWqMjNlb75TfP5jTeaAcwKaNZ3XbwoPfaYeTWkFGhHTp4szZ8f2N7ba86VSebaY5Mm2a+qDwAA\nEM6xIcwSqR1pJ5YlKiZNCmzLyJBycoaGsDNnzIrWhx+av1vrgGVnm3NkVgjr6wtUwiZOND87eE4M\nAAAgkrQKYbFUwsKH+W+6aehr7e3moxXCfD7z3pDZ2WZoO3vW3B7cjpw40Zw3++yz2P82AABw9XJ8\nCHO5AjNbsewbbYmKiROHbp81K7QSNn16YNHV4ErYF79ozqGFhzCrHTlxovSFL0jnzo3u7wQAAFcX\nx66YH8wuVNkZbrFWa8g/2E03BUJYZqZ5laM1eP/hh+a6YP390m23SX/+5+ZNu7u7zWDW12eGNivg\n3XADIQwAAMQmJULYxIkja0dOnhy65IRkBqXgeTDLffcFlqzIyjKH9YND2JUroSFwwgRzn64usxI2\nebL5fqsS9vHHo/87AQDA1SMlQphdZcuO1Y585pnAPSctkyaZa4uF+9M/DTzPzDQDlmTOgAWHsGBW\nS9IKYZMnUwkDAAAjk1Yh7I47zHaitf5XsJwc6be/Hf57rBCWn2+GMJ8vcgjr6zNnwqwQRiUMAADE\nKmVCWCwzYXfdFf11u3AWLLgSlp8v/f73ZiUsfJYsvBJmtSNvuMF8DwAAwHAcf3WkFHslLB7fE14J\ns2tHzpplLmPR22sGsOBKGO1IAAAQC0JY2PfMnGlWxPLzpY8+MoNWeCWsuFhqbJQ6OszQdtdd5kr8\nN9wwunakYcTl8AEAQApJiRAW69WRY5WZaQ7vT51qti6/+EXp5MmhlbDly6W33jJ//uzPpMpK8xZK\n4ZWwTz4J3H8yXEeHuSq/z2euP2atSQYAAK4OKRHCYp0Ji8f3TJ1q/lx/vfTHfyw995y0YEHofl6v\n2YacPz+wYr4UWgk7eFByu6W1a4d+j2GYa44dPmyGvN/9TnrhhfH7uwAAgPMkNITV1dUpPz9feXl5\n+v73vx/z+6ZOtV/jK94mTzavrqytlebNk5YulV591X7gf/ly6ctfDt32hS+YLcz+fumJJ6SaGuno\nUenSpdD9mprMtcgaGswrNhctkn7yk+S0Jevr6xP/pVc5znnicc4Tj3OeeJzz1JOwEDYwMKCHHnpI\ndXV1am5u1osvvqjfx3gp4c9+Zgai8bZ3r/QXf2Gujp+RYVbCJPsQVlkpPfJI6LYpU8x1x4qKzArZ\nvfdKt94qvf66+fru3dLf/Z1UVWVW195+22xpPvKIGdQaG6V335UOHBjfvzMY/0ebeJzzxOOcJx7n\nPPE456knYUtUHD9+XHPnzlVubq4k6d5779XBgwe1ILzXZ8PtHueD+1x2dujvt94qfe975mxYuLlz\n7T+jtlb6p3+Svvtds4VaViY99pi5/ZVXzOrZ+fPS889Ld99tVvh27ZI2b5a2bJE6O81bI/X0SC+/\nLN1yi9nizMiQHnxQmj3bnDV75BHpO98xl8t4+23zQgJrgdr+/sA9NwEAgDMlLIR1dHRo9uzZ/t+9\nXq8aGhoS9fWjcs010o4dI3vPjTdKTz0V+P3BB82g1NMjPfRQoLommVdi3nOP2fq8/37pv/5L+sUv\npJ//XHr4Yenxx6Uf/UiaNk0qLDSrgT095vv+6I/Mlqi1REZbmznHNnOmdOqU2cKdM8fcPmmSeaFB\nb695r8vLl81Qd+6cGehqa83frRulhz9a83jhj7E+j8XVtP8HH0jHjjnjWBKxvxO8/77Z/kds4vHf\nuKVFOn587J+D2MV6zn/5S/6fdKdwGUZiJpF+/vOfq66uTs8//7wk6YUXXlBDQ4OeeeaZwMGk4r/u\nAADgqjWWGJWwSpjH41FbW5v/97a2Nnm93pB9EpQHAQAAki5hg/lLly5VS0uLTp8+LZ/Pp3379qm8\nvDxRXw8AAOAoCauEZWZm6oc//KHuvPNODQwMaMuWLTEN5QMAAKSjhK4Tdtddd+l///d/9f777+ux\nxx4LeW20a4ghugceeEBut1uFhYX+befPn1dZWZnmzZunlStXqru72//anj17lJeXp/z8fB05ciQZ\nh5zS2tradPvtt2vhwoVatGiRnn76aUmc8/HU19enZcuWqaioSAUFBf5/Wzjn429gYEDFxcW6++67\nJXHOx1tubq4WL16s4uJilZSUSOKcj7fu7m7dc889WrBggQoKCtTQ0BDfc244QH9/v3HzzTcbra2t\nhs/nM5YsWWI0Nzcn+7DSwuuvv26cOHHCWLRokX/b3/7t3xrf//73DcMwjMrKSuPv//7vDcMwjPfe\ne89YsmSJ4fP5jNbWVuPmm282BgYGknLcqaqzs9NoamoyDMMwLly4YMybN89obm7mnI+zS5cuGYZh\nGFeuXDGWLVtmvPHGG5zzBHjyySeNr33ta8bdd99tGAb/toy33Nxc4+OPPw7ZxjkfXxs3bjSqq6sN\nwzD/fenu7o7rOXdECHvzzTeNO++80//7nj17jD179iTxiNJLa2trSAibP3++cfbsWcMwzNAwf/58\nwzAMY/fu3UZlZaV/vzvvvNN46623EnuwaearX/2q8corr3DOE+TSpUvG0qVLjd/97nec83HW1tZm\nrFixwvjNb35j/OVf/qVhGPzbMt5yc3ONc+fOhWzjnI+f7u5uY86cOUO2x/OcO+LekXZriHV0dCTx\niNJbV1eX3J+vgOt2u9XV1SVJOnPmTMgVq/x3GJvTp0+rqalJy5Yt45yPs8HBQRUVFcntdvvbwZzz\n8fU3f/M3+ud//mdlZAT+Z4RzPr5cLpfuuOMOLV261L/cE+d8/LS2turGG2/U/fffr1tuuUUPPvig\nLl26FNdz7ogQxvpgyeNyuaK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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(spectrum(wave))" ] }, { "cell_type": "code", "execution_count": 34, "id": "b9ee82ab", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(transform(wave))" ] }, { "cell_type": "code", "execution_count": 35, "id": "55dc9508", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.1805691881113141e-13" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# the inverse transform actually works\n", "norm(wave-itransform(transform(wave)))" ] }, { "cell_type": "markdown", "id": "45cb3d68", "metadata": {}, "source": [ "Signals after the Fourier Transform\n", "=====================================" ] }, { "cell_type": "code", "execution_count": 36, "id": "20edfbcf", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plotting signals only differing by phase\n", "for phase in [0.0,pi/2,0.3,0.7]:\n", " frequency = 100\n", " plot(transform(sin(2.0*pi*arange(1024)*frequency/1024.0+phase)))" ] }, { "cell_type": "code", "execution_count": 37, "id": "cd5a2cec", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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z8OWX8GSiw7lZ9W2Mg1hns/FPd93FrKFD+UNlZfc/NCMDsrNJSXGuYIqI9EUKXCLSbdu2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\n/wNuNVfh7Lu0PwAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plotting signals only differing by phase (magnified)\n", "for phase in [0.0,pi/2,0.3,0.7]:\n", " frequency = 100\n", " plot(transform(sin(2.0*pi*arange(1024)*frequency/1024.0+phase))[95:105])" ] }, { "cell_type": "code", "execution_count": 38, "id": "51fca63d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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AXphxaPvjH/+o4eFhSdKtW7fU3t6u/Px8VVZWqqWlRZLU0tKizZs3S5IqKyvV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\nkAYIbQAAAGng/wNwR1oTvXjPJgAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plotting spectrum of signals only differing by phase\n", "for phase in [0.0,pi/2,0.3,0.7]:\n", " frequency = 100\n", " signal = sin(frequency*x+phase)\n", " plot(spectrum(signal))" ] }, { "cell_type": "code", "execution_count": 39, "id": "20a1c128", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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T7T/gRhOuOXDiGRFZP5YzIjI5fa8eJUEheFkqM9kxoicF4aPRpit/RETmwsuaRGRyh77I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\nvqo2dJmX5QAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# magnified spectrum of signals only differing by phase\n", "for phase in [0.0,pi/2,0.3,0.7]:\n", " frequency = 100\n", " signal = sin(frequency*x+phase)\n", " plot(spectrum(signal)[95:105])" ] }, { "cell_type": "code", "execution_count": 40, "id": "e67be3d7", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plotting transform of signals differing by frequency\n", "for frequency in [1,10,100,500]:\n", " signal = sin(frequency*x)\n", " plot(transform(signal))" ] }, { "cell_type": "markdown", "id": "856d6c0c", "metadata": {}, "source": [ "Complex Numbers\n", "================" ] }, { "cell_type": "markdown", "id": "b9767ea9", "metadata": {}, "source": [ "(Complex Numbers)\n", "\n", "Recall that we can define complex numbers by introducing an abstract symbol for some unknown imaginary quantity $j$, such that $j^2=-1$.\n", "In fact, that's how complex numbers are defined: as a kind of simplest solution to the simplest polynomial equation that doesn't have a\n", "solution over the reals.\n", "\n", "We can then write numbers like:\n", "\n", "$c = x + jy$\n", "\n", "and derive formulas for addition, multiplication, etc. For example:\n", "\n", "$$c_1 \\cdot c_2 = (x_1 + jy_1)(x_2 + jy_2) = x_1x_2 + x_1 jy_2 + jy_1 x_2 + jy_1 jy_2 = (x_1x_2-y_1y_2) + j(x_1y_2+x_2y_1)$$" ] }, { "cell_type": "markdown", "id": "e12739e3", "metadata": {}, "source": [ "(Complex Numbers and Trigonometric Functions)\n", "\n", "Complex numbers are closely tied to trigonometric functions.\n", "That's because complex numbers can be thought of as 2D vectors and how they behave under multiplication.\n", "\n", "We can write a complex number also as a _phase angle_ and _magnitude_:\n", "\n", "$c = x + jy = r (\\cos \\alpha + j \\sin \\alpha)$\n", "\n", "In fact, a shorter way of writing this is as _Euler's formula_:\n", "\n", "$c = r e^{i\\alpha} = r (\\cos \\alpha + j \\sin \\alpha)$\n", "\n", "There are many ways of seeing that this identity is true, but the simplest one is probably\n", "by thinking of $\\sin$ and $\\cos$ as solutions to differential equations and seeing that\n", "Euler's formula satisfies these equations." ] }, { "cell_type": "markdown", "id": "28db7555", "metadata": {}, "source": [ "(Polar and Cartesian Representations)\n", "\n", "To convert between the two representations, note that\n", "\n", "$$\\alpha = \\arctan \\frac{y}{x}$$\n", "\n", "$$r = \\sqrt{x^2+y^2}$$\n", "\n", "(Note that you get get these values with `numpy.angle` and `numpy.abs`.)\n", "\n", "From Euler's formula, we also immediately see that:\n", "\n", "$$c_1 \\cdot c_2 = r_1 e^{j\\alpha_1} \\cdot r_2 e^{j\\alpha_2} = r_1 r_2 e^{j(\\alpha_1+\\alpha_2)}$$" ] }, { "cell_type": "markdown", "id": "fbd46412", "metadata": {}, "source": [ "(Complex Basis of Fourier Transform)\n", "\n", "With complex numbers, we can also now write the basis functions for our transform in a more compact way:\n", "\n", "$$b(n,k) = e^{-2\\pi~\\frac{kn}{N}~j}$$\n", "\n", "If you expand this, you'll see that this gives rise to the same sine and cosine-based components we have\n", "been using above, except for the odd behavior for $k=0$ and $k=N/2$ (we don't have to worry about those\n", "with complex numbers, since they are both important there).\n", "\n", "Note that complex numbers behave otherwise very much like real numbers; in particular, we can\n", "also apply most of linear algebra. So we can perform expansions just like before." ] }, { "cell_type": "code", "execution_count": 41, "id": "a7c323e7", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def b(k,n,N):\n", " return exp(-2*pi*1j*k*n/N)\n", "N = 420\n", "n = arange(0,420)" ] }, { "cell_type": "code", "execution_count": 42, "id": "efaf7d99", "metadata": { "collapsed": true }, "outputs": [], "source": [ "s = b(3,n,N)" ] }, { "cell_type": "code", "execution_count": 43, "id": "105e892a", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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sRdixA8jPF4dFFkpDfwNGp0axLmAdbymyOHBg5kksdnksnA3OqO2t1V7UArj1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\njHJV1q4FYoWpYkhIACwt+bIoxsTokq++vfri5bEv47OMz/T+3YocBWw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g4GC4uroiJCQE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\nrkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ylim(-1.1,1.1)\n", "plot(real(s))\n", "plot(imag(s))\n", "plot(abs(s),color='r')" ] }, { "cell_type": "markdown", "id": "ddde1d7e", "metadata": {}, "source": [ "(Discrete Fourier Transform with Complex Numbers)\n", "\n", "The formal definition of the discrete Fourier transform is now:\n", "\n", "$$X_k = \\sum_{n=0}^{N-1} x_n e^{-\\frac{2 \\pi i}{N} k n} \\quad \\quad k = 0, \\dots, N-1$$" ] }, { "cell_type": "markdown", "id": "8aa705e9", "metadata": {}, "source": [ "As before, we can put the Fourier transform into a matrix, call it `F`.\n", "\n", "This is now a complex matrix, but its real and complex components operate completely separately\n", "(provided we give it real input vectors)." ] }, { "cell_type": "code", "execution_count": 44, "id": "767f26db", "metadata": { "collapsed": true }, "outputs": [], "source": [ "F = array([b(k,n,N) for k in range(0,N)])" ] }, { "cell_type": "code", "execution_count": 45, "id": "ebc1fbe9", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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zgUOH1IwpDBGqX0JqWfSF5bSWIxkmiCjANVZuUGWsWlrofpUtMxDVAz8CLdEM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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a1 = 1.5\n", "a2 = 2.3\n", "omega1 = 6*2*pi/N\n", "omega2 = 14*2*pi/N\n", "y = a1*sin(n*omega1) + a2*sin(n*omega2)\n", "plot(y)" ] }, { "cell_type": "code", "execution_count": 46, "id": "ea95f608", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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EDQ2NhLbZs1lxc4xwHpVyAC8AAOYId8WN4OZAkVaVum2pFQAA04RbnBAMbrNm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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Y = dot(F,y)\n", "plot(abs(Y)**2)" ] }, { "cell_type": "code", "execution_count": 47, "id": "ff087250", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[6, 14, 406, 414]" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[i for i in range(N) if abs(Y[i])>100]" ] }, { "cell_type": "markdown", "id": "79bcc609", "metadata": {}, "source": [ "Fourier Transform of Common Signals\n", "===================================" ] }, { "cell_type": "markdown", "id": "dffb530d", "metadata": {}, "source": [ "There are some common signals that you should recognize the Fourier transform of.\n", "\n" ] }, { "cell_type": "code", "execution_count": 48, "id": "5010a86b", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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lwTffmJWBISHwz3/CNdfYHZWInC/PFhrVKkIRkdOsWmUSq/R0U3KhZ08z30pEfJcmuYuI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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def max1(x): return x*1.0/amax(abs(x))\n", "\n", "signal = n\n", "transform = dot(F,signal)\n", "plot(max1(signal))\n", "plot(max1(abs(transform)))" ] }, { "cell_type": "markdown", "id": "4dbd9b9b", "metadata": {}, "source": [ "Remember that the Fourier transform implements convolutions with circular boundary conditions. Therefore, the signal that the Fourier transform sees isn't the nice-looking smooth signal above, but one with a sharp discontinuity. We can see this by shifting the signal circularly.\n", "\n" ] }, { "cell_type": "code", "execution_count": 49, "id": "fc9a4d1c", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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gSUqKHSzF5bvv4Pbbw8iFzz+HmTPhlltg773jrkxyk7ukJBmwVNPKy+HRR+GG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\nJKmKGbAkSZKq2P8Dpk4B0gmJ1YUAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(roll(max1(signal),200))" ] }, { "cell_type": "markdown", "id": "75aebbe7", "metadata": {}, "source": [ "A double sawtooth illustrates this as well and is similar.\n", "\n" ] }, { "cell_type": "code", "execution_count": 50, "id": "aa167a9a", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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OmDgR/v5329WIP1PA8n/Fxeb9oHlzeO89zb4TORyvBiwtEfqnX381X6kOGwbX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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "signal = concatenate([n,n])[2*n]\n", "transform = dot(F,signal)\n", "plot(max1(signal))\n", "plot(max1(abs(transform)))" ] }, { "cell_type": "markdown", "id": "7c282b16", "metadata": {}, "source": [ "The Fourier transform of an impulse is a flat spectrum.\n", "\n" ] }, { "cell_type": "code", "execution_count": 51, "id": "7bcbce31", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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yAJiLSqVSlEqlZNc7ZMCqr6+PcrlceVwul6NYLB407sUXX4wbbrghBgYGYv78+RNe6+MB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\nAgBITMACAEhMwAIASOx/AcvpGHHGERWWAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "signal = (n==100)\n", "transform = dot(F,signal)\n", "ylim(-0.1,1.1)\n", "plot(max1(signal))\n", "plot(max1(abs(transform)))" ] }, { "cell_type": "markdown", "id": "b2b6432d", "metadata": {}, "source": [ "Again, we're actually looking at a circular convolution, so what the Fourier transform \"sees\" is this.\n", "\n" ] }, { "cell_type": "code", "execution_count": 52, "id": "facdd2d7", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ZE7ZYdwDAK/oFgCCxJmzBxXoUAF7RLwD/EbYsxFE7AK/oFzjfufnAvCgva8IWR2cAvKJf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\nADDofwFR1RBSueAP8wAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ylim(-0.1,1.1)\n", "plot(max1(concatenate([signal for i in range(8)])))" ] }, { "cell_type": "markdown", "id": "465a3d81", "metadata": {}, "source": [ "If the signal isn't a perfect impulse but a little broader, the transform changes significantly.\n", "\n" ] }, { "cell_type": "code", "execution_count": 53, "id": "a3da4442", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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HHjAyMIJnmCe29d6Glp+2lG3fHNNAROpEkiT8FPsTtl7dirj+cTArayY6EumAD76LMDo6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\niIhkxoJFREREJDMWLCIiIiKZ/T9yKooiY0M7uQAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "signal = (n>=100) * (n<102)\n", "transform = dot(F,signal)\n", "plot(max1(signal))\n", "plot(max1(abs(transform)))" ] }, { "cell_type": "code", "execution_count": 54, "id": "969e6607", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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qQY2knCQuEdaASQQsHycfXMi6IHUZ9C9t2jQAnMUiIpKrtPw02Ne2R12bulKXYnRMImC1\ndGyJpJwkqAW2BJcDbWawAAYsIiK54gb3mjOJgFXXpi4cbB2Qmp8qdSkEBiwiIlPB/Vc1ZxIBC2DD\nUTlhwCIiMg3x2fHwdfKVugyjZDIBi08SygcDFhGRaWCT0ZoznYDlyI3ucqFNmwbg3rVqbp8jIpId\n7sGqOZMKWJzBkgfOYBERGb/bxbeRXZCNpg2aSl2KUTKdgOXkwz1YMqFtmwYLCwYsIiK5SchOgNJB\nyUOea8hk/q01bdAUOYU5uF18W+pSzB5nsIiIjF98Fje468JkAlbZoc8J2QlSl2L2GLCIiIwf91/p\nxmQCFvDvPiwuE0qOAYuIyPjxkGfdmFbAYqsGyZUFJQYsIiLjFp8Vj5aOLaUuw2iZVMDydvBGYk6i\n1GWYtZoGLLZpICKSD0EQkJSTBG8Hb6lLMVqmF7CyGbCkVJOZKM5gERHJS1ZBFqwsrGBvay91KUbL\npAKW0kGJpJwkqcswa9q2aADYpoGISG6ScpKgdFBKXYZRM6mA5VTHCWpBjeyCbKlLMVvabnAHOINF\nRCQ3ybnJ8HLwkroMo2ZSAUuhUHAWS2IMWERExo8zWLozqYAFAN6O3OguJQYsIiLjl5ybDKU9A5Yu\nTC9g8UlCSTFgEREZv6ScJC4R6qjagBUeHg5fX194e3tjyZIlFV4TERGBdu3aoU2bNggJCRG7Rq1w\niVBaanXNAhbbNBARyUdyTjKXCHVkVdUHVSoVQkNDcfDgQbi5uaFjx44YMmQI/Pz8yq/Jy8vDtGnT\n8Ntvv8Hd3R1ZWVl6L7oq3g7eWBa9TNIazBlnsIiIjNvNopsoKCmAi52L1KUYtSpnsKKjo6FUKuHp\n6Qlra2uMHj0aO3fufOCajRs34umnn4a7uzsAwMnJSX/VakDpoERiTiIEfseWBNs0EBEZt+Sce08Q\nKrT9aZkeUOUMVnp6Ojw8PMr/7O7ujqioqAeuSUxMRElJCXr16oVbt27h1Vdfxbhx4yocb/78+eW/\nDwkJ0ctyolMdJwiCgJzCHDjWcRR9fKoaZ7CIiIxbUk4SvOzNb/9VREQEIiIiRBuvyoClSXotKSnB\nqVOn8Pvvv6OgoABdunRB586d4e39aHv9+wOWvigUivInCRmwDI8Bi4jIuCXnmuf+q4cnfhYsWKDT\neFUu5ri5uSEtLa38z2lpaeVLgWU8PDzwxBNPwNbWFo6OjnjssccQExOjU1G64kZ36TBgEREZN3Od\nwRJblQErKCgIiYmJSElJQXFxMbZs2YIhQ4Y8cM1TTz2FyMhIqFQqFBQUICoqCq1atdJr0dVhqwbp\nMGARERk3c53BEluVS4RWVlZYtmwZ+vXrB5VKhYkTJ8LPzw8rVqwAAEyZMgW+vr7o378//P39YWFh\ngUmTJkkesJQOSoQnhUtag7liwCIiMm7sgSUOhWCgx+0UCoXBnuz7O+1vvBr+KqInRRvkfvSf7GxA\nqQRyczV/jacn8McfQPPmeiuLiIg0UFhSCPsl9rjz9h1YWlhKXY6kdM0tJtfJHfjvuBy2ajA8zmAR\nERmvS3mX0KxhM7MPV2IwyYDlaOsIQRCQXZgtdSlmh32wiIiMFzu4i8ckA1ZZqwY+SWh4nMEiIjJe\nfIJQPCYZsIB/O7pn80lCQ2PAIiIyXnyCUDwmG7DYqkEaDFhERMaLM1jiMemAxSVCw2PAIiIyXpzB\nEo/JBqyyQ5/JsNTqmgUstVo/9RARkWZKVCVIzU+FZ0NPqUsxCSYbsLwdvZGYzVYNhsYZLCIi45Sa\nnwrXuq6oZVVL6lJMgskGLEfbewc9s1WDYbFNAxGRcUrOTWYHdxGZbMAqa9XAJwkNizNYRETGKSkn\nifuvRGSyAQsAvOy9kJybLHUZZoUBi4jIOCXnJvMJQhGZdsBy8EJyDgOWITFgEREZJ85gicu0AxZn\nsAyOAYuIyDgl53AGS0wMWCQqtmkgIjI+akGNi7kXucldRKYdsLhEaHCcwSIiMj7Xbl1D/Vr1Udem\nrtSlmAyTDlhN6jVBflE+bhfflroUs8E2DURExof7r8Rn0gHLQmGB5g2b42LuRalLMRucwSIiMj7s\ngSU+kw5YAJcJDY0Bi4jI+CTlJEFpzxksMZl8wFI6KLnR3YAYsIiIjA9nsMRn8gGLTxIaFgMWEZHx\n4R4s8ZlHwOISocGwTQMRkXERBIE9sPTA9AOWA2ewDIkzWERExiW7MBsKhQIOtg5Sl2JSTD5geTb0\nxJWbV1CiKpG6FLPANg1ERMalbPZKoe1Px1Qlkw9YNpY2cK3ritT8VKlLMQucwSIiMi7cf6UfJh+w\ngHvLhEk5SVKXYRYYsIiIjAufINQP8whYfJLQYBiwiIiMC3tg6QcDFomKAYuIyLgk5yZziVAPzCNg\nsZu7wbBNAxGRcUnKSeISoR6YR8DiDJbBcAaLiMh43Cq6hdvFt+Fa11XqUkyOeQQsBy9czL0Igd/F\n9Y4Bi4jIeCTnJqOFfQu2aNADswhY9WvVRx3rOrh++7rUpZg89sEiIjIebNGgP2YRsAAe+mwonMEi\nIjIePCJHf8wmYPFMQsNgwCIiMh5JuZzB0hfzCVg8k9AgGLCIiIwHZ7D0x3wCFp8kNAgGLCIi48E9\nWPpjXgGLS4R6xz5YRETG4W7pXWTcyYBHAw+pSzFJ5hOwuERoEJzBIiIyDpdyL6Fpg6awsrCSuhST\nZDYBy8XOBYUlhbhZdFPqUkwa2zQQERkHHvKsX2YTsBQKBVrYt+AyoZ5xBouIyDhw/5V+mU3AArhM\naAgMWERExiE5l08Q6pN5BSxudNc7BiwiIuPAGSz9MruAlZSbJHUZJo0Bi4jIOLAHln6ZV8By4AyW\nvrFNAxGR/JWqS5Gan4rm9s2lLsVkmVXA4nmE+scZLCIi+UvLT4OznTNqW9WWuhSTZVYBq2mDprh+\n+zqKSoukLsVksU0DEZH8cf+V/plVwLKysIJHfQ+k5KVIXYrJ4gwWEZH8sQeW/plVwALYqkHfGLCI\niOQvKScJSnvOYOlTtQErPDwcvr6+8Pb2xpIlSyq97vjx47CyssKOHTtELVBsbNWgXwxYRETyxxks\n/asyYKlUKoSGhiI8PBxxcXHYtGkTzp8/X+F1s2fPRv/+/SHI/Dullz1nsPSJAYuISP64B0v/qgxY\n0dHRUCqV8PT0hLW1NUaPHo2dO3c+ct3XX3+NESNGoFGjRnorVCxcItQvtmkgIpI3QRBwMfcie2Dp\nWZVHaKenp8PDw6P8z+7u7oiKinrkmp07d+LQoUM4fvw4FFV8d50/f37570NCQhASElKzqnXAJUL9\n4gwWEZG8Xbt9DXVt6qJerXpSlyIrERERiIiIEG28KgNWVWGpzIwZM7B48WIoFAoIglDlEuH9AUsq\nLexb4FLeJagFNSwUZrfHX+/YpoGISN7Ywb1iD0/8LFiwQKfxqgxYbm5uSEtLK/9zWloa3N3dH7jm\n5MmTGD16NAAgKysL+/btg7W1NYYMGaJTYfpiZ2OHhrUb4uqtq3Cv7179C0grnMEiIpI37r8yjCoD\nVlBQEBITE5GSkoImTZpgy5Yt2LRp0wPXXLx4sfz3EyZMwODBg2UbrsqULRMyYImPAYuISN6SczmD\nZQhVLuZYWVlh2bJl6NevH1q1aoVRo0bBz88PK1aswIoVKwxVo+i40V1/GLCIiOSNM1iGUeUMFgAM\nGDAAAwYMeODvpkyZUuG1a9asEacqPWOrBv1hwCIikreknCT2wDIAs9zlrXRQ8klCPWGbBiIi+RIE\ngTNYBmKWAYszWPrDGSwiIvnKKcyBAAGOto5Sl2LyzDNgOXghKSdJ6jJMEgMWEZF8JecmQ+mg1KgN\nE+nGLAOWo60j1IIaOYU5UpdictgHi4hIvpJykvgEoYGYZcBSKBTs6K4nnMEiIpKv5Jxk7r8yELMM\nWABbNegLAxYRkXwl5XIGy1DMN2BxBksvGLCIiOSLM1iGY94BizNYomObBiIi+WKLBsMx24CldFAy\nYOkBZ7CIiOTpdvFt3Cy6Cdd6rlKXYhbMOmCxVYP4GLCIiOQpOScZLexbwEJhtt/6Dcps/y271XdD\nTmEOCkoKpC7FpLBNAxGRPCXnJvOIHAMy24BlobBA84bNcTH3otSlmBTOYBERyRP3XxmW2QYsgMuE\n+sCARUQkT8m5yWzRYEBmHbB4ZI74GLCIiOSJM1iGZdYBS2nPJwnFxjYNRETylJzDGSxDMu+AxSVC\n0XEGi4hIfopKi3Dt9jU0a9hM6lLMhlkHLC4Rio8Bi4hIflLyUuBR3wNWFlZSl2I2zDpgNWvQDFdv\nXUWxqljqUkwG2zQQEckP918ZnlkHLGtLa3jU90BKXorUpZgMzmAREckPe2AZnlkHLIDLhGJjwCIi\nkp+knCQo7TmDZUhmH7C40V1cDFhERPLDGSzDY8BiqwZRMWAREckP92AZntkHLC4Riot9sIiI5EWl\nVuFy3mU0b9hc6lLMitkHLC4RioszWERE8pJ2Mw2N7BrB1tpW6lLMitkHrBb2LXA57zJUapXUpZgE\ntmkgIpKXpJwkdnCXgNkHrNpWteFs54y0m2lSl2ISOINFRCQvyTnc4C4Fsw9YAPdhiYkBi4hIXpJy\nk+Dt4C11GWaHAQvchyUmBiwiInlJzE7kE4QSYMACWzWIiQGLiEheknI4gyUFBixwiVBMbNNARCQf\nakHNJqMSYcAClwjFxBksIiL5SL+ZDvva9qhrU1fqUswOAxYAL3svJOckQ+B3eZ0xYBERyQc7uEuH\nAQtAvVr1UK9WPVy7fU3qUowe+2AREclHYk4ivB25/0oKDFj/4jKhODiDRUQkH0k5SVDacwZLCgxY\n/2LAEgcDFhGRfCTmsEWDVBiw/uVlzycJxcCARUQkH0k5SVwilAgD1r+UDuyFJQa2aSAikge1oL53\nTA7PIZQEA9a/uEQoDs5gERHJw9VbV9GgdgPUq1VP6lLMEgPWv8qWCNmqQTcMWERE8sAWDdJiwPqX\ng60DLBQWyC7MlroUo8Y2DURE8pCYncgjciTEgPUvhULBZUIRcAaLiEgeknI5gyUlBqz78ElC3TFg\nERHJA2ewpGUldQFyIuUMVqm6FCeunkB8Vjwa1m6Ix5o9Bntbe0lq0QUDFhGZu6ScJJy8ehIqQYWO\nTTpK1iaBe7CkxYB1H6WDEgcuHjD4fXde2IlZB2bB1soW/i7+yC7MxvO/Po/n/J/Dol6LjCposU0D\nEZmrszfOYnr4dJzPPI8ezXoAAF7f/zoCGwdiaf+laOnY0mC1CIKA5NxkBiwJMWDdp6VjS3x7/FuD\n3U8QBLwX8R7Wx6zH6qdWo3fz3uUfyynMwdu/v42glUHYM2YP/Br5GawuXXAGi4jM0YYzG/Dab6/h\n/V7v48X2L8LK4t6312JVMb6J/gbdV3fHT8N/Ql+vvgap5+qtq6hnU48tGiTEgHWflo4tkZiTCEEQ\noNA2JdTAR5EfYVf8LhyfdByN7Bo98DEHWwd8N+g7rP1nLXr92AsRL0TA18lX7zXpigGLiMzND6d+\nwMIjC/HH+D/QxrnNAx+zsbTBa11eQ1CTIDz989PYPWY3gt2D9V4Tlwelp9Em9/DwcPj6+sLb2xtL\nlix55OM//fQTAgIC4O/vj27duuHMmTOiF2oIjraOUECBrIIsvd9rd/xurDi5AuFjwx8JV/d7IfAF\nLOmzBP029EPGnQy916UrtmkgInOyL3Ef5v4xFwfGHXgkXN2vR7MeWDt0LYZtGWaQr+WJOYk8Ikdi\n1X4rVKlUCA0NRXh4OOLi4rBp0yacP3/+gWtatGiBI0eO4MyZM3j33XcxefJkvRWsTwqFAi0dWyIh\nO0Gv97lx+wYm75mMn4b/BNd6rtVePz5wPJ7zfw5jd4yFSq3Sa2264gwWEZmL1PxUvLDzBWx9ZqtG\n+6sGeg/E+MDxmLhrot6bWiflJEFpzxksKVUbsKKjo6FUKuHp6Qlra2uMHj0aO3fufOCaLl26oEGD\nBgCA4OBgXLlyRT/VGoC3o7feA9abB9/EOP9x6N60u8avWRCyAEWlRfjy2Jd6rEx3DFhEZA7UghrP\n//I8Xuv8mtZfyy/nXcb289v1WB1nsOSg2oCVnp4ODw+P8j+7u7sjPT290ut/+OEHDBw4UJzqJNDS\noSUScvQcfbuEAAAgAElEQVQXsKKuROHgxYN497F3tXqdlYUV1jy1Bh9FfiTrXl0MWERkDr4/+T0K\nSwvxRtc3tHqdjaUNvuz/JWbtn4XCkkI9Vcc9WHJQ7SZ3bTZ7//HHH1i9ejX+/PPPCj8+f/788t+H\nhIQgJCRE47ENpaVjS/wc97Pexp99cDbe7/V+jZ7s8HLwwpzucxAaForw58L1UJ3u2KaBiExddkE2\n5h6ai4gXImBpYan163s37412ru2w/MRyzOwyU/T6BEFAcg5bNGgrIiICERERoo1XbcByc3NDWlpa\n+Z/T0tLg7u7+yHVnzpzBpEmTEB4eDnv7ivs23R+w5KqlY0skZifqZeyjl48i7WYang94vsZjTA+e\njpWnViIsMQwDveU3U8gZLCIydR8c/QAjWo2oclN7deb1nIeBPw3E1KCpsLW2FbE64Nrta7CzsUP9\nWvVFHdfUPTzxs2DBAp3Gq3aJMCgoCImJiUhJSUFxcTG2bNmCIUOGPHBNamoqhg8fjg0bNkCpNO7E\n7O3ojaScJKgF8adUFh1dhLe6v1XeH6UmbCxt8NkTn2HW/lmy3PDOgEVEpiwlLwU/xvyI+SHzdRon\nsHEggpoEYfXp1eIUdp+E7ASDNjWlilUbsKysrLBs2TL069cPrVq1wqhRo+Dn54cVK1ZgxYoVAICF\nCxciNzcXU6dORbt27dCpUye9F64vdW3qwt7WHlduirtRPy4zDjHXYzDOf5zOYz3p/STq16qv902S\nNcE2DURkyuYemovQTqFoXLexzmO92e1NLI1aKvoP9PFZ8QxYMqDRVMqAAQMwYMCAB/5uypQp5b9f\ntWoVVq1aJW5lEipr1dC0QVPRxvzm+DeY3GEyalnV0nkshUKBeT3n4Y0Db2BEqxGwUMjnzG7OYBGR\nqfrn+j/4/dLvWP7kclHG6+bRDXWs6+BA8gH0U/YTZUwASMhJgI+jj2jjUc3I5zuzjIjdC+tW0S1s\nOrsJLwW9JNqY/ZX9Uce6Dnac3yHamGJgwCIiU7U4cjFmdZkl2vEzCoUCr3R6BcuOLxNlvDLxWfEM\nWDLAgFUBbwdxe2FtjduKnp490aReE9HGLJvFWnh4oV72i9UUAxYRmaJLuZdw4OIBTOowSdRxR7cZ\njcjUSFy7dU20MeOzuUQoBwxYFSg7k1Asa/9Zi/EB40Ubr8xA74GwsbTB3oS9oo9dUwxYRGSKvjj2\nBSa1nyT6k3l2NnYY5jsMP539SZTxilXFSMtPg5eDlyjjUc0xYFVAzCXCi7kXcSHrgl5aKigUCrzW\n+TV8Ff2V6GPXFPtgEZGpyS7IxoYzGzA9eLpexn8h8AWs/WetKMfnXMy9CI8GHrCxtBGhMtIFA1YF\nWti3QFp+GopVxTqPtensJoxsPVJv/7E/0/oZnMs4h7jMOL2Mry3OYBGRqVl+YjmG+g4VdZvH/Xo0\n7YHbxbdxLuOczmNx/5V8MGBVwMbSBu713XEp95LOY/0c9zNGtR4lQlUVs7G0weQOk7EsWtxNkjXF\nNg1EZEpKVCX49vi3eL3L63q7h0KhwDOtnxHlFBHuv5IPBqxKiLFMGJ8Vj6yCLHRr2k2kqir2UoeX\nsPncZuTdzdPrfTTBGSwiMiW74nfB29EbrZ1b6/U+I1uNxM+xP+u8TBifzRksuWDAqoQYAWtr3FY8\n7fe03vtUudZzRX9lf6w5vUav99EEAxYRmZLvTn6HKR2mVH+hjoKaBKFYVYyzGWd1GichOwE+TgxY\ncsCAVQlvB2+dnyTck7AHQ32HilRR1UI7hWL5ieWibJLUBQMWEZmKpJwkxFyPwdN+T+v9XgqFAk/5\nPIU9CXt0God7sOSDAasSus5gZd7JxIWsC+jetLuIVVWui3sXWFlYITI10iD3qwwDFhGZiu9Pfo/x\ngeNFOYFDEwO9ByIsMazGr88tzMXd0ruiHONDuqv5qcMmTteA9Vvyb+jdvLfBHpVVKBSY2G4ifjj9\nA3o062GQe1bk4TYNGXcycOraKdwsugkHWwcENg6EUx2nB17DNg1E5kcQBCTlJOF81nkUq4rhWtcV\n7VzboY51HalLAwAUlRZh7T9r8ef//jTYPR9r9hjO3DiDnMIcONg6aP36sg3uCm1/yiW9YMCqhEcD\nD2QXZuN28W3Utamr9evDEsP00vuqKuMCxqHl1y1xs+im6M3wNFU2g7U/eT8WRy7G6eun0a5xOzjW\ncUTmnUycvn4andw6YXa32ejTog8AzmARmZOi0iKsOrUKX0d/jVvFtxDYOBC1rWojNT8VidmJGO43\nHHMfm4sW9i0krXNn/E60dWkLb0dvg92ztlVthHiG4Lek3zCm7RitX8/9V/LCgFUJC4UFlA5KJOUk\nIbBxoFavValV+C35N3zS9xM9VVcxZztn9G7eG5vPbcbkDpMNeu8yRYo8fJc9GXlhp7EwZCGG+w1/\nYHq9sKQQ289vx8t7X0Zbl7b47snvoFA0YsAiMgPHrhzDC7++AC8HL/ww5Ad09ej6wGxLxp0MLD++\nHB1XdsTb3d/GzC4zJZuNWRezDi8EvGDw+w70HoiwpLAaBSw+QSgv3INVhZaOLRGfFa/166LSo+BR\n3wNu9d30UFXVJrabiNWnVxv8vsC9s7r2uHZCAytnnJt6DmPajnlk74KttS2e838OZ6aegZe9F4JW\nBuFy0T8MWEQmbuXJlRiyaQgW9V6Evc/uRbem3R4JT852zpgXMg8nJ5/E1ritGLN9jCgNn7WVcScD\nkamRGOY3zOD3HqAcgPCkcKjUKq1fG5/FHlhywoBVBV8nX8Rnax+wpFgeLNNP2Q9Xbl5BbEasQe97\nMfciHlv7GPzyX8U4x2XVbgqtbVUbH/f9GJ/0/QQLLz2B7Dp/GahSIjK0j45+hCV/LkHk/yIxotWI\naq/3bOiJiBciUKQqwvAtw1GiKjFAlf/ZfG4zBvsMrtH2EF01a9gMLnYuOHH1hNav5QyWvDBgVcHX\n0Rfns85r/TopA5aVhRWebfusaAeHaiLzTib6beiHt7u/jZb507R6inBk65GY0XQ9opoPxalrp/RX\nJBFJ4ou/v8CPMT/iyIQjWs2u1Laqja3PbIVCocCLu180aAuadTHr8Lz/8wa738PKlgm1oRbUSMpJ\nMuieMaoaA1YV/Br54ULWBa1ek3EnA5fyLqGze2c9VVW9sW3HYuPZjVAL+n80r1RdilHbRuFpv6cx\ntePUGrVpaN+gH/xTV2DQxkFIy0/TT6FEZHDb4rbhi2Nf4MC4AzU6x8/KwgpbRmxBbEYsvjj2hR4q\nfFRcZhyu3b6G3s17G+R+Femv7I/wpHCtXpOanwpHW0dJZt2oYgxYVfBx9EFCdoJWQeVwymF0b9od\nVhbSPT/g7+IPOxs7/JWm/2W3BYcXwNLCEh/0/gDAo20aNKFQAC45wzCj8wyM3DZSkj0XRCSu+Kx4\nTN07Fb+O/hUeDTxqPE4d6zrYPnI7Pv7zY4N8TVt/Zj3Gth0LSwtLvd+rMl3cuyA2Ixa3im5p/Jr4\nrHg+QSgzDFhVqFerHuxr2yM1P1Xj1xy+fBg9m/XUY1XVUygUGNt2rN6XCf9O+xsrT67EhmEbyr8Y\n6dJodFbXWWhUpxHePPCmHqoVl0qtQmFJoUFmCYnKqNQqFJQUSH5iQ3XuFN/B0z8/jQ97f4j2ru11\nHq9Zw2ZYMWgFnv/ledwuvi1ChRVTC2r8dOYnjPMfp7d7aMLW2hbtXdtrFSi5/0p+GLCqoe0yoRwC\nFgA82/ZZbIvbprfZoGJVMSbsnIBvBn4Dl7ou5X+vS8CyUFjgx6E/Ylf8LmyL2yZyxboRBAF/pv6J\nKXumoOXXLWH7gS0cPnaA3Yd26PB9B7xz6B0kZut2tBLRwwRBwMGLBzFx10R4feWF2h/UhuPHjrD7\n0A7Bq4IxP2I+LuddlrrMR4TuC0WHJh3wYvsXRRvzKd+n0L1pd8w9NFe0MR92OOUwHOs4oq1LW73d\nQ1M9PXviSOoRja9PyE5gwJIZBqxq+Dr54nymZhvdswqykJqfinau7fRcVfU8G3rCx9EH+5P362X8\nr6K+Qgv7FhjuN/yBvxcEwELL/6osLP5rNGpva4/NIzYjNCwUmXcyRapWNyevnkTPtT0xYecEeNl7\nYdvIbbj99m0UvlOIrDeysLT/UhSritF1dVeM2T5Glt/wyPgcunQI7b9vjxnhM9DWuS12j9mNwncK\nUfhOIW7MuoElfZYgpzAHHb7vgJf2vISsgiypSwYA7I7fjcjUSHw78FvRe1h90vcTbDy7Eecyzok6\nbpl1Z9ZJPntVpmeznjiccljj68u6uJN8MGBVw8/JDxeyNZvBOnr5KLp6dJV0/9X99PU04bVb17A4\ncjG+7P/lI19AxTiLsJNbJ4z1H4sZv80QodqaUwtqLIhYgIEbB2J8wHicn3Yeb3Z7E/4u/uVHINnZ\n2KF70+74pO8nSHk1BT6OPghaGSRZLzIyfgUlBZiyZwom7JyAd3q8g7NTz2JG5xlo1ahV+deWerXq\nIcQzBF8N+AoJrySgllUt+C/3x29Jv0lae/7dfLwc9jJWDl4JOxs70cdvZNcI7/V8D9P3TRd9mbSw\npBC/XvgVY9po3+BTH7q4d8E/1/9BQUmBRtdzD5b8yCMJyJivky82n9us0bVyWR4sM7L1SLz1+1u4\nVXQL9WrVE23c2Qdn48X2L1b405JYhz0vDFkI/+/8sTdhL55s+aQO1dZMQUkBRm8bjfyifPwz5R+4\n1nOt9jV2NnaYHzIfI1qNwKhtoxCdHo2vB3wNa0trA1SsvaLSIuyK34W9iXtx6topXL11FWpBjcZ1\nG6OdazsMUA7AUN+hRvVU0uW8y/g59mf8kfIH4jLjkHc3D7WtasPLwQtdPbpiuO9wdHbvLNuz2jLv\nZGLwpsFobt8cZ6ee1ejIKwdbByztvxTDfYdjzPYxmNV1FmZ2mWmAah81++BsDPQeiBDPEL3d46Wg\nl/D9ye+x/fx2jXpqaSosMQwdXDto9P+6IdjZ2MHfxR/Hrhyr9onGW0W3kF2YjWYNmhmoOtIEZ7Cq\n4evkq/EeLLkFLKc6TujRtAd+vfCraGNGp0fj0KVDmPtYxfsgxApYdjZ2WDl4JabunarXTa0VuVV0\nC/029IO9rT0Ojjuo9RfcNs5t8PfEv3E5/zJGbx9t8CaJ1blbehef/fUZmn7ZFN+d/A6d3Dph7dC1\nOD/tPBJeScDmEZvR2/PekUueX3ri3T/eNfjnQFuJ2YkYtW0UOnzfAUm5SZjUfhIOPn8QF1+9iJOT\nT+LD3h/CztoOz//6PDp83wH7EvdJXfIjErMT0XV1V/T16ouNwzdqfZ5oT8+eiHoxCitPrdTrPqXK\nHLl8BHsT9+LjPh/r9T5WFlb4esDXeH3/6ygqLRJt3C2xWzCq9SjRxhNDT8+eOHy5+mXCC1kX4OPo\nI+mTj1QBwUAMeCtRqdVqof5H9YWsO1lVXpdTkCPU+7CeUFxabKDKNLPxzEah/4b+oo03YMMAYfnx\n5ZV+fNgwQdi6Vbsx9+8XhMcfr/hjY7ePFd75/R3tBtRBcWmx0HddX2HSrkmCSq3Saay7JXeFQRsH\nCUM3DxWKSotEqlA3x9KOCT5f+wiDNg4Szt44W+31yTnJwnM7nhPcPnMTwhLCDFChdkpUJcKCiAWC\n4xJH4aOjHwk3796s8nqVWiXsiNshtPy6pTB8y3Ah43aGgSqt2qXcS4LbZ27CihMrdB4r43aG0Oqb\nVsLnf30uQmWaKVWVCgHLA4Qt57YY7J4DNgwQvo3+VpSxbhXd0ujrvKHtS9wn9FzTs9rr1p5eKzy7\n/Vn9F2RmdM0tnMGqhkKh0GgWKzI1EsHuwbJbDhriMwR/p/0tyobx6PRonMs4hwmBEyq9RqwZrDKL\n+yzG8hPLkZKXot2gNSAIAl7c/SJqW9XGt09+CwuFbv971LKqhW3PbINaUGPsjrGSt3RYc3oNBm8a\njPd7vY/dY3ajjXObal/Twr4F1g9bj/XD1uOlvS9h7qG5smkRkFOYg77r+yIyNRIxL8VgTvc51S6F\nWygsMMxvGGJeikEL+xbotKoTzt44a6CKK5ZxJwNPrH8Cc7rPEeWQ9kZ2jbBv7D58fuxz/Bz7swgV\nVm/16dWoX6s+nmn1jEHuBwDzes7DR5EfiTKLtSdhD7p6dIVjHUcRKhNPN49uOHH1BO6W3q3yuris\nOLRyamWgqkhTDFga8HOqvlXD0dSjeKzpYwaqSHN2Nnbor+yPHed36DzWgsML8Fb3t6o8Z1DsgOVe\n3x0zgmcYpDfWgsMLEJ8Vj80jNov2oEItq1r4ecTPuHrrKuZHzBdlTG2pBTVe3/86Poz8EEcmHMEz\nrbX/JtireS8cn3Qcv1/6HWN3jK32C76+Jecko+sPXdHBtQP2jd2n9cHqta1q45O+n+CD3h+g97re\n2BW/S0+VVu128W08ufFJjGozCqGdQkUbt2mDptgzZg9Cw0L13pwz/24+3ot4r8KHXvQp2D0YrZ1b\nY80/a3QeS47Lg8C9hxn8GvnhePrxKq+Ly4xDq0YMWHLDgKUBX6fqzyQ8duWYpMfjVGVU61HYErtF\npzGi06Nx9sZZ/K/d/6q8Ttc2DRWZ1XUWotOjceSy5j1htHXw4kGsPLUSO0fvRB3rOqKOXcuqFn4Z\n9QvWxazT+IEJsQiCgKl7pyI6PRpRL0bB18m3xmM52znj0POHUKouxYCfBqCwpFDESjUXmxGL7mu6\n49XgV/HpE5/qtO/k2bbPYu+zezF592T8cv4XEausniAImLx7Mlo1aoWFIQtFHz+gcQBWP7UaY7aP\nQU5hjujjl1l0dBEGeg8UpaGotspmsXTp93ez6CYOXTqEob5DRaxMPJ3dOyMqParKa85nnodfIz8D\nVUSaYsDSQHVLhKXqUpy6dgod3ToasCrN9Vf2x6lrp3D99vUaj7HoyCLM6T6nytkrQPwZLOBeV+OP\nHv8Ibxx4Qy/LUxl3MjD+1/FYN3TdA01TxeRs54xdY3bhlX2vIOZ6jF7u8TBBEDBz/0zEXI9B2LNh\ncLB10HlMW2tbbB6xGU3qNcGIrSMMfqzRxdyL6LehHz7t+ymmdpwqypid3Dph77N7MWXPFK3Pf9PF\nN8e/QVxmHL578ju9zfwMajkIw/2GY+KuiXr5f+dy3mWsPr26/KgsQ+vs3hl+Tn748Z8fazzGzgs7\n0bNZTzSs3VDEysQT7BZcZcAqLClE+q10eNl7GbAq0gQDlgb8nPwQlxlX6cfPZZxD0wZNZfs/qK21\nLQa1HITtcdtr9PrE7EQcu3Ksyr1XZfQRsABgVJtRKCotws74ndoNXg21oMb4X8djfMB4PN7icVHH\nfpi/iz++6PcFRm8fjTvFd/R6L+BeKI5IicC+sftEbdNhobDA2qfWwsrCCs//8jxUapVoY1fl6q2r\n6Lu+L+Y+Nhdj/ceKOnaHJh3w6+hfMe6XcQY57+7YlWNYeHghto/cDltrW73ea/Hji3E57zK+Pf6t\n6GMvOLwALwW9hMZ1G4s+tqbe7PYmvoz6ssYBUq7Lg2U6u3dG1JXKA1Z8djy87L1kt/+XGLA04uXg\nhWu3r1X6TTHqShSC3YMNXJV2dFkm/Cr6K0zuMFmjbwT6ClgWCgt80PsDvHPoHVG/oa86tQo5hTlY\nELJAtDGr8pz/cwhqEoTXfntNr/fZcX4HVp5aiX1j98He1l708a0trbFlxBZcv30dc//Qf0uAwpJC\nDN40GBPbTcRLQS/p5R5dPbrix6E/4pmtzyD9Zrpe7gHcawMyZvsYfD/4e3g56H/WoZZVLWwZsQXz\nIuYhOSdZtHEvZF3A7oTdeKPrG6KNWRO9PHvBUmGJgxcPav3a3MJcHE09iiE+Q/RQmTi87L1QUFKA\na7euVfhx7r+SLwYsDVhZWMHH0afSfVhR6VEIdpN3wHrC6wmcyzin9TeOvLt5+OnMT3i548saXa9W\n1yxgqTV4wG6g90A0rN1QtO70125dwzuH3sGqwasM+tPfNwO/waFLh2o8o1idcxnnMGXPFOwYtUOv\nMwu1rWpj28ht2Hxus16fVhMEAZP3TIavky/e6v6W3u4D3PtvLLRjKIb/PFxvG/ln7p+Jx5s/btA9\nP96O3pjdbTZe2vuSaEuF7/7xLmZ1mSX5zL1CocCMzjPwxbEvtH7tLxd+QZ8WfUSd4RWbQqFAJ7dO\nlS4Tns/i/iu5YsDSUGvn1ojNiK3wY8euHJN9wKplVQtDfIZofYjyqlOrMNB7IJrUa6LR9fqawbp3\nnQIfPf4R5kXME2Xvz/Tw6ZjSYYrBD3atX6s+fhr+E6aFTRP9vMX8u/kYtmUYPn/icwQ1CRJ17Io4\n1XHCjpE7MC1smt72li2NWopzGeewcvBKgzylNqf7HDRr0AzTwqaJPvbehL04ePEgPu/3uehjV+e1\nLq8hqyALG85s0HmsU9dO4c/UP/FK8CsiVKa7Z9s+i5PXTmrcFLqM3JcHywS7BePYlWMVfiwuky0a\n5IoBS0OtG7XGucxHDxjNv5uP1PxUWZy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fj9H629bIL8pH0wZNMcx3mNQl6STYLRgbMzfi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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "signal = (n>=100) * (n<110)\n", "transform = dot(F,signal)\n", "plot(max1(signal))\n", "plot(max1(abs(transform)))\n", "\n" ] }, { "cell_type": "markdown", "id": "21df7238", "metadata": {}, "source": [ "The Fourier transform of the Gaussian is very important in practice.\n", "\n" ] }, { "cell_type": "code", "execution_count": 55, "id": "3af7081e", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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NDhbgLJZl6WTnSQJWABwZsOhgAaFFBwtAINr62zQ3bq6S5ySbLsX2CFgACFgA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\nyXmcpv+d6Bz32Xc+ivg1e3/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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "signal = exp(-(n-200)**2/100.0)\n", "signal /= amax(signal)\n", "transform = dot(F,signal)\n", "plot(max1(signal))\n", "plot(max1(abs(transform)))" ] }, { "cell_type": "markdown", "id": "8cb8a372", "metadata": {}, "source": [ "It's kind of difficult to see what's going on here. It becomes easier if we shift the output of the transform to overlap with the original signal. Then it becomes pretty clear that the Fourier transform of a Gaussian is again a Gaussian. Some experimentation shows that the wider the original Gaussian, the narrower its transform and vice versa.\n", "\n" ] }, { "cell_type": "code", "execution_count": 56, "id": "99c9d84b", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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KFaqqqtKOHTsCHtPQ0KB169Zp9erVqq2tDXeNAKIonEs0ePAkIQCrSZpup8vl0h133KGX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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(max1(signal))\n", "plot(roll(max1(abs(transform)),200))" ] }, { "cell_type": "markdown", "id": "e533792f", "metadata": {}, "source": [ "# Inverse Fourier Transform" ] }, { "cell_type": "markdown", "id": "e01c9954", "metadata": {}, "source": [ "Of course, we can transform back as well. $F$ is a matrix, so we just take its inverse.\n", "\n" ] }, { "cell_type": "code", "execution_count": 57, "id": "6fa5e149", "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib/python2.7/dist-packages/numpy/core/numeric.py:320: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return array(a, dtype, copy=False, order=order)\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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pcph8GaF25dq4lHqJJx5VwLIjEZF1YMlRO0y+jFDCsQQ8y3niwu0LWodi81h2\nJCKyDjzpqB0mX0Zi6VEdcq8XAnJXvlh2JCJSF086aofJl5ECnAMQncwTj0rpuPJFRGQVWHbUDpMv\nI9V1rouYm1z5UuJRAsUN90RE2tIb9Dh78ywv1NYIky8jceVLOdOTLx0guPJFRKSWy2mX4VzKGWWL\nl9U6lCKJF2sbqU7lOriYehHZ+mw4OThZ/Pknk04iMjESmfpM1KpYC+1qtEMpp1IWj0MJYRAwQJKd\n8QtJAlh2JCI7cOPeDYTFhSElIwUuZVzQtnpbuJV1s3gcLDlqiytfRirpVBIe5TwQezvWos8NTwhH\n8x+bI2R1CPZe2YtTyacwdf9UeM7xxOdhn+NB9gOLxqOEIccAAfmXt7LsSES27lLqJfT/tT/8v/XH\n2ui1OHfrHFafXo26C+ti4IaBSM5Itmg8TL60xZUvGeq71MeppFMWq5F/fehrzDo0C3O6zEG/uv3g\noHN4/LVLqZfw8c6PEfRDEH7r9xv8qvhZJCYlcle+dHAofOhTDNBx5YuIbNaa02vw7p/v4v0W7+PH\nkB9RpliZx19Lz0zH1P1T0eD7Bvj9td/RwqOFRWKKTolGd5/uFnkWPU/xyldoaCj8/Pzg6+uLGTNm\nPPf1lStXokGDBqhfvz5at26NkydPKn2kZgKrBuJU8imLPGtK2BQsOb4EkcMjMSBwwFOJFwDUqlgL\na19di/dbvI/gn4IRkRhhkbiUEAZh8soXTzsSkS2aGz4XH+34CDvf3IlP2376VOIFAOWKl8P0F6dj\nScgS9FzdE/uv7LdIXFz50pai5Euv12Ps2LEIDQ1FTEwMVq9ejTNnzjw1platWti3bx9OnjyJSZMm\nYcSIEYoC1lJg1UCcTDJ/8rg8ajl+jvoZYYPD4FneM99xkiRhWONhWNxzMXqu7mn1fcgMOYbcVSyZ\nBHQQepYdici2/HD0B8w7PA8H3j6ABq4NChzb3bc7Vr2yCn3X9zV7Q+9sfTYu3L5gExUTe6Uo+YqI\niICPjw+8vLzg5OSE/v37Y9OmTU+NadmyJcqXLw8AaN68ORISEpQ8UlP1XeqbfeUrJiUGE7ZPwNbX\nt6Jq6apGvSakTghmd5qNHqt64Nb9W2aNTwmTV74krnwRkW3ZeWkn/h32b2wfuB3Vy1c36jWdvDth\nYruJ6Le+n1mvs4u9HQvPcp4o6VTSbM+ggilKvhITE+Hp+b+VGQ8PDyQmJuY7fsmSJeje3XZrzLUq\n1kJKRgrpQa+BAAAgAElEQVTSM9PNMn+2Phtv/v4mpnacKntf2ZsN3sSrAa/i9Q2vwyCsc5WIZUci\nKgri78Rj4IaBWPXKKvhW9pX12jFNx6Ba2Wr4Yu8XZoqOJUdroGjDvSQZ/410z549WLp0KQ4ePJjn\n1ydPnvz418HBwQgODlYSmlk46BwQ4ByA08mn0cqzlerzfxv5LSqVrIThjYeb9PppHaeh3bJ2+C7y\nO4xpNkbl6JQz5JjSaOKfDfc87UhENkAIgWFbhmFM0zFoX7O97NdLkoQfQ35E4HeBGFh/oFlKg0y+\n5AsLC0NYWJhq8ylKvtzd3REfH//44/j4eHh4eDw37uTJkxg+fDhCQ0NRsWLFPOd6MvmyZoEugTiV\ndEr15Cs5Ixlf7f8K+wbvk5XUPslR54glIUvQdllbvFT7JdSoUEPVGJXKXb0y5b1JbLJKRDbh56if\nkZyRjI/bfGzyHK5lXPFpm0/xXuh7CH0j1OTvCfk5nXwar9V9TdU57d2zi0JTpkxRNJ+ismNQUBBi\nY2MRFxeHrKwsrF27FiEhIU+NuXr1Kl555RX88ssv8PHxURSsNahftT5OJqu/6f6r/V/h9cDX4e/s\nr2gef2d/fNDyA4zYOgLCyhIWoTexz5fEPl9EZP2u372Oj3Z8hGW9liluxj222VhcTr2M3Zd3qxTd\n/0QlRRV6AIDMS1Hy5ejoiAULFqBLly4ICAjAa6+9Bn9/fyxatAiLFi0CAHzxxRdITU3F6NGj0ahR\nIzRr1kyVwLXyaOVLTQnpCVgRtQKftPlElfk+bPUhUjJSsOLkClXmU0vuni/Tyo7c80VE1m5c6DiM\naDICDV0bKp7LycEJn7/wOSbtmaTqD9J3M+/ixr0b8K0kby8aqUsSVrA8IkmS1a3S5CclIwW1F9TG\n7Y9uq7YUPO7PcSjmUAyzO89WZT4AiEiMwCtrX8G5sedQulhp1eZVIvXibUi+3qhgSJX1ugRHLyAs\nDB5tvMwSFxGRUvuv7Mebv7+Js2PPooRjCVXm1Bv0CPwuEHO7zkVn786qzHko/hDeC30PkcMjVZmv\nqFKat/B6IZmcSzujhGMJJKSr0zLj9oPb+OXkL5jQcoIq8z3SzL0Z2lRvg7nhc1WdVwmTrxdi2ZGI\nrJgQAh/u+BBfdfhKtcQLyD3k9VHrj/D131+rNufJpJNo4MKSo9aYfJlAzU73i44sQkidEFQrW02V\n+Z40teNUzAmfY/E7w/Lz6HohuVh2JCJrtj5mPXIMORgQOED1uQfUG4BTSadwOvm0KvNFJUWhvkt9\nVeYi0zH5MkF9l/qqdLrPMeTg28hv8X6L91WI6nm1KtbCmw3exJS9yk5lqMXUPl887UhE1iozJxOf\n7PoEszrNgk5S/1tqccfieKfpO5h3eJ4q80XdiOLKlxVg8mUCtVa+/jj/B2pUqGHWUycT207E2tNr\ncTn1stmeYazc044mrHxJOpYdicgqLT2+FL6VfNGhZgezPWNY42FYH7NecYNvgzDgVPIprnxZASZf\nJlBr5WvR0UUY2WSkChHlr3KpyhgZNBIzD80063OMIQwCwoRDCgK2cyCDiIqObH02ph+cjs9f+Nys\nz3Et44qONTti1alViua5nHoZFUtURMWSeffbJMth8mUCf2d/XLh9QdHdWwnpCTiceBh9A/qqGFne\nxjcfj7Wn1yIxPf+rnyzB1A33kCQIrnwRkZVZcXIFfCv5oqVnS7M/a3jj4fjx2I+K5jiZdJKrXlaC\nyZcJSjiWgFcFL5y7ec7kOdaeXovefr0tcrGpc2lnDGk0BLMOzTL7swokFGy458oXEVmRHEMOph2Y\nhkntJlnkeS/WehEJ6QmIvRVr8hxsrmo9mHyZSGnpcfXp1RhQT/2TMfn5sOWHWB61HEn3kiz2zGc9\ne72QEAKJ6YkITwhHeEI4rt29lneSJUkATzsSFSk5hhzE3orFwasHceTaEdx5eEfrkJ6yLnodXMu4\nol2NdhZ5noPOAf3q9sPq06tNnuNk0knUr8qVL2ug6G7HokzJpvvYW7FISE9Aey/5l66ayq2sGwYE\nDsA3h7/B1I5TLfbcJxlyDNBJEq6kXcG8iHlYF70OmTmZ8KrgBQGBuLQ4lClWBn0D+uKdpu/Aq4IX\ngH/2fOlZdiQqCvZd2YfvjnyHP2P/RMWSFeFaxhUPcx4i9lYs/J398Vb9tzC08VCUciqlWYxCCEw7\nMA2zO81W/d7FggyoNwBvb34bk9pNMum5UUlRmv37T0/jypeJlKx8rT69Gv3q9oODzkHlqAo2ocUE\n/HDsB2RkZVj0uY9k5jxETrF0NF7cGDpJh78G/oXkfyUjYngEIodHIvnDZGzuvxkGYUCTxU3wwV8f\nICMrA0LSceWLyM7F3opF5xWdMXTzULT2bI1zY8/h8nuX8ffQv3F85HGkfZyG6R2nY0/cHvjO98Wv\nMb9qFuuuy7sghFCt67yxWni0wMOch4hKipL92kfXCvlUsv07lu0Bky8T1Xepb9L/AEIIi5ccH/Gu\n5I221dvi56ifLf7sy6mX8c6eVyAccnB69GnM6jTruUvEJUlCoEsgZneejZh3YpCckYyGixpC75DJ\nJqtEduznEz+j1dJW6O7bHTHvxGBss7FwKePy1BhHnSM61uqIDa9twNpX1+Kz3Z9h+JbhyMzJtHi8\nc8PnYnyL8RZd9QJy/43sX6+/SaXHU8mnEOAcAEcdC17WgMmXiWqUr4H72feRkpEi63VRSVF4kP0A\nLTxamCmygk1oOQFzwufAICxXxou6EYU2y9qgi/vL0D2sCreyboW+xqWMC1a8vAL/af8fZJa+iMik\n3RaIlIgsSQiBSXsm4Yt9X2Df4H0Y32I8nBycCn1dm+ptcGT4Edy6fws9VvXA3cy7Fog21/lb5xF5\nLRJvBL5hsWc+aUC9AVhzeo3sf8N50tG6MPkykSRJaOjaECdunJD1unXR69C/Xn+L/8T0SGvP1qhY\noiK2nt9qkeedSjqFLr90wZwuc9Cn1mDZpx1fq/canO77YMm5LzUtMxCRuvQGPd7a+BZ2XtqJ8KHh\nz62EF6Zs8bJY33c9alasiR6reuB+9n0zRfq0eYfnYUSTERY5qZ6XwKqBKO1UGocTDst6XVQSO9tb\nEyZfCjR0bYjjN47Les2W81vQ26+3mSIqnCRJmNBygqoXtebn6p2r6LayG+Z0mYN+dfs9d9rRWDp9\naXxUbwHGbhuLNafXqB8oEVmUEAKj/hiF63evY/dbu+Fc2tmkeRx0Dlj00iJ4VfBC/1/7m31FP/VB\nKladWoXRQaPN+pyCSJKE3n69sTVW3g/QvFbIujD5UqCRayNZK19X0q4g6V4SmlZrasaoCtfHvw8u\n3r6oSpf+/GRkZaDXml54r/l7jy+bNegNMJhw95lB0qF6SV/seHMH3gt9D3su71E7XNWkPUzDwasH\nsfHsRmw9vxXHrh/Dg+wHWodFdi4lIwX7r+zHprObsPX8Vhy/flxRE2hz+2z3Z4i6EYXfX/td8QqS\nTtJhScgS3H5wG//Z9x+VIszbkuNL0KN2D1QrW82szylMD98esqoXvFbI+nDnnQINXRti2oFpRo//\nI/YPdPPtZvFTjs9ycnDCiCYjsDByIb5/6XuzPGPCXxMQ4ByAD1t9+L9Pmnqx9j99vgJdArHqlVXo\n/1t/HBhyAL6VfdULWIHUB6lYcnwJVp9ejfO3ziPAOQAupV2gF3okpCfg4u2LaOHRAm81eAuv1X0N\nxR2Lax0y2YEb927gx2M/Ym30WsTfiUeAcwAql6oMvUGPq3eu4nLaZbT3ao/BDQejt19vq9lo/f2R\n77HhzAYcePsAyhYvq8qcTg5OWN93PYJ+CELTak3RzbebKvM+KceQg/kR87Gh3wbV55arhUcLJKYn\nIv5OPDzLexY6ntcKWSFhBawkDNmycrJEyf+UFPcy7xk1vtsv3cTa02vNHJVxrqVfExWmVxBpD9JU\nn3vjmY2i5tya4s7DO099PnZztLhYrI7s+U6VbiZO/fD344+/j/xe1JlfR6Q+SFUcqxIPsh+I/+z9\nj6g0o5IYuGGg2HN5j8jWZz837m7mXbE+er3ovKKz8Pivh/gl6hdhMBg0iJjsQeqDVPF+6Pui4vSK\nYuSWkeLg1YMiR5/z3Li0B2nil6hfRKslrUTt+bXFprObNIj2aeHx4cJ5prM4f/O8Webff2W/qDqr\nqriSdkX1uddHrxdtlrZRfV5TvfHbG+K7yO+MGrshZoPosbKHmSMqWpTmLdbxo5CNcnJwgr+zP04l\nnyr09GJGVgYOXD2AVX2UXYyqFreybujs3RnLo5bj3ebvqjbvjXs3MHLrSPzW7zeUK17u6S8aTLte\n6Nk+XyODRuJU8ikM2zwM6/uu1+TwQtSNKLy+4XX4VvJFxLAIeFfyzndsmWJl8GrAq3g14FWEJ4Rj\n5NaRWH5yOb7v8T1qVqxpwajlSclIwY5LOxCRGIHLaZdxP/s+SjmVgmc5TzRxa4LO3p3hXs5d6zCN\nJoTAiRsnsPvybpxOOY0b925Ab9CjYsmKqFO5Dlp7tkawV7BVr0zuvrwbb/3+Frr7dseZMWeea8fw\npPIlyuON+m/gjfpvYPuF7RgXOg6rTq3CopcWoXyJ8haMOldKRgr6/doPP/T8wWyr1m2qt8G7zd7F\nqK2j8Mfrf6j6b8O3kd/i3Wbq/Vup1Eu1X8LKUysxKmhUoWOP3ziORm6NLBAVGYt7vhQy9sTj7su7\n0aRaE1QoUcECURlnTNMxWHhkoWr3JgohMHzLcIxoMgKtq7d+/usGkVtClE0CnolxdufZuHD7AhYf\nXWxitKbbeHYjXlzxIj5p8wl+f+33AhOvZ7XwaIEjw4+gg1cHNP+xOf66+JcZIzVNZGIkeq/p/biR\npXtZdwxqMAj/avUvDG4wGN4VvbH94nbU/74+Oi7viO0Xtlv13Zv3s+9j8dHFCPwuEH3X98WltEto\n5dEKY5uOxQctP0BI7RAYhAFf7vsSbl+74d0/30VcWpzWYT8lx5CDibsnYuCGgVjWaxkW91xcYOL1\nrC4+XXBi5AlULFkRLZe0xMXbF80Y7fMMwoA3NryB1wNfRy+/XmZ91ketP0Li3USsOqXeD7pnUs7g\n7M2zmh6WelYX7y7YG7fXqFOex64fQ2PXxhaIioymwuqbYlYShknmH54vRmwZUei4EVtGiNkHZ1sg\nIuMZDAZR99u6YtelXarMt+nsJuG3wE9k5mTm+fVz66PE+eJ1Zc8bVbaViPp2/3OfP5NyRlSZWUWc\nTjote05TGAwGMX3/dOHxXw8RmRipeL69cXuF62xXMffvuVZRhrxw64LovrK7cP/aXcw/PL/QcvrD\n7Idi5cmVos78OiL4p2ARkRBhoUiNYzAYxKqTq4TbbDfRc1VPsfPizkJ/n6+mXRUf7/xYVJ5RWfx7\nz79FRlaGhaLN3/2s+6LX6l6iw88dxI27NxTPt+DwAuEyy0Xsi9unQnTG+Sb8G9Hyx5Z5luXNITIx\nUrjMchHJ95JVme+9P98Tn+36TJW51NRuWTux9dzWQse5zXYTcalxFoio6FCat1hF1mPLydf+K/tF\nsx+aFTjGYDAI96/dxdmUsxaKyngLIxaKV9a+onie+1n3Rc25NcWOizvyHXN27QlxrkSg7LlPlGsj\nTszP+xvFkmNLRODCwHwTPjV9ufdLUffbuiLhToJqc15OvSzqfltXTNw9UbMEzGAwiO8jvxdVZlYR\nsw7OEg+zH8p6fbY+W/xw9AfhMstFfL7nc4t9gy1I/J140WVFF1H/u/ri7/i/C3/BM66mXRX91vcT\nXnO9THq9WtIepIl2y9qJ/r/2V/Xv+PYL20WVmVXEgSsHVJszPzHJMaLKzCoi9las2Z/1pA//+lC8\nueFNxfNkZGWIyjMqW2XyMvPATDF66+gCx1xLvyYqzahkFT/g2RMmXxpLf5guSn1VqsBvONHJ0aLG\nnBpW+Zc//WG6qDi9ooi/E69ons/3fC5eXfdqgWPOrjkuzpaoL3vuE+XaihPz9ub5NYPBIF5a9ZL4\nfM/nsueV4+tDXwvfeb7i+t3rqs+dfC9ZBC4M1CQBu5d5T7y85mXRZFETEZMco2iuxPRE8eLyF0Wr\nJa1UTVDl2n9lv3Cb7Sa+3PulyMrJUjTXxjMbhfNMZ/FtxLcW/7O58/COCFocJMb8MUboDXrV5w+N\nDRXOM51VWcXNT1ZOlghaHGT0xnA13c28K9xmuylekV16bKl4adVLKkWlrpM3Tgrvb7wLHPPH+T/E\ni8tftFBERYfSvIV7vhQqW7wsqpWthvO3zuc7Zvfl3ehYq6NmXe0LUrZ4Wbwe+DoWHV1k8hxxaXFY\nELEA/+383wLHGXIMMKXJqpAkCH3ezRMlScL3Pb7HwsiFZutbtuz4MsyPmI9db+2CaxlX1ed3Lu2M\nXW/twqazm/DF3i9Unz8/SfeS0P7n9ihbvCwODT0ku8P4s6qVrYbtA7eju093tFraCtHJ0SpFarzF\nRxejz7o+WNZrGSa2m2jUVTUF6eXXCwffPojvjnyHUX+Mgt6gVynSgj3MeYjea3qjiVsTzO82HzoT\n+uMVpotPF/zQ8we8tOqlAv/9UmLWoVmoXLIyRjYZaZb5C1KmWBl80f4LfPDXB4r2JH5/9HuMalL4\npnYt1K1aF+mZ6biSdiXfMceuH0NjN+73sjZMvlTQyLURjl0/lu/Xd1/ejQ5eHSwYkTyjg0ZjybEl\nyNZnm/T6z8M+x5hmYwrvNyOESU1WhaQr8GJt93LumP7idLy96W3kGHJkz1+Qg1cP4v92/h/+fONP\no/rpmMq5tDN2vrUTy08ux7Ljy8z2nEfi0uIeX2T8U6+fUMyhmCrz6iQdPmv3Gb7q8BU6LO+AfVf2\nqTKvMWYcmIEZB2fgwJAD6OLTRbV5fSv74u+hf+P8rfN4a+Nbqv8de1aOIQcDfhuAqqWr4tvu35r1\nh7Zefr3wZfsvEbI6BHce3lF17thbsfjv3//FopcWafaD55CGQ5D2MA0bz2406fXHrh9D0r0kdPXp\nqnJk6tBJOrSv2R574vJvPM3N9taJyZcKgqoF4ej1o3l+TW/QIywuDO1rtrdwVMarW7UufCr5YPO5\nzbJfG50cjdALofig5QeFjjXoTVv5AvJf+XpkSMMhqFiyIuYdnmfC/HmLvxOPvuv74qfeP8Gvip9q\n8+anaumq2Pb6Nnyy6xPsvLTTbM+JvxOPDj93wPst3sfk4Mlm+cY4sP5ArHxlJfqs64P9V/arPv+T\nhBCYHDYZy04sw77B+8zSxqBMsTLY9vo2pD5IRb/1/Uz+QcUY/9rxL9zNvIvlLy+3SEPm4U2Go2Ot\njnhjwxuqreyJf64P+qztZ6hRoYYqc5rCQeeA2Z1n46OdH5nU8f/7I99jRJMRmjfGLkgHrw7YfXl3\nvl/nypd1YvKlgqBqQThy7UieX4tKioJLGRfNr6MozKigUfj+qPxu95P2TMJHrT56vqdXXgymr3w9\n22riWZIkYWH3hZh2YBoS0xNlP+NZmTmZeGXdK3iv+Xvo7ttd8XzGqlOlDtb1XYfXf3sdZ2+eVX3+\n63evo+PyjhjTdAzGNhur+vxPerHWi1jdZzX6rOsj+xJgOabun4rfzvyGvYP3mrXvWEmnktjYfyOy\n9FkYunmoWe4RXHp8Kf44/wfW912v2mqkMeZ2mYu7WXcxee9kVeZbHrUcaQ/TVO0haKrO3p1Rs0JN\n/HTiJ1mvu/PwDtbHrMfbjd42T2Aq6VAzN/nKq7R66/4t3H5wW1Y7HLIMJl8qaOzWGCdunMjzp8bd\nl3ejY82OGkQlTx//Poi6EYXYW7FGvyYiMQIRiRF4p+k7Ro0XwrQ+X0KSCiw7PuJb2Rejgkbhg78K\nX4UrzMQ9E1GtbDV81PojxXPJ1a5GO0zrOA0vr30ZdzPvqjbvvax76LayG96s/yY+aKX898gYL9Z6\nEct6LUPImhCcSjql+vw/HvsRS44vwV8D/5LV98pUxRyKYV3fdbhw+wI+3vmxqnMfij+Ej3d+jE39\nN1n8GhgnByese3UdlhxbgrC4MEVzpT5IxUc7P8LilxZbzZVGk4MnY+r+qbJWv345+Qs61epkln2e\navKp5AOdpEPs7ef/7X7UXNUcewZJGf6JqKBCiQpwK+OW50rFrsu70KGm9e73eqS4Y3EMbjgYi48Z\n37R00p5JmNRuktEX44ocg2l3OxpRdnzkkzaf4HDiYey6tMuE5+TacXEHVp9ajSUhSzTbqzK08VC0\nqd4Gb29+W5UGpnqDHgN+G4Cm7k0xsd1EFSI0Xo/aPTCnyxz0XN0T1+9eV23ezec24997/o3tA7fD\nraybavMWppRTKWwZsAVbz29VrcydkpGCfuv7YVmvZYoPPpjKpYwLlvZaijd/fxO3H9w2eZ4pe6fg\nZb+X0aRaExWjU6aVZyvUrlwbP5/42ajxQgh8d+Q7jA4abebIlJMkCR1qdsjz3zyWHK0Xky+V5FV6\nzNJn4eDVg3ihxgsaRSXPiCYj8NOJn/Aw52GhY49cO4KYlBgMaTTE+AcIkVtClMmYsuMjpZxK4Zuu\n32DMtjHIzMmU/ayUjBQM3jQYP/f+GVVKVZH9ejXN7zYfcWlxmBM+R/FcH+74EPez72Nh94WaJJSv\nB76OoY2GImRNCDKyMhTPdzLpJIZtHobNAzZrcsF65VKVse2NbZi6f6qiRB/I7f4+aOMgDKw/ED1q\n91ApQtN09emKPv59MHzLcJOS/piUGKw8tRJftv/SDNEp8/kLn2PqAeNWvw7GH0SOIQfBXsHmD0wF\nHWp2wO645/d9cbO99WLypZKgakE4cv3p5CsyMRI+lXxQuVRljaKSx6eSDxq5NsJvMb8VOnbagWn4\nsOWHsval5JYOTSw7yvhG0LN2T/hU8jEpaRkXOg4D6g1Ax1ral4pLOJbAr31/xfQD03H0Wt4HOoyx\nImoF/jj/B37t+6vi1gtKTGw3EQHOARi0cZCi1bxb92+h95re+KbrNwiqFqRihPJ4VfDC6j6r8caG\nN3Ap9ZLJ83x96GukPUyzmoRl+ovTcf7WednX8wghMD50PCa2nQjn0s5mis50rau3hm8lXyyPWl7o\n2O+OfIeRTUZaZXugvLT3ao89l/c8tw/x6PWjXPmyUky+VNLErclzK1974vZY9SnHvIwKGlVoz68z\nKWdw4OoBDGs8TNbcQm+AMOUfswL6fOU9XMK8bvMw69AsJKQnGP26ree3IjIxEl+0t1yvrcLUqFAD\n87rNw4DfBuBe1j3Zr49OjsaEvybgt36/WXwf0bMkScLilxbj6p2rmH1otklz5Bhy0P+3/ng14FUM\nCBygcoTyta/ZHp+2/RS91/Q26o69Z4UnhGP237Oxus9qTRPjJ5VwLIGlIUsx4a8JSLqXZPTrtpzf\ngoT0BKP3gGphUrtJmHFwRoGnOlMyUvDH+T8wqOEgC0amjGd5T1QqWempfZW3H9xG0r0ki5zUJvmY\nfKmkkVsjnEw6+dQR9ANXD6Bd9XYaRiVfz9o9ceH2hQIbZM44OAPjmo1D6WKl5U2upOxoxIb7J9Wq\nWAujg0YbvSk6PTMdo/8YjcU9F6OUUynZMZpT/3r90bp6a4wPHS/rdfey7qHv+r6Y+eJMBLoEmik6\neYo7Fsev/X7F139/bdLG7o93fgydpMO0jtPUD85E7zZ7F4EugXh/+/uyXpf6IBUDfhuARS8t0rQd\nQ16aujfFoAaD8O6fxp1WzMzJxITtEzC361yrSSLz0qZ6G1QuWRmbzm3Kd8xPJ35Cb7/eqFSykgUj\nU65tjbY4GH/w8cdHrh1Bk2pNrLpNRlHG5Esl5YqXQ/Xy1RGTEgMgd4Pz3wl/o5VnK40jk8fJwQnD\nGg/Ld/XrStoVbDm/BWOajZE9t6llR0Ayes/Xkz5u8zHC4sIQnhBe6NhPd32Kzt6drfZwxLyu87D3\nyl6sj15v1HghBEZtHYUWHi3k7cuzgOrlq2PFyyvw+m+vy2oLsvrUamw8uxGr+6y2qm8okiThux7f\nYdelXVgXvc7o143ZNgY9fHugt19vM0ZnuinBU3Dixgn8fub3QsfODZ+LulXrorN3ZwtEZjpJkvCv\nVv/CrEOz8ix9G4QBi44usomN9s9q7dkaB64eePxxRGIEmrk30zAiKgiTLxU9uen+dPJpuJZxtcq9\nD4UZ1ngYVp5amefG6AWRCzCowSBUKFFB9ry5ZUcTVr50Olllx0fKFCuDqR2n4r3Q9wrsyXTw6kFs\nOLMBszuZVgqzhLLFy2LVK6swZtsYXL1ztdDxPxz7ASeTTmJB9wUWiE6+Tt6dMKbpGPT7tZ9RG6Av\n3r6IcaHj8Gu/X61yRaJc8XJY8+oajN02FpdTLxc6fl30Ohy9fhQzO820QHSmKelUEj/0/AHjQscV\nWPK+fvc6Zh2aha87f23B6EzX2683bt6/+dQq0SM7L+1E2eJlbTJpae3Z+qn3FJEYgWbVbO99FBVM\nvlQU5Pa/TfcH4w+itWdrjSMyTfXy1dHaszXWRq996vP3su5h2fFleLeZiY0ThTBtz5eJK19Abqd1\nAFh5cmWeX8/MycSwLcMwr9s8zfdEFaape1OMbzEeQzYNKTCZPHvzLD7b/RnW911vdSXUJ33S9hNU\nKlkJn+76tMBxWfos9P+tP/7d7t9o6NrQQtHJF1QtCJ+0+QT9f+tfYAf863ev490/38WKl1dY9Z8P\nALzg9QKCvYLx5b78DwN8susTDGs8DD6VfCwYmekcdA6Y0GICZh2a9dzXvj+Se4+jrWy0f1LtyrVx\nP/s+EtITIITgypeVY/KloqBqQYhMjASQm3y1qd5G44hMNypoFL4/8nTH++VRy9G2RlvUrFjTpDmF\nidcLFXSxdmF0kg5zu8zFJ7s+yfOn97nhc+Fd0Rt9/PuYNL+lfdT6o9yWEZEL8/x6tj4bAzcMxJft\nv0SdKnUsHJ08OkmHZb2WYW30Wmy/sD3fcZ/t/gxuZdzM3pFfDeNbjIdzKWdM3JN3LzUhBIZvGY4R\nTWLGkpkAAA9ZSURBVEbYzDfGWZ1mYenxpY+3VDwpIjECOy7twGdtP9MgMtMNbjgY4QnhT10onpie\niLC4MLwe+LqGkZlOkqTc1a+rBxGfHg9JkuBRzkPrsCgfTL5U1MitEWJSYvAw5yEOXrXdlS8A6OLd\nBckZyY9bHBiEAfMOz8P45vI2fT9JGEzfcK+kNUFLz5Z4wesFzDg446nPJ6YnYuahmZjbda7N/KTr\nqHPEz71/xuSwyXneRvDlvi9RtXRVjGwyUoPo5KtSqgqW916OIZuG5HmybvuF7Vhzeg2W9lpqE39G\nkiRhWa9lWBG1Is9LxZccX4Jrd69hUrtJGkRnGtcyrpjUbhLGbhv71P+HBmHAuD/HYWqHqShbvKyG\nEcpX0qkkhjUehgUR/yvL/3jsR/Sv19/m3suTWnu2xoH4A49XvWzh/5miismXiko5lYJfFT9sObcF\nGdkZqF25ttYhmcxB54ARTUY83ni//cJ2lHAsgXY1FJzeNLXsKEmyTzs+a3rH6VgYuRBX0q48/ty/\ndvwLo4NG20y55JHalWvj3y/8G4M2DnrqyHx4QjgWH12saWd+U7Sv2R5DGg3B4E2Dnyqn3rh3A0M2\nDcGKl1do3vBWDufSzlj00iIM3jj4qeuhLqdexie7PsHyl5db9N5GNbzT9B2kPkzFmtNrHn9u5cmV\nEBB4s8GbGkZmutFBo/HLyV+QnpmOHEMOfjj2A0YFjdI6LEVaV89d+eJ+L+unOPkKDQ2Fn58ffH19\nMWPGjDzHjBs3Dr6+vmjQoAGOHz+u9JFWrYVHC8wJn4NWnq1s6htgXoY2Gor1Metx5+EdfHP4G4xv\nMV7RezK17AhIEAZllxh7lvfEuGbj8H87/w8AsO/KPhy4egCftPlE0bxaGdtsLEo4lnjcLysjKwNv\n/v4mFvZYaNGrdtQy+YXJSH2Qim/CvwGQu6ry1u9vYWjjoTbTZfxJPev0RIeaHTDhrwkAct/P4E2D\n8VGrj1Cvaj2No5PPUeeIhd0X4sMdHyI9Mx13M+/i410fY17XeTZ7b6BHOQ908u6En078hK3nt6JG\nhRqo71Jf67AUaeLWBOduncOuy7tspqxdVCm69VSv12Ps2LHYuXMn3N3d0bRpU4SEhMDf/393k23b\ntg0XLlxAbGwsDh8+jNGjRyM8vPCj/7aquXtzfHfkO8x80XpPMRnLpYwLOnt3xsQ9E3H8xnFs7L9R\n0Xy5F2ubdtpR6coXAPyr9b/gt8APe+P24t0/38XszrPl9yqzEjpJh6W9lqLpD03R3bc7Fh5ZiNae\nrfGK/ytah2YSJwcnrOqzCs1/bI5gr2DsuLQD97Pv4/MXPtc6NJPN6TIHDb5vgC3ntiD2diwMwoAJ\nLSdoHZbJWnq2RBfvLvhy35dw0jnhxVovorlHc63DUmRcs3EYvGkwalaoiVFNbHvVC8jto9fYrTEO\nXD2g6e0PVDhFyVdERAR8fHzg5eUFAOjfvz82bdr0VPK1efNmDBqU2ym4efPmSEtLQ1JSElxcXJ6a\n68wvpl+fYk087pdB42tA7ROVceay7b+nfmkdMPXUKLxbfRgur8m/8aox7p+IRSkTTztmnbmoyt+R\nyWIkPpvZHQ3KBKBemVo4c9y2/4y+kEbhg/+8CEnSYWrjNTb//9EMh/H4eFp3ZBsyMa3hcsSuitI6\nJEW+dvwUcxcMhl4Y8GWDn3B+1QmtQ1JkeOZr+PjYawCAaXbw962iKI76cY64+fAw6hsm48wp234/\nANAhwRvlU6/ixm+XcEPrYFRQwc8VbkHuWoehOkXJV2JiIjw9PR9/7OHhgcOHDxc6JiEh4bnk69sh\nPR//uqmuDJo52OamRzcAS0pVRLFfFgDCtsuOAOAPYEmpyij2MAIwHFM0V1UASc1DZL8uq2FTuOxc\nBRwo/M7JwrQA0KRUKThm3oekt41N6QV5AUCrkgIO2eXg8KPtrqo80hJAk5ICDjmV4LDUdle9HvED\nMKd4SUiiGByXWs+1VaaqAGBBsQoABByX2dYJx7xIAKY45cCgKw+nZSa20LEyfR0z0MdRDyweoXUo\nqojtNQxuq7VvehsWFoawsDDV5lOUfBm7/+fZk2p5vW5B9jUloZCN8C98yHOCN38A4AO1QyEiIitn\nyvcMcwgODkZwcPDjj6dMmaJoPkU7Jd3d3REfH//44/j4eHh4eBQ4JiEhAe7u9reESERERGQMRclX\nUFAQYmNjERcXh6ysLKxduxYhIU+XlUJCQrB8+XIAQHh4OCpUqPBcyZGIiIioqFBUdnR0dMSCBQvQ\npUsX6PV6DB06FP7+/li0KLc31MiRI9G9e3ds27YNPj4+KF26NJYtW6ZK4ERERES2SBJKWoerFYQk\nKepgTkRERGQpSvMW2+yOR0RERGSjmHwRERERWRCTLyIiIiILYvJFREREZEFMvoiIiIgsiMkXERER\nkQUx+SIiIiKyICZfRERERBbE5IuIiIjIgph8EREREVkQky8iIiIiC2LyRURERGRBTL6IiIiILIjJ\nFxEREZEFMfkiIiIisiAmX0REREQWxOSLiIiIyIKYfBERERFZEJMvIiIiIgti8kVERERkQUy+iIiI\niCyIyRcRERGRBTH5IiIiIrIgJl9EREREFsTki4iIiMiCmHwRERERWRCTLyIiIiILYvJFREREZEFM\nvoiIiIgsiMkXERERkQUx+SIiIiKyICZfRERERBbE5IuIiIjIgph8EREREVkQky8iIiIiC2LyRURE\nRGRBTL6IiIiILMjk5Ov27dvo1KkTateujc6dOyMtLe25MfHx8Wjfvj3q1q2LevXqYd68eYqCtTdh\nYWFah6AJvu+ihe+7aOH7LlqK6vtWyuTka/r06ejUqRPOnz+Pjh07Yvr06c+NcXJywpw5cxAdHY3w\n8HB8++23OHPmjKKA7UlR/UvL91208H0XLXzfRUtRfd9KmZx8bd68GYMGDQIADBo0CBs3bnxujKur\nKxo2bAgAKFOmDPz9/XHt2jVTH0lERERk80xOvpKSkuDi4gIAcHFxQVJSUoHj4+LicPz4cTRv3tzU\nRxIRERHZPEkIIfL7YqdOnXDjxo3nPv/VV19h0KBBSE1Nffy5SpUq4fbt23nOc+/ePQQHB2PixIno\n3bv380FIkimxExEREWmigPSpUI4FfXHHjh35fs3FxQU3btyAq6srrl+/jqpVq+Y5Ljs7G3369MHA\ngQPzTLwAZW+AiIiIyJaYXHYMCQnBzz//DAD4+eef80yshBAYOnQoAgICMH78eNOjJCIiIrITBZYd\nC3L79m3069cPV69ehZeXF9atW4cKFSrg2rVrGD58OP744w8cOHAA7dq1Q/369R+XFqdNm4auXbuq\n+iaIiIiIbMX/t3f+ME30YRz/lqSL0QAmQgolKSlFoh7XS4g44AI4GTBGBzDWQVkciSGEjYW/hoEQ\nJgKDLDARDLakGiE0OjRqGxMZJPFMWqyDjQOg5KA878S9Ane8CIV7+d3zmXp/hufT7/Xy5C6/p4d+\n8nX+/Hm8evUKnz9/RjgcRl5eHgCgqKgIL168AADU1NRga2sL8XgcsVgMsVhsT+M1OzuLiooK+Hw+\n9PX1HUHl/4/H40FlZSUURcHVq1cBHGxe2mnj4cOHKCwshCRJ+r79PHt6euDz+VBRUYFwOGxFyVnB\nyLuzsxNutxuKokBRFIRCIf2YKN5m8/xEz9zMW/TM19fXUV1dDb/fj0uXLqGjowOA+HmbeYueNwBk\nMhkoioKGhgYA4me9zW7vrGZNFrK5uUler5dUVSVN00iWZVpcXLSypGPF4/FQOp3esa+trY36+vqI\niKi3t5fa29utKC2rLCws0IcPH+jKlSv6PjPPT58+kSzLpGkaqapKXq+XMpmMJXUfFSPvzs5OGhgY\n2HOuSN6pVIpisRgREa2srFB5eTktLi4Kn7mZtx0yX1tbIyKijY0Nqq6upkgkInzeRMbedsh7YGCA\n7t27Rw0NDURkj/s50V7vbGZt6d8LRaNRlJWVwePxwOl0oqmpCdPT01aWdOzQrre8B5mXdtq4fv06\n8vPzd+wz85yenkZzczOcTic8Hg/KysoQjUZPvOZsYOQNGC8oEcnbaJ7f8vKy8JmbeQPiZ37mzBkA\ngKZpyGQyyM/PFz5vwNgbEDvvZDKJYDCIlpYW3dMOWRt5E1HWsra0+VpeXkZJSYm+7Xa79ZuXiDgc\nDtTX16OqqgojIyMA/n5e2mnFzPPbt29wu936eSJeA0NDQ5BlGY8ePdIfz4vq/ec8Pztlvu197do1\nAOJnvrW1Bb/fj8LCQv3Vqx3yNvIGxM67tbUVT58+RU7Ov+2CHbI28nY4HFnL2tLmy27zvd68eYNY\nLIZQKITh4WFEIpEdxx0Ohy2+k//yFOk7ePz4MVRVRTweh8vlwpMnT0zPPe3eq6uruHPnDgYHB3Hu\n3Lkdx0TOfHV1FXfv3sXg4CDOnj1ri8xzcnIQj8eRTCaxsLCAubm5HcdFzXu39/z8vNB5z8zMoKCg\nAIqimI6EEjFrM+9sZm1p81VcXIxEIqFvJxKJHd2jaLhcLgDAhQsXcPv2bUSjUX1eGoB956Wddsw8\nd18DyWQSxcXFltR4HBQUFOg3p5aWFv1RtGje2/P8AoGAPnbGDpkbzTG0S+YAkJubi5s3b+L9+/e2\nyHubbe93794Jnffbt2/x/PlzlJaWorm5Ga9fv0YgEBA+ayPvBw8eZDVrS5uvqqoqLC0t4evXr9A0\nDZOTk2hsbLSypGPj169fWFlZAQCsra0hHA5DkqQDzUsTATPPxsZGTExMQNM0qKqKpaUlfSWoCKRS\nKf3z1NSUvhJSJG8ymecneuZm3qJn/uPHD/11y+/fv/Hy5UsoiiJ83mbef/4LjGh5d3d3I5FIQFVV\nTExMoLa2FuPj48JnbeT97Nmz7P62s7Ys4JAEg0EqLy8nr9dL3d3dVpdzbHz58oVkWSZZluny5cu6\nazqdprq6OvL5fHTjxg36+fOnxZUenaamJnK5XOR0OsntdtPY2Ni+nl1dXeT1eunixYs0OztrYeVH\nY7f36OgoBQIBkiSJKisr6datW/T9+3f9fFG8I5EIORwOkmWZ/H4/+f1+CoVCwmdu5B0MBoXP/OPH\nj6QoCsmyTJIkUX9/PxHtfy8T2Vv0vLeZn5/XV/2JnvWfzM3N6d7379/PWtaHHrLKMAzDMAzD/D2W\nvnZkGIZhGIaxG9x8MQzDMAzDnCDcfDEMwzAMw5wg3HwxDMMwDMOcINx8MQzDMAzDnCDcfDEMwzAM\nw5wg/wBB//oArHl1iQAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "signal = (n>=100) * (n<110)\n", "transform = dot(F,signal)\n", "reconstructed = dot(inv(F),transform)\n", "\n", "plot(max1(signal))\n", "plot(max1(abs(transform)))\n", "plot(max1(reconstructed))" ] }, { "cell_type": "markdown", "id": "b44a737e", "metadata": {}, "source": [ "What happens if we apply the Fourier transform matrix $F$ twice?\n", "\n" ] }, { "cell_type": "code", "execution_count": 58, "id": "28c9ec2c", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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MsVjMy9QAAHmAtiPyQTKZVDKZHLXX8xS+gsGg0ul09nE6nVYoFBowbt++fVq+fLkSiYQm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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "double = dot(F,transform)\n", "plot(max1(double))" ] }, { "cell_type": "code", "execution_count": 59, "id": "559370ae", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "imshow(abs(dot(F,F))); gray()" ] }, { "cell_type": "markdown", "id": "703a3aec", "metadata": {}, "source": [ "(Inverse Fourier Transform)\n", "\n", "So, from $F \\cdot F$, we see that the Fourier transform is almost its own inverse, except for a reflection.\n", "\n", "The actual formula for the inverse discrete Fourier transform (IDFT) is\n", "\n", "$$x_n = \\frac{1}{N} \\sum_{k=0}^{N-1} X_k e^{\\frac{2\\pi i}{N} k n} \\quad \\quad n = 0,\\dots,N-1.$$\n", "\n", "Note the sign change and the normalization factor. Other than that, the formula is the same as for the regular disrete Fourier transform." ] }, { "cell_type": "markdown", "id": "f04b6e96", "metadata": {}, "source": [ "(Properties of the Fourier Transform)\n", "\n", "The Fourier transform has a number of important properties; you should know these by heart.\n", "\n", "The Fourier transform is linear:\n", "\n", "$$ {\\cal F}[a f + b g] = a {\\cal F}[f] + b {\\cal F} [g] $$\n", "\n", "The Fourier transform turns translations into multiplications with a complex number (and the other way around):\n", "\n", "$$ {\\cal F} [ f(x - x_0) ] ( \\omega ) = e^{ -2\\pi i x_0 \\omega} {\\cal F} [ f(x) ] (\\omega)$$\n", "\n", "The Fourier transform computes inverse scaling:\n", "\n", "$$ {\\cal F} [ f(ax) ] (\\omega) = \\frac{1}{|a|}{\\cal F} [ f(x) ] (\\frac{\\omega}{a}) $$\n", "\n", "The Fourier transform turns convolutions into multiplication:\n", "\n", "$$ {\\cal F}[f * g] = {\\cal F}[f] \\cdot {\\cal F}[g] $$" ] }, { "cell_type": "markdown", "id": "343623fe", "metadata": {}, "source": [ "Fast Fourier Transform\n", "=======================\n", "\n", "\n" ] }, { "cell_type": "markdown", "id": "89eeddfc", "metadata": {}, "source": [ "## Thomasson-Lanczos-Cooley-Tukey-Gauss Lemma" ] }, { "cell_type": "markdown", "id": "4a67e4ea", "metadata": {}, "source": [ "(DFT)\n", "\n", "Let's look again at the definition of the discrete Fourier transform:\n", "\n", "$$ X_k = \\sum_{n=0}^{N-1} x_n e^{-\\frac{2 \\pi i}{N} k n} \\quad \\quad k = 0, \\dots, N-1 $$\n", "\n", "We also wrote this as a set of dot products:\n", "\n", "$$ X_k = \\sum_{n=0}^{N-1} x \\cdot b_k $$\n", "\n", "where\n", "\n", "$$ b^{(k)}_n = e^{-\\frac{2 \\pi i}{N} k n} $$" ] }, { "cell_type": "markdown", "id": "e62b5e07", "metadata": {}, "source": [ "(Complexity)\n", "\n", "Or we can write it as a matrix multiplication:\n", "\n", "$$ X = F \\cdot x $$\n", "\n", "where\n", "\n", "$$ F_{kn} = b^{(k)}_n $$\n", "\n", "For a signal of length $N$, this takes $N^2$ operations.\n", "\n", "It turns out that we can compute this particular matrix product in time $\\log N$." ] }, { "cell_type": "markdown", "id": "de0ac5fb", "metadata": {}, "source": [ "(Thomasson-Lanczos Lemma)\n", "\n", "The key observation is the Thomasson-Lanczos Lemma, or the Cooley-Tukey Lemma. Gauss also knew this.\n", "\n", "The insight is that we can write the DFT $S$ of a sigal $s$ as the weighted sum of two half-length DFTs. In particular,\n", "\n", "$$S_j = S^e_j + e^{\\frac{2\\pi i j}{N}} S^o_j$$\n", "\n", "$$S_{j+\\frac{N}{2}} = S^e_j - e^{\\frac{2\\pi i j}{N}} S^o_j$$\n", "\n", "Here, $S^e$ and $S^o$ are the even and odd elements of $S$, respectively." ] }, { "cell_type": "code", "execution_count": 60, "id": "da538767", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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3JTP/jfn88x//ZMf2HQwYOACd7ux/ih0OB5WmSnJycqix1K41ZbPaMJYZyc/LR1Ubfjaj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\nEhpC9q5siouLOXnyJNOnT2fXrl1a82hSIj169GDbF9vIzc2lq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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,10); xticks([]); yticks([]); imshow(imread(\"Figures/fft-image.png\"))" ] }, { "cell_type": "markdown", "id": "4e06e7bf", "metadata": {}, "source": [ "This observation is easy to translate into a recursive function for computing the Fourier transform. Note that this function only works for input signals whose length is a power of two. \n", "\n", "For other kinds of input lengths, there are more complicated decompositions, or such signals need to get padded. For signals of prime lengths, there is no decomposition like this (i.e., we can only decompose the problem into subproblems whose lenghts are factors of the original length)." ] }, { "cell_type": "code", "execution_count": 61, "id": "7ade558e", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 2.00000000+0.j , 1.70710678+0.70710678j,\n", " 1.00000000+1.j , 0.29289322+0.70710678j,\n", " 0.00000000+0.j , 0.29289322-0.70710678j,\n", " 1.00000000-1.j , 1.70710678-0.70710678j])" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def myfft(s): \n", " N = len(s)\n", " if N<=1: return s\n", " Se = fft(s[::2])\n", " So = fft(s[1::2])\n", " e = exp(arange(0,N/2)*2j*pi/N)\n", " return r_[Se+e*So,Se-e*So]\n", " \n", "myfft(array([1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0]))" ] }, { "cell_type": "code", "execution_count": 62, "id": "b1cd3565", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Knzwbrupa6xTmOxQSiHAFoLfaFs5c+ZEnw1VqcqrSk9PV1N5kdynwCTpXAHrr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\nkXkkBJo+MdisbEZKEHvNQ3Vx47khKywLdQPmlwYvKy5jb9R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pL/pn4p9xqVKyK0DFlWth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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k = arange(256)\n", "signal = 1.0*(k>=100)*(k<110)\n", "transform = myfft(signal)\n", "plot(max1(signal))\n", "plot(max1(abs(transform)))" ] }, { "cell_type": "markdown", "id": "5e1fe7a4", "metadata": {}, "source": [ "# Fourier-Based Audio Filtering" ] }, { "cell_type": "markdown", "id": "2538e841", "metadata": {}, "source": [ "Let's do a simple Fourier-based audio filter. Let's try to filter out the high frequency components.\n", "\n" ] }, { "cell_type": "code", "execution_count": 63, "id": "34d3dd7c", "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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HrFwJNDbOfow5mUI0Pydv2aL+fP/7dr5flEUZAHzkI8D996vbmj7knZXx8TTFND+Wy2Xg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\nABaglAEAAFjgb7s/FBa4X5xXAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mix = data32+data128\n", "plot(mix[:100])\n", "play(mix,r=10)" ] }, { "cell_type": "markdown", "id": "c5d1483b", "metadata": {}, "source": [ "We can see the two components in the frequency domain.\n", "\n" ] }, { "cell_type": "code", "execution_count": 64, "id": "fe7ade7f", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Lv8QFF1xQ/LmLx9UHeQ8sRm/Xrl2xZMmSuPDCC2Px4sUR8e7/29m2bVtERGzd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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(abs(fft(mix)))" ] }, { "cell_type": "markdown", "id": "76722fc0", "metadata": {}, "source": [ "Now let's zero out the two high frequency peaks.\n", "\n" ] }, { "cell_type": "code", "execution_count": 65, "id": "1428d261", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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11lvjN7/5TUydOjWeeeaZuPXWW0dirQAA2TvqbcG1a9ce9vENGzYkX0yEY1EAoGzZvUI7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\nAAmJKwCAhMQVAEBC4goAICFxBQCQ0P8Ak4RRbSP5c6QAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "transform = fft(mix)\n", "transform[120:130] = 0\n", "transform[-130:-120] = 0\n", "plot(abs(transform))" ] }, { "cell_type": "markdown", "id": "f1437ee4", "metadata": {}, "source": [ "We can now see the result of the filtering operation.\n", "\n" ] }, { "cell_type": "code", "execution_count": 66, "id": "e8385274", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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LlwL/9E/AyIj2Z9AAeBstaXIznLJEAvjnfwbOPx/4h38A1l2TwOplHSgUgJUr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\ne+5R/F0ZOzzZ6YWlTqvDiQQikCRpSjZPLfIxNf1Jb3b6yH9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MLmG6Yddad7QboUCoaL1A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\nTgAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(real(ifft(transform))[:100])\n", "plot(mix[:100])" ] }, { "cell_type": "markdown", "id": "d9c5cc09", "metadata": {}, "source": [ "The original sound...\n", "\n" ] }, { "cell_type": "code", "execution_count": 67, "id": "b9bae4ff", "metadata": { "collapsed": true }, "outputs": [], "source": [ "play(mix,r=10)" ] }, { "cell_type": "markdown", "id": "11a7862b", "metadata": {}, "source": [ "The filtered sound...\n", "\n" ] }, { "cell_type": "code", "execution_count": 68, "id": "4b05189d", "metadata": { "collapsed": true }, "outputs": [], "source": [ "play(real(ifft(transform)),r=10)" ] }, { "cell_type": "markdown", "id": "2a5316b9", "metadata": {}, "source": [ "Removing Noise in the Fourier Domain\n", "=====================================" ] }, { "cell_type": "markdown", "id": "1a40158b", "metadata": {}, "source": [ "Let's generate a signal corrupted by an interfering sound.\n", "\n" ] }, { "cell_type": "code", "execution_count": 75, "id": "af4e9bae", "metadata": { "collapsed": false }, "outputs": [], "source": [ "test = numpy.fromfile(\"test.raw\",\"int32\")[::2]\n", "test = test*1.0/amax(abs(test))\n", "noise = test+2*sin(arange(len(test))/5.0)\n", "play(noise)" ] }, { "cell_type": "markdown", "id": "22801664", "metadata": {}, "source": [ "We perform a Fourier transform and look for the spectral location of the interference.\n", "\n" ] }, { "cell_type": "code", "execution_count": 76, "id": "49c298e6", "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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vnlZcXKzevXurb9++WrJkSeJKDQAAkMYiBrBrrrlGixcvDhhXUlKioqIirVu3TiNHjlRJ\nSYkkqaKiQnPnzlVFRYUWL16s66+/Xk1NTYkrOQAAQJqKGMBGjBihzp07B4xbsGCBJk6cKEmaOHGi\n5s2bJ0maP3++JkyYoKysLOXl5alXr14qLy9PULEBAADSV5vbgNXV1Sk7O1uSlJ2drbq6OknSpk2b\nlJub2zxfbm6uampq4lRMAACAzNGxPQt7PB55PJ6I00OZOnVq8/PCwkIVFha2pxgAAABxUVZWprKy\nsoRvp80BLDs7W7W1terWrZs2b96srl27SpJycnJUVVXVPF91dbVycnJCrsM/gAEAAKSKlhVD06ZN\nS8h22nwKcsyYMSotLZUklZaWauzYsc3j58yZo4aGBlVWVmr9+vUaNmxYfEsLAACQASLWgE2YMEHL\nly/Xli1b1KNHD915552aMmWKxo8fr5kzZyovL09PP/20JCk/P1/jx49Xfn6+OnbsqBkzZkQ8PQkA\nAHCo8hhjjNMNejyKdZPHHSfV10tuSwwAQPrweKTly6XvfS/ZJckM7cktkdATPgAAgGMEMAAAAMcI\nYAAAAI4RwAAAABwjgAEAADiWVgGMqx8BAEAmSKsABgAAkAkIYAAAAI4RwAAAABwjgAEAADhGAAMA\nAHCMAAYAAOAYAQwAAMAxAhgAAIBjBDAAAADHCGAAAACOEcAAAAAcI4ABAAA4RgADAABwjAAGAADg\nGAEMAADAMQIYAACAYwQwAAAAxwhgAAAAjhHAAAAAHCOAAQAAOEYAAwAAcIwABgAA4FhaBTCPJ9kl\nAAAg9fF9mfrSKoABAABkAgIYAACAYwQwAAAAxwhgAAAAjhHAAAAAHCOAAQAAOEYAAwAAcIwABgAA\n4BgBDAAAwDECGAAAgGMEMAAAAMcIYAAAAI4RwAAAABwjgAEAADhGAAMAAHCMAAYAAOAYAQwAAMAx\nAhgAAIBjBDAAAADHCGAAAACOEcAAAAAcI4ABAAA4RgADAABwLK0CmDHJLgEAAED7xRzAiouL1b9/\nfxUUFOiKK67Q/v37VV9fr6KiIvXp00ejRo3S9u3b41lWAACAjBBTANu4caMef/xxrV69Wu+//74a\nGxs1Z84clZSUqKioSOvWrdPIkSNVUlIS7/ICAACkvZgC2NFHH62srCzt2bNHBw8e1J49e3TCCSdo\nwYIFmjhxoiRp4sSJmjdvXlwLCwAAkAliCmDHHnusbrnlFn3nO9/RCSecoG9/+9sqKipSXV2dsrOz\nJUnZ2dmqq6uLa2EBAAAyQcdYFvr000/1wAMPaOPGjTrmmGN0+eWX68knnwyYx+PxyOPxhFx+6tSp\nzc8LCwtVWFgYSzEAAADiqqysTGVlZQnfTkwB7K233tKZZ56p4447TpJ06aWX6vXXX1e3bt1UW1ur\nbt26afPmzeratWvI5f0DGAAAQKpoWTE0bdq0hGwnplOQffv21RtvvKG9e/fKGKMXX3xR+fn5uuii\ni1RaWipJKi0t1dixY+NaWAAAgEwQUw3YoEGDdPXVV+u0005Thw4ddMopp+jaa6/VV199pfHjx2vm\nzJnKy8vT008/He/yAgAApD2PMW67N/V4PIp1k8ceK23bRoesAACE4/FIK1ZII0YkuySZoT25JZK0\n6gkfAAAgExDAAAAAHCOAAQAAOEYAAwAAcIwABgAA4BgBDAAAwDECGAAAgGMEMAAAAMcIYAAAAI4R\nwAAAABwjgAEAADhGAAMAAHCMAAYAQIZJwL2jEWcEMAAAAMcIYAAAAI4RwAAAABwjgAEAADhGAAMA\nIMPQCD/1EcAAAAAcI4ABAAA4RgADAABwjAAGAADgGAEMAIAMQyP81EcAAwAAcIwABgAA4BgBDAAA\nwDECGAAAGYY2YKmPAAYAAOAYAQwAAMAxAhgAAIBjBDAAAADHCGAAAGQYGuGnPgIYAACAYwQwAAAA\nxwhgAAAAjhHAAAAAHCOAAQCQYWiEn/rSKoBxQAEAgEyQVgEMAAAgExDAAAAAHCOAAQAAOEYAAwAg\nw9BmOvURwAAAABwjgAEAADhGAAMAAHCMAAYAAOAYAQwAgAxDI/zURwADAABwjAAGAADgGAEMAADA\nMQIYAAAZhjZgqS+tApjHk+wSAACQ+vi+TH1pFcAAAAAyQcwBbPv27brsssvUr18/5efna9WqVaqv\nr1dRUZH69OmjUaNGafv27fEsKwAAiAI1YKkv5gB200036YILLtCHH36o9957T3379lVJSYmKioq0\nbt06jRw5UiUlJfEsKwAAQEbwGNP2pno7duzQkCFDtGHDhoDxffv21fLly5Wdna3a2loVFhbqo48+\nCtygx6MYNilJOu44qb6exoUAAITj8UhLl0rnnZfskmSG9uSWSGKqAausrFSXLl10zTXX6JRTTtFP\nf/pT7d69W3V1dcrOzpYkZWdnq66uLq6FBQAAyAQdY1no4MGDWr16taZPn66hQ4fq5ptvDjrd6PF4\n5AlzEnrq1KnNzwsLC1VYWBhLMQAAAOKqrKxMZWVlCd9OTKcga2trdcYZZ6iyslKS9Oqrr6q4uFgb\nNmzQsmXL1K1bN23evFnnnHMOpyABAHCIU5DxlVKnILt166YePXpo3bp1kqQXX3xR/fv310UXXaTS\n0lJJUmlpqcaOHRu/kgIAgKhwFWTqi+kUpCQ9/PDDuvLKK9XQ0KCePXtq1qxZamxs1Pjx4zVz5kzl\n5eXp6aefjmdZOaAAAIgCZ4pSX0ynINu1wXZU5R1/vLR1KwcWAADhcAoyvlLqFCQAAEhdnDFKfQQw\nAAAAxwhgAABkGGrAUl9aBTAOKAAAWkdb6dSXVgEMAAAgExDAAADIMJwxSn0EMAAAAMfSKoCR6AEA\nQCZIqwAGAACQCQhgAAAAjhHAAAAAHCOAAQCQYWgznfrSKoBxQAEAgEyQVgEMAAAgExDAAAAAHCOA\nAQAAOEYAAwAgw9BmOvWlVQDjgAIAoHXGJLsEaE1aBTAAAIBMQAADACDDcMYo9RHAAAAAHCOAAQAA\nOEYAAwAAcIwABgAA4BgBDACADEMj/NRHAAMAAHAsrQIYiR4AAGSCtApg9OwLAAAyQVoFMAAAgExA\nAAMAAHCMAAYAQIahzXTqS6sAxgEFAEDraDOd+tIqgHFAAQCATJBWAQwAALSOM0apjwAGAADgGAEM\nAIAMQw1Y6kurAMYBBQBA62gznfrSKoABAABkgrQKYCR6AABaxxmj1JdWAQwAACATpFUAI9EDAIBM\nkFYBDAAAIBMQwAAAABwjgAEAADhGAAMAIMPQZjr1EcAAAAAcI4ABAAA4RgADAABwjAAGAADgGAEM\nAIAMQyP81EcAAwAgw3Dv5NRHAAMAAHCMAAYAQIbhFGTqa1cAa2xs1JAhQ3TRRRdJkurr61VUVKQ+\nffpo1KhR2r59e1wKCQAAkEnaFcAefPBB5efny/N11C4pKVFRUZHWrVunkSNHqqSkJC6F9CLRAwCA\nTBBzAKuurtbChQv1k5/8RObr1n4LFizQxIkTJUkTJ07UvHnz4lPKr9GoEAAAZIKYA9h//dd/6b77\n7lOHDr5V1NXVKTs7W5KUnZ2turq69pcQAAAgw3SMZaHnn39eXbt21ZAhQ1RWVhZyHo/H03xqsqWp\nU6c2Py8sLFRhYWEsxQAAACHQZCd2ZWVlYbNNPHmMafuJvdtvv12zZ89Wx44dtW/fPu3cuVOXXnqp\n3nzzTZWVlalbt27avHmzzjnnHH300UeBG/R4FMMmJUndu0u1tZyKBAAgHI9HWrlSOvPMZJckM7Qn\nt0QS0ynIu+++W1VVVaqsrNScOXN07rnnavbs2RozZoxKS0slSaWlpRo7dmxcC0uiBwAAmSAu/YB5\nTzVOmTJFS5cuVZ8+ffTyyy9rypQp8Vh9M2q+AABAJojpFGS7NsgpSAAAEoZTkPGVUqcgAQBA6qGC\nIn0QwAAAABxLqwBGI3wAAJAJ0iqAAQCA8LynIDkVmfrSKoBxQAEAgEyQVgEMAACER0VF+kirAEYb\nMAAAkAnSKoABAIDWUROW+ghgAABkCIJX+kirAMaBBQAAMkFaBTAAAIBMkFYBjEb4AACEx5mi9JFW\nAQwAALSOIJb6CGAAAACOEcAAAMgQ1HylDwIYAACAYwQwAAAyBDVg6YMABgBAhiGIpT4CGAAAgGME\nMAAAMgQ1X+mDAAYAAOAYAQwAAMAxAhgAABnCewqSU5GpjwAGAADgGAEMAADAsZQJYBs3SqtXR57H\n43FSFAAA0lK0px7nzZOamhJbFkSWMgHsggukU0+NPA/ntAEAaL9LLpE++ijZpTi0pUwA27kz2SUA\nACC9RdMI3zst1FmlO+6Qjj8+/uVCsJQJYDU1yS4BAACZ7+OPw097/XVp61Z3ZTmUJSWAbd+ejK0C\nAIBINWAdUqZaJvMlZVfX1sa2HI3wAQAIj7bS6SMpASzWA4QDCwCA1kX6voxUmcGVke5Q2QgAACQR\nwFyiBgwAgAzR3u9JApg7aRXAAABA+3hPQYY6Fcn3sztpFcA4MAAASBxqwNwhgAEAkCGi6Yg1muWR\neDTCBwDgEMIpyNRAAAMAIEPQCD99cAoSAABIIoC5lBYBrLFR+uwzAhgAANGqrGz7MgQwd9LiFOQf\n/yjl5RHAAACIxPs9+e670ne/Kx08GDzPzp2tL4/ES4sasP/+78SUAwCATLR3r328887gaS+9ZB9D\nNcKnBsydtAhgAAAgeh2+/navrg6eFulekHw/u5NyAezZZ2NbDgCAQ533e/LAAfv4wQfB8/zmN/aR\nbiiSK+UC2OWXx7YcAACwSkrs45tvhp8n1HcqpyDdSYtG+F4EMAAAWhepMiMSApg7KVcDBgAAYuP9\nfu3du/V5OQWZXCkfwD7/PHHlAAAgE0VqaB8JNWDuJCWAteUPXF/ve759e/zLAgBApvBWcBDAUl/K\nBzAAANA20QSwZ54JHscpSHdS/hRka7Zskfbsid/6AABIF5s3h+7tPpoAVlUVPI4A5k5a14AdOCB1\n6SL9+MfxWR8AAOnkhBOk66/3vW5LgKIbiuSKKYBVVVXpnHPOUf/+/TVgwAA99NBDkqT6+noVFRWp\nT58+GjVqlLaHabTVlj9wpIPpgQe85Yl+fQAAZJLHHw8eF2tNFgHMnZgCWFZWlv70pz9p7dq1euON\nN/TII4/oww8/VElJiYqKirRu3TqNHDlSJd6e4FqI1x942zb7GGtjQwAAMlGsAYxTkO7EFMC6deum\nwYMHS5I6deqkfv36qaamRgsWLNDEiRMlSRMnTtS8efNCLh+vANaxY3zWAwBAJvAGKGrAUl+724Bt\n3LhRa9as0fDhw1VXV6fs7GxJUnZ2turq6kIuE6+E/Y1v2MfXX4/P+gAAyATRfM/+5S/B4whg7rSr\nDmnXrl0aN26cHnzwQR111FEB0zwejzxhzg2Wlk7VK6/Y54WFhSosLAy7jUgHkTeAAQAAn5UrY1vu\njDOkCy6Ib1nSTVlZmcrKyhK+nZgD2IEDBzRu3DhdddVVGjt2rCRb61VbW6tu3bpp8+bN6tq1a8hl\nr7xyqkaPjnXLPgQwAAB8vG2jFy0KPb21Gq5jj5UGDoxvmdJNy4qhadOmJWQ7MZ2CNMZo8uTJys/P\n180339w8fsyYMSotLZUklZaWNgezluJVxUkAAwDA59lnI09/4onI05uapA5J6aDq0BNTDdjKlSv1\n5JNPauDAgRoyZIgkqbi4WFOmTNH48eM1c+ZM5eXl6emnnw65fFvagNXWhp9GAAMAwCfcDba94zdv\njrw8AcydmALYWWedpaYw1Vgvvvhiq8u3pQbswgvDT6P7CQAAfEJVcCxfLkVoah2AAOZOWveEDwAA\nfEIFsAMHol+eAOZOWgewt96Kz3oAAMgE7f1+JYC5k9YB7Kmn4rMeAADSzWefBY8LVQPWlnbXTU00\n73ElKQGMWx0AANA+DQ2+51/fkrnd36/GUAPmSlrXgAEAcKjyD0o33WQfQ32/tqVGi1OQ7hDAAABI\nQ6GCVajv16VLo18nAcwdAhgAAGkoVFDaty943H33Rb9OApg7KdEGzHWbsMMPDzx3DgBAsv3jH9KP\nfhT9/KE6I//DH9pXhmeeoYcBV1KiBqyxse3raE9o27dP2rs39uUBAIi3mTOlv/89+vljqan66qvW\n55k1q+05kuSIAAAgAElEQVTrRdulRABrqa6u9XXEGsC4AhMAkIpefrlt88fSXUQ0pyPPPrvt60Xb\nJSWAtby/Y8tQFOocdkuxtiPzbosgBgBIZ4loq3XeedK118Z/vQiWlAD2m98Evm4ZhloLV+vXS2++\nGXmeXbtChyzv6U4CGAAgXezdKx08GDiuZQ1YRUX7t9PUFLptGeIvJa91aK1N2Lp10plnRp7nqKNC\nn8f2hjsCGAAgXXTrJk2cGHme/v3bv53GRq6CdCUldvPGjYGvp0+PPH+oGrKtW4PHhbpNg3fZWBr+\nAwCQDDt3Sh98EDguHoGrpeXLpfr6+K8XwZISwH7728DX+/cHvn733bY3LpwzJ/y07dvtOiVfAHvh\nhbatHwAAl1asCHzd8sxNqIqHcJYsif57tbUmPoiPpASwf/wj8HXLGq2yMvv43nuhl1+3Lnjctm3B\n47wH64knSoMH28b93pqvlqEPAIBUYIzti+vss+PXZ+XNN0c/L23A3EhKANuwIfB1uEb3H38cevzz\nzwePC7WO3/3OPu7caR8PP9w3309/2no5AQBw7ZlnpKFD7XP/77YtW2JfZ1sqHbZvj307iF5KtAEL\n1yC+5fnuePB2cUEjfABAKvr3v33P/QPY5s2xr7NlxUck1IC5kdIB7M4747s+SSosjG2dAAC44N+m\nORn3Th440P02D0UpHcDC8bYR8+ffuHDcuPDL+p/WfP/9wGmvvhpbz8IAAETjjTdCf8/8+Meh528Z\nwD78MO5FCkINmBtJC2D+B2C8E75/9W0kN94Y+HrEiPiWAwAAf+E6Sy0tDT2+5fdjuLbR7fXpp77v\n5UR0b4FgKVED1p6GhV73329rvv72t+iXKSuLvrHhnj00TAQARCdce60jjggeF6kH+5YB7JJLpKlT\npR49Yi5aSDNn+p4PGRLfdSO0lAhgsbb18rdjh/Svf7XeU3BLoa6GPHAgeNzYsdIJJ8RWNgDAoeWE\nE0LXVtXU2Ef/pjeRapzef19avTpw3LRpUnV1+8voz7/3e5riuJESASyRjQxDhSl/3g5a/d12W/C4\npUvtvbgAAIjGffcFj/v1r+1jy1AVTlWVtHZt/MoUDgHMvZQIYIm8LVBrV3OsXx88btWq+Gx79myp\nd+/4rAsA4F5DQ9sDiffHuv9pvZZOOy26dV11lXT11W3bfnsRwNxIagDr10/64ovgO7zH00cftX2Z\ntpanvj50TdvSpdInn7R9+wCA1BCpJ/pwn/1tuUVQKpg+3ddxuUQAcyWpAeyjj+wlteFuOZQsbamR\n27lTOu446Ze/DJ5GZ68AkN4ihZHjjpMOOyx4fFZW4soTb8bYNmX+CGBuJP0UZCJPP8Yq0o1Iu3cP\nvJG39x6Ujz0WPC8BDAAyQ7RtlS+4QCopiX69ya6A2L07uds/lHVMdgEaG6Xjj49PVxTtcf750c1X\nWyt9//u+cBXpn/Lvf29/uQAAyfPWW/bxs8+kk06KPO8XX0iLFtkhGo88krh+vaJlDJUFyZISASzZ\ntWChqlunTw99WrGlZNwmwuvgQXvlSoek12MCQPI0NNjTfok4dVZXZx83bgwMYKFqrtatC7+e+npp\n3rzAcdF8xySaMenXZi1TJP2r+8EHfafxUskNN0R349M77gh8vWqVdOWVgeNefz1+5fLXs6f7q2MA\nINV885vSM88kZt3ez9jdu+3VjQUF9rX/WRtvR6qROgLv10+aPDkxZWyP3/422SU4dCU9gC1enOwS\nhDdggP1FFSpA/eUv9tH/NOOGDdK110r/+EfgvK+8EnsZPv44fA/8n3/OaU4AkKQ1a0KPf++99vXh\nuH+/fbz1Vumll6QPPpCeey7wavmXXrKPjz8evPzZZ9vvkS++iL0MifTww8kuwaEr6QEsldXX28fv\nfS94WsuqZMnWSIWqlm7P+fW+faXOnYPH79gR+zrbor7e3oYpnF27In+4/ec/ie1mBEBiffJJ5I5A\nv/wy8mdcba2bZiYlJaGbhAwaJB15ZPvX/9FH0osv2udjxkijR7e+TH6+tGJF+7eNzEQAi0KoALFy\nZfTByvvLrLpamjs3/HyffNL6Os86y36gffvb0W27vY47TvrhD8NPP/lke2+zzz4LPf3//l8+gIB0\nNny4PRsQyu23S127Sv/+d/jlu3eX/vznxJStpdGjpUcflf7wh8DxLT9Xt271/cBuqalJ+tOf2r7t\n2trgcZHu8QikVAC7995klyB6u3ZJy5ZFN6+3YebPfhYYZvbskX71K9/r3r19V898+GFgw8h9++zj\nypXtO6UZyh13RK7Fev/98NM2bbKPGzaEn+fll+1jdTW3cwLSgf//arigItmwI9lasEjCTX/1VWn+\n/LaXL5wXX5SmTLGnC6XALhbefdd+bku2VuyUU+zzqirp97/3zbdgge9zOdof2cbYH8fp5Oijk10C\npFQA894jK114/5lbs2aNdNNN0sKF9rUxNrwdeaT9pfX4474q+jlz7Adffr40apRvHYcf7jsVGOpX\n1fDhkT8oI7nzzsi/1DZu9AXAcEaPDg5X3v3j/YDt0cP3wQggdUXzv/r8877PnJ//PHj6wYO+H5/h\nrk4cN04aO7bt5TPG3urtd78L7one22Z2506pUyff+MGDpS5d7LI1Nb5a++98R/qf//GV0fvD+vzz\npZEjA9cd7n0Y03oITTXx/iGPGBjHJBlfzyOBQ1NT6PGpOpxySvhps2aFnzZxojF33x1+XUOHhl6u\nb9/Wy2SMMR98YMzWrb593thozLJlgX+H114z5k9/MubgQbvcypW+aVdeaczy5cYMGhS47rPPttMb\nGozZvdv79/QNU6YY07GjMa++asyqVcY8/bQd/61v+eYdNCj+xxSA+PL/PPF//q9/GbNwYfjPnh07\n7OOaNcHT//hHYyZPNmbx4uDtbN9uzM9+Zj9bvPbuDfxc8q53xw5jpk6N/XN73z7f83vvDX4PkZb9\nwQ+S/70Tr2H9+sjfI/BJVFRyvqsjBTA7/dAYunRJzHr377ePF19s92dNjS8I+Tv11OBlq6pa/xt8\n9pkxOTn2+RtvRF+uKVPs47HHujvW0sWmTXa//v73yS7JoaOhwZibbzamttaYPXuSXZrUE+ozedmy\nyP/jX31lH7/8MvT0rl0D1/vII8HzbNzoK8Of/+z7zKmt9ZVlwoTEfS7n5SX/uyEewz33RJ5+8832\nfyDcdARKVABLqVOQh5JEVVd/85v2cc8eqX9/KSdHGj/ejrvoIunuu233FcYEL/vII62v/4svbPW9\nJJ1+evTl8t6ao77ed0XV55+Hnvfzz8P3wbZwoW0k29iY3E5w22vlSl+njiecIJ14oq8/nnnzQv99\n0H5VVfZWYwsXSg88IHXrJv30p7YBtceT3vvde7HQxo22q4RQ3n479EVFu3b5TieG69rmnHMib9/b\npipcW6iW3TD84hfB8zQ2SjNm2Eb0111nx514ov07LVliXz/1VORytMfGjYlbt0utdUhbWOikGGhN\nQmJdBFLkGrCsrOT/esiEIVQNV2vDj3/sOyUZbjjuuPiUb+dO+1hREXyMfOMbdtq+fcZUV7c8foz5\ny1+MGTzYmMsuC3+cNTba95IsBw7YMrRUXm6n+R/zLf8HJF9tZEt1dYkpbyZpagq/n8480+7ff/87\ncL+//rp9vP12WwvT8rgzxtYYNDUltuyR+J+eC0UyprQ08Fjy2rDBd+qttDR42XPPtf93770X+niM\n9xBuvZlSA5Xs4Q9/iDx9/nxqwNoiUVEpZWvATjwx2SVIb2+/3fZl/vpXqWMrN6eK1y0rvFfgPPqo\nLWt5uf1lvmeP74KEa6+VcnPt8717bY2eZBv8vvOO9Oyz4dc/dmzr7yVW0ezbY4+1XXBI9opWj8d2\n0DtsWOAv+NtvD7384sV2mQcftK9nzbIXqWRnt6/sh4Knn7b7aeJE31W6vXrZ/dnQYF/7X/Um+Wp/\n7r5bysuzx11Bga8mYc8e6bDDpP/938jb3rHDdieTCIcd1npnnhMn+p5PmGAfd++Wvvtd6dJL7eud\nO+2wf7+9QOjZZ+2Vyo2N0sCBget74YX4ld/flCmhx2dKDVSyJeKWTEiAhMS6CKTINWAdO9rnRUXR\nJX1v2yKGzB1+/evw07x27/bVTvjXMJ1/vv3l39L69YGvt20z5uWXjXnuOdsg+OKLjdm1yzY4nj+/\n5TFsa/C8zjnHtrk4eNAu451HsjWRf/+7fX7CCbG9f//1Sb62d/v325qcQ93evfZv9Oyzxgwfbswt\nt/j21axZtiayPcdfy1phY3yNzbt1M2bBAl9Zxo4NPC6NMaakxF4Ys3atbfdUXm7Mxx8H/+127Qpd\n8/b558Ycc0zwMd/U5Gu/tnVr+PI/91zy/4cZEjd861vB4/74x8jLzJ8f/mzHKae0698xIyUqKiVm\nrZE2qOgC2PbtwdN79Qoed9ttyf8HYEjecPnlxlRW+l7bYyx48L/yyTv86Ef2Q8gbkFoO/o19p083\n5qabfK+3bfM/pgOHtWsDXz/0UPve409/Gnr8hRf63nNbVVXZxs2p5PXXQ5+2bY33iuNjjw29n7wX\nocQ6/Pa3oY+lb3/bPt56q68s3nkefdRe8ffoo75xF18cev0HD9pTf/4hSzLmxhuNefvt4Pk//zxw\nW/7PGQ69IdTV8X/6U+h5vRdIeH9UhpqHABbskAtgdl473H+/ffze94KXIYAxrFjR+jzeY6jlMH9+\nbNv84AN7jB59dPLf/2ef2ZqT2lq7L957L5r/Qzvk59vHcNata9//uzE2sIQLeytX2u3/7W/28Ve/\nan19//iHMfX1xrzzjg0v2dnJ/xtMn27LFsuymzcbc8QRsW+7ZeBnOLQG7w8x/+GBB+zj0KHGvPSS\nb7z3GPXW2oZa39Ch7f+fzzSHdAAzxv46/NWvgpe5/fbk/wMwHJrDa68lvwzhhn37jLnrLnvK60c/\nsr+ITzrJmKuvtpegt5z/+eeNmTbNmIEDjRkzxv7Pbd7sm/7Pf9r+m4YM8f0v+/c1d+CA77SctzuC\npiZjBgzwrePAAWM+/NCY666zr8OdNvMG6rlzjenf354aHjPG9gFVX2+nXXpp8vex/zByZPiaVAaG\nRA6RAthf/hL8XSpFDmBnnBH/7/10l/EBbPVqO/3RR415+GHvvL6DprExdEetBDAGhvgP0Z62q6+3\n/59nn+0b162bfbz++uD5vVchSq1fqcXAwBB+GD3aPoYKYA8+6PvObPldOmqU7XvQf7z/cNZZTqJA\nWklUAEuZqyCHDLGP114r/fKXwdM7dAh9ZUe4qz28/U61dPjhsZUvknS6hyUQDW/fca059ljbZ9Py\n5b5x3psSz5gRPP9rr/mep9utxwBX7r8/eFx5eeDr1q50DPed+cIL9gbpku0Dr6WTT46ujGi/pASw\nbdukmTN9r1veud7ftdcGvg532b4k3Xab73lennTPPb7XI0bYfH/GGb4OA+Pl4ovjuz4gnXB/TyC+\nzj7bfl/5Gzo08PUJJ9jHUCHr3HOj28599wV2PbJhg/TnP0dfTrRPUgLYt79t+6uZNMn2K3XLLeHn\n9fYO7nXXXfZmq5WV9rX/wXfRRb7n3/lO4AHs7T/phRekN96wz709qZ97buCNr1vz3e8Gvs7Kin7Z\nWB1zTPC4Cy9M/HYBIB3MnZvsElgrV9rHnj3DzzN6tH18/XXfuEsusY9790qnnuob739Dcf+7ERxx\nRPB66+psf24DBgSOv+kme3Pxlo45xt4Z4o037Jmck05y832GryXkxGYE8dzkiBG+q6gk33Ovl16y\nPevX1NiGwf5mz/a1KSsrs1dhHXlk+PPt//M/vud79wZO27Ah8ef7f/zjwNd33GHLnex2CAwMDAyp\nMNjvF7fDK68Evn70UV85br01/HLevg39y1xdbS848VdZacynn/rmNcbXwP6jj+zj5Mn2RuaPPx63\nr1a0kKiolJi1RtpgAt5IdbW96sv7z9C28tj+h7zeeMP2LdXyH2bnTtsf0Dnn2Pn87yT/6afGfPOb\nrf+zem8uG2548knbeDLUtOnTA1/v3+8m+J1+uvsPNQYGBoa2DsYE/1ANNUydah9ffTX8PD/7me9q\n3da26X3u332DZMwXX9irir3Tvf1YPvFEYD+C3g6ao+UNYMbYxvTcTD7xEhXAUqYRfnvk5NibUMdy\nc+YZMwLbhA0fbqtrDzsscL5vfUv63e/sLTske2uTpibbzuykk0K3Y2t5McHPfx654eSVV0o33uh7\nbYw9Ry/5bkzrvYnqYYfZ7VZUSC+9ZMdNnx7xreqhh4LHtdbg8oorIk9vC/+Gpa3dUgWAe97bFUnR\n3Q7uzjvt47RpkecrLY08/a67gsetWRN5mTPOsI8NDb7bP3Xr5pt+1lnSiy/a594YJNlTesZIffuG\nX/fIkdJpp0Xevtenn9rbX/k3kjdG6tJFuuYa37jBg+3jNdfYZjhezz8vLVsW3bZa6t49MReWwZGE\nxLoIErlJb61UvLT8VRPJM88E/jLasye42wzvOiXb55J/54uzZgVut2dP+3zHDtsHk3e8t/+jlvbu\nDVz/uefax+7dfeP8b9Eze7Y9Nfv970c+9frww+GnPfKIMcXF9rm31tAY3422pcA+p7xV5i33RTSD\n/016o/mVG+tQWmpM586JW39bhqOO8j1ftiz0ccYQevDeEioVOmltOfzmN7Etd/750c3n7Y/ssMPa\ntv4LL7THmfe199RXy8EYWwMv+W5nc+BA6I6yPR77uGRJ6HV5bzn38ce2jzjv+JUrfev2/3zyvxuK\n/+ee1xNP+KafdZa94fTs2YGfrX/4g33e2GibcviXx3sLn3/+M7ifuoaG4BtYR0sKvGNCeyxd2rZt\no/0SlVvivtZFixaZk08+2fTq1cuUlJQEbzCNjpznnouuV3FjfF+MGzfaDy4v7wfhtGn2dXm5MatW\n+aYfPGj/qf1JvgDm78ILjXnggWVBHzr+Nm2yy//3f4f+J/V+SHpv+bJnjw15p50W+gPS+4FsjO+u\nA/PmBa933DjffN6g99BD9ovQuy7/e48ZE3wK9fDDfc9btrO76CLf8/nzjend2z6/6y77eOWVob8o\nvPvTNyyL+CXk/bC+4ILgaZ06BY977bXQt4v54gsb5rzl6NPHPj/5ZPtB7H0//fv7lvnPfwJPf/vf\nxsb79zpwwI7fu7ftX7DRDv/7v5GmR95/rQ2JKrNkf1CsX2/3rddnnwXO07OnfVy92pjc3OB1vPyy\n/WF033329Qcf+L7Uv/zS3h6o5TLPPWfMvfcGj//97+3j4MG+fdeyX6ZwQ3m57/lVV9llVq+Obj94\nm2L494Au2R+TX3xhnw8bFrzMzp2+YPWvf/nCRqdOxrz5pjFduviOZ+97aHnrqH37fJ8l//mPDVbe\nZUKV9f/9P3sHBy9v33C7dweu1/b3uMzceKM9rbdlS/BnkDH2R+++ffb2XX//e/B0yf6t/LX8PJ01\ny7d9yQbAo4/2TV++3Hfnhmj97W/2+EymZd5fcWiztAhgBw8eND179jSVlZWmoaHBDBo0yFRUVARu\nMEFvJNm8twOJhxNPNOaKK0JPu+OOO6JaR7hfSU1NtiYqnKFD7a/V3//eftC1dPBg6OX8a8CamuxF\nC17799sPfmNs2wr/ctXX2x7Wf/c7Gyw+/dT3oV5b67sf4+zZ9obX3mW99wo1xj6uWmXMjBm+D/bX\nXgssn2TvpHDbbXeYm26y25kzJ/jL4fnn7etf/tI37aST7POvvrKBta7Od99B//WPHm3fj7f2xf9v\nMGuWrfnwd/fdvi/uK66wX4BNTXZ/rV1rw1anTvZLKpRt22zgb2qyoePOO415913bHjFUr+yXXWYf\nTz3V9yUn+d6r5Oshe88eG6pbtoecMOGO5p7uQw1z5tiyP/ts4PiZM30/QoyxnUH6h5Sbbw4MHaGG\nk06yx+SNN9pj5he/sCHfGPu+wznpJLuva2rsF7f35uwLFvjKMXu27YHfX+/e9jjzP06amuzf1xtk\nfvADO957w+sbbrCvv/jCVwP++efe+0fe0bzuHj187+s///E9PvmkMY895jum/D8HmpqMeeEF33IH\nDti/0bXX+n6IGOO7Q4Mx9kIlyf4Y8P7vfvGFfV9FRXa/zZjh24b3x5OXf2j46CMbJLxCBTBvOUON\nl+z/9E9+YmvPQ2lstKGtJftj7Y7QC7WBZH8st9c778Tv896VaL87ECwtAthrr71mRo8e3fy6uLjY\nFBcXB24w3Y7aJDhwIPxNiVP1n+iLL+wXaGt27TLmk09i28bbbwfeJuPLLwOnr11rTEFB6GU//dSG\ninD77/337Relt4Zi1y5bm+J93vLXa0WFPR3i9eKLwfc7bGpqvQb1qacS/0H+f/6PvYhj2zZbe+l9\nj/7Wrg3/C/3EE20t0MGDgfvvn//0BYQjjgg+Zj/5xNZETJkSer0rVwbXdBhj/w5vvWWn/9d/2dPc\nieLt8T+SxkZ7fLS0aJGvR/HKSmNycoLn8R5Dxhjz85/f0fx82zZ7vFRVhd9uZWXw1dvG2GXy8gLH\nHTzouyvBl1/a2r1YRQqz/hYujH0bsYjHZ9/+/aGP/0NBqn53pINE5ZaO8WxPVlNTox49ejS/zs3N\n1apVq+K5iUNCx7j+Vdzo0sUOrTnyyMj940RyyimBPakff3zg9Px86b33Qi/bsu+2llr2m3PkkfZC\nC+/zI48MnN6vn7R+ve/1yJHB6/R4pIKCyNu9+GJpzpzI87TXq68Gbi+U/Pzwy2/cGHr8pZf6Gm3v\n3h08vWdP6bHHwq/3zDNDj+/Rww6R5omXiy6Snnoq8jwdOgQfH5L0/e/7nuflSdXVwfN4jyHJ1xeh\nZBth+zfEDiUvL/T43FxfP4he3/iG1LmzfX788VJVVeR1R+LfMWckofqVSnUtL64CksnzdbqLi3/+\n859avHixHn/8cUnSk08+qVWrVunhhx/2bbC1+ycAAACkkDhGpWZxrWvJyclRld9Pr6qqKuXm5gbM\nk4g3AQAAkE7i2g/YaaedpvXr12vjxo1qaGjQ3LlzNWbMmHhuAgAAIO3FtQasY8eOmj59ukaPHq3G\nxkZNnjxZ/fr1i+cmAAAA0l7ce8I///zz9fHHH+uTTz7RbbfdFjBt8eLF6tu3r3r37q177rkn3ptO\nW3l5eRo4cKCGDBmiYcOGSZLq6+tVVFSkPn36aNSoUdq+fXvz/MXFxerdu7f69u2rJUuWNI9/++23\nVVBQoN69e+umm25y/j5cmTRpkrKzs1Xg18I9nvtr//79+sEPfqDevXvr9NNP12effebmjTkSav9N\nnTpVubm5GjJkiIYMGaJFixY1T2P/+VRVVemcc85R//79NWDAAD309e0lOP6iE27/cfxFZ9++fRo+\nfLgGDx6s/Pz85u9Yjr/Whdt3ST32EnJtZQjR9BF2qMrLyzNbt24NGHfrrbeae+65xxhjTElJifnN\n151IrV271gwaNMg0NDSYyspK07NnT9P09XXVQ4cONau+7uX1/PPPN4sWLXL4LtxZsWKFWb16tRkw\nYEDzuHjur0ceecRcd911xhhj5syZY37g7ewpQ4Taf1OnTjX3339/0Lzsv0CbN282a9asMcYY89VX\nX5k+ffqYiooKjr8ohdt/HH/R2/113y0HDhwww4cPN6+88grHX5RC7btkHnvO7gVZXl6uXr16KS8v\nT1lZWfrhD3+o+fPnu9p8yjMtLk5YsGCBJk6cKEmaOHGi5s2bJ0maP3++JkyYoKysLOXl5alXr15a\ntWqVNm/erK+++qq5Bu3qq69uXibTjBgxQp2919x/LZ77y39d48aN00vem21miFD7Twp9gQz7L1C3\nbt00+Oub+nXq1En9+vVTTU0Nx1+Uwu0/ieMvWkcccYQkqaGhQY2NjercuTPHX5RC7TspeceeswAW\nqo8w7z/eoc7j8ei8887Taaed1tyFR11dnbK/7jgoOztbdXV1kqRNmzYFXFnq3Y8tx+fk5BxS+zee\n+8v/WO3YsaOOOeYY1dfXu3orSfPwww9r0KBBmjx5cvMpDPZfeBs3btSaNWs0fPhwjr8YePff6aef\nLonjL1pNTU0aPHiwsrOzm0/ncvxFJ9S+k5J37DkLYPT/Fd7KlSu1Zs0aLVq0SI888oheeeWVgOke\nj4f91wbsr7a77rrrVFlZqXfeeUfdu3fXLbfckuwipbRdu3Zp3LhxevDBB3XUUUcFTOP4a92uXbt0\n2WWX6cEHH1SnTp04/tqgQ4cOeuedd1RdXa0VK1Zo2bJlAdM5/sJrue/KysqSeuw5C2DR9BF2qOre\nvbskqUuXLrrkkktUXl6u7Oxs1dbWSpI2b96srl27Sgrej9XV1crNzVVOTo6q/brirq6uVk5OjsN3\nkVzx2F/e4zEnJ0eff/65JOngwYPasWOHjj32WFdvJSm6du3a/MH9k5/8ROXl5ZLYf6EcOHBA48aN\n01VXXaWxY8dK4vhrC+/++9GPftS8/zj+2u6YY47RhRdeqLfffpvjr428++6tt95K6rHnLIDRR1ho\ne/bs0VdffSVJ2r17t5YsWaKCggKNGTNGpaWlkqTS0tLmD6oxY8Zozpw5amhoUGVlpdavX69hw4ap\nW7duOvroo7Vq1SoZYzR79uzmZQ4F8dhfF399nx7/dT377LMaGeo+Qxlm8+bNzc///e9/N18hyf4L\nZIzR5MmTlZ+fr5tvvrl5PMdfdMLtP46/6GzZsqX5FNnevXu1dOlSDRkyhOMvCuH2nTe4Skk49tpz\nRUFbLVy40PTp08f07NnT3H333S43nbI2bNhgBg0aZAYNGmT69+/fvF+2bt1qRo4caXr37m2KiorM\ntm3bmpe56667TM+ePc3JJ59sFi9e3Dz+rbfeMgMGDDA9e/Y0N9xwg/P34soPf/hD0717d5OVlWVy\nc3PNE088Edf9tW/fPnP55ZebXr16meHDh5vKykqXby/hWu6/mTNnmquuusoUFBSYgQMHmosvvtjU\n1n2NyX0AAACBSURBVNY2z8/+83nllVeMx+MxgwYNMoMHDzaDBw82ixYt4viLUqj9t3DhQo6/KL33\n3ntmyJAhZtCgQaagoMDce++9xpj4fl9k6v4Lt++SeezF9V6QAAAAaJ2zU5AAAACwCGAAAACOEcAA\nAAAcI4ABAAA4RgADAABwjAAGAADg2P8HBneBXzX41eUAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Noise = fft(noise)\n", "plot((abs(Noise)**.5))" ] }, { "cell_type": "code", "execution_count": 77, "id": "1e2f69e2", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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yc3N33Zebm6uysrL4RgcAQJrgqkME0Sz2Q8L7/e9/r3333VfDhw+P+JhQKBT29jFjxuz6\nc35+vvLz84MOAwCABhGpR4tm+MalqKhIRUVFCTteoKD197//XS+//LJee+21Xbe1b99epaWlu/6+\nevVqtW/fPuzz6wYtAAAyAT1aTUP9AtDYsWPjOp7vqcOZM2fq3nvv1bRp07T//vvvun3QoEGaNGmS\nKisrtWLFCpWUlKh3795xDQ4AgHTB1CGCiFrRGjZsmObMmaONGzeqQ4cOGjt2rAoLC1VZWamCggJJ\nUp8+fTRhwgTl5eVp6NChysvLU7NmzTRhwoSIU4cAAGSacFOHNMMjlpBzzjXoCUMhNfApAQCIW6dO\n0syZ9nutNWukU06x39E4xZtbWBkeAAAPIvVo0QyPaAhaAAB4QI8WgiBoAQDgAVvwIAiCFgAAHoSb\nOqQZHrEQtAAA8ICpQwRB0AIAwINwQWuffSxocTE9IiFoAQDgQbgeraws+1VdnZoxIf0RtAAAiKGm\nxn5lhXnXZPoQ0RC0AACIoXbaMNyGJzTEIxqCFgAAMYSbNqxFRQvRELQAAIghXCN8LVaHRzQELQAA\nYgi3hlYtKlqIhqAFAEAMsSpaBC1EQtACACCGaD1aNMMjGoIWAAAxMHWIoAhaAADEQDM8giJoAQAQ\nAz1aCIqgBQBADPRoISiCFgAAMdCjhaAIWgAAxMDUIYIiaAEAEAPN8AiKoAUAQAzsdYigCFoAAMQQ\nrUeLZnhEQ9ACACAGerQQFEELAIAYYk0d0qOFSAhaAADEQEULQRG0AACIgXW0EBRBCwCAGKJVtGiG\nRzQELQAAYmB5BwRF0AIAIIZYU4c0wyMSghYAADHQDI+gCFoAAMRA0EJQBC0AAGKI1qNFMzyiIWgB\nABADyzsgKIIWAAAxxJo6pBkekRC0AACIgR4tBEXQAgAgBtbRQlAELQAAYojWo0UzPKIhaAEAEANT\nhwiKoAUAQAyxpg5phkckBC0AAGJgeQcERdACACAGpg4RFEELAIAYogUtmuERDUELAIAYWN4BQRG0\nAACIIVaPFs3wiISgBQBADPRoISiCFgAAMdCjhaAIWgAAxECPFoIiaAEAEAPraCEoghYAADHE6tGi\nGR6RELQAAIiBqUMERdACACCGaFOHNMMjGoIWAAAxsLwDgooatEaNGqWcnBz16NFj122bNm1SQUGB\nunTpov79+6uiomLXfYWFhercubO6du2qWbNmJW/UAAA0IHq0EFTUoDVy5EjNnDlzj9vGjx+vgoIC\nFRcXq1+/fho/frwkacmSJZo8ebKWLFmimTNn6vrrr1dNTU3yRg4AQAOhRwtBRQ1affv2VatWrfa4\nbfr06RoxYoQkacSIEZo6daokadq0aRo2bJiys7PVsWNHderUSQsWLEjSsAEAaDgs74CgfPdolZeX\nKycnR5KUk5Oj8vJySdKaNWuUm5u763G5ubkqKytL0DABAEgdVoZHUBHyuTehUEihUCjq/eGMGTNm\n15/z8/OVn58fzzAAAEgqmuGbjqKiIhUVFSXseL6DVk5OjtatW6e2bdtq7dq1OvzwwyVJ7du3V2lp\n6a7HrV69Wu3btw97jLpBCwCAdBerR4tm+MajfgFo7NixcR3P99ThoEGDNHHiREnSxIkTNXjw4F23\nT5o0SZWVlVqxYoVKSkrUu3fvuAYHAEA6oEcLQUWtaA0bNkxz5szRxo0b1aFDB91555267bbbNHTo\nUD3xxBPq2LGjpkyZIknKy8vT0KFDlZeXp2bNmmnChAlRpxUBAMgUTB0iqJBzzjXoCUMhNfApAQAI\nrKZG2mcf+z1c/WDDBikvz35H4xNvbmFleAAAoti506pWkSZpqGghGoIWAABRRJs2lGiGR3QELQAA\novAStKhoIRKCFgAAUURb2kEiaCE6ghYAAFFEW9pBsvuqqyWu80I4BC0AAKKINXUYCtlVidXVDTcm\nZA6CFgAAUcQKWhIN8YiMoAUAQBSxerQk+rQQGUELAIAoYvVoSRbECFoIh6AFAEAUXqcOCVoIh6AF\nAEAUBC3Eg6AFAEAUXnu0aIZHOAQtAACi8NKjRUULkRC0AACIwsvUIc3wiISgBQBAFCzvgHgQtAAA\niIKpQ8SDoAUAQBSsDI94ELQAAIiC5R0QD4IWAABReOnRohkekRC0AACIgh4txIOgBQBAFPRoIR4E\nLQAAoqBHC/EgaAEAEAXraCEeBC0AAKLw0qNFMzwiIWgBABAFU4eIB0ELAIAoaIZHPAhaAABEsXMn\nyzsgOIIWAABRMHWIeBC0AACIwkvQohkekRC0AACIguUdEA+CFgAAUXjdgodmeIRD0AIAIAp6tBAP\nghYAAFHQo4V4ELQAAIiCHi3Eg6AFAEAUXnu0CFoIh6AFAEAUrAyPeBC0AACIgmZ4xIOgBQBAFF62\n4KEZHpEQtAAAiIKKFuJB0AIAIAqCFuJB0AIAIAqa4REPghYAAFF46dGiooVICFoAAETByvCIB0EL\nAIAo6NFCPAhaAABEwRY8iAdBCwCAKLxuwUMzPMIhaAEAEAVTh4gHQQsAgChohkc8CFoAAETB8g6I\nB0ELAIAomDpEPAhaAABEwcrwiAdBCwCAKKhoIR4ELQAAovDSo0UzPCIJHLQKCwvVvXt39ejRQ8OH\nD9eOHTu0adMmFRQUqEuXLurfv78qKioSOVYAABqUc1J1Nc3wCC5Q0Fq5cqX+8pe/6IMPPtDHH3+s\n6upqTZo0SePHj1dBQYGKi4vVr18/jR8/PtHjBQCgwdQuVhoKRX8cPVqIJFDQatGihbKzs7V9+3bt\n3LlT27dvV7t27TR9+nSNGDFCkjRixAhNnTo1oYMFAKAhedl+R6KihcgCBa3WrVvrZz/7mY488ki1\na9dOLVu2VEFBgcrLy5WTkyNJysnJUXl5eUIHCwBAQ/Ky/Y5E0EJkHr599rZ8+XLdf//9WrlypQ45\n5BD94Ac/0DPPPLPHY0KhkEIRaq1jxozZ9ef8/Hzl5+cHGQYAAEnl5YpDiWb4xqSoqEhFRUUJO16g\noPXee+/p9NNP16GHHipJGjJkiObNm6e2bdtq3bp1atu2rdauXavDDz887PPrBi0AANKV16BFRavx\nqF8AGjt2bFzHCzR12LVrV82fP1/ffPONnHOaPXu28vLyNHDgQE2cOFGSNHHiRA0ePDiuwQEAkEpe\nlnaQaIZHZIEqWieccIKuuOIKnXLKKcrKytJJJ52ka6+9Vl999ZWGDh2qJ554Qh07dtSUKVMSPV4A\nABoMFS3EK+Sccw16wlBIDXxKAAAC+fRTaeBAqbg4+uMqKqSOHe13NC7x5hZWhgcAIAIqWogXQQsA\ngAj89GgRtBAOQQsAgAj8VLRohkc4BC0AACLwGrT22UeqqbFfQF0ELQAAIvAatEIhq2pVVyd/TMgs\nBC0AACLw2qMl0aeF8AhaAABE4LWiJRG0EB5BCwCACPwGLRriUR9BCwCACHbupKKF+BC0AACIoKrK\ne49WdjZBC3sjaAEAEAE9WogXQQsAgAgIWogXQQsAgAhohke8CFoAAESwaZPUurW3x1LRQjgELQAA\nIti4UTrsMG+PpRke4RC0AACIwE/QoqKFcAhaAABEQNBCvAhaAABE4Ddo0QyP+ghaAABEQEUL8SJo\nAQAQAc3wiBdBCwCAMKqqpK++klq29PZ4KloIh6AFAEAYtWtoZXl8p6RHC+EQtAAACMPPtKFERQvh\nEbQAAAjDb9CiRwvhELQAAAiDihYSgaAFAEAYBC0kAkELAIAwggQtmuFRH0ELAIAwqGghEQhaAACE\nQTM8EoGgBQBAGFS0kAgELQAAwtiwgaCF+BG0AAAIY+NGqU0b74+nGR7hELQAAAiDqUMkAkELAIB6\nvvnGqlPNm3t/Ds3wCIegBQBAPV9+adWsUMj7c6hoIRyCFgAA9fidNpQIWgiPoAUAQD1BgxbN8KiP\noAUAQD1UtJAoBC0AAOoJErRohkc4BC0AAOqhooVEIWgBAFAPQQuJQtACAKAemuGRKAQtAADqoaKF\nRCFoAQBQD83wSBSCFgAA9VDRQqIQtAAAqMM5C1qHHurveQQthEPQAgCgjm3bpH32kQ480N/zaIZH\nOAQtAADq2LDB/7ShREUL4RG0AACoI0h/lkQzPMIjaAEAUEfQoEVFC+EQtAAAqGPjRqlNG//Pa9FC\n2rw58eNBZiNoAQBQR9CK1pFHSqWliR8PMhtBCwCAOoIGrVatpOpqacuWxI8JmStw0KqoqNAll1yi\nbt26KS8vT++88442bdqkgoICdenSRf3791dFRUUixwoAQNIFDVqhkFW1Vq1K/JiQuQIHrZtuukkX\nXnihli5dqkWLFqlr164aP368CgoKVFxcrH79+mn8+PGJHCsAAEkXNGhJBC3sLVDQ2rJli958802N\nGjVKktSsWTMdcsghmj59ukaMGCFJGjFihKZOnZq4kQIA0AAIWkikQEFrxYoVatOmjUaOHKmTTjpJ\n11xzjbZt26by8nLl5ORIknJyclReXp7QwQIAkGwELSRSsyBP2rlzpz744AM9/PDD6tWrl26++ea9\npglDoZBCoVDY548ZM2bXn/Pz85Wfnx9kGAAAJFy8QeuVVxI7HjSsoqIiFRUVJex4Ieec8/ukdevW\nqU+fPlqxYoUk6a233lJhYaE+//xzvfHGG2rbtq3Wrl2rc845R8uWLdvzhKGQApwSAICkq6mR9ttP\n2r7dVnr3a+5c6Ze/lN56K/FjQ2rEm1sCTR22bdtWHTp0UHFxsSRp9uzZ6t69uwYOHKiJEydKkiZO\nnKjBgwcHHhgAAA1tyxbpoIOChSyJqUPsLVBFS5I++ugjXX311aqsrNQxxxyjJ598UtXV1Ro6dKhW\nrVqljh07asqUKWrZsuWeJ6SiBQBIUyUl0oAB0mefBXt+VZUFte3bbUseZL54c0vgoBX4hAQtAECa\nmjdPuuUWaf784MfIzZX+8x+rbiHzpWTqEACAxiieRvhaTB+iLoIWAAD/laig9cUXiRkPMh9BCwCA\n/9qwIf6gddRRVLSwG0ELAID/YuoQiUbQAgDgvwhaSDSCFgAA/0XQQqIRtAAA+K+NG6U2beI7Rm0z\nPCsZQSJoAQCwSyIqWi1bWsjasiUxY0JmI2gBAPBfiQhaoRBXHmI3ghYAAJJ27pS2brWKVLzo00It\nghYAAJI2bZJatZL22Sf+YxG0UIugBQCAEjNtWIughVoELQAAlPigxTY8kAhaAABIoqKF5CBoAQCg\nxAYtrjpELYIWAABKbNBq104qL5eqqhJzPGQughYAAEps0MrOlnJypDVrEnM8ZC6CFgAASmzQkmiI\nhyFoAQCg5AQt+rRA0AIAQNKGDQQtJB5BCwAAJb6ixZWHkAhaAABIYuoQyUHQAgA0eV9+KWVlSS1a\nJO6YBC1IBC0AAFRSInXuLIVCiTtm7VWHziXumMg8BC0AQJNXG7QS6ZBDLLhVVCT2uMgsBC0AQJOX\njKAVCjF9CIIWAABJCVoSVx6CoAUAQNKCFhUtELQAAE2ac8kNWmzD07QRtAAATdqGDdI++0iHHpr4\nY1PRAkELANCkJauaJRG0QNACADRxBC0kE0ELANCkffaZ1KlTco7dvr20fr1UVZWc4yP9EbQAAE1a\nMitazZpJbdtKZWXJOT7SH0ELANCkJTNoSVx52NQRtAAATVYyl3aodfTRUnFx8o6P9EbQAgA0WeXl\n0n77Sa1aJe8cffpIb7+dvOMjvRG0AABNVrKrWZJ01lnSm28m9xxIXwQtAECT1RBBq1s3qaKChvim\niqAFAGiyGiJoZWVJfftS1WqqCFoAgCarIYKWRNBqyghaAIAmqyGD1ty5yT8P0k/IOeca9IShkBr4\nlAAA7MU5qXlzae1aqUWL5J6rqso2rV65UmrdOrnnQmLFm1uoaAEAmqQ1ayxoJTtkSVJ2tnTqqSzz\n0BQRtAAATVJDTRvWOusspg+bIoIWAKBJauigRUN800TQAgA0SQ0dtE49Vfr4Y2nbtoY7J1KPoAUA\naJIaOmgdcIB04onS/PkNd06kHkELANAkffZZwwYtienDpoigBQBocmpqpOXLpU6dGva8rKfV9BC0\nAABNTlmZ1LKlLe/QkM44Q3r3XamysmHPi9QhaAEAmpyG7s+q1bKldMwx0vvvN/y5kRoELQBAk5Oq\noCXZelo3Iu3WAAAgAElEQVT0aTUdcQWt6upq9ezZUwMHDpQkbdq0SQUFBerSpYv69++vioqKhAwS\nAIBEKilp+P6sWjTENy1xBa0HHnhAeXl5CoVCkqTx48eroKBAxcXF6tevn8aPH5+QQQIAkEiprGj1\n7Su99ZY15KPxCxy0Vq9erZdffllXX331rs0Wp0+frhEjRkiSRowYoalTpyZmlAAAJFAqg1bbtlKb\nNtInn6Tm/GhYgYPWLbfconvvvVdZWbsPUV5erpycHElSTk6OysvL4x8hAAAJVF0trViRuqlDienD\npqRZkCfNmDFDhx9+uHr27KmioqKwjwmFQrumFOsbM2bMrj/n5+crPz8/yDAAAPCttFQ69FDpwANT\nN4azzpJeflkaPTp1Y0B4RUVFEbNNECFXO+/nwy9/+Us9/fTTatasmb799ltt3bpVQ4YM0bvvvqui\noiK1bdtWa9eu1TnnnKNly5btecJQSAFOCQBAQrz6qjRunPTGG6kbw+ef25paa9ZIEWoSSBPx5pZA\nU4fjxo1TaWmpVqxYoUmTJuncc8/V008/rUGDBmnixImSpIkTJ2rw4MGBBwYAQDKksj+r1ne+YxW1\njz9O7TiQfAlZR6t2ivC2227Tq6++qi5duuj111/XbbfdlojDAwCQMMuWSV26pHYMoZA0YID0yiup\nHQeSL9DUYVwnZOoQAJBCp50m3X23dPbZqR3HjBnSH/4gJbAdCEkQb24haAEAmowdO6TWraX166WD\nDkrtWLZts6UeysqkFi1SOxZElpIeLQAAMtGHH9q0YapDlmRj6NNHeu21VI8EyUTQAgA0GfPn29Rh\nuqBPq/EjaAEAmox0C1oXXCDNnCnRUdN4EbQAAE1GugWtrl2lrCxpyZJUjwTJQtACADQJ69ZJW7ak\nfg2tuljmofEjaAEAmoR33pFOPdUqSOmkdvoQjVOafbsBAJAc6TZtWOvccy0Efv11qkeCZCBoAQCa\nhHQNWgcfLPXuLb3+eqpHgmQgaAEAGr2dO6X33rNAk46YPmy8CFoAgEZv8WIpN1dq1SrVIwmvtiGe\nZR4aH4IWAKDRS9dpw1rdu1vV7dNPUz0SJBpBCwDQ6M2fb1ccpqtQiOnDxoqgBQBo9NK9oiWxnlZj\nFXLxbEkd5IRx7oINAIAfmzdLRx5pvzdrlurRRLZli/WRlZdLBx6Y6tGgVry5hYoWAKBRW7BAOvnk\n9A5ZknTIIdJJJ0lFRakeCRKJoAUAaNQyYdqw1uWXSzfdJH3ySapHgkQhaAEAGrV33smcoHXNNdJv\nfyudc440eXKqR4NEoEcLANBoOScddphViI44ItWj8e7DD6UhQ6SLL5buvjv9pz0bM3q0AACIoKTE\ntrjJpJAlSSeeaCvZL1kiFRRI69enekQIiqAFAGi0Mqk/q77WraUZM6S+faVTTpFWr071iBAExUgA\nQKOVyUFLkvbZR7rzTik7W7rySmnWLCmLEklG4eUCADRamR60at1+u7Rtm/TQQ6keCfyiGR4A0Ch9\n/bWUkyNt2iTtt1+qRxO/5cstNM6ZI+XlpXo0TQfN8AAAhPHrX0vf+17jCFmSdMwxUmGhdNllUmVl\nqkcDr6hoAQAanZkzpWuvtWUSWrdO9WgSxzlp8GCpe3dp3LhUj6ZpiDe3ELQAAI3Khg3SCSdI//iH\nLfzZ2Kxfb1/fc89JZ56Z6tE0fkwdAgDwX85JV10l/ehHjTNkSdLhh0uPPy5dcYW0dWuqR4NYqGgB\nABqNxx6zEDJvnrTvvqkeTXJde60t+/DII6keSePG1CEAAJKWLbPFPd98U+raNdWjSb7166Vjj5VW\nrpQOOSTVo2m8mDoEADR5lZXS8OHSXXc1jZAl2RRiQYH0z3+meiSIhooWACCjVFVJa9bYljSlpfb7\n3LlSKCRNnWq/NxWzZ0s//7m0cGHT+robElOHAIAmY9o06Yc/lNq0kXJzpQ4ddv9+5ZVSq1apHmHD\nqqmROneWJk2SevVK9WgaJ4IWAKBJqKmRevSQ/vhH6YILUj2a9DF+vK0a/5e/pHokjRM9WgCAJuH5\n56WDD5bOPz/VI0kvV15p/zZffZXqkSAcghYAIO3V1Ehjx0p33EEvUn1t20rnnis9+2yqR4JwCFoA\ngLT3/PNS8+ZMGUZy7bW2fhjSD0ELAJDWamqkO++UxoyhmhVJQYG0caP0/vupHgnqI2gBANLaCy9I\nBx1ENSuarCzpmmtoiE9HXHUIAEhbNTXS8cdL99wjXXhhqkeT3taskY47Tlq1yqZZkRhcdQgAyGhL\nl0qzZtmG0PW98IJ04IHSgAENP65M066ddPbZtqYW0gdBCwCQMkVFFg5+9jPpxBMtJFRX2330ZvlH\nU3z6IWgBAFLixReloUOlyZOlRYukwkLpoYdsr8InnrDQdcABVLP86N9fKi+XPvww1SNBLXq0AAAN\n7q9/lX7zG+mll6STTtp9u3PSm29K48ZJ//63NGOG9N3vpm6cmeiOO6SKCumBB1I9ksaBLXgAAClT\nVSW9/bZ0yCG2/2CbNtJ++0V+vHO2Zczjj1tfVufOkR+7erXtYwh/VqyQeveWysqkffdN9WgyX7y5\npVkCxwIAaEJ27LANnouL7Q19/Xpby+mAAyxwHX64/ar75yVLpP/8x8JZu3bRj0/ICuY737GrD2fM\nkIYMSfVoQNACAPi2fbt08cVSixbWD1RbOXHOpq3Wr5c2bLBf69fbr88+k7KzpblzpVatUjv+xu7K\nK6UnnyRopQOmDgEAvnz1lTRwoNShg72ZN+Mje9rZts0qgkuX2l6ICI51tAAADaaiwq5s69JFmjiR\nkJWuDjrIKo7PPJPqkYCgBQDwZONG6dxzrdH6scds2xekr5EjreLotxjz+efS979v65ctWGDrmSE4\n/psAAGLavt02Lj7/fOn++1lANBOceaZdsPDee96f8/HHUt++tu3Rtm3SqFFSTo70ox9J//ynbe9D\n8PKHHi0AQFTOSSNG2Bvs008TsjLJXXfZHogTJsR+7Pz50ve+Z0F62LDdt69aJb3yiv16911p0yap\nY0fp6KOlY46xBWavuir6sh6ZjHW0AABJ9eij9mvePOv9QeZYtUrq2dPW1Np//8iPe/VV6bLLpL//\nPfbm3du321pdy5fbrylTpAsusIVSG6OUBK3S0lJdccUVWr9+vUKhkK699lrdeOON2rRpk374wx/q\niy++UMeOHTVlyhS1bNkyoQMGADSc+fOlQYNs7atOnVI9GgRRUCBdfbWteRbO889L118v/etfNt3o\n1+rVtk/lm29K3brFN9Z0lJKgtW7dOq1bt04nnniivv76a5188smaOnWqnnzySR122GH63//9X919\n993avHmzxo8fn9ABAwAaxvr10sknS488YmELmemf/5SeekqaOXPP27/+2vaWfOgh6eWXLSwF9fDD\nVtkqKmp8F0mkZHmHtm3b6sT/viLNmzdXt27dVFZWpunTp2vEiBGSpBEjRmjq1KmBBwYASJ2dO6VL\nL7XeLEJWZrv4Yrt6sKzM/r5hg/Tb39oK8gsXWiUqnpAlSdddJ1VW2mbg2FPcPVorV67U2WefrU8+\n+URHHnmkNm/eLElyzql169a7/r7rhFS0ACDt3XqrvQm/8oq0zz6pHg3i9eMfW4+Wc3ZBww9+IP3i\nF9H3mvRr0SKpXz/7/YgjEnfcVEvpXodff/21vv/97+uBBx7QwQcfvNfAQhEuTRkzZsyuP+fn5ys/\nPz+eYQBA3GpqpK1bpXptpU3SG29IkyfbsgCErMbhmmusV+uaa6TFi2PvMxnE8cfb8W++2b5/MlVR\nUZGKiooSdrzAFa2qqipddNFFGjBggG6++WZJUteuXVVUVKS2bdtq7dq1Ouecc7Rs2bI9T0hFC0Aa\nGjNGmjZN+uCD4MsX3HOPvYFdfnlCh+ZLZaX1ylx2WfCv49pr7ZL9//mfxI4Njd8331jguu8+6aKL\nUj2ava1ZI/3739K330o/+Ym3/yMp6dFyzumqq65SXl7erpAlSYMGDdLEiRMlSRMnTtTgwYMDDwwA\nGkpZmTUEf/mlXWUXxIoV0t13S7fcYldhpcrMmba45AsvBHu+czZdGOsSfyCcAw6wXQNGj7Zm+1Tb\nsUN67TWbJj3+eKlHD/s/8uc/S3fe2TBjCFTReuutt3TWWWfp+OOP3zU9WFhYqN69e2vo0KFatWoV\nyzsAyBgjRkjt20uHHip99JFdoeXXZZdJxx5rU5Affii9+GJqFvYcPtym+15/XVqyRDrkEH/P//hj\na37//HMWJkVwI0dKrVpJf/pTasfRu7f9fuGFttZXr172/6O83JayuOUWW9oiGhYsBZBwTz8tHXyw\nveE2tku163vvPWngQKm42KbdOnWSSkqkww7zfoz33999jOxsu4Lrrrtsv7iGtG2bBcaSEunXv7YN\nnx95xN8x7rlH+uIL/88D6lq/3qafP/kkOf1gXixdan1pq1aF/zn2+efSWWdZGBw6NPJxUjJ1CGBv\n//63dN55dul0Jnv7bSuz//73Vmp/9lmpujrVo0oO56wP6c47LVgeeqhtQfLkk/6O8YtfWI9X8+a2\nDclf/iLdeKNUUZG0oYc1Y4Z02mlSmzbS+PFWVZs3z98xXn5ZGjAgOeND03H44dKVV0r33pu6MTz3\nnH3YifRh8eij7fv9hhtsZfxkIWgBcVq1SrrkEis/b98uTZqU2ONv2mRv/kF7bvzYutX6ex5/3Nbd\n+eMfbY+0rl1tfZzKyuSPoSG9+KKFoVGjdt923XXWY+J149xXXpHWrt3zGGeeaRWuW29N7HhjefZZ\nW/tK2j1t8+MfS1VV3p6/ZYtV5845J3ljRNPx859LEydadSsVnn/efjZHc/zx9rjLLrN9HJOBoAUE\nVFlpVYOTTrIGy8WLpd/8RvrHPxJ3jiVLrMdg+XJbcTnZbrrJqnKDBll/zvnn22KGTzxhV7Idf7xU\nb2m8hPAaBBJpxw7pf//XwkjdJQx695ZatPD2Cbe62o5x9902TVfX3XdLL70kzZ2b2HFHUlFhyzJc\nfPHu2374Q5tK9NonM3u2dMYZ7GeIxGjXzoL/ffc1/Lk//VTauNG+n2Pp29d+xg0aJNVbKCEhCFpp\nzDmb3x4/XhoyxKolSA8ffWSh4623rPJzxx22GGBBgV199tln8Z9jxgzp7LMtvN13n30vJNMLL9jX\nE+5N+ayzbGr0/POtcuOlXaGoyBqrd+4Mf//69VY5699fOvBAaezYuIbv28MPW6XuvPP2vD0UsqrW\no4/GPsbEiVLr1la9qu+QQ6QHH7SlEnbsSMyYo3nxRencc/dsfg+FrCJ5773WjxLLK68wbYjEuvVW\n+3++aZO/51VU2M+92bODnTfWtGF9Awfaz76k/F91DSwFp8wo27c798orzo0e7dxRRznXsaNzP/2p\nc8cc49y8eakeHWpdeaVzY8eGv++GG5wbMyb4sWtqnBs/3rl27Xa/5mvWOHfooXZfMpSVOXf44bG/\nx7791rlTTnHu/vujP27cOOeOPNK5rl2dO/BA53r3du4nP3Hu8cede+QR5845x7kWLZz74Q+de+45\n55Yvt8cWFibua4pmwwbnDjvMuaVLw9//9dfOtW7t3KpVkY+xbZtz7ds7N39+5MfU1Dj3ve8599vf\nxjdeL/r3d27y5PD33X23c+efH/37p6bGuSOOcK64ODnjQ9M1apRzd9zh7bGff+7cTTc516qVc0OH\n2s+lmTP9n/P4452bM8f/88KJN7cQtFJo507nFi1y7q9/de7HP3auZ0/nDjjAuTPOsDfaTz7Z/YNx\n5Ejn/vzn1I43XlVVzk2ZYm9yme7oo537+OPw982f71znzsFCUWWlc8OHO3fyyc6Vlu6+vabG3vjX\nrQs23miqq50rKPAeDpcvd65NG+cWLAh//8MP279PWZn9fetW595807kHHnBuxAjnfvQj51580T5U\n1FVWZv9uf/pT4C/Fs9Gj7QNMNDfc4Nyvfx35/rvucu4HP4h9rtWrLSR/+qm/MfpRXu7cIYdY+Aun\nstLeeP75z8jHWLjQPtABiVZSYh9stmyJ/Jj585275BL7OfeLX+z++ff22/bzpqjI+/k+/dS5tm3t\nPTYRCFoZauNGS+pdujh3+eXOPfigfaN98034x99/v3PXXdewY0yUnTud+8c/7Gs9/HDnbrkl1SOK\nT1mZ/TCorg5/f02NvWFFCiLRPP20c3367B1CnHPurLOce+01/8eM5YEHnDv1VAvCXj3/vHPf+Y5z\nmzfveftTTzmXm2ufSoNYtcqO+/DDwZ7vxcSJznXoEDvwL15sP6wrK/e+7403LDyVlHg75733Onfh\nhb6H6tkjj1hAj+Y//7EqaaQ3u3HjLFwCyXDZZfY9Vt/XXzt37bX2f/L+++2DWX2vvWZhy+uszl13\n2YepRCFoZahXX3Xu7LO9P/6NN5w7/fRkjSY5qqvtDbl7d+dOO82+5tWrrSS8cWOqRxfcpEnODRwY\n/TF33OHcjTf6P/bppzv3r3+Fv+/66y0UJVJxsX3SDDJdNHq0c0OG7K7c/etfFkyWLIlvTCtW2LTj\nY4/Fd5xwpk93LifH+xjPPtuqsLU++si5AQOsYvfii97Pu2OHfdCYMcPXcD0780z72mIZNSryB50z\nz7S2BSAZFi+2D9pff737toULrWXgssuiV7ucc+6ll+z5CxfGPtcJJ/irgMVC0MpQf/yjv0+PmzY5\nd/DBkaso6Wb5cudOPNG5k06y/yB1p9Guuiq+HqZUGz3auXvuif6Y4mJ7Q/dTJfroI+v5ifScRx5x\n7pprvB/Pix//2HvvRH3ffGPT3Q895NysWfaJ8/33EzOukhKrjE2cmJjjOWf9GtGmPMOZNMn6yVau\ntCnPnByrPu/Y4f/8L79sU6Pffuv/udGsWmUVVi9jWr/e/g0WLdrz9tqfL+EqqUCifP/71hpQXe3c\nfffZh7ynn/b+/Oeftw9zixdHfkztz95ETRs6R9DKWCNGOPeXv/h7TocOzn32WVKGk3BXXOHcrbeG\n71Natsx+2Nf9ZJNJjj/eWwm7d29/TZzXXRc9gM6ZY9OKifLll861bOnc2rXBj1Hbe9GmjfVhJdLH\nH9v0XJBQU98HH9gYZ8/297wdO+wHe+vWzv3mN7E/dcdy0UXWmJ5I995rH168mjDBub599/y/OXly\ncqc2Aefs/2G7ds5dcIG1KwR5P3v6aftAGqkKP25c4ttsCFoZqmfP6FcrhXPRRc698EJyxpNIK1fa\nG1P9/p26LrnEPtFkms2bnWve3Nub/wMPWP+dF1u32pTq6tWRH7Nxo1UdEnXl4d13W5UmXrNnJ+7q\nnvrOPNO5adPiO0ZxsV1NF/T/zvvv21WfiVBSYuExUcdzzi6c8BMgd+605zz11O7brrzSKpNAsl19\ntXO/+lX43kevnnjCKt7hwlbPns69/nrwY4dD0MpAVVV2deFXX/l73q9+1TCXicfrhhvsqpFo3n3X\n/qMkolrRkGbMsKkkL9atsyvBvFTuHn3UuYsvjv24I45w7osvvJ0/mqoq64N67734j5VMjz5ql3gH\ntXq1LZHy178mbkzxuu02q/jWV1Pj3LPP2sUAzzzj7VjFxcGurnrnHXve5s02jZOTY9P9QKZ44gmb\n5al7Qcpnn1kfVyKnDZ2LP7ekZMFSr1tbNFYlJbZac/Pm/p53wgm2UGY627BBeuYZ2xE9mlNOscUi\n//nPhhlXorz5pq0i7EVOjtSnjzR9evTHOWeLY153XexjHnecrUAfr2nTpNxc6eST4z9WMv3gB9LM\nmbY1UBB33GGro191VWLHFY9f/Up67bU99yD87DPpggukceOk3/3Oti557rnYx3r6afs3qruyvRe9\ne9sCjXfcIX34oS1yevTR/o4BpNKoUfb9e+65uxeIfu45W9zb7/+HZEtJ0HrzzVScNX0sWmSrivuV\nCUHrgQdsF/Qjjoj92Ntvt21KMil4+wlaku2f9cwz0R8zb56t+t+vX+zjHXdcYlaIf+AB224n3R16\nqK2OP3Wq/+du22ar3d94Y+LHFY/mze37/sYbpW+/le66yzaCLiiwfQYvu8zC5U9/aoE4nJ07LbA9\n8YTtsRnEuHG2N+L48dKFFwb/eoBUueoq6be/3R22nnvOPnikm5QErUyrYiRa0KB1zDFWMdqyJfFj\nSoStW6U//1n6xS+8Pf6cc6SDD478ZlJZGXn7llT45hv79N+nj/fnDB4svf22vW6R/PnP0k9+4m2r\niO7d4w9aCxfaNkF198RLZ5ddFmz/yBdekE4/3fZbSzfDh0v77isddZRt4fT++1bFys62+084wfZJ\nvOYa2xanrtWr7f/Oe+/Za9m1a7AxHHaYhbznniNoIXNdfbVtU3bWWVJpqf2eblIStF54wd5Em6qg\nQWuffayisWiR/+eWlkp/+IO3PeqCeuwx+1R+zDHeHh8KSbfdZp+o645r/XorCbdrZ/+B0sWCBfbv\n72fD3ebNpe9+V5o8Ofz9X34p/d//SVde6e14Xipa77wj/e1vke9/8EGrgtS+qae7gQPt337dOn/P\ne/JJaeTI5IwpXqGQ7ZP45JP2QeOoo/Z+zCmn2LTziBG793t76SW7/bvftQB2+OHxjePqq+3/Xzq+\nOQFeXXON9Pvf24f8+pu7p4UE9Yp5Jsnz4np+rFwZ31UMifD119ZkGsuRRwZfpuHaa/1fHfTVV7aA\n2xFHOHf77cHOG8s339jxP/zQ3/Oqq5079li7SmTZMvv6Wra0319+2ZYOSJe1fX73O+d+9jP/z3v7\nbbvSbNy4vZv/7703fGN0JFu32t6B0Zo9L73UuYMOcu7mm/ded6283P59M23B2CuuiL2/Yl3Ll9v3\nTqLXrEqFuXPtaxkxwpp/E72MBoDo4o1KKaloDR+e2OlD56y/JUgfRyL97W+2W3i0qlFFhVUxvvOd\nYOfw26dVU2OfiE86yZ73/PPWeJ1oTz0l9exp4/MjK8t2d//BD6z3qW1b6dNPrTo2YIDUq1fkalBD\n89ufVev0022a56237HV4+227vaZm97ShVwcfbFWMFSvC319Zaf09775r00o//KH1AdV6/HHpkkus\n9ymTDB/ub/pw4kRp2DBpv/2SN6aG0revNGWKVcEWLpTOPDPVIwLgS4ICn2eS3IYNzrVo4X95g0je\ness5KfaSAsnWt69zWVnOLV0a+TFz59pCbUG99ZZzvXp5f/xvfmObVNd+sl++3CpPU6cGH0N9VVW2\nt9/cucGeX1lpaxyF2xD3pZdsdflErR0VVFWVfc/GUwmqqbHtXNq1s4rd5MlWafT7tV10UeTtX159\ndff317ffWnXrjDNs3Dt22LnrrwqeCaqqbAkCL1sFVVc7d9RRtjgiAMQr3qiUkorWYYfZp7JITdB+\nPfWUXZn03nveHv+vf0mjR0sPPyy9/rq0dm38vUtlZdY7M3y49OqrkR/38cfB+rNq9ehhl/dXV8d+\n7OTJ9m/zr3/t/mR/9NHW93H11XteXh6P55+3SlSQao9kvUJDhkgHHrj3fRdcYFXAd96Jb4zx+ugj\nWw4hnkpQKGSVu8WLrd/u0kttSYdQyN9xojXET58uDRpkf95vP6sCnXGG/frDH6Rjj7XvoUzTrJlV\n57xUtd54Q2rZ0iqsAJBqKQlaUuKmD7/91t7o77/frtzxslTAI49YsPrkE2nMGHvjad3aGrk3bQo2\njhdesKbd7343etAK2ghfq0ULW5+ppCT64957b/fl4fUbZk85xQLYxRdLxcXBxyJZCBo71pZqSIas\nrN2hOIhNmxJzAUDQacNwWraUJkyQli4Ntr5TpIZ45/YMWpL9+919t3TDDXZhQSYs6RBJ7dWHsV7P\ndG6CB9AEJaiy5lntKb/6yqZi1q+P73hTpjjXr5/9uWNHa6iOpqrKtjH58ss9b1+/3rnrr3du8OBg\n01RnnGGrhq9fb19XpMb8Pn3i365k8GDb7DaS1att1fVI00u1nnjCVqFety7YOL780rbyuPHG5E7t\nbdpkDdx+xrlqle3/tu++9v2xYkV8YxgyxPtq3cm2cKFz3bvvfftHH9nrGem1WL489VOw8aipca5T\np+ibQldU2Gr8GzY03LgANG7xRqWUVbSaN7e1W55/Pr7jPPWUdMUV9udTTok9ffjJJ7Yqe+vWe97e\npo30pz9Jq1ZZtcGPsjJpyRKriLVpY8sbhJvqqqmxqcN4p26iNcQ7Z5/8f/ITW8MpmlGjpP79gzXH\nf/mldN55NmV7//3+p7/8aNXKGrj/+ldv4/r5z+3fqE0be20KCqyp/tFHI1c8nbM1ssKtUeZcYita\n8eraVVq+fO8lUmqrWZFei6OPTu7rlGyhUOw1tSZPtgtjDjus4cYFANGkLGhJNn347LPBn79+vb0B\nDhlif/cStP7zH7sKLJz99pMmTbLpRD9X9j3/vPS979kChJK9sYebPly50kJDq1bejx1OtKBVVGQ9\nZ7fd5u1YQ4fuvSBiLBs22Eq8BQXW99MQb96jR9sVepEWMN2+3dZROfZYWxH8k0+kwkJ7w731Vmnu\nXAvl/fpJn39uz6mpsSsBb7lF6tjRXsOePe2KvbqKi6UDDpCOPDKpX6Jn++9v6y7Vnz6uP23YGF12\nmYWpSN8HTBsCSDcpDVrnn2+VoFWrgj1/0iTri6rdM7BXr9hBa968yEFLkjp3lu67zxpvt23zNo4p\nU/Zc9j9S0Fq0KDGNyCecEHnR0rvukn75S+97PZ15prRsWfSVy+tav95C1kUX2UKHDVUhOfFEC0Ph\n9g0sKZFOPVX64AN7fR99dO/VwLt1s1B10UW2z9vll1tz+/XXW8/Uyy9bEL7nHqu0PvTQ7l6guXPT\np5pVq36f1po1tgVFuo0z0Tp3ljp0sA9D5eV73rd0qb2GF1yQipEBQHgpDVr77mvrTk2atPd9n3xi\nlYZoq0HXnTaUbI2ihQujb9sSraJV6/LLbe8xL3uklZZaUDnvvN23nXmmTRFWVOz52HivOKzVsaNN\ncU2lvVEAAAwoSURBVNVv3J83z6o1w4d7P9a++9p2HtEa+GuVl9tjhwyxQNfQ01DhmuKnTbMr6kaP\ntspi586Rn7/PPtLPfmbrWPXqZdW/RYtsFfru3e3rueQS+3d88kmr9m3Zkl7ThrXqX3k4Y4YFjExZ\n7T0eTz5p29Ace6xVIadOtWnUv/9d+tGP0nRlaABNVkqDlrT31YeLFll1qF8/W5Rx8GDbY66+xYtt\niuzcc3ff1rKlVTKWLQt/rvJyafNm+wEdy8MPWwUk1tTmCy/sOW0o2dROnz52mXld8V5xWCsry45T\nf/rw97+3aTK/b7YXXOBt+vB3v7PXZezY1PT6DBlir23t8ha/+pVdTfd//2c9aV7HdOyxdvVdly7h\n7+/UyQJ5mzbSySdLs2alX9CqX9FqCtOGtbp3t1BVWmo/H/70J6tyPfYY04YA0k/Kg1bfvtLGjVbV\nGjLEmrNPPdUqMy++aA28I0fu3cT89NNWeao/RRatT2vePKtUedm8t3lzG9ONN1rjcST1pw1r9e+/\nd5UoUUFL2rtPa+FC++V1z7y6BgyQ/v3v6EtjVFVZb8wtt/g/fqLsu6907bXSuHE25vnz7bU+9dTE\nn2v//e2iiLvuskDWrVvizxGPukFr2zab3mxqU2YHH2w/G+bOtSrlY4+l3+sEACkPWllZVu6/5RYL\nXZ9/bleNHXSQVSj+9jfpiy+sJ6NWdbX0zDP2vPqiBS0v04Z19exp1ZsLL7SpivpWrbLtYvr12/u+\n+n1a27fbJ/BIVRS/6get2g0199/f/7GOOsqaxj/4IPJj/v1vqwQF3TooUa691qqIJ59sY4p3U91Y\nLr3U3sjT7Wq9Tp3se3L7dvs+693bKrpNVadO1lcJAOkm5UFLsimpL76wsFV/dfD997cejKef3n1Z\n9xtv2KKdxx2397GiNcT/5z82pefH9dfbzuBnnbX3/nLPP29TF3WnDWv16CFt3WrNuZJNdx17bOJ6\naOoGrcWLbZrzmmuCH2/AgOjTh888Y1d8pVq7dtaQX1jYtHtxsrMttC9b1rSmDQEg06RF0GrWLHxY\nqZWTY304t9xiUwT1m+Dr6tnTms7rrzFUWWnrJPXu7X98P/+5NVGfffaeK6k/95w1TIeTlWUN8rVV\nrUROG0oWMpctsym9wkLp5putChhUtD6trVvtvkhfa0Nr0SLVI0gPxx1nYXvGDLv6FgCQftIiaHlx\n3HEWsC65xD7BDxsW/nHNm9tVeYsX73n7woV2RdrBBwc7/+jRNn15zjl27C++sGUF6jbj11d3+jAR\nC5XWddBB1gD88svSzJlWeYvHWWdZz0+4LYhefFHKz49vnz8kXvfu0hNP2D6TqZ7SBQCElzFBS7Kq\nyx132JIQ0XpzwvVp+e3PCmfUKFug87zzrHdr8ODoU4EFBdJrr1lPWaIrWpJNH153nYXAeKs8++1n\nFbtwyzyky7Qh9nTccVbhZdoQANJXRgUtyS7jf+KJ6I+JFLT89meFM2yYbUr9zDOxp9Lat7dpz4UL\nkxe0vvrK23pfXoSbPlyzxv4tmZpKP7U9igQtAEhfGRe0vKjfEO9cYipatYYMscb4goLYjy0okCZO\ntJ6tnJzEnL/W0KHS448nbkpvwACbhqy7zMOkSdLFF9sWNEgvHTtKv/mNfbAAAKSn0H93pm64E4ZC\nSvYpv/nGwsemTXbV4qpV1gS/dm3DX6Y/Y4Zddt6njzR7dsOeO4hjj7VFWk86yf5+0knSvfeGX8IC\nAIDGLt7c0igrWgccYJe+1+4HWFvNSsVaSPn5dmVgoqcNk6W2qiXZPpTl5fY1AAAA/xpl0JL27NOa\nNy8x/VlBNG9uIe+EE1Jzfr/q9mn94x/Wk+Z1g2oAALCnRhu06vZpJbI/K4gpUyIvR5Fuzj7b1mba\nvNmC1uWXp3pEAABkrkbZoyVJ779v+6DNn2+bA3/5ZbDtaZqiCy+0qdfZs239r3TbfgYAgIZCj1YE\nxx0nffaZNGeOLRRKyPLuggukBx+0tbMIWQAABNdoK1qSTR+2bWsrwv/pTw1yykahpMQqWitX2obT\nAAA0VVS0ojjlFOmll1Lbn5WJOne2sEXIAgAgPo06aPXqZYuVErT869Qp1SMAACDzNeqg1aePTYG1\na5fqkQAAgKaoUfdoSdLOnVKzZg12OgAA0IjQoxUDIQsAAKRKow9aAAAAqULQAgAASBKCFgAAQJIQ\ntAAAAJKEoAUAAJAkBC0AAIAkSXjQmjlzprp27arOnTvr7rvvTvThkWJFRUWpHgLiwOuXuXjtMhuv\nX9OV0KBVXV2tn/70p5o5c6aWLFmiZ599VkuXLk3kKZBi/LDIbLx+mYvXLrPx+jVdCQ1aCxYsUKdO\nndSxY0dlZ2fr0ksv1bRp0xJ5CgAAgIyR0KBVVlamDh067Pp7bm6uysrKEnkKAACAjJHQDWpCoVBC\nH4f0NHbs2FQPAXHg9ctcvHaZjdevaUpo0Grfvr1KS0t3/b20tFS5ubl7PKaB97AGAABImYROHZ5y\nyikqKSnRypUrVVlZqcmTJ2vQoEGJPAUAAEDGSGhFq1mzZnr44Yd1/vnnq7q6WldddZW6deuWyFMA\nAABkjISvozVgwAB9+umn+uyzz3T77bfvcR9rbGWO0tJSnXPOOerevbuOO+44Pfjgg5KkTZs2qaCg\nQF26dFH//v1VUVGR4pEimurqavXs2VMDBw6UxOuXSSoqKnTJJZeoW7duysvL0zvvvMPrlyEKCwvV\nvXt39ejRQ8OHD9eOHTt47dLYqFGjlJOTox49euy6LdrrVVhYqM6dO6tr166aNWtWzOM32MrwrLGV\nWbKzs3Xfffdp8eLFmj9/vh555BEtXbpU48ePV0FBgYqLi/+/vXt5SW0N4zj+c1Oj2BBFamWBSCom\nZdEFGiYihNrFBjUwkGjipKK/IS2a5DgIpAY2jSgpkSDQBmFRYFCEguFlYDkwAq2eMzjgobPR9uEc\nzcV5PjOXstYLX5QHL6/Q6/VYW1v77qWyMtxuNzQaTfEHKNxPOBYXFzE2Nobb21tcX19DrVZzPwGI\nxWLY2tpCOBzGzc0N3t/f4fV6uV0Ns9vt8Pl8n46V6hWJRLC3t4dIJAKfzweHw4GPj4/yF6AqCQaD\nZDQai7ddLhe5XK5qXZ79S+Pj43RyckIqlYpSqRQRESWTSVKpVN+8MlZKPB4nvV5PgUCATCYTERH3\nE4hsNktyufyX49yv9mUyGVIqlfT09ESFQoFMJhMdHx9zuxoXjUZJq9UWb5fq5XQ6aW1trfg4o9FI\noVCo7Lmr9o4W77ElXLFYDJeXlxgeHkY6nYZEIgEASCQSpNPpb14dK2V5eRkbGxv48eOvpzn3E4Zo\nNIqWlhbY7Xb09/djYWEBLy8v3E8AmpqasLKygs7OTrS1taGxsREGg4HbCUypXolE4tNuCr8zy1Rt\n0OK9s4Qpl8vBarXC7Xbj58+fn+4TiUTctUYdHBxALBajr6+v5JYq3K92vb29IRwOw+FwIBwOo6Gh\n4ZePmrhfbXp4eMDm5iZisRgSiQRyuRx2d3c/PYbbCctXvb5qWbVB63f22GK1pVAowGq1wmazYWJi\nAsCfk30qlQIAJJNJiMXi71wiKyEYDGJ/fx9yuRyzs7MIBAKw2WzcTyBkMhlkMhkGBwcBANPT0wiH\nw5BKpdyvxl1cXGBkZATNzc2oq6vD1NQUQqEQtxOYUq+Vf59lHh8f0d7eXvZcVRu0eI8tYSEizM/P\nQ6PRYGlpqXjcYrHA4/EAADweT3EAY7XF6XQiHo8jGo3C6/VidHQUOzs73E8gpFIpOjo6cHd3BwDw\n+/3o7u6G2WzmfjVOrVbj/Pwcr6+vICL4/X5oNBpuJzClXistFgu8Xi/y+Tyi0Sju7+8xNDRU/mT/\n9RfKyjk8PCSlUkkKhYKcTmc1L83+obOzMxKJRNTb20s6nY50Oh0dHR1RJpMhvV5PXV1dZDAY6Pn5\n+buXyr5wenpKZrOZiIj7CcjV1RUNDAxQT08PTU5OUjab5X4Csb6+ThqNhrRaLc3NzVE+n+d2NWxm\nZoZaW1upvr6eZDIZbW9vl+21urpKCoWCVCoV+Xy+L88vIuL/xGGMMcYYq4SqfXTIGGOMMfZ/w4MW\nY4wxxliF8KDFGGOMMVYhPGgxxhhjjFUID1qMMcYYYxXCgxZjjDHGWIX8AXpqfG+WTgU+AAAAAElF\nTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot((abs(Noise)**.5)[900:1000])" ] }, { "cell_type": "markdown", "id": "cf91b080", "metadata": {}, "source": [ "Now we zero out the region containing the interfering signal.\n", "\n" ] }, { "cell_type": "code", "execution_count": 78, "id": "87663473", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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o6eBOPz34e5J2XXj/fZETToi7FMnTr18/6WcLJzfeeKOW/RR1N2JVVZWsWbNG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\nkbFji9/X4sWq9qmQuaiK0aKF+xAVDz1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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "Noise[970:980] = 0\n", "Noise[-980:-970] = 0\n", "plot(abs(Noise)**.5)" ] }, { "cell_type": "markdown", "id": "99e8fcbe", "metadata": {}, "source": [ "Finally, we transform back. Note that this doesn't get rid of the noise completely, in part because a value of 0 isn't quite correct either.\n", "\n" ] }, { "cell_type": "code", "execution_count": 79, "id": "c825652e", "metadata": { "collapsed": false }, "outputs": [], "source": [ "denoised = ifft(Noise)\n", "play(real(denoised))" ] }, { "cell_type": "markdown", "id": "3142c3dd", "metadata": {}, "source": [ "For comparison, here is the original.\n", "\n" ] }, { "cell_type": "code", "execution_count": 74, "id": "01c943ed", "metadata": { "collapsed": true }, "outputs": [], "source": [ "play(noise)" ] }, { "cell_type": "code", "execution_count": null, "id": "0848018f", "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }