{ "cells": [ { "cell_type": "code", "execution_count": 369, "id": "eb80f6da", "metadata": { "collapsed": true }, "outputs": [], "source": [ "from pylab import *" ] }, { "cell_type": "code", "execution_count": 494, "id": "743eb581", "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": "e0a3fff6", "metadata": {}, "source": [ "Simple Sine Waves, Frequencies and Phase\n", "========================================" ] }, { "cell_type": "markdown", "id": "e95f22c5", "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": 371, "id": "f7b0121e", "metadata": { "collapsed": true }, "outputs": [], "source": [ "x = 2*pi*arange(1024,dtype='d')/1024.0" ] }, { "cell_type": "markdown", "id": "110e83f6", "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": 372, "id": "8fe61209", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 372, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlkAAAE1CAYAAADUJvX7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(x,sin(x))\n", "plot(x,cos(x))" ] }, { "cell_type": "markdown", "id": "add445db", "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": "f3988847", "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": 495, "id": "f38085e0", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmkAAAExCAYAAAAnRDXVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAwkP8HWdjq5PDDkG8AAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data128 = sin(128*x)\n", "data128 /= norm(data128)\n", "plot(data128)\n", "play(data128,r=10)" ] }, { "cell_type": "code", "execution_count": 417, "id": "55abc63d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmkAAAExCAYAAAAnRDXVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBEEQBCEQLNIIgiAIgiAE4v8DXGq859oq5HwAAAAASUVORK5CYII=\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": "code", "execution_count": 418, "id": "6623c901", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmkAAAExCAYAAAAnRDXVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ny0ZSjV4AAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data32 = sin(32*x)\n", "data32 /= norm(data32)\n", "plot(data32)\n", "play(data32,r=10)" ] }, { "cell_type": "code", "execution_count": 376, "id": "b659998d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmkAAAExCAYAAAAnRDXVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n" }, "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": "e7fe1e39", "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": "code", "execution_count": 421, "id": "6b55daa5", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmIAAAE1CAYAAABENYw0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nyaIkGYhlyZIlS5YsWbIoyf8HIBWb5WJh4zIAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dataodd = sin(31.3*x)\n", "plot(dataodd)\n", "play(dataodd,r=10)" ] }, { "cell_type": "markdown", "id": "0545adbf", "metadata": {}, "source": [ "Orthogonality Relationships\n", "==============================" ] }, { "cell_type": "markdown", "id": "c9a1bd61", "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." ] }, { "cell_type": "code", "execution_count": 379, "id": "725dfddd", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 379, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32,data32)" ] }, { "cell_type": "markdown", "id": "fcac1056", "metadata": {}, "source": [ "The dot product of a sine signal and a cosine signal is 0; the two signals are _orthogonal_ as vectors." ] }, { "cell_type": "code", "execution_count": 380, "id": "921c5a1d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-3.6831216008103521e-17" ] }, "execution_count": 380, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32,data32c)" ] }, { "cell_type": "markdown", "id": "0bc2b5dc", "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\n", "half frequencies; this gives rise to the _cosine transform_)." ] }, { "cell_type": "code", "execution_count": 381, "id": "ce785589", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.7017035905939927e-15" ] }, "execution_count": 381, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32,data64)" ] }, { "cell_type": "code", "execution_count": 422, "id": "7be9a382", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-4.9462849353357798" ] }, "execution_count": 422, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32,dataodd)" ] }, { "cell_type": "markdown", "id": "e3cd1012", "metadata": {}, "source": [ "Quadrature\n", "============" ] }, { "cell_type": "markdown", "id": "2df7b39e", "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. \n", "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": 382, "id": "deac3b12", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmIAAAE1CAYAAABENYw0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEun/A+aNaQLgnYoIAAAAAElFTkSuQmCC\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": 383, "id": "25564230", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "21.616797112821242" ] }, "execution_count": 383, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32,data32p)" ] }, { "cell_type": "code", "execution_count": 384, "id": "e3762422", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "6.6868589474523219" ] }, "execution_count": 384, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32c,data32p)" ] }, { "cell_type": "code", "execution_count": 385, "id": "c410f0b0", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.7017035905939927e-15" ] }, "execution_count": 385, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(data32,data64)" ] }, { "cell_type": "code", "execution_count": 387, "id": "7e4efe2b", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.48311824805e-13" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 387, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmIAAAE1CAYAAABENYw0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEARBEDLxf7F/M9Ex/L57AAAAAElFTkSuQmCC\n" }, "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": "8d4c7101", "metadata": {}, "source": [ "A Complete Basis\n", "===============" ] }, { "cell_type": "markdown", "id": "5d57f1d2", "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": 512, "id": "f7d974f9", "metadata": { "collapsed": false }, "outputs": [], "source": [ "sins = [sin(i*x) for i in range(1,513)]" ] }, { "cell_type": "code", "execution_count": 513, "id": "85386b06", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 513, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtIAAAHcCAYAAAD7iE1HAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nikIAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12,8)\n", "plot(sins[0])\n", "plot(sins[1])\n", "plot(sins[2])" ] }, { "cell_type": "code", "execution_count": 514, "id": "090ab98b", "metadata": { "collapsed": true }, "outputs": [], "source": [ "coss = [cos(2.0*pi*arange(1024)*i/1024.0) for i in range(0,512)]" ] }, { "cell_type": "code", "execution_count": 515, "id": "efa1a934", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 515, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtIAAAHcCAYAAAD7iE1HAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRESFwEKaiIiIiKgQ/h9Svf4l+oJQYgAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12,8)\n", "plot(coss[0])\n", "plot(coss[1])\n", "plot(coss[2])" ] }, { "cell_type": "code", "execution_count": 516, "id": "8d7e02cc", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 516, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsEAAAHYCAYAAACsgDW6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCAYAIB0RDABAOiIYAIB0RDAAAOn8L7b2iIRpgsd3AAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ylim(-0.1,1.1)\n", "plot(sin(0*x)[-10:])\n", "plot(cos(0*x)[-10:])" ] }, { "cell_type": "code", "execution_count": 517, "id": "1f89f87c", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 517, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAskAAAHcCAYAAAAkxjdYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAQAAgFn+f/TjHNyYTYHQAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(sin(512*x)[-10:])\n", "plot(cos(512*x)[-10:])" ] }, { "cell_type": "markdown", "id": "168e33b5", "metadata": {}, "source": [ "Let's construct matrices out of these basis functions." ] }, { "cell_type": "code", "execution_count": 530, "id": "590e63c9", "metadata": { "collapsed": false }, "outputs": [], "source": [ "sins = array(sins)\n", "coss = array(coss)" ] }, { "cell_type": "markdown", "id": "e9bdb880", "metadata": {}, "source": [ "Now let's verify the orthogonality conditions." ] }, { "cell_type": "code", "execution_count": 531, "id": "8f4f7fc4", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-2.03463569425e-11 512.0\n", "-2.88673035129e-11 1024.0\n", "-2.14634190463e-11 2.21060387877e-11" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABV8AAAGnCAYAAACgrSd3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n4gAAAABJRU5ErkJggg==\n" }, "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": "6c08f4ba", "metadata": {}, "source": [ "We can also look at these matrices themselves" ] }, { "cell_type": "code", "execution_count": 532, "id": "ff2a172d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 532, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAU4AAAFNCAYAAABvx4bHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nzAAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12,12)\n", "subplot(121); imshow(sins[:100,:100])" ] }, { "cell_type": "markdown", "id": "6d272147", "metadata": {}, "source": [ "Now we can perform transforms with this matrix." ] }, { "cell_type": "code", "execution_count": 533, "id": "4a09401f", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 533, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlUAAAE1CAYAAADOGhV1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAIAERBUAQAKiCgAggf8PYMMRcZ7B0TYAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,5)\n", "plot(dot(sins,data32))\n", "plot(dot(coss,data32))" ] }, { "cell_type": "markdown", "id": "6b582370", "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." ] }, { "cell_type": "code", "execution_count": 534, "id": "705161db", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 534, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl8AAAE1CAYAAADZOIW8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\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": "7f768717", "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_." ] }, { "cell_type": "code", "execution_count": 400, "id": "c9c7bbbd", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 400, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlsAAAE1CAYAAADQ0yXGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n" }, "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": "b9f0a44f", "metadata": {}, "source": [ "Invertible Transform\n", "=======================" ] }, { "cell_type": "code", "execution_count": 450, "id": "aae52f94", "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": 451, "id": "1562fb2d", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def spectrum(signal):\n", " return dot(sins,signal)[:-1]**2+dot(coss,signal)[1:]**2" ] }, { "cell_type": "code", "execution_count": 452, "id": "884e741a", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 452, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmIAAAE1CAYAAABENYw0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.ndimage import filters\n", "wave = filters.gaussian_filter(randn(1024),5.0)\n", "plot(wave)" ] }, { "cell_type": "code", "execution_count": 453, "id": "5898e687", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 453, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmEAAAE1CAYAAACvAjc3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(spectrum(wave))" ] }, { "cell_type": "code", "execution_count": 454, "id": "3d7e82eb", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 454, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl8AAAE1CAYAAADZOIW8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nZND/B/lXMMNIFq94AAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(transform(wave))" ] }, { "cell_type": "code", "execution_count": 455, "id": "80cf92b9", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "2.4632919247364998e-14" ] }, "execution_count": 455, "metadata": {}, "output_type": "execute_result" } ], "source": [ "norm(wave-itransform(transform(wave)))" ] }, { "cell_type": "markdown", "id": "3ecffa4e", "metadata": {}, "source": [ "Signals after the Fourier Transform\n", "=====================================" ] }, { "cell_type": "code", "execution_count": 456, "id": "838f253c", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmUAAAE1CAYAAACm6ZdNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nWKWGk68ws30AAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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": 457, "id": "b81fc84f", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlwAAAE1CAYAAAAyDz6/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nuERERETcTIFLRERExM0UuERERETc7P8DXhsND/LQh+IAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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": 458, "id": "0e27ac79", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAm0AAAE1CAYAAAC1Pte5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n8JYnaWt5pq4AAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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": 459, "id": "e33f4244", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmcAAAE1CAYAAACiHEdwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XlUVGeiNvqnpAonAiXIoBRSDFUMipFokO4+pkkQNNri\ngMFgohjN0Hr7XGPyrevJvW0cvm9Fz3dubh+Tbjomh06j6QiGqJgYEWOCMSbCkWAnHRQKKIYqBgUE\nmaSgqPsHxzoxKiIW9dbw/NbKWmRX7V3PlqTW4/u+e2+JyWQygYiIiIhswhjRAYiIiIjov7GcERER\nEdkQljMiIiIiG8JyRkRERGRDWM6IiIiIbAjLGREREZENGbKc3bhxA3PnzsWsWbMQGRmJ1157DQDQ\n2tqKhIQEqNVqJCYmoq2tzbzP7t27oVKpEB4ejvz8fPP24uJiREVFQaVSYfPmzebtvb29WLVqFVQq\nFWJjY1FTU2N+LTMzE2q1Gmq1Gvv377fYSRMRERHZqiHL2bhx4/Dll1/i4sWL+P777/Hll1/i66+/\nxp49e5CQkIDy8nLEx8djz549AIDS0lJkZ2ejtLQUeXl52LRpE27eRm3jxo3IyMiARqOBRqNBXl4e\nACAjIwNeXl7QaDTYsmULtm7dCmCwAO7atQtFRUUoKirCzp07bymBRERERI7ontOaEyZMAAAYDAYY\njUZMmjQJx44dQ1paGgAgLS0NR48eBQDk5uYiNTUVMpkMSqUSoaGhKCwsRENDAzo6OhATEwMAWLt2\nrXmfnx4rOTkZp0+fBgCcPHkSiYmJkMvlkMvlSEhIMBc6IiIiIkclvdcbBgYG8Mgjj6CyshIbN27E\n9OnT0dTUBF9fXwCAr68vmpqaAAD19fWIjY0176tQKKDX6yGTyaBQKMzb/f39odfrAQB6vR4BAQGD\nYaRSeHh4oKWlBfX19bfsc/NYPyWRSEZ63kRERERWN5wHM91z5GzMmDG4ePEidDodvvrqK3z55Ze3\nvC6RSISWJJPJ5HT/bN++XXgGnjfPm+fN8+Z587x53vf3z3AN+2pNDw8PLF68GMXFxfD19UVjYyMA\noKGhAT4+PgAGR8Tq6urM++h0OigUCvj7+0On0922/eY+tbW1AID+/n60t7fDy8vrtmPV1dXdMpJG\nRERE5IiGLGfNzc3mRfg9PT04deoUoqOjkZSUhMzMTACDV1QuW7YMAJCUlISsrCwYDAZotVpoNBrE\nxMTAz88P7u7uKCwshMlkwoEDB7B06VLzPjePlZOTg/j4eABAYmIi8vPz0dbWhmvXruHUqVNYsGDB\n6PwpEBEREdmIIdecNTQ0IC0tDQMDAxgYGMCaNWsQHx+P6OhopKSkICMjA0qlEocOHQIAREZGIiUl\nBZGRkZBKpUhPTzdPeaanp2PdunXo6enBokWLsHDhQgDAhg0bsGbNGqhUKnh5eSErKwsA4OnpiW3b\ntuHRRx8FAGzfvh1yuXzU/iDsSVxcnOgIQvC8nQvP27nwvJ2Ls573cElM9zMJamMkEsl9zeESERER\niTLc3sInBBARERHZEJYzIiIiIhvCckZERERkQ1jOiIiIiGwIyxkRERGRDWE5IyIiIrIhLGdERERE\nNoTljIiIiMiGsJwRERER2RCWMyIiIiIbwnJGREREZENYzoiIiIhsCMsZERERkQ1hOSMiIiKyISxn\nRERERDaE5YyIiIjIhrCcEREREdkQljMiIiIiG8JyRkRERGRDWM6IiIiIbAjLGREREZENYTkjIiIi\nsiEsZ0REREQ2hOWMiIiIyIawnBERERHZEJYzIiIiIhvCckZERERkQ1jOiIiIiGwIyxkRERGRDWE5\nIyKb9Mf9HyHzo+OiYxARWR3LGRHZpA+btdivKREdg4jI6qSiAxAR/ZzB0IfLoWF4qKtTdBQiIqvj\nyBkR2Zz/yD4Gj84OdI+fgBNffCs6DhGRVXHkjIhszlcV/0Co6xj0jHXFx12X8eQTvxAdiYjIajhy\nRkQ2p3qSG9SmcQjqMKBy7IDoOEREVsWRMyKyKZ1dPbgUGoY3fQJRVafDa8brMPYb4SJ1ER2NiMgq\nOHJGRDbl3ayj8Gltxq9iorB6aSL6pFIczT8rOhYRkdUMWc7q6urw+OOPY/r06ZgxYwbeeustAMCO\nHTugUCgQHR2N6OhonDhxwrzP7t27oVKpEB4ejvz8fPP24uJiREVFQaVSYfPmzebtvb29WLVqFVQq\nFWJjY1FTU2N+LTMzE2q1Gmq1Gvv377fYSROR7fq2tgzB//U94CJ1QVhFOT4pOic4FRGR9Qw5rSmT\nyfCHP/wBs2bNQmdnJ2bPno2EhARIJBK88soreOWVV255f2lpKbKzs1FaWgq9Xo/58+dDo9FAIpFg\n48aNyMjIQExMDBYtWoS8vDwsXLgQGRkZ8PLygkajQXZ2NrZu3YqsrCy0trZi165dKC4uBgDMnj0b\nSUlJkMvlo/enQUTC1Xh5ILbzv9eZBXUboR3PQX4ich5DfuP5+flh1qxZAAA3NzdERERAr9cDAEwm\n023vz83NRWpqKmQyGZRKJUJDQ1FYWIiGhgZ0dHQgJiYGALB27VocPXoUAHDs2DGkpaUBAJKTk3H6\n9GkAwMmTJ5GYmAi5XA65XI6EhATk5eVZ6LSJyBa1X+/E5RA11i5ebN62ePYvUB6qhrHfKDAZEZH1\nDPuCgOrqapSUlCA2Nhbnzp3D22+/jf3792POnDl48803IZfLUV9fj9jYWPM+CoUCer0eMpkMCoXC\nvN3f399c8vR6PQICAgbDSKXw8PBAS0sL6uvrb9nn5rF+bseOHeaf4+LiEBcXN+yTJyLb8s7Bw5g6\ntg9zflLOkp+Mw8tHPkb2J6exenmiwHRERPenoKAABQUF973fsMpZZ2cnVq5cib1798LNzQ0bN27E\n66+/DgDYtm0bXn31VWRkZNz3h1vCT8sZEdm3ovoqBLlIbtnmInWBuqoCeT1GljMisis/HzTauXPn\nsPa750KOvr4+JCcn49lnn8WyZcsAAD4+PpBIJJBIJHj++edRVFQEYHBErK6uzryvTqeDQqGAv78/\ndDrdbdtv7lNbWwsA6O/vR3t7O7y8vG47Vl1d3S0jaUTkeGq8JyFirMdt24NvANqJMgGJiIisb8hy\nZjKZsGHDBkRGRuLll182b29oaDD/fOTIEURFRQEAkpKSkJWVBYPBAK1WC41Gg5iYGPj5+cHd3R2F\nhYUwmUw4cOAAli5dat4nMzMTAJCTk4P4+HgAQGJiIvLz89HW1oZr167h1KlTWLBggWXPnohsxtXm\nNpQFq/Dc0qTbXlsaOw+Xue6MiJzEkNOa586dwwcffICZM2ciOjoaAPDGG2/g4MGDuHjxIiQSCYKC\ngrBv3z4AQGRkJFJSUhAZGQmpVIr09HRIJINTFOnp6Vi3bh16enqwaNEiLFy4EACwYcMGrFmzBiqV\nCl5eXsjKygIAeHp6Ytu2bXj00UcBANu3b+eVmkQO7J2sjzFtvBFRixbd9trSBfPwz1kHkZnzGdY/\nvURAOiIi65GY7nTZpZ2QSCR3vGqUiOzPsh070CcBjm/fccfXn9j9vzDlxgD+tvN16wYjIrKQ4fYW\n3jyIiGxCje9kTJ8w+a6vh/ZLUe0+zoqJiIjE4LM1iUg4fUMzNMoQHAqPuut7nvr1E/j4WgMMhj64\nuvLiACJyXBw5IyLh9h06jKC6GqiC7n5FdsJjMXDv6kDGoU+smIyIyPpYzohIuIvX6qFsaLzn+0Kq\ntTij+cEKiYiIxGE5IyLhaqb4IMrd957vUw2MRY18ohUSERGJwzVnRCSUtq4RldOC8NuZs+/53tT5\niTh4tQ49Pb0YP36sFdIREVkfR86ISKj3Dh1GSE0Vpvn73PO9j8XOwuS2VrybddQKyYiIxGA5IyKh\nvu+8AmXj1WG/P6SmBl9XXxrFREREYrGcEZFQ1f5T8IjX8J+bqx4zEbVe7qOYiIhILJYzIhLmckUt\nqv2n4aVVK4a9z5onF+FyiBrt1ztHMRkRkTgsZ0QkzH8cPgp1lQZ+Pp7D3icmOgJ+V69g38Ejo5iM\niEgcXq1JRMKU3riGwO77fz5uUF0dCvv5XF0ickwcOSMiYbSKqZjjE3jf+0XI3FEzWT4KiYiIxGM5\nIyIhvv+xAjo/f2xMTb7vfZ9bsgRlIWq0Xrs+CsmIiMRiOSMiId7/5BOEVZbDc9L9X3k5c3ooFI16\n/Pngx6OQjIhILK45IyIhLvVdR2DzyNeNBenqcWGA686IyPFw5IyIhNAGBGDu1JAR7x85bhJqvId/\nlScRkb2QmEwmu/2rp0QigR3HJ3Ja54t/xIJGLfRx8XCbOH5Ex7hcUYs5mh9RMXvufd2Kg4hIlOH2\nFo6cEZHVfZB3AuEV5SMuZgAQHjoNSl0N/nwwx4LJiIjE45ozIrK6clM3AlsffNRbWd+Iixw8JyIH\nw5EzIrK6qsBA/EoZ/sDHmenmg2o/bwskIiKyHSxnRGRVX52/iGa5J158etkDH+uFlBWoDAxGrf6K\nBZIREdkGljMisqqDn+cjoqIM48ePfeBjBQX4IaRWi3cO8X5nROQ4uOaMiKxKM6YXgW0DFjteYMMV\n/CCx2OGIiIRjOSMiq6pUBiF5YILFjjdr0lQcGW+5skdEJBqnNYnIak4WFOL6xIewIWWJxY75UsoK\naAMCodHqLHZMIiKRWM6IyGpyvvoCERVlcHWVWeyY/lMmQ62twLs5Ryx2TCIikTitSURWUykbQOD1\nPosfN/BKC0q57oyIHATLGRFZjSY4GGvGuFv8uLO9p+HDcUaLH5eISAROaxKRVeSePIte17FYu3yh\nxY/90qoVqJvijx8uV1n82ERE1sZyRkRWkXv+LMIqyuEidbH4sb0nyxFWpcH7uccsfmwiImvjtCYR\nWUXVOCCoy/LrzW4KvHoNl1y48IyI7B/LGRGNOmO/EeXBoXhRKh+1z4iZGoz3x45e+SMishZOaxLR\nqPv4RAFMY8Zg1ZL4UfuM36auQL23Hy78/fKofQYRkTWwnBHRqDte/C3Uo7Te7CYPdzeEV5Zj//Hj\no/YZRETWwGlNIhp12gkuCO4e/UcsBba0o0zKdWdEZN9YzohoVBn7jbisCsOW8V6j/lm/CgzHH6W9\no/45RESjidOaRDSqPjiSB1eDAcsX/nrUP+ul1OVonuSJs0Xfj/pnERGNliHLWV1dHR5//HFMnz4d\nM2bMwFtvvQUAaG1tRUJCAtRqNRITE9HW1mbeZ/fu3VCpVAgPD0d+fr55e3FxMaKioqBSqbB582bz\n9t7eXqxatQoqlQqxsbGoqakxv5aZmQm1Wg21Wo39+/db7KSJyHpO/fgd1FWVVvms8ePHIqKyDB/m\n51nl84iIRsOQ5Uwmk+EPf/gDfvzxR5w/fx5/+tOfcOnSJezZswcJCQkoLy9HfHw89uzZAwAoLS1F\ndnY2SktLkZeXh02bNsFkMgEANm7ciIyMDGg0Gmg0GuTlDX55ZmRkwMvLCxqNBlu2bMHWrVsBDBbA\nXbt2oaioCEVFRdi5c+ctJZCI7EO1myuCDdYbpA+81oUKCac2ich+DfmN6efnh1mzZgEA3NzcEBER\nAb1ej2PHjiEtLQ0AkJaWhqNHjwIAcnNzkZqaCplMBqVSidDQUBQWFqKhoQEdHR2IiYkBAKxdu9a8\nz0+PlZycjNOnTwMATp48icTERMjlcsjlciQkJJgLHRHZB4OhD5dVYUieF2e1z3wsdAYqlEqrfR4R\nkaUN+4KA6upqlJSUYO7cuWhqaoKvry8AwNfXF01NTQCA+vp6xMbGmvdRKBTQ6/WQyWRQKBTm7f7+\n/tDr9QAAvV6PgICAwTBSKTw8PNDS0oL6+vpb9rl5rJ/bsWOH+ee4uDjExcUN95SIaJRl5nyGiZIu\nPLn0F1b7zOdXJeH3eZ/h9NkLiJ83x2qfS0T0cwUFBSgoKLjv/YZVzjo7O5GcnIy9e/fioYceuuU1\niUQCiUTcpes/LWdEZFu+KLuI0LGjd2+zO3F1lSG8ogzZXZdYzohIqJ8PGu3cuXNY+91zIUhfXx+S\nk5OxZs0aLFu2DMDgaFljYyMAoKGhAT4+PgAGR8Tq6urM++p0OigUCvj7+0On0922/eY+tbW1AID+\n/n60t7fDy8vrtmPV1dXdMpJGRLavxmMCQo3Wv2OPsr0HlS79Vv9cIiJLGLKcmUwmbNiwAZGRkXj5\n5ZfN25OSkpCZmQlg8IrKm6UtKSkJWVlZMBgM0Gq10Gg0iImJgZ+fH9zd3VFYWAiTyYQDBw5g6dKl\ntx0rJycH8fGDj3dJTExEfn4+2tracO3aNZw6dQoLFiyw/J8AEY0Kg6EPl1RheDo+0eqf/Xj4LFQE\nBVv9c4mILEFiunk55R18/fXXeOyxxzBz5kzz1OXu3bsRExODlJQU1NbWQqlU4tChQ5DLBx9o/MYb\nb+Avf/kLpFIp9u7day5UxcXFWLduHXp6erBo0SLzbTl6e3uxZs0alJSUwMvLC1lZWVD+12Le999/\nH2+88QYA4Pe//735wgFzeIkEQ8QnIoH+uP8j/GFMDyqfXWv1zzb2G+H3SS7+4uaDJQn/ZPXPJyK6\nk+H2liHLma1jOSOyXSnbd6JNJkH+718X8vnz/t89UHcNIGP7/y3k84mIfm64vYVPCCCiUVHj6QaV\nZLywz1d29KFyLP/yRkT2h8/WJCKL6+zqweWQMOydEiQsw4JZMdja3wZjvxEuUuteMUpE9CA4ckZE\nFrfvw8PwbbmK2NnThWVIXTIfxjEuOJx3RlgGIqKRYDkjIos7r9Mg6L9ukSOKi9QFYZUaHL/wjdAc\nRET3i+WMiCyuerIHwqUP3fuNoyyo2wjtBE5pEpF94ZozIrKo9uudKAtW491pKtFRsHjOL/HPva1c\nd0ZEdoUjZ0RkUX/+28eYeqUR0VFq0VGwYuGv4TJgxMFPPhcdhYho2FjOiMiiihq1CKrT3fuNVuAi\ndYGqsgInLxaJjkJENGwsZ0RkUTU+nogcKxcdwyzEIIH2IVfRMYiIho1rzojIYq42t6E8KBT7QyNF\nRzFb8as4rOto4rozIrIbHDkjIotJP5iDafU6TFcrRUcxWxz/S0zo6cFfPvpUdBQiomFhOSMiiylp\n0UGprxcd4zah2ip8efmi6BhERMPCckZEFlPtOxkzJk4WHeM2IUYpqj3EPeeTiOh+cM0ZEVmEvqEZ\nFcoQHI54WHSU26yKm4+ca3oYDH1wdZWJjkNENCSOnBGRRbyTnYPgumoEK6eKjnKb+Hlz4NFxHf+R\nfUx0FCKie2I5IyKL+HtbIwIbmkTHuKvQ6mp8VfEP0TGIiO6J5YyILKJ6ig8edvcTHeOuQk1jUTNp\nougYRET3xDVnRPTAqqrrUTUtCC/OnC06yl2tTlyIg0016OzqgdtEXhxARLaLI2dE9MD25RxGaHUl\npvn7iI5yV/NiZsL7WgvezToqOgoR0ZA4ckZED+wfXc1QdopOcW/BNTX4tt8kOgYR0ZA4ckZED6za\nfyqivRSiY9xTmIsbarw8RMcgIhoSyxkRPZAfy6tRO1WBTakrRUe5p7WLF+NyiBrt1+1gmI+InBbL\nGRE9kL8cyYVaWwHvyXLRUe5pzsPhmHq1Ee8cPCw6ChHRXXHNGRE9kEu9bQjstp91XEG1OhQZ7Scv\nETkfjpwR0QPRKvwxx08pOsawRYz1QI33JNExiIjuiuWMiEas5Idy6H2n4LdPrxAdZdieW5qEsmAV\nrja3iY5CRHRHLGdENGKZx48jrEoDz0nuoqMMW1R4MAIa9NiXzXVnRGSbuOaMiEbsUt91KJvtb/1W\nkE6PC/YXm4icBEfOiGjEtNOmIVahEh3jvk2fMBk1vpNFxyAiuiOWMyIakfPFP6LJyxsvrbaf9WY3\nvbByGTTKEOgbmkVHISK6DcsZEY3IgbzPEF5ZZpcPEVcFKRBUV4N9h7jujIhsD9ecEdGIaEw9CGy1\n34VbyoZGXLTf+ETkwFjOiGhEKpVKbO4fJzrGiEW5++L4BLYzIrI9nNYkovv25TffodVDjhdWLRUd\nZcR+m5KMymlB0NY1io5CRHQLljMium/Zp08hvKIM48ePFR1lxKb5+yCkpgrvcd0ZEdkYTmsS0X2r\ncDFA2TYgOsYDUzZexfcS0SmIiG7FckZE961CGYynTBNEx3hgsyZNxccT7L9kEpFjGXJac/369fD1\n9UVUVJR5244dO6BQKBAdHY3o6GicOHHC/Nru3buhUqkQHh6O/Px88/bi4mJERUVBpVJh8+bN5u29\nvb1YtWoVVCoVYmNjUVNTY34tMzMTarUaarUa+/fvt8jJEtGDO/HFt+icOBHPPfUb0VEe2MbUlahW\nBOJyRa3oKEREZkOWs+eeew55eXm3bJNIJHjllVdQUlKCkpISPPnkkwCA0tJSZGdno7S0FHl5edi0\naRNMpsEroTZu3IiMjAxoNBpoNBrzMTMyMuDl5QWNRoMtW7Zg69atAIDW1lbs2rULRUVFKCoqws6d\nO9HWxocUE9mCj88WIFxTBldXmegoD8zPxxPqKg3+4/BR0VGIiMyGLGfz5s3DpEmTbtt+s3T9VG5u\nLlJTUyGTyaBUKhEaGorCwkI0NDSgo6MDMTExAIC1a9fi6NHBL8Jjx44hLS0NAJCcnIzTp08DAE6e\nPInExETI5XLI5XIkJCTcVhKJSIwq1wEoOw2iY1hM4NVWlN64JjoGEZHZiNacvf3229i/fz/mzJmD\nN998E3K5HPX19YiNjTW/R6FQQK/XQyaTQaFQmLf7+/tDr9cDAPR6PQICAgaDSKXw8PBAS0sL6uvr\nb9nn5rHuZMeOHeaf4+LiEBcXN5JTIqJhKg8OQdqYh0THsJg5PoH4YFy/6BhE5IAKCgpQUFBw3/vd\ndznbuHEjXn/9dQDAtm3b8OqrryIjI+O+P9hSflrOiGh0Hck7gz6ZDM8mLRQdxWI2piZjz7df4/sf\nKzBzeqjoOETkQH4+aLRz585h7Xff9znz8fGBRCKBRCLB888/j6KiIgCDI2J1dXXm9+l0OigUCvj7\n+0On0922/eY+tbWDC3H7+/vR3t4OLy+v245VV1d3y0gaEYlxrPBrhFVq4CJ1ER3FYjwnuSOsshzv\nf/KJ6ChERABGUM4aGhrMPx85csR8JWdSUhKysrJgMBig1Wqh0WgQExMDPz8/uLu7o7CwECaTCQcO\nHMDSpUvN+2RmZgIAcnJyEB8fDwBITExEfn4+2tracO3aNZw6dQoLFix44JMlogejHSeBssvxpgAD\nm9twqe+66BhERADuMa2ZmpqKM2fOoLm5GQEBAdi5cycKCgpw8eJFSCQSBAUFYd++fQCAyMhIpKSk\nIDIyElKpFOnp6ZBIBu/umJ6ejnXr1qGnpweLFi3CwoWDUyIbNmzAmjVroFKp4OXlhaysLACAp6cn\ntm3bhkcffRQAsH37dsjl8lH7QyCiezP2G1EWosJLMsf7f3Hu1BBkjO0THYOICAAgMd3p0ks7IZFI\n7njlKBFZ3sHcU3ilrw26ZSscaloTANqvd2La2QKcmhqCmOgI0XGIyEENt7fw2ZpENCwnSs473Hqz\nmzzc3RBeUY79nx0XHYWIiOWMiIZHO1GG4BuiU4yewNYOlJu6RccgIuKzNYno3oz9RpSFqvE/JniL\njjJqfqUMx9tSB26fRGQ3OHJGRPe0/0gexhp6sXTBPNFRRs2LTy9Ds9wTX52/KDoKETk5ljMiuqfP\n/1EMVVWV6Bijavz4sYioKMPBz/NFRyEiJ8dyRkT3VOM+DiF9jv91EdjWBc2YXtExiMjJcc0ZEQ3J\nYOjDpdAwbPPwEx1l1P1aFYX/PYYXBRCRWI7/V2EieiDvf/QpHurqxIK4uaKjjLoNKUtwfeJDOPVV\nkegoROTEWM6IaEgF5d8jtNqx15vd5OoqQ3hFGT4684XoKETkxFjOiGhI1fIJCDW6io5hNcrrN1Ah\ndbznhxKR/eCaMyK6q56eXlwKDce/egeIjmI182fMxusDfAg6EYnDkTMiuqt3s45iclsrHoudJTqK\n1axdvhC9rmORe/Ks6ChE5KRYzojors5VX0ZwTY3oGFblInVBWEU5cs+znBGRGCxnRHRXNZ4PQS2Z\nIDqG1QV19aFqnOgUROSsuOaMiO6os6sHl0PVeHtqiOgoVrfw4bn4H/1tMPYb4SJ1ER2HiJwMR86I\n6I7e+fAwfJuvIiY6QnQUq1u1JB6mMWPw8YkC0VGIyAmxnBHRHZ3XaRBcWys6hhAuUheoK8pxvPhb\n0VGIyAmxnBHRHdVMliNc5i46hjBBPSZoJ3BKk4isj2vOiOg2rdeuoyxYhQxlmOgowiyJ+RU23Wjh\nujMisjqOnBHRbd7JOgz/pnrMnB4qOoowyxLnQdbXhw9z80VHISInw3JGRLf5z6ZqBOnqRccQykXq\nAnVVJU7+cEF0FCJyMixnRHSbGm9PRI6bJDqGcMGGMah2c57nihKRbeCaMyK6ReOVVpQHq/Charro\nKMIlz4vDmo4mGAx9cHWViY5DRE6CI2dEdIt92Yeh1NciPHSa6CjCPfnELzCxuwuZOZ+JjkJEToTl\njIhu8V2LDkp9g+gYNiNUq8UXZRdFxyAiJ8JyRkS3qPHzxgw3b9ExbEaoUYoaD+d7vigRicM1Z0Rk\nVqu/gorAYLwY8bDoKDbj6fhEHGrRcd0ZEVkNR86IyOzdQ4cRXKtFsHKq6Cg24/FfPoJJ7e14N+uo\n6ChE5CRYzojI7O/XG6FsuCI6hs0JqdHibGWp6BhE5CRYzojIrHqKH2ZN4qjZz6kxHtWebqJjEJGT\nYDkjIgCARquDNiAQL6WsEB3F5qxZuAiXQ8LQ2dUjOgoROQGWMyICALyXcxSq6kr4T5ksOorNiZ09\nHb4tV7Hvw8OioxCRE+DVmkQEAPixuxmBXaJT2K6g2lqc7zeJjkFEToAjZ0QEAKhWTMXsyQGiY9is\ncOlDqJ7sIToGETkBljMiwo/l1aidosBvn04WHcVmrfvNb1AWrEb79U7RUYjIwbGcEREyjuRCXaWB\n92S56Cg2KzpKjalXGvHnv30sOgoROTiuOSMiXOptQ2A311PdS1CdDkVG/jkR0ejiyBkRQRugQIxf\nkOgYNi+M9smSAAAXuUlEQVRirBw13pNExyAiBzdkOVu/fj18fX0RFRVl3tba2oqEhASo1WokJiai\nra3N/Nru3buhUqkQHh6O/Px88/bi4mJERUVBpVJh8+bN5u29vb1YtWoVVCoVYmNjUVNTY34tMzMT\narUaarUa+/fvt8jJEtHtLvz9Mup9/LDxGa43u5cNy5eiPFiFq81t934zEdEIDVnOnnvuOeTl5d2y\nbc+ePUhISEB5eTni4+OxZ88eAEBpaSmys7NRWlqKvLw8bNq0CSbT4PD/xo0bkZGRAY1GA41GYz5m\nRkYGvLy8oNFosGXLFmzduhXAYAHctWsXioqKUFRUhJ07d95SAonIcvYfP47wynJ4uPMO+PcyXa3E\ntHod0g/miI5CRA5syHI2b948TJp06xD+sWPHkJaWBgBIS0vD0aODDwPOzc1FamoqZDIZlEolQkND\nUVhYiIaGBnR0dCAmJgYAsHbtWvM+Pz1WcnIyTp8+DQA4efIkEhMTIZfLIZfLkZCQcFtJJCLLKDN2\nIrClXXQMu6HU16OkRSc6BhE5sPu+IKCpqQm+vr4AAF9fXzQ1NQEA6uvrERsba36fQqGAXq+HTCaD\nQqEwb/f394derwcA6PV6BAQM3ldJKpXCw8MDLS0tqK+vv2Wfm8e6kx07dph/jouLQ1xc3P2eEpFT\nqwoMxMa+saJj2I0ZEyfj5ETRKYjIHhQUFKCgoOC+93ugqzUlEgkkEsmDHOKB/bScEdH9OVf0A654\nTsaLj8eLjmI3Xlq5An+69HfoG5r5qCsiGtLPB4127tw5rP3u+2pNX19fNDY2AgAaGhrg4+MDYHBE\nrK6uzvw+nU4HhUIBf39/6HS627bf3Ke2thYA0N/fj/b2dnh5ed12rLq6ultG0ojIMj7Mz0NERRnc\nJo4XHcVuBCunIriuGu9kc90ZEY2O+y5nSUlJyMzMBDB4ReWyZcvM27OysmAwGKDVaqHRaBATEwM/\nPz+4u7ujsLAQJpMJBw4cwNKlS287Vk5ODuLjB//2npiYiPz8fLS1teHatWs4deoUFixYYJETJqL/\nVi7pQeA13vH+fgU2NOHvbY2iYxCRgxpyWjM1NRVnzpxBc3MzAgICsGvXLvzLv/wLUlJSkJGRAaVS\niUOHDgEAIiMjkZKSgsjISEilUqSnp5unPNPT07Fu3Tr09PRg0aJFWLhwIQBgw4YNWLNmDVQqFby8\nvJCVlQUA8PT0xLZt2/Doo48CALZv3w65nHcuJ7K0ysAgLB0YJzqG3XnY3Q/HJgyIjkFEDkpiunm/\nCzskkUhgx/GJhDp99gJWttWjacGTcHWViY5jV2r1VxD5fTG+j3gYwcqpouMQkZ0Ybm/hEwKInNSh\ngs8RoSljMRuBaf4+CK2pwrsfHxEdhYgcEJ+tSeSkKlz6oWzvFR3Dbikbr+IHsRerE5GDYjkjclIV\nQcF4Grxh10hFeylwaDzXnRGR5XFak8gJHT/9DbrHj8f6p34jOord2pS6ErVTFfixvFp0FCJyMCxn\nRE7o8LkChFWUw0XqIjqK3fKeLIdaW4G/HMkVHYWIHAynNYmcUJWrCUEdBtEx7F7glVZccuHCMyKy\nLJYzIidj7DdCExyK9S7uoqPYvTl+ShwY2y86BhE5GE5rEjmZo/ln0SeVYvXSRNFR7N5vn14Bve8U\nlPxQLjoKETkQljMiJ/NJ0TmuN7MQz0nuCKvSIPP4cdFRiMiBcFqTyMlox0sQ1G0UHcNhBDa34bKU\n686IyHJYzoiciLHfiPJQNX431lN0FIfxC4UK+1x5cQURWQ6nNYmcyMFPPseYASNWLPy16CgO46XV\nK9Dk5Y3zxT+KjkJEDoLljMiJnLxYBFVlBdebWZDbxPEIryzDgbzPREchIgfBckbkRKofkiGkl+uj\nLC2wtRMaU4/oGETkILjmjMhJGPuNuByixv/l5iM6isP5p6AI7JXeEB2DiBwER86InERmzmcY39uL\nJQn/JDqKw3lh1VK0esjx5TffiY5CRA6A5YzISZy+VIJQbaXoGA5p/PixCK8oQ/bpU6KjEJEDYDkj\nchLV7uMQ2s+VDKNF2daNChfeUoOIHhy/qYmcgMHQh8uhYdgxaYroKA4rTj0TuyXdomMQkQPgyBmR\nE8g49AncuzqQ8FiM6CgO67mnfoPOiRNx4otvRUchIjvHckbkBM5ofkCoVis6hkNzdZUhXFOGj88W\niI5CRHaO5YzICdRMmohQ01jRMRyestOAKtcB0TGIyM5xzRmRg+vp6cWlkDD8b99A0VEcXsL0R/D/\nDHSIjkFEdo4jZ0QObt/BI5h8rRXzYmaKjuLwnl2+EH0yGY7knREdhYjsGMsZkYM7V3MZIbU1omM4\nBRepC8IqNThW+LXoKERkx1jOiBxcrZc71GMmio7hNJRd/dCO4/NLiWjkuOaMyIG1X+/E5RA13p4a\nIjqK03gyei5e6WuDsd8IF6mL6DhEZIc4ckbkwPYdPAK/q1cQEx0hOorTSFn8BADg0PEvBCchInvF\nckbkwArrKxFUVyc6hlO5ue7sREmh6ChEZKdYzogcWM1kOSJdPUTHcDrBN4DqiVw1QkQjw28PIgd1\ntbkNZSFqvB8cLjqK01kaOw8vdF/lujMiGhGOnBE5qH3ZhxHQoEdUeLDoKE5n6YJ5GGvoxf4jeaKj\nEJEdYjkjclDFV2sRpNOLjuG0VFVV+PwfxaJjEJEdYjkjclA1Pl6InOAlOobTCukbgxr3caJjEJEd\n4pozIgfUeKUV5UGhyA6PEh3Faa187Amsbm+EwdAHV1eZ6DhEZEc4ckbkgP58MAdKXQ1UQQrRUZzW\ngri5eKirE+9/9KnoKERkZ1jOiBzQxWv1UNY3io7h9EKrq1BQ/r3oGERkZ0ZczpRKJWbOnIno6GjE\nxMQAAFpbW5GQkAC1Wo3ExES0tbWZ3797926oVCqEh4cjPz/fvL24uBhRUVFQqVTYvHmzeXtvby9W\nrVoFlUqF2NhY1NTwwc1Ew1Xt542Zbj6iYzi9UKMrquUTRMcgIjsz4nImkUhQUFCAkpISFBUVAQD2\n7NmDhIQElJeXIz4+Hnv27AEAlJaWIjs7G6WlpcjLy8OmTZtgMpkAABs3bkRGRgY0Gg00Gg3y8gYv\nPc/IyICXlxc0Gg22bNmCrVu3Pui5EjmFWv0VVAYG44WUFaKjOL1V8Qm4HBqGnp5e0VGIyI480LTm\nzYJ107Fjx5CWlgYASEtLw9GjRwEAubm5SE1NhUwmg1KpRGhoKAoLC9HQ0ICOjg7zyNvatWvN+/z0\nWMnJyTh9+vSDRCVyGu8c+hghNVUICvATHcXpPf7LR+DVdg3vZeeKjkJEdmTEV2tKJBLMnz8fLi4u\neOmll/DCCy+gqakJvr6+AABfX180NTUBAOrr6xEbG2veV6FQQK/XQyaTQaH47wXL/v7+0OsH78uk\n1+sREBAwGFIqhYeHB1pbW+Hp6XlLjh07dph/jouLQ1xc3EhPicghfH+9Ccp20SnopuCaGnzdZ8L/\nKToIEVldQUEBCgoK7nu/EZezc+fOYcqUKbh69SoSEhIQHn7rI2IkEgkkEslIDz9sPy1nRARUT/VD\ncjev9bEVaskE/Kcnfx9Ezujng0Y7d+4c1n4j/saYMmUKAMDb2xvLly9HUVERfH190dg4eIVYQ0MD\nfHwGFyT7+/ujrq7OvK9Op4NCoYC/vz90Ot1t22/uU1tbCwDo7+9He3v7baNmRHQrjVaHakUgNqau\nFB2F/svaRYtxOVSNzq4e0VGIyE6MqJx1d3ejo6MDANDV1YX8/HxERUUhKSkJmZmZAIDMzEwsW7YM\nAJCUlISsrCwYDAZotVpoNBrExMTAz88P7u7uKCwshMlkwoEDB7B06VLzPjePlZOTg/j4+Ac+WSJH\n927OEai1FfDz4V9kbEVMdAR8m6/inQ8Pi45CRHZiRNOaTU1NWL58OYDBUa1nnnkGiYmJmDNnDlJS\nUpCRkQGlUolDhw4BACIjI5GSkoLIyEhIpVKkp6ebpzzT09Oxbt069PT0YNGiRVi4cCEAYMOGDViz\nZg1UKhW8vLyQlZVlifMlcmil3S0I7BKdgn4uuLYW5/tN934jEREAiennl1zaEYlEctsVo0TOLDLj\nPay+4YLf/x/rRUehn3h5zx9wbqIE//nPL4uOQkQCDbe3cJUqkYP44XIV6qb446VVvL+ZrVm/ZAnK\nglVovXZddBQisgMsZ0QO4v3cYwir0sB7slx0FPqZmdND4d/UgHeyuO6MiO5txLfSICLbcqm3HYHd\nnOa3VUE6PS4Y+fshonvjyBmRg6iaFoC5U0NEx6C7iBw3CdW8ipaIhoHljMgBFJVcQqO3D15KXS46\nCt3F8yuWoTxYhcYrraKjEJGNYzkjcgAHTnyG8MpyeLi7iY5CdxEeOg1KfS32ZXPdGRENjWvOiBxA\n+UAXprUMiI5B96DUN+A7LjsjontgOSNyAJXTAvG7/rGiY9A9zHDzRt5E0SmIyNZxWpPIzp0t+h7N\nkzy53swOvJi8HBWBwajVXxEdhYhsGMsZkZ37MD8PEZVlGD+eI2e2Llg5FcG1Wrx7iOvOiOjuOK1J\nZOcqJL0IvMb1ZvZC2XAFf5eITkFEtozljMjOVSiVWD4wQXQMGqaH5X7IncCrAojo7jitSWTHTn1V\nhOtu7nh+VZLoKDRMv121ElUBSmi0OtFRiMhGsZwR2bGPznyB8IoyuLrKREehYfKfMhmq6kq8l3NU\ndBQislGc1iSyYxXSfiivc72ZvQlsasaPXHdGRHfBckZkxyqCQvAs+FQAezN7cgCyxhtFxyAiG8Vp\nTSI79cmpr9EzdizSVi4SHYXu02+fTkbtFAV+LK8WHYWIbBDLGZGdOvrNVwivLIeL1EV0FLpP3pPl\nUFdpkHEkV3QUIrJBnNYkslOVY01QdvSJjkEjFHj1Gi65cOEZEd2O5YzIDhn7jdCEhOJ5qVx0FBqh\nGL8g/HVcv+gYRGSDOK1JZIcO552BcYwLUpfMFx2FRmjjM8mo9/FDyQ/loqMQkY1hOSOyQ8cvfIOw\nCq43s2ce7m4IryzHXz/9VHQUIrIxnNYkskNVE1wQ3M37m9m7wJZ2XJZy3RkR3YrljMjOGPuNKAtV\nY/M4L9FR6AH9YloY/izrFR2DiGwMpzWJ7MyHufmQ9fdjWeI80VHoAb349DJc8ZyMc0U/iI5CRDaE\n5YzIzuR/fwGqqgquN3MAbhPHI6KiDB/m54mOQkQ2hOWMyM5oH3JFsIHrlBxF4LVOlEt6RMcgIhvC\nNWdEduTmerPXHvIVHYUsZF5IJP6/MTdExyAiG8KRMyI78pePPsWEnh4sjv+l6ChkIS8+vQzXPDxw\n+uwF0VGIyEawnBHZkS8vX0Sotkp0DLIgV1cZIjRlOFTwuegoRGQjWM6I7Ei1x3iEGLkawdEEtnej\nwoWPciKiQfyWJ7ITBkMfLoeG4X9O8hcdhSzsifBZ+F/oFB2DiGwER86I7MS7WUchv34d8fPmiI5C\nFrb+qd+ge/wEHD/9jegoRGQDWM6I7MTZylKE1GhFx6BR4CJ1QVhFOQ6fKxAdhYhsAMsZkZ2omeQG\ntWm86Bg0SoI6DKhyNYmOQUQ2gGvOiOxAZ1cPLoWG4U2fQNFRaJQkzpyD14zXYew38ukPRE6OI2dE\nduDdrKPwaW3Gr2KiREehUbJ6aSL6pFIczT8rOgoRCcZyZocKCgpERxDCmc/729oyBNfUiI5iVc72\n+7657uy9Qx+IjiKEs/2+b+J5053YdDnLy8tDeHg4VCoV/vVf/1V0HJvhrP9RO/N513h5IMzFTXQU\nq3LG33dQtxGX9c550Ycz/r4Bnjfdmc2WM6PRiN/97nfIy8tDaWkpDh48iEuXLomORWR1vb0GXA5R\nY+3ixaKj0ChbPPsXaPH0grHfKDoKEQlks+WsqKgIoaGhUCqVkMlkePrpp5Gbmys6FpHVXfjHJUy9\n2og5D4eLjkKjLPnJOEhMJmR/clp0FCISSGIymWzy2u2cnBycPHkS7733HgDggw8+QGFhId5++23z\neyQSiah4RERERPdtOLXLZm+lMZziZaO9koiIiGjEbHZa09/fH3V1deZ/r6urg0KhEJiIiIiIaPTZ\nbDmbM2cONBoNqqurYTAYkJ2djaSkJNGxiIiIiEaVzU5rSqVS/PGPf8SCBQtgNBqxYcMGREREiI5F\nRERENKpsduQMAJ588kmUlZWhoqICr7322i2vOeM90NavXw9fX19ERTnXXeLr6urw+OOPY/r06Zgx\nYwbeeust0ZGs4saNG5g7dy5mzZqFyMjI2/4fcHRGoxHR0dFYsmSJ6ChWo1QqMXPmTERHRyMmJkZ0\nHKtpa2vDypUrERERgcjISJw/f150pFFXVlaG6Oho8z8eHh5O8922e/duTJ8+HVFRUVi9ejV6e3tF\nR7KKvXv3IioqCjNmzMDevXuHfrPJDvX395tCQkJMWq3WZDAYTA8//LCptLRUdKxR99VXX5m+++47\n04wZM0RHsaqGhgZTSUmJyWQymTo6Okxqtdopft8mk8nU1dVlMplMpr6+PtPcuXNNZ8+eFZzIet58\n803T6tWrTUuWLBEdxWqUSqWppaVFdAyrW7t2rSkjI8NkMg3+t97W1iY4kXUZjUaTn5+fqba2VnSU\nUafVak1BQUGmGzdumEwmkyklJcX017/+VXCq0ffDDz+YZsyYYerp6TH19/eb5s+fb6qoqLjr+216\n5OxunPUeaPPmzcOkSZNEx7A6Pz8/zJo1CwDg5uaGiIgI1NfXC05lHRMmTAAAGAwGGI1GeHp6Ck5k\nHTqdDp999hmef/55p7sq29nOt729HWfPnsX69esBDC5p8fDwEJzKuj7//HOEhIQgICBAdJRR5+7u\nDplMhu7ubvT396O7uxv+/v6iY426y5cvY+7cuRg3bhxcXFzw61//GocPH77r++2ynOn1+lv+I1Yo\nFNDr9QITkbVUV1ejpKQEc+fOFR3FKgYGBjBr1iz4+vri8ccfR2RkpOhIVrFlyxb827/9G8aMscuv\nqBGTSCSYP38+5syZY77Ho6PTarXw9vbGc889h0ceeQQvvPACuru7RceyqqysLKxevVp0DKvw9PTE\nq6++imnTpmHq1KmQy+WYP3++6FijbsaMGTh79ixaW1vR3d2N48ePQ6fT3fX9dvnNx5vPOqfOzk6s\nXLkSe/fuhZubczxncsyYMbh48SJ0Oh2++uorp3ge3aeffgofHx9ER0c73SjSuXPnUFJSghMnTuBP\nf/oTzp49KzrSqOvv78d3332HTZs24bvvvsPEiROxZ88e0bGsxmAw4JNPPsFTTz0lOopVVFZW4t//\n/d9RXV2N+vp6dHZ24m9/+5voWKMuPDwcW7duRWJiIp588klER0cP+ZdPuyxnvAea8+nr60NycjKe\nffZZLFu2THQcq/Pw8MDixYtx4cIF0VFG3TfffINjx44hKCgIqamp+OKLL7B27VrRsaxiypQpAABv\nb28sX74cRUVFghONPoVCAYVCgUcffRQAsHLlSnz33XeCU1nPiRMnMHv2bHh7e4uOYhUXLlzAL3/5\nS3h5eUEqlWLFihX45ptvRMeyivXr1+PChQs4c+YM5HI5wsLC7vpeuyxnvAeaczGZTNiwYQMiIyPx\n8ssvi45jNc3NzWhrawMA9PT04NSpU4iOjhacavS98cYbqKurg1arRVZWFp544gns379fdKxR193d\njY6ODgBAV1cX8vPzneLKbD8/PwQEBKC8vBzA4Pqr6dOnC05lPQcPHkRqaqroGFYTHh6O8+fPo6en\nByaTCZ9//rnTLNe4cuUKAKC2thZHjhwZcirbZu9zNhRnvQdaamoqzpw5g5aWFgQEBGDXrl147rnn\nRMcadefOncMHH3xgvsUAMHgp9sKFCwUnG10NDQ1IS0vDwMAABgYGsGbNGsTHx4uOZXXOsoyhqakJ\ny5cvBzA41ffMM88gMTFRcCrrePvtt/HMM8/AYDAgJCQE77//vuhIVtHV1YXPP//cadYXAsDDDz+M\ntWvXYs6cORgzZgweeeQRvPjii6JjWcXKlSvR0tICmUyG9PR0uLu73/W9NvvgcyIiIiJnZJfTmkRE\nRESOiuWMiIiIyIawnBERERHZEJYzIiIiIhvCckZERERkQ1jOiIiIiGzI/w/l7GcJR+LcFgAAAABJ\nRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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": 460, "id": "6bbd2f71", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmUAAAE1CAYAAACm6ZdNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for frequency in [1,10,100,500]:\n", " signal = sin(frequency*x)\n", " plot(transform(signal))" ] }, { "cell_type": "markdown", "id": "5ecae29e", "metadata": {}, "source": [ "Complex Numbers\n", "================" ] }, { "cell_type": "markdown", "id": "0cdaf498", "metadata": {}, "source": [ "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": "aae676df", "metadata": {}, "source": [ "Complex numbers are closely tied to trigonometric functions.\n", "That's because complex numbers can be thought of as 2D values 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.\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": "8a7115f5", "metadata": {}, "source": [ "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": 556, "id": "90132617", "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": 557, "id": "44c033c1", "metadata": { "collapsed": true }, "outputs": [], "source": [ "s = b(3,n,N)" ] }, { "cell_type": "code", "execution_count": 558, "id": "bfe73c08", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 558, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl8AAAExCAYAAABCqceqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\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": "cae80412", "metadata": {}, "source": [ "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": "aafa45e9", "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": 559, "id": "a8208df5", "metadata": { "collapsed": true }, "outputs": [], "source": [ "F = array([b(k,n,N) for k in range(0,N)])" ] }, { "cell_type": "code", "execution_count": 560, "id": "a333719b", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 560, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlYAAAE1CAYAAAAlLa52AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYGPFMAzDMAyjCDZWDMMwDMMwivj/VhI17dDt5nIAAAAASUVORK5CYII=\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": 564, "id": "ca0859f2", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 564, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAm4AAAE1CAYAAABeCWy6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFaDU1fX8MwAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Y = dot(F,y)\n", "plot(abs(Y)**2)" ] }, { "cell_type": "code", "execution_count": 565, "id": "4659cd5b", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 565, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl8AAAE8CAYAAAD+N9R0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(Y) # ???" ] }, { "cell_type": "code", "execution_count": 566, "id": "bdfbb70f", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[6, 14, 406, 414]" ] }, "execution_count": 566, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[i for i in range(N) if abs(Y[i])>100]" ] }, { "cell_type": "markdown", "id": "9419a455", "metadata": {}, "source": [ "Fourier Transform of Common Signals\n", "===================================" ] }, { "cell_type": "code", "execution_count": 572, "id": "d4ce87a4", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def max1(x): return x*1.0/amax(abs(x))" ] }, { "cell_type": "code", "execution_count": 573, "id": "f8534703", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 573, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAE1CAYAAAA75J7FAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIiIe9v8BP2eM9kwRJU0AAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "signal = n\n", "transform = dot(F,signal)\n", "plot(max1(signal))\n", "plot(max1(abs(transform)))" ] }, { "cell_type": "markdown", "id": "d72d8a4e", "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." ] }, { "cell_type": "code", "execution_count": 574, "id": "894319bf", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 574, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAE1CAYAAAA75J7FAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLEmSpBQzYEmSJKWYAUuSJCnF/h83kgN8HQH01gAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(roll(max1(signal),200))" ] }, { "cell_type": "markdown", "id": "4636f22e", "metadata": {}, "source": [ "A double sawtooth illustrates this as well and is similar." ] }, { "cell_type": "code", "execution_count": 576, "id": "78f1796a", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 576, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAE1CAYAAAA75J7FAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDKNlbILFMAzDMAyjZf8GjGFElj8DB3AAAAAASUVORK5CYII=\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": "c93e19d0", "metadata": {}, "source": [ "The Fourier transform of an impulse is a flat spectrum." ] }, { "cell_type": "code", "execution_count": 579, "id": "3eab0154", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 579, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAExCAYAAACgddzTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngAUAkJiABQCQmIAFAJCYgAUAkNj/AUevGfe7Ip54AAAAAElFTkSuQmCC\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": "c53015a0", "metadata": {}, "source": [ "Again, we're actually looking at a circular convolution, so what the Fourier transform \"sees\" is this." ] }, { "cell_type": "code", "execution_count": 581, "id": "1dce3919", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 581, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlsAAAExCAYAAABLQmfQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAQAAWETYAgAAsOj/AYJwJ2eK/oB6AAAAAElFTkSuQmCC\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": "f4a4d601", "metadata": {}, "source": [ "If the signal isn't a perfect impulse but a little broader, the transform changes significantly." ] }, { "cell_type": "code", "execution_count": 583, "id": "1bb383a0", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 583, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAE1CAYAAAA75J7FAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XlcTfnjP/DXbaHs2UI1ExUVSUSWQdYShREyo2nGHtkG\n0yyYrJ9pZhhGluw72WuoEKKxZWfUmBCSZTCZItN6fn/MT9+JSnTufd/l9Xw8eozrns55vedwe3mf\nc99XIUmSBCIiIiKSjZ7oAERERETahgWLiIiISGYsWEREREQyY8EiIiIikhkLFhEREZHMWLCIiIiI\nZFZiwRoyZAhMTU3h4OBQ7Dbjxo2DjY0NHB0dceHCBdkDEhEREWmaEgvWZ599hujo6GKfj4yMxPXr\n15GUlITly5fD399f9oBEREREmqbEgtW+fXuYmJgU+3xERAT8/PwAAC4uLnj69CkePnwob0IiIiIi\nDWNQlm9OTU2FhYVFwWNzc3PcvXsXpqamhbZTKBRlOQwRERGRSpX1g27KVLCKClBcmdqVsAvZednI\nzstGVl4WsnKzkJ6Vjicvnvz7lfkEjzMf4276XTx8/hB1K9WFZTVLWFazhG1NWzjUdoCDqQMsqlho\nTGELCgpCUFCQ6Bgq16ZNENLTg2BlBUREiE6jOrp6vjlu3cJx65aSxp2Vm4U/nvyBhEcJSHyciIRH\nCbj+13WkpKcgIysDZlXMYFHFAnUq1YGJsQmqGVVDtfLVUM2oGiqWq4jy+uVRTr8cPBt5Qk+hXu+5\nk6NnlKlgmZmZISUlpeDx3bt3YWZmVuS2fe36lnq/2XnZuJt+F7ee3kJyWjISHidg4emFuPLnFbzI\neYEmtZugpVlLtDVvizYWbWBexbwswyCZSRJQq9a//yUiIs2Xm5+Lq39eRXxqPE6nnkZ8ajz+ePIH\n6pvUh30te9jXskdf276wqWEDiyoWqFWxltqVJlUrU8Hy8vJCSEgIfHx8cOrUKVSrVu21y4Pvopx+\nOTQwaYAGJg2A+oWfe5z5GFceXkF8ajw2XtmI0ZGjYWxgjLYWbdG5fmd0t+oOy2qWZc5AZaOvz4JF\nRKSp8vLzcPHBRRy/cxzdN3THybsnYVbZDC7mLmhVrxVGOY+CQ20HlDcoLzqq2iqxYA0aNAhHjx7F\n48ePYWFhgRkzZiAnJwcAMHLkSHh4eCAyMhLW1taoWLEi1qxZo/TANSvURKf6ndCpficA/16ivP7X\ndfx651ccSj6EqYenwsTYBG5Wbuhu1R1d6neBsaGx0nMVxdXVVchxRatXzxXPnulewdLV881x6xaO\nW3s9ev4Ie//Yi31J+3Dk1hGYVjSFbSNb+LX0Q5h3GEyMi3/TG71OIZX1Lq7SHEShKPPNYqWVL+Xj\n0oNL2H9jP6KvR+Pig4vobtUd3vbe8LDxQKVylVSSQ5eNHQskJQF6ekBkpOg0RERUnOS0ZOz5fQ/2\nXNtT8PPSs6EnujboinqV64mOJ4wcvUXrCtarHj1/hPBr4diZuBPH7xxH5/qdMbjpYHg29OTUppIE\nBAA3b/47gxUVJToNERH916Pnj7D1t63YeGUjktOS4dXIC31t+6JLgy4wMjASHU8tsGC9pbQXaQi/\nFo4Nlzfg0oNL8GniAz9HPzjXc9aYdyZqgtGjgTt3gJwcYP9+0WmIiCgrN6vg51/c7Tj0bNgTvk19\n0bVBVxjolXlBAa3DglUGt57ewoZLG7D20loYGRhhVItR8Gvmhyrlq4iOpvH8/YHUVOCff4ADB0Sn\nISLSXTfTbiL0XCjWXFgDB1MH+Dn6oa9tX1QuX1l0NLXGgiUDSZJw9PZRLDmzBDE3Y/Bx048xpuUY\n2Na0FR1NY40aBTx4ADx/Dhw8KDoNEZFuyZfyEZkUiSVnliA+NR5+zfwwssVINKzRUHQ0jSFHb9H5\neUGFQgFXS1e4WrribvpdhJ4LhetaVzQ1bYopbaega4OuvHz4liSJyzQQEanaP7n/YMOlDfjx5I+o\nUr4KxrQcg50Ddgp7J72u0/kZrKJk5WZh629bEXw8GBUMK+DLD75EX9u+0NfTFx1NI4wYATx9Cjx5\nAhw6JDoNEZF2S3uRhqVnl2JR/CI0r9scX7T9Ah3e78DJgTLgJUIly5fyEXEtAv/79X94+s9TBLYL\nhG9TXxjqG4qOptaGDwcyMoA//wQOHxadhohIOz3JfIJ5J+dh2dll8GzkicltJsPB1EF0LK0gR2/R\n7XXs30BPoYc+tn1waugpLOu5DJuubILdYjtsurwJefl5ouOpLUn6dw0sDezURERqL+1FGqYdmYaG\nIQ3xOPMxLoy8gHV91rFcqRkWrFJQKBToVL8TDn1yCCs8V2DxmcVwXOaI3Ym7NXJmTtlYsIiI5JeR\nlYGZR2fCZpEN7mXcw9nhZ7Hcczner/a+6GhUBBast9SpficcH3IcwV2DMePoDLRa2QrHbh8THUut\n5Of/W7Dy80UnISLSfLn5uVhxbgUahTTCtSfXcHLoSazyWoX6JvXf/M0kjM6/i/BdKBQK9GzYEz1s\neiDstzD47vZFy3ot8X237//9gGodxxksIqKykyQJ0dejMeXgFNSsUBMRgyLgXM9ZdCwqJc5glYGe\nQg+DHAbh9zG/w6mOE1quaInAmECkZ6WLjiYUl2kgIiqbxEeJcN/kjon7J2Jul7k44neE5UrDsGDJ\nwNjQGN90+Aa/+f+Gx5mP0SikETZc2qCz92exYBERvZtn2c8QGBOIDms7oKdNT1zxvwKvRl5cckED\nsWDJqG7luljltQoRPhFYcHoBOq/vjMRHiaJjqRwvERIRvR1JkrAjYQfsF9vjXsY9XPG/gnEu47gs\nkAbjPVhK0NKsJeKHxWPJmSVov6Y9RjqPxDftv0EFwwqio6kECxYRUendTLsJ/33+SE1PxcYPN6LD\n+x1ERyIZcAZLSfT19DHWZSwu+1/Gjb9uoMmSJjicrBurbrJgERG9WV5+HhacWoBWK1qhS/0uuDDy\nAsuVFuEMlpLVq1wPW723IjIpEn57/NDTpie+7/Y9qpSvIjqa0nCZBiKikiU8SsDQiKEop18OJ4ee\nhE0NG9GRSGacwVIRDxsP/Ob/G3Lzc9F0aVMcuHFAdCSl4QwWEVHRcvJyMOvoLHRc2xF+jn444neE\n5UpLcQZLhaoaVcVKr5U4cOMAhv8yHN2tumN+9/moXL6y6GiyYsEiInrdtcfX4LvbF9WNq+P8iPOw\nqGohOhIpEWewBOhu1R1X/K9AkiQ4hTrh1N1ToiPJiss0EBH9H0mSsOTMErRb3Q6fNvsUUR9HsVzp\nAM5gCVKlfBWs9FqJXYm70GdrH4xuORpft/8aBnqaf0pYsIiI/nU/4z6GRAzB48zHOD7kOBrVbCQ6\nEqkIZ7AE+9DuQ5wfeR6/3vkVHdd2xM20m6IjlRkvERIRAfv+2AenUCe0rNcSJ4acYLnSMSxYaqBe\n5XqIHhyN/vb90Xpla2y/ul10pDJhwSIiXZadl43JBybDf58/dgzYgZmdZnLBUB2k+dejtISeQg8T\nWk9A+/faY8COATh6+yjmdZ+H8gblRUd7a1ymgYh0VXJaMnx2+qB2xdq4MPICalSoIToSCcIZLDXT\nol4LnB9xHg+ePUDb1W1x468boiO9Nc5gEZEu2pW4Cy4rXeDT2AcRPhEsVzqOBUsNVTWqiu39t+NT\nx0/RZlUb7ErcJTrSW2HBIiJdkpufiy8OfoFJByZh70d7MbHNRH44M/ESobpSKBQY6zIWrc1bo//2\n/jh77yxmdZoFfT190dHeiO8iJCJd8TjzMXx2+EChUODs8LOctaICnMFScy3NWuLM8DM4efckPLd4\n4uk/T0VHeiMWLCLSBefunYPzcmc413NG9MfRLFdUCAuWBqhVsRYODD6AhjUaotWKVkh4lCA6Uol4\niZCItN26i+vgvskdP3b/Ed91/U4jri6QavESoYYw1DfEAvcFaF63OVzXuiK0Vyj62vUVHatILFhE\npK1y8nIwcf9EHLhxALF+sWhcu7HoSKSmWLA0zCeOn8C+lj0+DPsQFx5cQJBrEPQU6jURyYJFRNoo\n7UUa+m/vj/IG5RE/PB7VjKqJjkRqTL1+MlOpONdzxpnhZ3A4+TB8dvjgRc4L0ZEK4TpYRKRtbvx1\nA21WtYGDqQMifCJYruiNWLA0lGklU8R8EgMDPQN0Xt8Zfz7/U3SkApzBIiJtEnc7Du1Wt8OE1hPw\nk9tPvN+KSoUFS4MZGRhh04eb0K1BN7Re2RqJjxJFRwLAdxESkfZYf2k9+m3rh/V912OU8yjRcUiD\n8B4sDadQKDCz00xYmVih49qO2NJvC7o06CI0EwsWEWm6fCkf045Mw5YrWxD7aSzsa9mLjkQahjNY\nWsKvmR+29d+Gj3Z9hNUXVgvNwkuERKTJsvOy4bvbF7G3YnF62GmWK3onnMHSIq6Wrjj26TF4bPbA\nnb/v4NuO3wr5uAYWLCLSVBlZGei3rR8qGFZAjG8MjA2NRUciDcUZLC3TqGYjnBhyAuHXwjEmcgzy\n8vNUnoEFi4g00cNnD9FpXSfUN6mPHQN2sFxRmbBgaSHTSqaI9YtF4uNE+Oz0QVZulkqPz2UaiEjT\n3PjrBtqtbodeDXthWc9lMNDjBR4qGxYsLVXVqCqiPo5CvpQPj80eyMjKUNmxOYNFRJrk3L1zaL+m\nPSa3nYwg1yAht1aQ9mHB0mJGBkbY5r0NNtVt4LrOVWVrZfFdhESkKWJuxqDHph5Y7LGYyzCQrFiw\ntJy+nj6W9lyKXg17od3qdkhOS1b6MVmwiEgT/HLtF3y08yPsGLBDbT/blTQXLzLrAIVCgRmuM1DT\nuCY6ru2ImE9i0LBGQ6Udj5cIiUjdhf0WhvHR47Hvo31oadZSdBzSQixYOmSsy1hULFcRndZ1woHB\nB5T2KfAsWESkzlZfWI2ph6fioO9BOJg6iI5DWooFS8cMcRoCIwMjdN3QFZEfRcKprpPsx2DBIiJ1\ntej0Ivxw4gfEfhqr1Jl8IhYsHfSRw0cor18e7pvcEeETARdzF1n3z2UaiEgdfffrd1hxfgWOfXYM\nltUsRcchLffGm9yjo6Nha2sLGxsbBAcHv/b848eP4e7ujmbNmqFJkyZYu3atMnKSzPrZ98Nqr9Xw\n3OKJuNtxsu6bM1hEpE4kScL0I9Ox/tJ6xH0Wx3JFKlFiwcrLy0NAQACio6ORkJCALVu2IDExsdA2\nISEhcHJywsWLFxEbG4tJkyYhNzdXqaFJHj0b9sTmfpvx4bYPEXMzRrb9smARkbqQJAnTY6dj9++7\ncfTTo6hXuZ7oSKQjSixY8fHxsLa2hqWlJQwNDeHj44Pw8PBC29StWxfp6ekAgPT0dNSoUQMGBrzy\nqCm6NuiKnQN2YtDOQTicfFiWfXKZBiJSB5Ik4dvYb7Hn9z04/Mlh1KpYS3Qk0iElFqzU1FRYWFgU\nPDY3N0dqamqhbYYPH46rV6+iXr16cHR0xMKFC5WTlJSmw/sdsKP/DgzcMRCxt2LLvD8WLCJSB0FH\ng7ArcRcOfXKI5YpUrsSpptJ8XMDcuXPRrFkzxMbG4saNG+jWrRsuXbqEypUrF9ouKCio4Neurq5w\ndXV9p8CkHB0tO2Kb9zb0394fuwbsQvv327/zvniJkIhEC4oNwo6EHTjidwS1K9YWHYfUXGxsLGJj\nY2XdZ4kFy8zMDCkpKQWPU1JSYG5uXmibEydO4JtvvgEAWFlZoX79+rh27RqcnZ0LbfffgkXqqVP9\nTtjSbws+3PYh9gzcg3bvtXun/bBgEZFIM2JnYHvCdhz+5DDLFZXKqxM/M2bMKPM+S7xE6OzsjKSk\nJNy6dQvZ2dkICwuDl5dXoW1sbW0RE/PvDdIPHz7EtWvX0KBBgzIHIzG6NuiKjX03om9YX5xMOflO\n+2DBIiJRZh2dhbCrYTj8yWGYVjIVHYd0WIkFy8DAACEhIXBzc4O9vT0GDhwIOzs7hIaGIjQ0FADw\n9ddf4+zZs3B0dETXrl3x/fffo3r16ioJT8rhZu2GtX3WovfW3ohPjX/r7+c6WEQkwo8nfsTGKxtx\n2I/lisRTSJLy5xkUCgVUcBiS2d4/9mJI+BAc9D0IxzqOpf6+pk2BJUsANzfg+XMlBiQi+v+WnV2G\n4OPBOPbpMVhUtXjzNxCVQI7e8saFRkl39WrYCyEeIeixqQf+ePJHqb+P7yIkIlXaeHkjZh+bjRjf\nGJYrUhtcsIpKNKDxAGRkZaDbhm6I+ywO71V9743fw4JFRKqyO3E3Jh+YjMN+h2FV3Up0HKICLFj0\nRkObD0V6Vjq6beiGY58ee+O9DbzJnYhUYf/1/Ri5dySiPo6CfS170XGICuElQiqViW0mwqeJD9w2\nuiHtRVqJ27JgEZGyxd2Ow+Ddg7Fr4C60qNdCdByi17BgUakFdQyCq6Urem7uiefZxd+9zoJFRMp0\n4f4F9NvWD5s/3IwP3vtAdByiIrFgUakpFArMd5sP25q26BvWF1m5WUVux2UaiEhZbvx1Az0398TS\nnkvRzaqb6DhExWLBoreip9DDcs/lqFSuEj4N/xT50ustijNYRKQMD589hNtGN0zvOB397PuJjkNU\nIhYsemsGegbY3G8zUtNTMenApNfWCuG7CIlIbulZ6eixqQcGNx2MUc6jRMcheiMWLHonRgZGCPcJ\nx8EbB/HjiR8LPceCRURyysrNQt+wvnAxd8G3Hb8VHYeoVFiw6J2ZGJsgenA0Qs6EYMOlDQW///IS\nIRFRWeXl58F3ty+qGVVDSI8QKBQK0ZGISoXrYFGZmFcxR9THUei0rhNqV6wNN2s3SBLw8jXwv78m\nInobkiRhfPR4/Pn8T0QPjoa+nr7oSESlxnkGKjP7WvbYNWAXfHf74uy9s68VLCKidxF8PBhxd+IQ\n7hMOIwMj0XGI3goLFsmi3XvtsNJrJTy3eCKr4nUoFP+WLC7VQETvYutvW7HkzBJEfhSJqkZVRcch\nemu8REiy8WrkhXsZ9zD2bk88zToBhaIGZ7CI6K39eudXjIsah5hPYmBWxUx0HKJ3whksktUo51Ew\nuuOFUbF9oTDMYsEioreS9CQJ3tu8saHvBjQ1bSo6DtE7Y8Ei2VU5HYyaxrWR7zkE+flsWERUOo+e\nP4LHZg/M6jQLbtZuouMQlQkLFslP0sPCjhsAkxuYETdddBoi0gAvcl6g99be6G/fH8NbDBcdh6jM\nWLBIdpIEGBsaw3BHBLZe3YQ1F9aIjkREaixfyoffHj+8V/U9zO48W3QcIlnwJneS3ctlGvRe1MbO\nfvvQI8wV71V9D10adBEdjYjU0NeHvsa9jHuI+SQGegr+u5+0A/8kk+xeFiyFAmhU3Q5h3mEYtHMQ\nEh4liI5GRGpm+bnl2JW4C3t89nCtK9IqLFgku/x8FFoHy9XSFT90+wGeWzzxJPOJ6HhEpCYOJx/G\n9CPTse+jfahZoaboOESyYsEi2f13BuvlMg1+zfzQz64fvLd7IycvR2xAIhLu+l/X8dHOj7Cl3xbY\n1LARHYdIdixYJLuXH/asp1f4o3L+1+V/qGhYEWOjxkLiAllEOuvvf/6G1xYvBLkGoVP9TqLjECkF\nCxbJrqgZLADQ19PH5n6bEXcnDkvOLBEXkIiEycvPw6Cdg9C5fmeMch4lOg6R0rBgkeyKK1gAUKV8\nFfwy6BfMOjYLMTdjxAQkImECYwKRnZeNn9x+Eh2FSKlYsEh2JRUsAGhg0gBbvbfi410fI+lJkuoD\nEpEQay6sQfi1cGzrvw2G+oai4xApFQsWye5NBQv4952FszrNgtdWLzz956lqAxKRyh2/cxyBMYH4\nZdAvqG5cXXQcIqVjwSLZvbpMQ3FGtBiBbg26wWeHD3Lzc1UXkIhU6vbT2+i/vT/W910P25q2ouMQ\nqQQLFsmuNDNYL813m488KQ9TDk5RTTgiUqln2c/gtdULX7T7Au7W7qLjEKkMCxbJrrhlGopioGeA\nbd7bsPePvdh4eaNqAhKRSkiShKERQ9G8bnOMdxkvOg6RSvGzCEl2bzODBQAmxibYPXA3Oq3rhMa1\nGsOprpPyQxKR0v144kfcTLuJuM/ioFAoRMchUinOYJHs3rZgAUCT2k2w2GMxPtz2IR5nPlZuQCJS\nupibMZh/aj52DdjFzxgkncSCRbJ7l4IFAAMaD0B/+/4YtHMQb3on0mC3nt7C4F2DsaXfFlhUtRAd\nh0gIFiyS3bsWLACY22UuJEnCN4e/UU44IlKqzJxM9A3ri8B2gXC1dBUdh0gYFiySXWmXaSiKgZ4B\ntnpvxbar27Dt6jblBCQipZAkCSP3joR9LXtMaD1BdBwioXiTO8muLDNYAFCzQk3sGrAL3Td2h30t\nezSp3UT+kEQku0Xxi3Dl4RWcGHqCN7WTzuMMFsnubZZpKI5TXSfM7z4ffcP6Iu1FmrwBiUh2R28d\nxZy4Odg1cBcqGFYQHYdIOBYskl1ZZ7Be8nX0hYeNBwbvHox86S2vNRKRytxNv4tBOwdhQ98NaGDS\nQHQcIrXAgkWyk6tgAcCP3X5ERlYGZh6dKU84IpJVdl42vLd5Y2yrsehu1V10HCK1wYJFspOzYBnq\nGyLMOwzLzy3HgRsH5AlIRLKZcnAKTCuZIvCDQNFRiNQKCxYphVwFCwDqVq6Lzf02w2+PH+6m3y37\nDolIFtuvbscv137B2t5roafgjxOi/+LfCJLVy0IlZ8ECAFdLV4xrNQ4Dtg9ATl6OPDslond27fE1\njI4cje39t8PE2ER0HCK1w4JFsvrvulfvsg5WSQI/CER14+oIjOGlCCKRMnMy4b3dG7M7zUaLei1E\nxyFSSyxYJKuXSzQAZVumoSh6Cj2s77seu3/fjZ0JO+XbMRGVmiRJGL1vNBxNHTGixQjRcYjUFhca\nJVm9vMEdkPcS4UvVjatje//t8NjkgaamTWFTw0beAxBRiVZfWI0z987g9LDTXEyUqAScwSJZKbtg\nAYBzPWfMcJ0B7+3eeJHzQv4DEFGRLj64iC8PfYkd/XegUrlKouMQqTUWLJKVKgoWAIxyHoUmtZsg\nICpAOQcgokL+/udveG/zxqIei2BXy050HCK198aCFR0dDVtbW9jY2CA4OLjIbWJjY+Hk5IQmTZrA\n1dVV7oykQVRVsBQKBUJ7heJkykmsubBGOQchIgD/3nf1WfhncLN2g08TH9FxiDRCifdg5eXlISAg\nADExMTAzM0PLli3h5eUFO7v/+9fL06dPMWbMGOzfvx/m5uZ4/Pix0kOT+lJVwQKASuUqYceAHei4\ntiNambVC49qNlXcwIh22KH4R7vx9B1v6bREdhUhjlDiDFR8fD2tra1haWsLQ0BA+Pj4IDw8vtM3m\nzZvRr18/mJubAwBq1qypvLSk9vLzCxcsOZdpKIp9LXsEdw3GwB0DkZmTqdyDEemg8/fPY/ax2Qjz\nDkN5g/Ki4xBpjBJnsFJTU2FhYVHw2NzcHKdPny60TVJSEnJyctCpUydkZGRg/Pjx8PX1fW1fQUFB\nBb92dXXlpUQtpcoZrJc+a/YZDiUfwoToCVjuuVz5ByTSERlZGRi4YyAW9VgEq+pWouMQKU1sbCxi\nY2Nl3WeJBas0b8HNycnB+fPncejQIWRmZqJNmzZo3bo1bGwKv33+vwWLtJcy18EqjkKhwLKey9B8\neXOE/RaGgU0GKv+gRFpOkiSM2jcKnSw78e8Uab1XJ35mzJhR5n2WWLDMzMyQkpJS8DglJaXgUuBL\nFhYWqFmzJoyNjWFsbIwOHTrg0qVLrxUs0g0iZrAAoHL5ygjzDoP7Rnc413Pmv7aJymjNxTW49OAS\n4ofHi45CpJFKvAfL2dkZSUlJuHXrFrKzsxEWFgYvL69C2/Tu3Ru//vor8vLykJmZidOnT8Pe3l6p\noUl9iSpYANC8bnNM6zANPjt9kJ2XrboDE2mZhEcJCIwJxLb+21DBsILoOEQaqcSCZWBggJCQELi5\nucHe3h4DBw6EnZ0dQkNDERoaCgCwtbWFu7s7mjZtChcXFwwfPpwFS4eJLFgAENAqAOZVzPFlzJeq\nPTCRlniR8wIDdwzEd12+g30tvpYTvSuFJCn/R6BCoYAKDkNqIC0NqF8fePoUaNECCA0FnJ1Vm+Gv\nF3+heWhzhHiEoFfDXqo9OJGGG7l3JDKyMrDpw038KBzSWXL0Fq7kTrISPYMF/Pt5hZv7bcawiGG4\nm35X9QGINNS2q9twOPkwlvVaxnJFVEYsWCQrVa+DVZy2Fm0x3mU8Ptr5EXLzc8WEINIgN9NuIiAy\nAGHeYahSvoroOEQajwWLZCVimYbiBH4QiPIG5THn2BxxIYg0QE5eDgbtHIRv2n+D5nWbi45DpBVY\nsEhW6nCJ8CU9hR7W9VmHpWeX4kTKCXFBiNTczGMzUd24Osa5jBMdhUhrsGCRrNSpYAFAvcr1ENor\nFIN3DUZ6VrrYMERqKO52HFaeX4m1vdfyvisiGbFgkazUrWABQG/b3uhu1R1jIseIjkKkVp7+8xS+\nu32x0nMlTCuZio5DpFVYsEhW6liwAGC+23ycvXcWm69sFh2FSC1IkoRRe0fBs5EnejbsKToOkdYp\n8aNyiN6WuhasCoYVsPnDzei+sTvaWrSFZTVL0ZGIhNpweQN++/M3nBl+RnQUIq3EGSySlbos01AU\np7pOCGwXiMG7BnPpBtJpN/66gUkHJmFzv80wNjQWHYdIK7FgkazUaZmGonze5nMYGxpjbtxc0VGI\nhMjJy8HHuz7G1PZT0dS0qeg4RFqLBYtkpa6XCF96uXTDkjNLcDLlpOg4RCo389hMmBibcEkGIiVj\nwSJZqXvBAv5dumFZr2X4eNfHXLqBdMrLJRnW9F7DJRmIlIwFi2SlCQULAPrY9kE3q24IiAwQHYVI\nJV4uybDCcwXqVKojOg6R1mPBIllpSsECgPnd5yM+NR5brmwRHYVIqSRJgv8+f/Rq2Au9GvYSHYdI\nJ3CZBpKVJhWsiuUqYku/LXDb6IYP3vsAFlUtREciUorNVzbj8sPLODv8rOgoRDqDM1gkK3VepqEo\nTnWdMLH1RHwa/inyJTUPS/QOUv5OwcT9E7Gx70YuyUCkQixYJCt1X6ahKFPaTcGLnBdYdHqR6ChE\nssqX8vH8mQt0AAAgAElEQVRZ+GcY7zIeTnWdRMch0iksWCQrTbpE+JKBngHW912P2XGzkfgoUXQc\nItmExIfgec5zBH4QKDoKkc5hwSJZaWLBAgDr6taY3Wk2fHf7IicvR3QcojL7/fHvmHVsFjb03QAD\nPd5uS6RqLFgkK00tWAAwosUImFYyxey42aKjEJVJTl4OfHf7YlanWbCubi06DpFOYsEiWWlywVIo\nFFjpuRLLzi5DfGq86DhE72xO3BzUrFATI1uMFB2FSGexYJGsNLlgAUDdynUR0iMEvrt9kZmTKToO\n0VuLT43H0rNLscprFVdrJxKIBYtkpekFCwD6N+6PlvVaIjCGNwaTZsnMycQnuz/Boh6LUK9yPdFx\niHQaCxbJStPWwSpOiEcIwn8Px8EbB0VHISq1L2O+RIt6LTCg8QDRUYh0HgsWyUoT18EqSjWjaljT\new2GRAxB2os00XGI3ujgjYPY8/sehPQIER2FiMCCRTLThkuEL3Vp0AUf2n2IMZFjREchKlHaizQM\njRiKVV6rYGJsIjoOEYEFi2SmTQULAP7X5X84f/88wn4LEx2FqFhjo8ait21vdLPqJjoKEf1/LFgk\nK20rWBUMK2BD3w0YFz0OD549EB2H6DW7EnchPjUewV2DRUchov9gwSJZaVvBAoCWZi0xrPkw+O/z\nh6QNAyKt8TjzMcZEjsHaPmtRwbCC6DhE9B8sWCQrbSxYADC9w3Rc/+s6tvy2RXQUogIBkQH42OFj\ntLVoKzoKEb2CBYtkpS3LNLyqvEF5rO29FhP3T8T9jPui4xBh+9XtuPjgImZ1miU6ChEVgQWLZKUt\nyzQUpUW9FhjZYiRG7h3JS4Uk1J/P/8TYqLFY22ctjA2NRcchoiKwYJGstPUS4UtTO0zF7b9vY8Pl\nDaKjkI6SJAmj943Gp80+RWvz1qLjEFExWLBIVtpesMrpl8O6Pusw+cBkpKanio5DOmjb1W1IfJyI\nINcg0VGIqAQsWCQrbS9YANCsTjOMaTkGI/aO4KVCUqkHzx5gXPQ4rO29FkYGRqLjEFEJWLBIVrpQ\nsADg6/Zf417GPay9uFZ0FNIRkiTBf58/hjUfhpZmLUXHIaI3YMEiWelKwTLUN8S6PuvwRcwXSPk7\nRXQc0gFbftuC639dx/QO00VHIaJSYMEiWWnrMg1FaWraFONdxmPYL8N4qZCU6n7GfUzcPxFre69F\neYPyouMQUSmwYJGstHmZhqIEtgvEk8wnWHl+pegopKUkScLIvSMxssVItKjXQnQcIiolFiySla5c\nInzJUN8Qa/usxdeHv8btp7dFxyEttPHyRtz++zamdpgqOgoRvQUWLJKVrhUsAGhSuwkmuEzgAqQk\nuwfPHmDywclY03sNyumXEx2HiN4CCxbJShcLFgB80e4LPHz+EOsvrRcdhbTImMgxGOo0FM3rNhcd\nhYjeEgsWyUpXC5ahviFWe63GlINT+FmFJIsdCTuQ8CgB0zvyXYNEmogFi2SlqwULAJzqOmF4i+EY\nEzmGlwqpTJ5kPsHYqLFY5bWKC4oSaSgWLJKVLhcsAJjWYRoSHydiR8IO0VFIg03cPxEDGg9AW4u2\noqMQ0TtiwSJZ5ecXXqZBm9fBKoqRgRFWe63GuOhxeJL5RHQc0kCRSZH49c6vmNt5rugoRFQGLFgk\nK12fwQKANhZtMLDxQEzYP0F0FNIw6VnpGLV3FFZ4rkDFchVFxyGiMnhjwYqOjoatrS1sbGwQHBxc\n7HZnzpyBgYEBdu3aJWtA0iwsWP+a03kOjt85jsikSNFRSIMExgTCzdoNXRp0ER2FiMqoxIKVl5eH\ngIAAREdHIyEhAVu2bEFiYmKR2wUGBsLd3Z039+o4Fqx/VSxXESs8V2DU3lFIz0oXHYc0QOytWOz9\nYy9+7Paj6ChEJIMSC1Z8fDysra1haWkJQ0ND+Pj4IDw8/LXtFi1aBG9vb9SqVUtpQUkzsGD9ny4N\nusDN2g1fHPxCdBRSc5k5mRgWMQxLPJagqlFV0XGISAYGJT2ZmpoKCwuLgsfm5uY4ffr0a9uEh4fj\n8OHDOHPmDBQvf7q+IigoqODXrq6ucHV1fffUpLZYsAr7sduPaLK0CWJvxcLV0lV0HFJT045MQyuz\nVvBs5Ck6CpFOio2NRWxsrKz7LLFgFVeW/mvChAn47rvvoFAoIElSsZcI/1uwSHuxYBVW1agqlngs\nwbCIYbjsfxkVDCuIjkRq5vTd09h0eROu+F8RHYVIZ7068TNjxowy77PES4RmZmZISUkpeJySkgJz\nc/NC25w7dw4+Pj6oX78+du7cidGjRyMiIqLMwUgz5ecXLli6tkxDUTwbecLF3AXTjkwTHYXUTFZu\nFoZEDMEC9wWoVZG3WBBpkxILlrOzM5KSknDr1i1kZ2cjLCwMXl5ehba5efMmkpOTkZycDG9vbyxd\nuvS1bUh3SFLhdbB0fQbrpYXuC7H5ymacvnv6zRuTzpgTNwfW1a0xsPFA0VGISGYlFiwDAwOEhITA\nzc0N9vb2GDhwIOzs7BAaGorQ0FBVZSQNwkuERatZoSYWuC3AkIghyMrNEh2H1MClB5ew9OxSLO25\ntFS3YxCRZlFIKlhX4eX9WaT9du8G1q0D9uwBJk0C6tYFJk8WnUo9SJKEPmF90LxOc3zr+q3oOCRQ\nXn4eWq9qjZEtRmJY82Gi4xDRK+ToLVzJnWTFGaziKRQKLPZYjJAzIUh89Pp6cqQ7FsUvQkXDihjq\nNFR0FCJSEhYskhULVsnMq5gjqGMQhv8yHPkS3wGgi24/vY3Zx2ZjuedyXhok0mIsWCQrFqw3G+U8\nCnlSHlacWyE6CqmYJEnw3+ePia0nomGNhqLjEJESsWCRrLhMw5vp6+ljhecKTD0yFfcy7omOQyoU\ndjUMKekpmNJuiugoRKRkLFgkKy7TUDpNajfBKOdRGBs1VnQUUpG/XvyFifsnYoXnCpTTLyc6DhEp\nGQsWyYqXCEvvm/bf4Lc/f8Oe3/eIjkIqMOXgFHjbe6O1eWvRUYhIBViwSFYsWKVnZGCE5b2WY2zU\nWKRnpYuOQ0p0JPkIDt44iLmd54qOQkQqwoJFsmLBejsdLTvC3dodXx36SnQUUpIXOS8wYu8IhHiE\noHL5yqLjEJGKsGCRrFiw3t73Xb/H7sTdOJFyQnQUUoLZcbPRrE4zeDXiR4gR6RIWLJIVC9bbMzE2\nwQL3BRj+y3B+jI6WufzwMlacW4Gf3X8WHYWIVIwFi2TFgvVu+tv3RwOTBvj++Peio5BM8vLzMPyX\n4ZjTeQ7qVq4rOg4RqRgLFskqP7/wMg1cB6t0FAoFlngswc/xP+P3x7+LjkMyWHJmCYwMjDC0OT8O\nh0gXsWCRrDiD9e4sqlpgeofpGPHLCH6MjoZL+TsFM47OQGivUOgp+DJLpIv4N59kxYJVNqNbjkZ2\nXjZWnl8pOgq9I0mSMDpyNMa7jIdtTVvRcYhIEBYskhULVtm8/Bidbw5/g/sZ90XHoXewI2EHktOS\nEfhBoOgoRCQQCxbJigWr7BxMHTCixQiMix4nOgq9pbQXaZiwfwI/DoeIWLBIXixY8pjWYRouPbiE\nX679IjoKvYXAmED0se2DNhZtREchIsFYsEhWLFjyMDIwwrJeyzA2aiyeZz8XHYdK4fid44hMiuTH\n4RARABYskhmXaZBP5/qd0f799gg6GiQ6Cr1BTl4ORu0bhZ/cfkJVo6qi4xCRGmDBIllxBkte87rP\nw7qL63DpwSXRUagE80/Oh0UVC3jbe4uOQkRqggWLZMWCJa/aFWtjTuc5GLVvFNfGUlPJacn44cQP\nCPEIgeLlH34i0nksWCQrFiz5DW0+FHoKPSw/t1x0FHqFJEkIiArApDaT0MCkgeg4RKRGWLBIVixY\n8tNT6GFZz2WYdmQaHjx7IDoO/cfOxJ249fQWJrWdJDoKEakZFiySFQuWcjiYOmCI0xBMOsAf5Ooi\nPSsdE6InILRXKNe8IqLXsGCRrFiwlGd6h+k4kXICB28cFB2FAEw9PBXu1u744L0PREchIjXEgkWy\nYsFSnorlKiKkRwhGR47GP7n/iI6j087eO4ttV7chuGuw6ChEpKZYsEhWXAdLuXo27AlHU0fMjeNi\nlqLk5udi5N6RCO4ajBoVaoiOQ0RqigWLZMUZLOVb6L4QS88uxe+PfxcdRSctObMEVcpXwSeOn4iO\nQkRqjAWLZMWCpXxmVcwwrcM0jNo7ChL/B6tUanoqZh6diaU9l3LNKyIqEQsWyYoFSzXGtByDZ9nP\nsP7SetFRdMr46PEY3XI0bGvaio5CRGqOBYtkxYKlGvp6+ljWaxkCYwLxJPOJ6Dg6Yd8f+3Dp4SV8\n3f5r0VGISAOwYJGsWLBUx7meMwY0HoDAmEDRUbTe8+znCIgKwBKPJTAyMBIdh4g0AAsWyYoFS7Vm\nd56N6OvRiLsdJzqKVpt5bCbamLdBN6tuoqMQkYZgwSJZcZkG1apSvgoWuC/AqH2jkJ2XLTqOVrry\n8ApWX1iN+W7zRUchIg3CgkWy4gyW6vWz6wfLapaYd2Ke6ChaJ1/Kx8i9IzGr0yzUqVRHdBwi0iAs\nWCQrFizVUygUWOyxGPNOzsPNtJui42iVledXQoKEES1GiI5CRBqGBYtkxYIlhmU1S0xpOwVjIsdw\nbSyZ/Pn8T0w9PBXLei6DnoIvlUT0dviqQbJiwRJnYpuJuPP3Hez+fbfoKFrhi4NfwNfRF451HEVH\nISINxIJFsmLBEqecfjks9liMCdET8Cz7meg4Gi3udhxibsYgqGOQ6ChEpKFYsEhWLFhiuVq6oqNl\nR8w6Nkt0FI2Vk5eD0ZGjMd9tPiqXryw6DhFpKBYskhWXaRDvh24/YPWF1bj651XRUTTSovhFqFOp\nDvrb9xcdhYg0GAsWyYozWOLVqVQH33b8lje8v4PU9FTMjZuLxR6L+WHORFQmLFgkKxYs9eDv7I/0\nrHRsurJJdBSN8vmBz+Hf0h8NazQUHYWINBwLFsmKBUs96OvpY2nPpfji4Bd4+s9T0XE0woEbBxCf\nGo+vPvhKdBQi0gIsWCQrFiz14WLuAs9Gnph2ZJroKGovKzcLAZEBWNRjESoYVhAdh4i0AAsWyYoF\nS73M7TwX269ux7l750RHUWs/nPgBdrXs0KthL9FRiEhLsGCRrFiw1EuNCjXwvy7/w+jI0ciX+JbO\noiSnJWPBqQVY6L5QdBQi0iJvLFjR0dGwtbWFjY0NgoODX3t+06ZNcHR0RNOmTdGuXTtcvnxZKUFJ\nM0hS4WUaWLDE82vmBwM9A6w8v1J0FLU0LnocPm/zOSyrWYqOQkRapMSClZeXh4CAAERHRyMhIQFb\ntmxBYmJioW0aNGiAY8eO4fLly5g2bRpGjOCHouqy/PzCM1hcB0s8PYUelvZciqmHp+LR80ei46iV\niGsRSHqShEltJomOQkRapsSCFR8fD2tra1haWsLQ0BA+Pj4IDw8vtE2bNm1QtWpVAICLiwvu3r2r\nvLSk9niJUD01NW2KwU0HIzAmUHQUtZGZk4lxUeOw2GMxyhuUFx2HiLSMQUlPpqamwsLCouCxubk5\nTp8+Xez2q1atgoeHR5HPBQUFFfza1dUVrq6ub5eUNAILlvoKcg2C/WJ7HL9zHO3eayc6jnBz4uag\njUUbdGnQRXQUIhIsNjYWsbGxsu6zxIL1NisZHzlyBKtXr8bx48eLfP6/BYu0FwuW+qpSvgrmdZ8H\n/33+OD/yPAz0Svzrr9V+f/w7Qs+G4rI/7xklotcnfmbMmFHmfZZ4idDMzAwpKSkFj1NSUmBubv7a\ndpcvX8bw4cMREREBExOTMocizcWCpd4GNB4A00qmWHR6kegowkiShIDIAEztMBX1KtcTHYeItFSJ\nBcvZ2RlJSUm4desWsrOzERYWBi8vr0Lb3LlzBx9++CE2btwIa2trpYYl9ceCpd4UCgVCeoRgTtwc\npKanio4jRNjVMDzKfISAVgGioxCRFiuxYBkYGCAkJARubm6wt7fHwIEDYWdnh9DQUISGhgIAZs6c\nibS0NPj7+8PJyQmtWrVSSXBSTyxY6q9RzUYY5TwKkw7o3jvn0rPSMenAJCztuVSnL5ESkfIpJEn5\nPwIVCgVUcBhSA+PHA/XrAxMmAL/8AoSGAnv3ik5Fr8rMyUTjJY2xwnMFujboKjqOykzcPxHpWelY\n5bVKdBQiUmNy9Bau5E6y4gyWZqhgWAE/u/+MMZFjkJWbJTqOSlx6cAmbr2xGcNfXF0wmIpIbCxbJ\nigVLc3g28oRtTVv8eOJH0VGULl/Kx+jI0ZjVaRZqVqgpOg4R6QAWLJIVC5ZmWei+ED+d+gnJacmi\noyjVuovrkJufi2HNh4mOQkQ6ggWLZMWCpVksq1liYuuJmLB/gugoSvPXi7/w1aGvsLTnUugp+JJH\nRKrBVxuSFQuW5pncdjISHiUgMilSdBSl+PrQ1+jfuD+a120uOgoR6RAWLJIVC5bmKW9QHot6LMK4\nqHH4J/cf0XFkdSb1DMKvhWNWp1mioxCRjmHBIlnl5wN6//9PlZ7ev49J/blbu8PB1EGrbnjPl/IR\nEBWA77p8h2pG1UTHISIdw4JFsuIMlub6ye0n/HTqJ9x6ekt0FFmsvrAa+gp9+Dr6io5CRDqIBYtk\nxYKluV7e8D5x/0TRUcrsrxd/4ZvD32Cxx2Le2E5EQvCVh2TFgqXZJredjCsPryAqKUp0lDKZengq\nvO294VTXSXQUItJR/DAukhULlmYzMjDCzz1+xrjocfit/m8ob1BedKS3dv7+eexK3IXEMYmioxCR\nDuMMFsmKBUvzedh4oHGtxhp5w3u+lI+AyADM6TwHJsYmouMQkQ5jwSJZsWBphwXuC/DTqZ9w++lt\n0VHeyvpL65En5eEzp89ERyEiHceCRbKSpMLLNLBgaSbLapYY5zIOnx/4XHSUUnv6z1N8degr3thO\nRGqBr0Ikq/z8wjNYXAdLc33R7gtcfHAR+6/vFx2lVKYfmQ6vRl5wrucsOgoREQsWyYuXCLWHkYER\nfnb/GWOjxiIrN0t0nBJdfngZYVfDMLfzXNFRiIgAsGCRzFiwtEvPhj1hW9MW80/OFx2lWJIkYUzk\nGMx0nYkaFWqIjkNEBIAFi2TGgqV9FrgvwLyT83Dn7zuioxRp05VNyMzJxLDmw0RHISIqwIJFsmLB\n0j4NTBpgbKux+Hy/+t3wnp6VjsCYQCz2WAx9PX3RcYiICrBgkaxYsLTTF+2+wIUHF3DwxkHRUQqZ\ncXQG3K3d0dq8tegoRESFsGCRrLhMg3YyNjTGArcFCIgKUJsb3q/+eRUbLm3Ad12+Ex2FiOg1LFgk\nKy7ToL08G3nCproNfjr1k+gokCQJAVEBmN5xOmpVrCU6DhHRa1iwSFa8RKjdFrovxI8nfkTK3ylC\nc4RdDUPaizSMch4lNAcRUXFYsEhWLFjazaq6Fca0GoNJByYJy5CRlYHJByZjscdiGOjx8+qJSD2x\nYJGsWLC035ftvsSZe2cQczNGyPFnx81GlwZd0O69dkKOT0RUGixYJCsWLO1XcMN7ZACy87JVeuzf\nH/+O1RdWI7hrsEqPS0T0tliwSFYsWLrBq5EXrKpbYcGpBSo7piRJGBs1Ft+0/wZ1KtVR2XGJiN4F\nCxbJigVLNygUCix0X4jvj3+Pu+l3VXLMnYk78eDZAwS0ClDJ8YiIyoIFi2SVn194HSwu06C9rKtb\nw7+lv0pueH+e/Ryf7/+cN7YTkcZgwSJZcQZLt3z1wVeIT43HoZuHlHqcub/ORfv326PD+x2Uehwi\nIrmwYJGsWLB0SwXDCvjJ7SeMjRqrtBvek54kIfRsKH7o9oNS9k9EpAwsWCQrFizd07tRb7xf7X0s\nPLVQ9n1LkoRx0ePw5Qdfol7lerLvn4hIWViwSFYsWLpHoVDgZ/efEXw8GPcy7sm67/Br4bj99DbG\nu4yXdb9ERMrGgkWyYsHSTTY1bDDSeSSmHJwi2z4zczIxcf9EhHiEwFDfULb9EhGpAgsWyYoFS3d9\n/cHXiLsdh2O3j8myv+DjwWhl1gqd63eWZX9ERKrEgkWykqTCyzSwYOmOiuUqYl73eQiIDEBufm6Z\n9nXjrxtYHL8Y87rPkykdEZFqsWCRrPLzC89gcR0s3eJt741aFWth6ZmlZdrPhP0TMLntZJhXMZcp\nGRGRarFgkax4iVC3KRQKLOqxCDOPzcTDZw/faR97/9iLP578gc/bfC5zOiIi1WHBIlmxYJF9LXv4\nOfrhq0NfvfX3/pP7D8ZHj8eiHotQTr+cEtIREakGCxbJigWLAGB6x+nYf2M/Tt099Vbf98PxH9Cs\nTjN0t+qupGRERKrBgkWyYsEiAKhSvgqCuwYjIDIAefl5pfqeW09vYeHphZjffb6S0xERKR8LFsmK\nBYte+tjhYxgbGmPl+ZWl2n7i/omY0HoC3q/2vpKTEREpHwsWyYrLNNBLCoUCIT1CMD12Op5kPilx\n2+jr0bjy8Aomt52sonRERMrFgkWy4jIN9F+OdRwxoPEATD0ytdhtsnKzMC5qHH7u8TOMDIxUmI6I\nSHlYsEhWvERIr5rpOhO7E3fj/P3zRT4//+R82NWyg4eNh4qTEREpDwsWyYoFi15lYmyCOZ3nICAy\nAPlS4SnNO3/fwbyT87DAbYGgdEREysGCpUSxsbGiI6icJAEXL8YC0L2CpYvnGyjduD9z+gx5Uh7W\nX1pf6PcnHZiEgFYBqG9SX0nplIfnW7dw3PS23liwoqOjYWtrCxsbGwQHBxe5zbhx42BjYwNHR0dc\nuHBB9pCaShf/YEoScOFCLAAWLF1RmnHrKfQQ0iMEXx36Ck//eQoAiLkZg3P3ziGwXaCSEyoHz7du\n4bjpbZVYsPLy8hAQEIDo6GgkJCRgy5YtSExMLLRNZGQkrl+/jqSkJCxfvhz+/v5KDUzqjZcIqTgt\nzVrCs6EngmKDkJ2XjYDIACxwXwBjQ2PR0YiIZGdQ0pPx8fGwtraGpaUlAMDHxwfh4eGws7Mr2CYi\nIgJ+fn4AABcXFzx9+hQPHz6Eqamp8lKT2vpvoeIyDfSquV3mwn6xPTKyM2BV3QqeDT1FRyIiUg6p\nBNu3b5eGDRtW8HjDhg1SQEBAoW169eolHT9+vOBxly5dpLNnzxbaBgC/+MUvfvGLX/zil8Z8lVWJ\nM1iKl9d63kB6ZZri1e979XkiIiIibVbiPVhmZmZISUkpeJySkgJzc/MSt7l79y7MzMxkjklERESk\nOUosWM7OzkhKSsKtW7eQnZ2NsLAweHl5FdrGy8sL69f/+9brU6dOoVq1arz/ioiIiHRaiZcIDQwM\nEBISAjc3N+Tl5WHo0KGws7NDaGgoAGDkyJHw8PBAZGQkrK2tUbFiRaxZs0YlwYmIiIjUVpnv4nqD\nqKgoqVGjRpK1tbX03XffKftwQr3//vuSg4OD1KxZM6lly5aSJEnSkydPpK5du0o2NjZSt27dpLS0\nNMEpy+6zzz6TateuLTVp0qTg90oa59y5cyVra2upUaNG0v79+0VElkVR4/72228lMzMzqVmzZlKz\nZs2kyMjIgue0Zdx37tyRXF1dJXt7e6lx48bSwoULJUnS/nNe3Li1/Zy/ePFCatWqleTo6CjZ2dlJ\nX375pSRJ2n++ixu3tp9vSZKk3NxcqVmzZlKvXr0kSdL+c/3Sq+OW+1wrtWDl5uZKVlZWUnJyspSd\nnS05OjpKCQkJyjykUJaWltKTJ08K/d6UKVOk4OBgSZIk6bvvvpMCAwNFRJPVsWPHpPPnzxcqGsWN\n8+rVq5Kjo6OUnZ0tJScnS1ZWVlJeXp6Q3GVV1LiDgoKkefPmvbatNo37/v370oULFyRJkqSMjAyp\nYcOGUkJCgtaf8+LGrQvn/Pnz55IkSVJOTo7k4uIixcXFaf35lqSix60L53vevHnSRx99JHl6ekqS\npBuv55L0+rjlPtdK/aic/66jZWhoWLCOljaTXnnH5H/XCfPz88OePXtExJJV+/btYWJiUuj3ihtn\neHg4Bg0aBENDQ1haWsLa2hrx8fEqzyyHosYNFP0uWW0ad506ddCsWTMAQKVKlWBnZ4fU1FStP+fF\njRvQ/nNeoUIFAEB2djby8vJgYmKi9ecbKHrcgHaf77t37yIyMhLDhg0rGKcunOuixi39O+n02rbv\nOm6lFqzU1FRYWFgUPDY3Ny94gdJGCoUCXbt2hbOzM1asWAEAhRZdNTU1xcOHD0VGVJrixnnv3r1C\n7zzVxj8DixYtgqOjI4YOHYqnT//9GBhtHfetW7dw4cIFuLi46NQ5fznu1q1bA9D+c56fn49mzZrB\n1NQUnTp1QuPGjXXifBc1bkC7z/fEiRPxww8/QE/v/+qALpzrosatUChkPddKLVilXUdLWxw/fhwX\nLlxAVFQUFi9ejLi4uELPKxQKnfh/8qZxatP/A39/fyQnJ+PixYuoW7cuJk2aVOy2mj7uZ8+eoV+/\nfli4cCEqV65c6DltPufPnj2Dt7c3Fi5ciEqVKunEOdfT08PFixdx9+5dHDt2DEeOHCn0vLae71fH\nHRsbq9Xne+/evahduzacnJyKXa9SG891ceOW+1wrtWCVZh0tbVK3bl0AQK1atdC3b1/Ex8fD1NQU\nDx48AADcv38ftWvXFhlRaYobp7avk1a7du2CF6Bhw4YVTBtr27hzcnLQr18/+Pr6ok+fPgB045y/\nHPfgwYMLxq0r5xwAqlatip49e+LcuXM6cb5fejnus2fPavX5PnHiBCIiIlC/fn0MGjQIhw8fhq+v\nr9af66LG/cknn8h+rpVasEqzjpa2yMzMREZGBgDg+fPnOHDgABwcHODl5YV169YBANatW1fwIq1t\nihunl5cXtm7diuzsbCQnJyMpKQmtWrUSGVVW9+/fL/j17t274eDgAEC7xi1JEoYOHQp7e3tMmDCh\n4Pe1/ZwXN25tP+ePHz8uuDTy4sULHDx4EE5OTlp/vosb98uiAWjf+Z47dy5SUlKQnJyMrVu3onPn\nzkYJBfIAAAEeSURBVNiwYYPWn+uixr1+/Xr5/27Lcit+CSIjI6WGDRtKVlZW0ty5c5V9OGFu3rwp\nOTo6So6OjlLjxo0LxvrkyROpS5cuWrVMg4+Pj1S3bl3J0NBQMjc3l1avXl3iOOfMmSNZWVlJjRo1\nkqKjowUmL5tXx71q1SrJ19dXcnBwkJo2bSr17t1bevDgQcH22jLuuLg4SaFQSI6OjgVvX46KitL6\nc17UuCMjI7X+nF++fFlycnKSHB0dJQcHB+n777+XJKnk1zJtHre2n++XYmNjC95Np+3n+r+OHDlS\nMO7BgwfLeq4VksQPCiQiIiKSk1IvERIRERHpIhYsIiIiIpmxYBERERHJjAWLiIiISGYsWEREREQy\nY8EiIiIiktn/A2I1VU993zgQAAAAAElFTkSuQmCC\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": 585, "id": "0812c5d4", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 585, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAE1CAYAAAA75J7FAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\njDHGGGMu4wGLMcYYY8xlvwDCrQ7OS0gLTwAAAABJRU5ErkJggg==\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)))" ] }, { "cell_type": "markdown", "id": "888975ba", "metadata": {}, "source": [ "The Fourier transform of the Gaussian is very important in practice." ] }, { "cell_type": "code", "execution_count": 586, "id": "9c4993ef", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 586, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAE1CAYAAAA75J7FAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XtwXOV9//HP6mJrdb/Luo1lLNmWjZGd2JiEhioBYkzA\nSUuamkwIP2KoS+OmaZJO0qYtuJ1STMofNE4ap0kIJK1D02lraI2ANBYQSDAGGwJ2sAyWLcuyJa3u\nd2l1fn9sJVuWtNqVdvc55+z7NbMzkvZ4z/fxAc3H3+c5z/FYlmUJAAAAEZNgugAAAAC3IWABAABE\nGAELAAAgwghYAAAAEUbAAgAAiDACFgAAQIQFDVif+9znVFRUpLVr1856zBe+8AVVVVWppqZGR44c\niXiBAAAAThM0YN11112qq6ub9f0DBw7o5MmTamho0He/+13de++9ES8QAADAaYIGrA996EPKycmZ\n9f0nn3xSd955pyRp06ZN6urq0oULFyJbIQAAgMMkLeQPNzc3q7y8fPL7srIynT17VkVFRVOO83g8\nCzkNAABATC30QTcLXuR+eQGzhan8h/J1pOWILMuKm9d9991nvAbGzbij+RoetpSRcZ/WrbM0Pm6+\nHq4342bczhr3ux3vanx83Pg4L39FwoICVmlpqZqamia/P3v2rEpLS2c8dvcNu/WlZ760kNMBsJl/\n+zcpL08aHpYOHjRdDQAn6RzsVM13ajTsHzZdSlQsKGBt3bpVjz/+uCTpV7/6lbKzs6dND0741JpP\n6dVzr6p/pH8hpwRgI9/9rnTNNdIXvhD4GgBCdbDxoK4tv1YpSSmmS4mKoGuwbr/9dj3//PNqb29X\neXm5du3apdHRUUnSjh07dPPNN+vAgQOqrKxUWlqaHn300Vk/K31Rut5X/D69cPoFbanaEtlR2FRt\nba3pEoxg3PHBsqQ33pC+/OVaLVsm/eM/mq4otuLtek9g3PElmuN+7r3ndOMVN0bt803zWJGabAx2\nEo9HlmXpb5//W3UNd+nhjz4c7VMCiLLz56U1aySfTxoclHJypL4+KWlBt84AiBdV36zSv//ev6tm\nSY3pUqaZyC0LEdOd3G9cfqOee/e5WJ4SQJS88460cmXga69XWrJEamw0WhIAh2jsalTPcI/WFs2+\nkbnTxTRgvb/4/WroaNDg6GAsTwsgCk6cuBiwpMDXJ06YqweAc7x27jVdU3aNEjzufWJfTEeWnJis\n5TnLdcLHb2HA6S7tYEmBr995x1w9AJzjWNsxrSlYY7qMqIp5dFxdsFpvt70d69MCiDACFoD5ervt\nba0uWG26jKiKecBaU7BGx9qOxfq0ACKMgAVgvuhgRcHqgtUELMDhRkelM2ek5csv/mzFCtZgAZjb\n2PiYGjoatDJ/5dwHOxgBC0DYLlyQcnOlxYsv/qykRGptlcbGzNUFwP7e63xPJRklSk1ONV1KVMU8\nYFXlVel092kNj7lza3wgHpw/LxUXT/1ZUlLgsTltbWZqAuAMx9qOuX79lWQgYC1KXKSlWUt1suNk\nrE8NIELOnw/se3W5JUsC7wHAbI63HVd1frXpMqLOyAYUy3KWqbGr0cSpAUQAAQvAfDV2N2pZ9jLT\nZUSdkYC1NGupTnefNnFqABHQ0jJ7wGppiX09AJzjdNdpLc1earqMqDMWsOhgAc410xosKfAzOlgA\ngmnsatTSLAJWVCzNpoMFOBlThADmw7Isnek+QwcrWiqyK3S6i4AFOBVThADmo22gTanJqUpflG66\nlKhjDRaAsDFFCGA+4mX9lWQoYBVnFKtzsFNDY0MmTg9gASwrEKKKiqa/xxQhgGBOd5+Oi/VXkqGA\nleBJUGlmqZq6m0ycHsAC9PZKiYlS+gwdfgIWgGDoYMUAdxICzjTb+itJysiQ/H6pry+2NQFwhsbu\n+LiDUDIZsLiTEHCk2e4glCSPJ7AOi4XuAGZypvsMASvaSjNKda73nKnTA5in9napoGD29/PzJZ8v\ndvUAcI7mnmaVZpaaLiMmjAWskowStfTxz1zAaTo6Ag91nk1eHgELwMxa+lpUklFiuoyYMBawitOL\n1dJLwAKcxueTcnNnfz83NxDCAOBS/nG/2vrbVJQ2wy3ILmQuYGUUM0UIOFBHBwELQPjaBtqUnZKt\n5MRk06XEBFOEAMLi8zFFCCB8Lb3xMz0oGQxYS9KX6ELfBY1b46ZKADAPdLAAzMe53nMqzpjhERAu\nZSxgLUpcpMzFmWofaDdVAoB5YJE7gPlo6WtRcToBKyaKM1joDjgNi9wBzEdLbwsdrFgpyShhoTvg\nMKFMEdLBAnC5c33nVJLOGqyYKE4vZqE74CCWNXfAysujgwVgOjpYMcQUIeAsAwNSQoLk9c5+DB0s\nADNhDVYMlaSX6FwfU4SAU8y1wF2SsrKk/n5pdDQ2NQFwhnO959imIVaWpC+hgwU4yFwL3KVAhys7\nW+rqik1NAOzPsixd6LugovT42MVdMhywCtMK1TbQZrIEAGGYa/3VBKYJAVyqa6hL3mSvUpJSTJcS\nM+YDVj8BC3CKUKYIJRa6A5iqtb9VhWmFpsuIKeMBq7W/1WQJAMIQyhShRAcLwFRtA20ErFjK8eao\nd6RXI/4Rk2UACBEdLADzQQcr1if3JCg/NZ/H5QAO0dkZWMA+l5wcAhaAiwhYBjBNCDhHV1doASsr\nS+rujn49AJyBgGUAAQtwju7u0AJWdjYBC8BFrf2tKkwlYMUUAQtwjq6uQHdqLllZ7IMF4CI6WAYQ\nsADnoIMFYD4IWAYUphKwAKeggwVgPghYBrCbO+AcdLAAzAf7YBlQkFZABwtwiFA7WDyLEMCEsfEx\ndQ11Kdcbwi7FLmI8YLEGC3CG4WHJ75e83rmPZZsGABN8Az7lpOQoMSHRdCkxZYuAdaHvgukyAMyh\nuzsQnDyeuY+dCFiWFf26ANhba3+rCtIKTJcRc3MGrLq6Oq1atUpVVVXavXv3tPfb29t10003ad26\ndbryyiv1wx/+MKwC8lPz5RvkoWWA3YW6yagkLVokJSdLAwPRrQmA/bUPtKsglYA1hd/v186dO1VX\nV6djx45p3759On78+JRj9uzZo/Xr1+vo0aOqr6/Xl7/8ZY2NjYVcQMaiDA2PDfM8QsDmJjpYoWId\nFgApELDyU/NNlxFzQQPWoUOHVFlZqYqKCiUnJ2vbtm3av3//lGOKi4vV09MjSerp6VFeXp6SkpJC\nLsDj8SjXmyvfAF0swM7C6WBJrMMCEEDAmkFzc7PKy8snvy8rK1Nzc/OUY+655x69/fbbKikpUU1N\njR555JGwi8hLzeOBz4DN0cECMB/xGrCCtpo8IaxmfeCBB7Ru3TrV19fr3Xff1Y033qg33nhDGRkZ\nU467//77J7+ura1VbW3t5PeswwLsjw4WgPloH2zXsuxlpssIqr6+XvX19RH9zKABq7S0VE1NTZPf\nNzU1qaysbMoxL7/8sr7+9a9LkpYvX65ly5bpnXfe0YYNG6Ycd2nAulyeN48pQsDm6GABmI/2gXZt\nLNlouoygLm/87Nq1a8GfGXSKcMOGDWpoaFBjY6NGRkb0xBNPaOvWrVOOWbVqlX72s59Jki5cuKB3\n3nlHV1xxRVhF5KXm0cECbI4OFoD5aB9oV543z3QZMRe0g5WUlKQ9e/Zo8+bN8vv92r59u6qrq7V3\n715J0o4dO/QXf/EXuuuuu1RTU6Px8XE99NBDys0Nb7dWOliA/XV3S8uXh348HSwAUmCjUdZgzWDL\nli3asmXLlJ/t2LFj8uv8/Hw99dRTCyoiz5un8/3nF/QZAKIr3A4WzyMEIMXvInfjO7lL/7fInQ4W\nYGvhrsHKyqKDBYCAZRRrsAD7C/VBzxNYgwVgcHRQo+OjSl+UbrqUmLNHwGINFmB7vb1SZmbox2dm\nSv+3BzGAOOUb9CnPmxfStk9uY4+ARQcLsL2envADVm9v9OoBYH/xOj0o2SVgednJHbC7nh7psv2D\ng6KDBYCAZViON0fdQ93yj/tNlwJgFuFOEWZkELCAeBevWzRINglYSQlJylycqa4hbjkC7Gh0NPDy\nekP/M0wRAmgfaFdeavxtMirZJGBJrMMC7Ky3N9CRCmedKlOEACYWuccj+wQs7iQEbCvcBe6StHix\n5PdLIyPRqQmA/XUMdijXG97TXdzCPgErlYXugF1NdLDC4fEwTQjEOwKWDeSn5jNFCNjUfDpYEtOE\nQLwjYNkAU4SAfRGwAMwHAcsG8rwscgfsaj5ThBJbNQDxrmOwg0XupnEXIWBfC+lgsQYLiF90sGyA\n3dwB+5pvB4spQiB+WZalzqFO5XhzTJdihG0CVn5qPmuwAJuabweLKUIgfvWO9ColKUWLEheZLsUI\n2wQspggB+1pIB4spQiA+xfP0oGSngMVdhIBtcRchgHARsGxiooNlWZbpUgBchilCAOEiYNlESlKK\nkhKS1DfSZ7oUAJdhihBAuAhYNsJu7oA9MUUIIFwELBthHRZgT2w0CiBcBCwb4U5CwJ7YaBRAuDoG\nO5SbQsCyBTpYgD319jJFCCA8vkEfHSy7yEvNU8dgh+kyAFymp4cpQgDhYYrQRnK9uQQswGaGhyXL\nkhYvDv/P0sEC4hcBy0ZyU3LVMUTAAuxkYoG7xxP+n83ICPx5trcD4g8By0boYAH2M98F7pKUnBx4\nDQ5GtiYA9kfAshECFmA/892iYQLThED8sSyLgGW6gEvlenO5ixCwmYV0sCS2agDi0cDogBI9ifIm\ne02XYoztAhYdLMBe5rtFwwTuJATiT7x3ryQCFoA5zHeLhglMEQLxh4Bls4CV481R51CnLG45Amxj\noR0spgiB+EPAslnAWpS4SClJKeod4bcxYBcL7WAxRQjEHwKWzQKWxDQhYDeRWOROwALiCwGLgAVg\nDpHYpoEpQiC+ELAIWADmsNAOFlOEQPzpGCJgEbAABBWJRe4ELCC+0MGyYcDK8+YRsAAbYZsGAOEi\nYNkwYNHBAuwlEhuNsgYLiC8ELAIWgDnQwQIQLt+Aj4BluoDLEbAAe2GbBgDhooNFwAIwB6YIAYSL\ngEXAAhCEZTFFCCA8g6ODGhsfU1pymulSjCJgAZjV8LCUmCgtWjT/zyBgAfGlc6hTud5ceTwe06UY\nRcACMKuFdq8kKT1dGhiQxscjUxMAe2N6MMB2ASsnJUcdgx2yLMt0KUDcW+j6K0lKSJBSU6W+vsjU\nBMDeCFgBcwasuro6rVq1SlVVVdq9e/eMx9TX12v9+vW68sorVVtbu6CCvMleJXgSNDg2uKDPAbBw\nkehgSYGQ1t298M8BYH8dgx3KS80zXYZxScHe9Pv92rlzp372s5+ptLRUGzdu1NatW1VdXT15TFdX\nlz7/+c/rmWeeUVlZmdrb2xdc1MQ0YWpy6oI/C8D8LXSLhgncSQjEDzpYAUE7WIcOHVJlZaUqKiqU\nnJysbdu2af/+/VOO+dd//VfddtttKisrkyTl5+cvuCjWYQH2EIkpQinwGQQsID4QsAKCdrCam5tV\nXl4++X1ZWZleeeWVKcc0NDRodHRUH/7wh9Xb26s/+ZM/0R133DHts+6///7Jr2tra4NOJRKwAHuI\n5BQhdxIC8aFjsEO5Kc4KWPX19aqvr4/oZwYNWKHcYjk6OqrXX39d//u//6uBgQF94AMf0DXXXKOq\nqqopx10asOaS682Vb8AX8vEAoiNSHSymCIH40THYofLM8rkPtJHLGz+7du1a8GcGDVilpaVqamqa\n/L6pqWlyKnBCeXm58vPz5fV65fV6dd111+mNN96YFrDCQQcLsAc6WADCxRRhQNA1WBs2bFBDQ4Ma\nGxs1MjKiJ554Qlu3bp1yzMc//nH94he/kN/v18DAgF555RWtXr16QUURsAB7oIMFIFwErICgHayk\npCTt2bNHmzdvlt/v1/bt21VdXa29e/dKknbs2KFVq1bppptu0lVXXaWEhATdc889kQlYQwQswLSe\nHqmiYuGfQwcLiB8ErICgAUuStmzZoi1btkz52Y4dO6Z8/5WvfEVf+cpXIlZUrjdX73a+G7HPAzA/\nvb2RmSLMyGAfLCBeELACbLeTu8QUIWAXkdoHiw4WED8IWAEELACzitQi94wMAhYQD0b8IxoYHVDm\n4gj8y8zhCFgAZsVGowDC0TnYqRxvTkjbPLmdLQNWnjePgAXYANs0AAgH04MX2TJg0cEC7IFtGgCE\ng4B1kS0DVmpyqsbGxzQ0NmS6FCCuscgdQDgIWBfZMmB5PB7lenPVOdhpuhQgbllWZLdpoIMFuB8B\n6yJbBiyJaULAtMFBadEiKWnO3fLmRgcLiA8ErIsIWABmFKkF7pKUliYNDUljY5H5PAD21DHUoTxv\nnukybIGABWBGkVrgLkkej5SeLvX1RebzANgTHayLCFgAZhSpBe4TmCYE3I+AdREBC8CMIrXAfQIL\n3QH3I2BdZN+AlZKrjiECFmAKHSwA4SJgXWTfgEUHCzCKDhaAcBGwLiJgAZgRHSwA4SJgXUTAAjCj\nSG7TIAU+i4AFuJd/3K/e4V5lLc4yXYot2Dpg+QZ8pssA4lZPj5QVwd+TmZlMEQJu1jXUpczFmUpM\nSDRdii3YOmDRwQLMYYoQQDiYHpyKgAVgRpEOWCxyB9zNN+gjYF3CtgErc3GmBkYHNOofNV0KEJfo\nYAEIBx2sqWwbsDwej3K8Oeoc6jRdChCXursjuwaLDhbgbgSsqWwbsCSmCQGT6GABCIdvgCnCSxGw\nAMwoGmuwCFiAe/kGfcpLzTNdhm0QsADMqLs78h0spggB9/IN+pTnJWBNsHXAyvPmEbAAQyK9DxYd\nLMDdfAMErEvZOmDRwQLMGBmRxsaklJTIfSYdLMDdmCKcioAFYJre3kAg8ngi95kscgfcjQ7WVAQs\nANNEev2VJHm90uho4AXAfehgTUXAAjBNpNdfSYFuGHthAe5FB2sqAhaAaSK9RcMEAhbgTsNjwxr2\nDytzcRR+cTgUAQvANNGYIpRYhwW41cRzCD2RXLjpcAQsANNEs4NFwALch+nB6QhYAKaJxhosia0a\nALdigft0tg5YWYuz1DPcI/+433QpQFyJVgeLKULAnehgTWfrgJWYkKjMxZnqHu42XQoQV6K1BotF\n7oA70cGaztYBS2KaEDCBDhaAcHQMdtDBugwBC8A00VqDRQcLcCffoE/5qfmmy7AVRwQs34DPdBlA\nXKGDBSAcrMGazvYBKy81T75BAhYQS+yDBSAcrMGazvYBKz81X+0D7abLAOIKHSwA4aCDNZ39A5aX\ngAXEWrTWYGVlBbpjANyFDtZ09g9YdLCAmIvmFCEBC3AfOljT2T5gFaQVELCAGIvWFCEdLMB9LMtS\n51Cncr25pkuxFdsHLDpYQGwND0t+v5SSEvnPzspiDRbgNt3D3UpNTlVyYrLpUmzFEQGrbaDNdBlA\n3OjtDQQhjyfyn00HC3Afpgdn5oiARQcLiJ1orb+SAhuN9vcHOmQA3IEF7jOzfcDK8+apY7BD49a4\n6VKAuBCt9VeSlJAgpaWxmzvgJnSwZjZnwKqrq9OqVatUVVWl3bt3z3rcq6++qqSkJP3Hf/xHRAtM\nTkxWWnKauoeYVwBiIZoBS2IdFuA2dLBmFjRg+f1+7dy5U3V1dTp27Jj27dun48ePz3jcV7/6Vd10\n002yLCviRXInIRA73d3R2QNrAuuwAHehgzWzoAHr0KFDqqysVEVFhZKTk7Vt2zbt379/2nHf/OY3\n9clPflIFBQVRKZJ1WEDsxKKDRcAC3MM3SMCaSVKwN5ubm1VeXj75fVlZmV555ZVpx+zfv18///nP\n9eqrr8ozy61H999//+TXtbW1qq2tDblI7iQEYoeABSAcvkGfqvOrTZexIPX19aqvr4/oZwYNWLOF\npUt98Ytf1IMPPiiPxyPLsmadIrw0YIWLDhYQO9EOWDyPEHAXN0wRXt742bVr14I/M2jAKi0tVVNT\n0+T3TU1NKisrm3LMa6+9pm3btkmS2tvb9fTTTys5OVlbt25dcHETCFhA7LAGC0A4WOQ+s6ABa8OG\nDWpoaFBjY6NKSkr0xBNPaN++fVOOee+99ya/vuuuu3TrrbdGNFxJPPAZiKWeHqm0NHqfT8AC3MUN\nHaxoCBqwkpKStGfPHm3evFl+v1/bt29XdXW19u7dK0nasWNHTIosSCvQO753YnIuIN6xBgtAONoH\n2ulgzSBowJKkLVu2aMuWLVN+NluwevTRRyNT1WVY5A7ETk9P9KcIW1qi9/kAYseyLLUNtKkgNTq7\nCDiZ7Xdyl1iDBcRSNB+VIwU+mw4W4A59I31K9CQqbVGa6VJsh4AFYAqmCAGEqrW/VYVphabLsCUC\nFoApCFgAQtU20KaCNKYHZ+KIgJWdkq2+kT6N+kdNlwK4Hts0AAgVHazZOSJgJXgSlOvNVcdgh+lS\nAFezrOivwSJgAe5BwJqdIwKWxJ2EQCwMDkqJiVJKSvTOkZMjdXVF7/MBxA4Ba3aOCliswwKiq6tL\nys6O7jkyM6XeXml8PLrnARB9rf2tKkwlYM2EgAVgUmdn9ANWYqKUlsbzCAE3YJH77AhYACZ1dQWm\n8KKNaULAHZginJ1jAlZBagEBC4iyWEwRSoFzELAA5yNgzc4xAYtF7kD0xTJgdXZG/zwAoouANTtH\nBSw6WEB0dXbGZoqQDhbgfOPWuNoH2pWfmm+6FFsiYAGYFKsOVk4OHSzA6bqGupS+KF2LEheZLsWW\nHBWw2vqZIgSiKVaL3OlgAc7H9GBwjglYhWmFau1vNV0G4Gqx2KZBImABbkDACs5xAcuyLNOlAK7F\nFCGAUBGwgnNMwEpJSlFqcqq6hvhnLxAtTBECCFVbf5sKUtlkdDaOCVhSoIt1of+C6TIA12KKEECo\n6GAF56iAVZRepAt9BCwgWpgiBBCq1gECVjDOClhpRXSwgChiihBAqOhgBeesgJVexJ2EQJSMjwce\nwJyZGf1zEbAA52vtb2UNVhCOCliFqazBAqKlt1dKTZWSkqJ/LqYIAedr62+jgxWEowIWa7CA6InV\n9KAkpaVJw8PSyEhszgcg8pgiDM5ZASuNKUIgWmJ1B6EkeTxMEwJONjY+pu7hbuV6c02XYluOClhs\n0wBET0eHlBvD35W5uYFzAnCe9oF25XpzlZiQaLoU23JUwGKKEIgen0/Ky4vd+fLyAucE4DxsMjo3\nZwUstmkAooYOFoBQsf5qbo4KWOmL0mVZlvpG+kyXArgOHSwAoWrtb1VBGh2sYBwVsDwej5akL1FL\nb4vpUgDX8fli28HKy6ODBThVS1+LitOLTZdha44KWJJUklGilj4CFhBpHR2x7WDl5tLBApzqXO85\nlWSUmC7D1hwXsIoziulgAVFABwtAqOhgzc15ASu9mA4WEAV0sACEqqW3RcUZBKxgCFgAJJlZ5E4H\nC3AmOlhzc17AyijWud5zpssAXMfEFCEdLMCZ6GDNzXEBqySjhDVYQIRZVuBRObHeB4uABTjP4Oig\nhsaGlJMSo4eXOpTjAhZThEDk9fRIKSnSokWxOydThIAztfQFulcej8d0KbbmvIDFXYRAxMV6gbsk\npadLIyPS8HBszwtgYc71nmP9VQgcF7DyvHnqH+3X0NiQ6VIA14j1+itJ8nh4XA7gRKy/Co3jApbH\n41FRWhFdLCCCYn0H4QQWugPOwx2EoXFcwJL+b5qQdVhAxMT6Qc8T6GABzkPACo0jA1ZpRqmae5pN\nlwG4hokpQokOFuBEPCYnNI4MWGWZZWruJWABkdLWJhUWxv68BQWBcwNwjrM9Z1WeVW66DNtzbMA6\n23PWdBmAa7S2mglYhYWBcwNwjqbuJpVllpkuw/YcGbDKM8vV1NNkugzANdraAt2kWKODBTiLZVk6\n23OWgBUCRwYsOlhAZNHBAhCKzqFOLU5arPRF6aZLsT0CFgACFoCQMD0YOkcGrNLMUrX0tsg/7jdd\nCuAKLHIHEAqmB0M3Z8Cqq6vTqlWrVFVVpd27d097/1/+5V9UU1Ojq666Stdee63efPPNqBR6qUWJ\ni5TrzdWF/gtRPxfgdqOjUne3mW0a6GABzkLACl3QgOX3+7Vz507V1dXp2LFj2rdvn44fPz7lmCuu\nuEIvvPCC3nzzTf3VX/2V/uAP/iCqBU9gmhCIjPb2wH5UCQb62fn5gX2wxsdjf24A4WvqaVJZBgEr\nFEF/pR46dEiVlZWqqKhQcnKytm3bpv3790855gMf+ICysrIkSZs2bdLZs7EJPQQsIDJMTQ9KUnKy\nlJEhdXaaOT+A8LAHVuiSgr3Z3Nys8vKLf5FlZWV65ZVXZj3++9//vm6++eYZ37v//vsnv66trVVt\nbW14lV6mPKucgAVEgKkF7hMmpglNPAsRQHjcOkVYX1+v+vr6iH5m0IDl8XhC/qCDBw/qBz/4gV56\n6aUZ3780YEVCWUaZznSfiehnAvGotdXMHlgTJgJWdbW5GgCEpqnHnXcRXt742bVr14I/M+gUYWlp\nqZqaLm7o2dTUpLKy6X+xb775pu655x49+eSTysnJWXBRoajIrtDp7tMxORfgZqY7WAUFLHQHnGDc\nGteZ7jNamrXUdCmOEDRgbdiwQQ0NDWpsbNTIyIieeOIJbd26dcoxZ86c0e/+7u/qxz/+sSorK6Na\n7KUqsit0qvNUzM4HuJXJNVhS4Nxs1QDY3/m+88pcnKm0RWmmS3GEoFOESUlJ2rNnjzZv3iy/36/t\n27erurpae/fulSTt2LFDf/M3f6POzk7de++9kqTk5GQdOnQo6oUvy1mmxq7GqJ8HcLvWVmnjRnPn\nZ6sGwBkauxpVkV1hugzHCBqwJGnLli3asmXLlJ/t2LFj8uvvfe97+t73vhf5yuZQkFqggdEB9Q73\nKmNxRszPD7jFhQvmO1hvvWXu/ABCQ8AKjyN3cpcCC/BZhwUsXEuLVFJi7vwlJdK5c+bODyA0BKzw\nODZgSYF1WEwTAgvT3EzAAjC3xq5GLcteZroMx3B8wGKhOzB/Y2OBBeZFReZqIGABznCq6xQdrDA4\nPmA1djeaLgNwrIkNPpOTzdWwZEmgDj/PbgdsjSnC8Dg6YC3L5k5CYCHOnTM7PSgFwl1uLncSAnY2\nbo2rqbuaM8WfAAAP0UlEQVSJPbDC4OyAlbNM73W+Z7oMwLHsELAkpgkBu2vuaVaON0feZK/pUhzD\n0QGrMrdSDb4GWZZluhTAkc6dk0pLTVcRqIGABdhXQ0eDVuStMF2Gozg6YGWnZCs1OVUtfS2mSwEc\niQ4WgFCc8J1QVW6V6TIcxdEBS5Kq8qrU4GswXQbgSHYKWM3NpqsAMJuGjgYCVpgcH7BW5K1QQwcB\nC5gPOwUsOliAfTX4mCIMl+MDVlVuFQELmCcCFoBQNHQ0qCqPDlY4XBGwTvhOmC4DcCTTu7hPKCmR\nzp41XQWAmYyNj+lU5yktz1luuhRHcX7AYg0WMC/9/YGXyQc9T6iokM6cMV0FgJmc6T6jwrRCtmgI\nk/MDVm6V3u18V/5xtoEGwnH6tLR0qeTxmK5EysmRxselri7TlQC4XIOP6cH5cHzASluUpsK0QnZ0\nB8J06lSgc2QHHk+gllM8WhSwnWNtx7S6YLXpMhzH8QFLkq4svFJvtb5lugzAURob7ROwpEAtjY2m\nqwBwubfa3tKVBVeaLsNxCFhAnCJgAQjFW61v6cpCAla43BGwCq7UW20ELCAcBCwAcxm3xvV269ta\nU7jGdCmO44qAtaZwDR0sIEwELABzOd11Wtkp2cpOyTZdiuO4ImBV51frZMdJjfpHTZcCOAYBC8Bc\n3m57m+nBeXJFwPIme1WeWc6Go0CI+vrsswfWhImAZVmmKwEwgfVX8+eKgCVJNUtq9MaFN0yXATjC\nxBYNdtgDa0JOTqAen890JQAmHD1/VFcVXWW6DEdyTcDaULxBh88dNl0G4Ai/+Y20apXpKqbyeKSV\nK6V33jFdCYAJh88d1saSjabLcCT3BKwSAhYQquPHpepq01VMV10dqA2AeZ2DnWrtb9WKvBWmS3Ek\n1wSs9xW/T0fOH+GROUAI7NjBkgI1/eY3pqsAIEmvtbym9cXrlZiQaLoUR3JNwMrx5mhJ+hK942N+\nAZiLnTtYBCzAHg6fO6wNJRtMl+FYrglYEtOEQCjGx6UTJwLrnexm1SqmCAG7OHzusDYUE7Dmy1UB\na1PpJr3c9LLpMgBbO3NGys2VMjJMVzLdFVdIzc3S0JDpSoD4ZlmWfnn2l7q69GrTpTiWqwLWdUuv\n0wunXzBdBmBrx4/bc/2VJCUnB0LWCba0A4x6t/NdeeTRFTlXmC7FsVwVsGqKatTS16LW/lbTpQC2\n9dZb0hobP1ZszRrp1782XQUQ355vfF7XLb1OHjttlucwrgpYiQmJurb8WrpYQBCvviptsPGyig0b\npMMspQSMev708/rtpb9tugxHc1XAkpgmBOZy+DABC0BwL5x+Qb9dQcBaCNcFrI8s+4iee+8502UA\ntuTzBV4rbLxv4PvfLx09KvnZ0g4wosHXoBH/iFbm2fBWYwdxXcB6X/H71DXUpZMdJ02XAtjO4cPS\n+94nJdj4//zsbKm4mO0aAFOeOvGUbllxC+uvFsjGv2bnJ8GToFtW3KKn3nnKdCmA7Rw+LG10wGPF\nNm5kmhAw5akTT+nWFbeaLsPxXBewJOnWFbfqqRMELOByL78sXe2AbW02bZJeesl0FUD86Rzs1Gvn\nXtP1V1xvuhTHc2XAun7Z9Xq95XW2awAuMTwsvfii9JGPmK5kbjfcID33nGRZpisB4stTJ55SbUWt\nUpNTTZfieK4MWGmL0nTrylu179f7TJcC2MYvfxnYYDQ313Qlc6uulkZHpZMspQRi6rE3HtMdV91h\nugxXcGXAkqQ7a+7UY288ZroMwDaee0766EdNVxEajydQ63PcEAzEzJnuMzp6/qhuXcn6q0hwbcD6\ncMWH1T7QriMtR0yXAtjCs89KN95ouorQ3Xij9MwzpqsA4scPj/5Qn1rzKaUkpZguxRVcG7ASExL1\n+Y2f18O/fNh0KYBxJ08GHvL8wQ+ariR0W7ZI9fVSZ6fpSgD3Gxwd1Ldf/bZ2btxpuhTXcG3AkqQ/\n3PCHevrk02rsajRdCmDUj34k3X574GHKTpGTE5gm/OlPTVcCuN8Pj/5QV5derTWFNn5QqcO4OmBl\npWRpx/t3aNfzu0yXAhgzPi49/rj02c+ariR8n/1soHYA0TMwOqAHX3pQf/5bf266FFdxdcCSpK/9\n1tf07LvP6ldnf2W6FMCI//kfKStLWr/edCXhu+km6dQpNh0Founvf/H3urb8Wn2g/AOmS3EV1wes\nzMWZeuiGh3TPU/doYHTAdDlATFmW9Nd/Ld13X+DOPKdJTpb+/M8D9QOIvNdbXtd3Dn9H37jxG6ZL\ncR3XByxJ+vTaT6umqEZ/9D9/JIudCxFH9u0LBKtPfMJ0JfN3zz3Sr38tHTxouhLAXToGO/Spn35K\n37r5WyrNLDVdjuvERcDyeDz6zi3f0dttb+srz30lZiGrvr4+JuexG8ZtD6dPS1/8orR3b3S7V9Ee\n9+LF0j/9k3Tnnfa6o9Bu1ztWGLc7dA11afOPN+u21bfpU2s+Netxbht3LM0ZsOrq6rRq1SpVVVVp\n9+7dMx7zhS98QVVVVaqpqdGRI/bcdyp9Ubqe/cyz+sWZX+j3//331T3UHfVzxut/mIzbvPPnpVtu\nkb761eg/3DkW4/7Yx6RPflL6+Melnp6ony4kdrrescS4ne/NC29q0/c26bql1+nB6x8Meqybxh1r\nQQOW3+/Xzp07VVdXp2PHjmnfvn06fvz4lGMOHDigkydPqqGhQd/97nd17733RrXghcjx5uj5//e8\nCtIKtOpbq7Tn0B71jfSZLguIqIMHA/td/d7vSV/6kulqIucf/kFas0b6rd+SXnvNdDWA85zqPKU/\nfvqPdf3j1+svP/SXevijD8vjxMWZDpEU7M1Dhw6psrJSFRUVkqRt27Zp//79qq6unjzmySef1J13\n3ilJ2rRpk7q6unThwgUVFRVFr+oFSElK0bdu/pY+t+5zeuAXD+jrP/+6Plj+Qd2w7Aa9v+T9uiLn\nCpVmlCoxIdF0qUBIRkakEycCD3Lety8wNbhnj3Sry552kZAgffvb0o9/HOhorV8fCJGbNklXXCF5\nvaYrBOxjaGxIjV2NOtlxUi81vaSfvfczvdf5nu5ad5eO/dExFaQVmC7R/awgfvrTn1p333335Pc/\n+tGPrJ07d0455pZbbrFeeumlye+vv/566/Dhw1OOkcSLFy9evHjx4uWY10IF7WCF2jq8fNH45X+O\nO/cAAEA8CboGq7S0VE1NTZPfNzU1qaysLOgxZ8+eVWkpt3sCAID4FTRgbdiwQQ0NDWpsbNTIyIie\neOIJbd26dcoxW7du1eP/9yyLX/3qV8rOzrbt+isAAIBYCDpFmJSUpD179mjz5s3y+/3avn27qqur\ntXfvXknSjh07dPPNN+vAgQOqrKxUWlqaHn300ZgUDgAAYFsLXsU1h6efftpauXKlVVlZaT344IPR\nPp1RS5cutdauXWutW7fO2rhxo2VZluXz+awbbrjBqqqqsm688Uars7PTcJULd9ddd1mFhYXWlVde\nOfmzYON84IEHrMrKSmvlypXWM888Y6LkiJhp3Pfdd59VWlpqrVu3zlq3bp114MCByffcMu4zZ85Y\ntbW11urVq601a9ZYjzzyiGVZ7r/ms43b7dd8cHDQuvrqq62amhqrurra+trXvmZZlvuv92zjdvv1\ntizLGhsbs9atW2fdcsstlmW5/1pPuHzckb7WUQ1YY2Nj1vLly61Tp05ZIyMjVk1NjXXs2LFontKo\niooKy+fzTfnZn/3Zn1m7d++2LMuyHnzwQeurX/2qidIi6oUXXrBef/31KUFjtnG+/fbbVk1NjTUy\nMmKdOnXKWr58ueX3+43UvVAzjfv++++3Hn744WnHumncLS0t1pEjRyzLsqze3l5rxYoV1rFjx1x/\nzWcbdzxc8/7+fsuyLGt0dNTatGmT9eKLL7r+elvWzOOOh+v98MMPW5/+9KetW2+91bKs+Ph9blnT\nxx3pax3VR+Vcuo9WcnLy5D5abmZddsfkpfuE3Xnnnfqv//ovE2VF1Ic+9CHl5ORM+dls49y/f79u\nv/12JScnq6KiQpWVlTp06FDMa46EmcYtzXyXrJvGvWTJEq1bt06SlJ6erurqajU3N7v+ms82bsn9\n1zw1NVWSNDIyIr/fr5ycHNdfb2nmcUvuvt5nz57VgQMHdPfdd0+OMx6u9UzjtgJNp2nHznfcUQ1Y\nzc3NKi8vn/y+rKxs8heUG3k8Ht1www3asGGD/vmf/1mSpmy6WlRUpAsXLpgsMWpmG+e5c+em3Hnq\nxv8GvvnNb6qmpkbbt29XV1eXJPeOu7GxUUeOHNGmTZvi6ppPjPuaa66R5P5rPj4+rnXr1qmoqEgf\n/vCHtWbNmri43jONW3L39f7TP/1TfeMb31BCwsU4EA/XeqZxezyeiF7rqAaseNuC/6WXXtKRI0f0\n9NNP61vf+pZefPHFKe97PJ64+DuZa5xu+ju49957derUKR09elTFxcX68pe/POuxTh93X1+fbrvt\nNj3yyCPKyMiY8p6br3lfX58++clP6pFHHlF6enpcXPOEhAQdPXpUZ8+e1QsvvKCDBw9Oed+t1/vy\ncdfX17v6ev/3f/+3CgsLtX79+ln3q3TjtZ5t3JG+1lENWKHso+UmxcXFkqSCggL9zu/8jg4dOqSi\noiKdP39ektTS0qLCwkKTJUbNbON0+z5phYWFk7+A7r777sm2sdvGPTo6qttuu0133HGHPvGJT0iK\nj2s+Me7PfOYzk+OOl2suSVlZWfrYxz6m1157LS6u94SJcR8+fNjV1/vll1/Wk08+qWXLlun222/X\nz3/+c91xxx2uv9Yzjfuzn/1sxK91VANWKPtoucXAwIB6e3slSf39/Xr22We1du1abd26VY899pgk\n6bHHHpv8Je02s41z69at+slPfqKRkRGdOnVKDQ0Nuvrqq02WGlEtLS2TX//nf/6n1q5dK8ld47Ys\nS9u3b9fq1av1xS9+cfLnbr/ms43b7de8vb19cmpkcHBQzz33nNavX+/66z3buCeChuS+6/3AAw+o\nqalJp06d0k9+8hN95CMf0Y9+9CPXX+uZxv34449H/v/tiCzFD+LAgQPWihUrrOXLl1sPPPBAtE9n\nzHvvvWfV1NRYNTU11po1aybH6vP5rOuvv95V2zRs27bNKi4utpKTk62ysjLrBz/4QdBx/t3f/Z21\nfPlya+XKlVZdXZ3Byhfm8nF///vft+644w5r7dq11lVXXWV9/OMft86fPz95vFvG/eKLL1oej8eq\nqamZvH356aefdv01n2ncBw4ccP01f/PNN63169dbNTU11tq1a62HHnrIsqzgv8vcPG63X+8J9fX1\nk3fTuf1aX+rgwYOT4/7MZz4T0WvtsSweFAgAABBJUZ0iBAAAiEcELAAAgAgjYAEAAEQYAQsAACDC\nCFgAAAARRsACAACIsP8Pb74d/Q0ZQ5cAAAAASUVORK5CYII=\n" }, "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": "161ead62", "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." ] }, { "cell_type": "code", "execution_count": 588, "id": "7947d7db", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 588, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAE1CAYAAAA75J7FAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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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": "134ac963", "metadata": {}, "source": [ "Inverse Fourier Transform\n", "==========================\n", "\n", "Of course, we can transform back as well.\n", "\n", "$F$ is a matrix, so we just take its inverse." ] }, { "cell_type": "code", "execution_count": 590, "id": "42844a16", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 590, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl8AAAE1CAYAAADZOIW8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XlgTFf7B/DvnSTWWIJIIgkhCUmINXbV2LcKrVKUovaX\nqmrfvrrTxd5fFdWiKK291FaN2mJrI9YgCWIJSZAEiUSQZeb8/kipEMncmTtzZybfz1+SnDn3GVue\nnOec50hCCAEiIiIiMguN2gEQERERFSdMvoiIiIjMiMkXERERkRkx+SIiIiIyIyZfRERERGbE5IuI\niIjIjIxKvt588024uLggMDDwuWMmTJgAX19fNGjQACdPnjTmcURERERWz6jka9iwYQgNDX3u13fs\n2IGLFy8iNjYWixcvxtixY415HBEREZHVMyr5euGFF+Dk5PTcr2/duhVDhgwBADRv3hxpaWlISkoy\n5pFEREREVs3elJMnJibC09Pz8cceHh5ISEiAi4vL489JkmTKEIiIiIgUZezlQCZNvoBnAywo2fot\n5jccSTyCH0/8iLFBYzE1eKrNJ2VTpkzBlClT1A7D7D545wN8Oncuzny8Xq/x3l8NQ9bfJ1GtuWfR\ngy1Ycf3z5vsuXvi+ixdTve87D+6g/6/9kZiRiHld56FDrQ6KP8MYSuQnJk2+3N3dER8f//jjhIQE\nuLu7PzOut19v9PbrjXdavINea3vhesZ1LOm5xOYTsOJJIBsl0OyLnnqNTpxeBtDx+lEiouLg9v3b\naLO8DXr49sAfr/8BO42d2iGZhElbTYSEhGDlypUAgPDwcFSsWDFfyfFpVctWxe7Bu3Hy5knMOjzL\nlKGRSoROANA/qRaQILQ60wVEREQWIUebgz7r+6Bn7Z6Y03mOzSZegJErXwMGDMD+/ftx69YteHp6\nYurUqcjJyQEAjB49Gt27d8eOHTvg4+ODsmXLYvny5UXOWbZEWWzpvwVNFjdBh1odEFQtyJgQLVZw\ncLDaIaiiVdPW0ElL9B4vJI1NrHwV1z9vvu/ihe+7eFH6fU8/NB0l7Utieofpis5riSRh7K4xYwOQ\npAI3rq06vQozD8/EsVHHUMKuhAqRkSncPn8Lkn8dVNLd1mv8NYdawK7dqB5cy8SRERGRWqKSoxC8\nIhgnRp2AZwXL3uP7vLxFDovtcD8wcCBcHF3w44kf1Q6FFKTL1UGw7EhERE9498938WnbTy0+8VKK\nxSZfkiRhVsdZ+PLAl7iXfU/tcEgpQkAn46+dkDT/7BMjIiJbtO/KPsTeicXooNFqh2I2Fpt8AUAj\nt0ZoW6MtFh5dqHYopBCDNtwz+SIislmfhn2Kz4M/L1ZbjCw6+QKAyW0mY96RecjWZqsdCilAl6uD\nkNFChGVHIiLbFZ4QjsT0RLxW7zW1QzEri0++Gro2hL+zP9acWaN2KKQAoWPZkYiI8sz+azbeafEO\n7DUm7/luUSw++QKAd1q8gwVHF6gdBilBCPkb7tU9kEtERCYQfzce+67sw7BGw9QOxeysIvnq4t0F\nyZnJOHHjhNqhkJF0uTrI2fMFSYLIZdmRiMjWLDu5DAMCB8CxhKPaoZidVSRfdho7jGg0AktO6N+c\nkyyT0AnoJP3/2umg4coXEZGN0eq0WHpyKUY1HqV2KKqwiuQLAN5s9CbWnl2LBzkP1A6FjCC08vp8\nceWLiMj27LmyBy6OLmjg2kDtUFRhNcmXe3l3NHZrjB2xO9QOhYwgdCLvyiB9x0MDcOWLiMimrDqz\nCoMCB6kdhmqsJvkCgNcDX8eqM6vUDoOMIHQyN9xL7PNFRGRLHuQ8wNbzW4tde4knWVXy9Yr/K9hz\nZQ/SHqapHQoZSG7ZkX2+iIhsy/YL29G0WlO4OrqqHYpqrCr5qliqItrWaIvQi6Fqh0IGkl12ZJ8v\nIiKb8mvMr+hXt5/aYajKqpIvAAipHYKt57eqHQYZSLDPFxFRsfUw9yF2XtyJkDohaoeiKqtLvl6q\n/RJCL4YiR5ujdihkAJFrwGlHlh2JiGzC7su70dC1IaqWrap2KKqyuuTLrZwbfCv74uC1g2qHQgYQ\nQn7ZESw7EhHZhN/O/YaX/V5WOwzVWV3yBeSVHrec36J2GGQIuacdwdOORES2QAiBP2L/wEu1X1I7\nFNVZZ/JVJ2/fF/cCWR+dVid/wz3LjkREVu9M8hmULVEW3pW81Q5FdVaZfNWrWg8AcDb5rMqRkGwy\nV74AiU1WiYhsQOjFUHTx7qJ2GBbBKpMvSZIQUoelR2sktDpAktlklStfRERWL/RiKLr6dFU7DItg\nlckXAHTz6YZdl3epHQbJlNfhnn2+iIiKk4ysDBy9fhTBXsFqh2IRrDb5eqH6Czh+/TgyszPVDoVk\nyGuyyrIjEVFxsi9uH5q7N4djCUe1Q7EIVpt8lS1RFo3dGuPQtUNqh0IyyL5eiGVHIiKrx5Jjflab\nfAFAh5odsOfKHrXDIBkM6fPFsiMRkfUSQuCPi39ws/0TrDr5al+zPfZe2at2GCQHTzsSERUrl1Iv\nISs363GnArLy5Ku5R3NcuH0Bdx7cUTsU0hNPOxIRFS/74/ajXc12kGTt97VtVp18lbArgdbVWyMs\nLkztUEhPeRvuWXYkIiou9l/dj7bV26odhkWx6uQL4L4vayN3wz0gQei48kVEZK0OXD2AF71eVDsM\ni2ITyRf3fVkRuRvuNbxYm4jIWl1Nu4oHuQ9Qp3IdtUOxKFaffDVwbYDkzGTcyLihdiikh7wSosyL\ntbnhnojIKh24egBta7Tlfq+nWH3ypZE0aOXZCofjD6sdCulBaHXymqxKEsAN90REVon7vQpm9ckX\nALT2bM3ky1oY0ueLK19ERFZp/9X93O9VANtJvq4x+bIGcsuOkCTu+SIiskLXM67j9v3b7O9VAJtI\nvoKqBSEqJQr3c+6rHQoVQXbZEezzRURkjQ5cPYAXarwAjYxqR3FhE78jpR1KI7BqICISI9QOhYpi\nQNmRHe6JiKzPgasHuN/rOWwi+QKA1tVZerQGsk87SjztSERkjcITwtG6emu1w7BItpN8cdO9VeBp\nRyIi25eZnYlzt86hoWtDtUOxSEYlX6GhofDz84Ovry9mzpz5zNdv3bqFrl27omHDhqhXrx5++ukn\nYx5XqNaerfF3wt/QCX6jtmg87UhEZPOO3ziOQJdAlLIvpXYoFsng5Eur1WL8+PEIDQ1FdHQ01qxZ\ng5iYmHxjFixYgEaNGuHUqVMICwvDu+++i9zcXKODLoiLowsql66M6JRok8xPysjbPM+VLyIiWxae\nEI4WHi3UDsNiGZx8RUREwMfHB15eXnBwcED//v2xZcuWfGPc3NyQnp4OAEhPT0flypVhb29vXMSF\n4L4vyyeEyLsySN/xXPkiIrI64QnhaOHO5Ot5DM6EEhMT4enp+fhjDw8PHDlyJN+YkSNHon379qhW\nrRoyMjKwfv36AueaMmXK418HBwcjODjYoJhaebRCeGI4RgeNNuj1ZAY6Ie9ibfb5IiKyKkIIhCeE\n4+vOX6sdiiLCwsIQFham6JwGJ1/63NM0bdo0NGzYEGFhYbh06RI6deqEyMhIlCtXLt+4J5MvYzR1\nb4r5EfMVmYtMQ+h0Mu/4kgAdy45ERNYiIT0BWqGFV0UvtUNRxNOLQlOnTjV6ToPLju7u7oiPj3/8\ncXx8PDw8PPKN+euvv9C3b18AgLe3N2rWrInz588b+sgiBVYNxJW0K8jIyjDZM8hIOpkb7jUsOxIR\nWZNH+714mfbzGZx8BQUFITY2FnFxccjOzsa6desQEhKSb4yfnx92794NAEhKSsL58+dRq1Yt4yIu\nhIOdA+q71MeJGydM9gwykhB5pUR9sexIRGRVwhO536soBidf9vb2WLBgAbp06YKAgAC89tpr8Pf3\nx6JFi7Bo0SIAwIcffohjx46hQYMG6NixI2bNmoVKlSopFnxBmlZriqPXj5r0GWQ42acdWXYkIrIq\nPOlYNKOOHnbr1g3dunXL97nRo//d7F6lShVs27bNmEfI1sy9Gbae32rWZ5L+hBCAzLIjrxciIrIO\n2dpsnLp5CkHVgtQOxaLZTIf7R7jyZeF0Qn6He5YdiYiswtnks6jlVAvlSpYrenAxZnPJl29lX6Q+\nSEVKZoraoVABhE4na+ULkoZlRyIiK3Hs+jE0cWuidhgWz+aSL42kQVC1IK5+WSqZK1+8WJuIyHoc\nv3GcyZcebC75AvL6fR1NZPJlifJWvni9EBGRLTp+/TiaVGPyVRTbTL6478tyyezzBYkb7omIrEG2\nNhvRKdFo6NpQ7VAsns0mXxGJESxXWSJD+nzxz5GIyOKdTT4L70reKONQRu1QLJ5NJl8e5T2gkTRI\nSE9QOxR6itDJ6/MlJOmf1xARkSXjZnv92WTyJUkSGrk1wsmbJ9UOhZ6mE3m9u/Sl0bDVBBGRFeBm\ne/3ZZPIFAI1cG/GaIUskt+wIlh2JiKwBN9vrz2aTr8ZujbnyZYHklh3zmqyy7EhEZMm42V4em02+\nGrk2wskbTL4sjiFlR658ERFZtEed7bnZXj82m3zVdKqJu1l3cev+LbVDoSfJLDuyySoRkeU7dv0Y\nS44y2GzypZE0XP2yQLKvF9LweiEiIkt34sYJbraXwWaTLwA88WiJhAEXa3Pli4jIop26eQqNXBup\nHYbVsO3ky5XJl8XR8nohIiJbotVpcSb5DOq71Fc7FKth08lXY7fGbDdhaYSQV3bk9UJERBbt4p2L\ncCnrggqlKqgditWw6eTLr4ofEtITcC/7ntqh0D8ErxciIrIpp26eYosJmWw6+bLX2KOuc11E3oxU\nOxR6RKuTv+eLG+6JiCzWqSQmX3LZdPIFsPRocYTIO8GoL/b5IiKyaJE3I9HApYHaYVgVm0++Gro2\nxOnk02qHQY8IAdkd7pl8ERFZLJYd5bP55Ku+S32cTmLyZTF0Bpx2ZNmRiMgiJd1LwoPcB6heobra\noVgVm0++6lWth6jkKGh1WrVDIfyz4Z5lRyIimxCZFImGrg0hyfmhmmw/+SpfsjycyzrjcupltUMh\nANBxwz0Rka3gfi/D2HzyBbD0aFG48kVEZDN40tEwxSf54qZ7y6Bjny8iIlvBzfaGKR7JV9X6OJN0\nRu0wCOCGeyIiG/Ew9yEup16GfxV/tUOxOsUi+Qp0CWTZ0VLIvV6IZUciIot07tY5eDt5o6R9SbVD\nsTrFIvnyqeSDG/du8JohS8DrhYiIbEJUchTqVq2rdhhWqVgkX/Yae/hX8cfZ5LNqh0IsOxIR2YSo\nlCjUdWbyZYhikXwBPPFoMXjakYjIJkSlRCHAOUDtMKwSky8yL0PKjmDyRURkaaKSufJlqGKVfJ1J\n5olH1cktO2pYdiQisjT3c+4jMSMRPpV81A7FKhWb5Cuwat6JR8ESlrpYdiQisnrnb52HTyUfONg5\nqB2KVSo2yZdzWWeUsi+FhPQEtUMp3gzYcC9x5YuIyKJws71xik3yBXDfl0WQufIlceWLiMjiMPky\nDpMvMi/2+SIisnrs8WWc4pV8VeUdj6ozpM+XYNmRiMiScOXLOMUq+Qp0CeQdj2qTu+HejmVHIiJL\ncj/nPq5nXId3JW+1Q7FaRiVfoaGh8PPzg6+vL2bOnFngmLCwMDRq1Aj16tVDcHCwMY8zmn8Vf1xK\nvYSs3CxV4yjWWHYkIrJqMSkx8K3kC3uNvdqhWC2Df+e0Wi3Gjx+P3bt3w93dHU2bNkVISAj8/f+9\n3TwtLQ3jxo3Dzp074eHhgVu3bikStKFK2peEt5M3olOi0citkaqxFFsyy44SrxciIrIoUSnc72Us\ng1e+IiIi4OPjAy8vLzg4OKB///7YsmVLvjGrV69Gnz594OHhAQCoUqWKcdEqoF7VeohKiVI7jGLM\ngD5f7HBPRGQxolOiud/LSAavfCUmJsLT0/Pxxx4eHjhy5Ei+MbGxscjJyUG7du2QkZGBt99+G4MH\nD35mrilTpjz+dXBwsEnLk3Wd6zL5UpPcsqOGZUciIksSlRKFNxu+qXYYZhMWFoawsDBF5zQ4+ZL0\n+Aaak5ODEydOYM+ePbh//z5atmyJFi1awNfXN9+4J5MvU6tbtS5+OvWT2Z5HT9Hp8jbR60nSaFh2\nJCKyIMWtzcTTi0JTp041ek6Dky93d3fEx8c//jg+Pv5xefERT09PVKlSBaVLl0bp0qXRtm1bREZG\nPpN8mRNXvlTGDfdERFYrMzsTN+/dhLcTTzoaw+A9X0FBQYiNjUVcXByys7Oxbt06hISE5BvTq1cv\nHDp0CFqtFvfv38eRI0cQEBBgdNDG8K7kjRsZN3A/576qcRRXEvt8ERFZrZhbMahduTbsNHZqh2LV\nDF75sre3x4IFC9ClSxdotVoMHz4c/v7+WLRoEQBg9OjR8PPzQ9euXVG/fn1oNBqMHDlS9eTLXmMP\n38q+iEmJQZNqTVSNpVgSIq+UqCeJfb6IiCxGVHIUApzV/T5uC4xq0tGtWzd069Yt3+dGjx6d7+P3\n3nsP7733njGPUdyj0iOTLxWw7EhEZLXY2V4ZxarD/SMBzgHc96UWwbIjEZG1ik6JLlab7U2lWCZf\ndZ3rIiqZyZcqhJB32tFOA4krX0REFoErX8oonslXVZ54VIvEsiMRkVW6l30PSfeSUMupltqhWL1i\nmXx5O3kj6V4S7mXfUzuU4kfo9OoR9xjLjkREFiEmJQZ1qtThSUcFFMvky05jh9qVayMmJUbtUIof\nIe96IZYdiYgsA0uOyimWyRfA0qNaJJ0u78ogvV/AlS8iIksQlcI2E0opvskXO92rw4A+X1z5IiJS\nX1QyV76UUryTL554VIEBG+7B5IuISG1RKcXrTkdTKr7JF8uOqpB9vZBGynsNERGpJiMrAymZKahZ\nsabaodiEYpt81axYEymZKcjIylA7lOJFiLwrg/SUV6LkyhcRkZpibsXAr4ofTzoqpNgmX3YaO/hV\n8UN0SrTaoRQz8sqOkkbini8iIpVFJbPkqKRim3wBLD2qQXbZkacdiYhUxzYTyireyRdPPJqf3LIj\nTzsSEamOyZeymHzxxKOZ8bQjEZG1iUpmjy8lFe/ki2VHszPotCPLjkREqknPSsftB7dR04knHZVS\nrJMvr4peuPPgDu4+vKt2KMWI/LIjL9YmIlJPTEreSUeNVKxTBkUV699JjaSBfxV/nng0I7krX5LE\nlS8iIjVxv5fyinXyBbD0aH7ccE9EZE2YfCmPyRdPPJqX4IZ7IiJrwh5fymPyxROPZiUJHaCR22SV\nZUciIrVw5Ut59moHoDaWHc1LEgLQcMM9EZE1uPvwLlIfpKJGxRpqh2JTiv3KV/UK1ZGelY60h2lq\nh1JMCEgyVr5YdiQiUk90SjRPOppAsf/dfHTikaVH85B92pFlRyIi1USnRHO/lwkU++QLAAKcA9hu\nwmx42pGIyFpwv5dpMPlC3qb76FtMvsyCpx2JiKwGky/TYPIFrnyZkyR0Bqx8sexIRKQGtpkwDSZf\nyEu+uOfLPPJOO8rd88WVLyIic0t7mIa7WXdRvUJ1tUOxOUy+ANSoWCPvLxnveDQ5SeggySw7SuDK\nFxGRuUWnRMO/ij9POpoAf0eRd+LRr4ofYm7FqB1KMSBzw709+3wREakhKjkKAc4Baodhk5h8/aNu\nVXa6NwdJ5oZ7SZIgccM9EZHZcbO96TD5+kdAlQCeeDQDSejkNVllny8iIlWwx5fpMPn6Bzfdm4u8\nsqOGfb6IiFTBlS/TYfL1j7pV67LdhBnILTuyzxcRkfmlPUxDelY6TzqaCJOvf3hV9MLtB7eRnpWu\ndig2TW7ZUdJI0LDsSERkVo8228s6nU56Y/L1j8cnHlN44tG05F8vxJUvIiLzYsnRtJh8PYGd7k1P\nErxYm4jI0jH5Mi0mX0/giUfTk4QBF2tz5YuIyKzY48u0jEq+QkND4efnB19fX8ycOfO5444ePQp7\ne3ts2rTJmMeZHHt9mYOQveeLyRcRkXmxzYRpGZx8abVajB8/HqGhoYiOjsaaNWsQE/PsfimtVov/\n/e9/6Nq1K4SFtwxg2dH05JYd2eeLiMi8Uh+k4l72PXiW91Q7FJtlcPIVEREBHx8feHl5wcHBAf37\n98eWLVueGTd//ny8+uqrcHZ2NipQc6hZsSaSM5NxL/ue2qHYLAki78ogPWlYdiQiMquoFJ50NDV7\nQ1+YmJgIT89/s2IPDw8cOXLkmTFbtmzB3r17cfTo0ef+QU6ZMuXxr4ODgxEcHGxoWEax09ihTpU6\niEmJQVP3pqrEYPOEkPcPWiPxbkciIjOKSo5iyfEJYWFhCAsLU3ROg5Mvfb6BTpw4ETNmzIAkSRBC\nPLfs+GTypbZHpUcmX6ahETro5Oz5kiRIYNmRiMhceNIxv6cXhaZOnWr0nAYnX+7u7oiPj3/8cXx8\nPDw8PPKNOX78OPr37w8AuHXrFv744w84ODggJCTE0MeaXF3nuohK4aZ70xHQyLleyF7DlS8iIjOK\nSolCD98eaodh0wxOvoKCghAbG4u4uDhUq1YN69atw5o1a/KNuXz58uNfDxs2DD179rToxAvIW/n6\n8cSPaodhsyQICF4vRERksVh2ND2Dky97e3ssWLAAXbp0gVarxfDhw+Hv749FixYBAEaPHq1YkObE\nE4+mJQld3j4ufcdrWHYkIjKX2/dv40HuA7iXc1c7FJtmcPIFAN26dUO3bt3yfe55Sdfy5cuNeZTZ\n1HKqhZv3biIzOxNlS5RVOxybI0EALDsSEVmk6JRonnQ0A3a4f4q9xh6+lX1x7tY5tUOxSXIv1gY3\n3BMRmQ0325sHk68CsPRoOpLMi7U19uzzRURkLky+zIPJVwF44tGEhAHXC7HsSERkFtxsbx5MvgrA\nlS/T0UDehnuWHYmIzIcrX+Zh1IZ7W8WVLxMSBvT5YtmRiMjkbt2/hazcLFQrV03tUGweV74K4F3J\nG9czruN+zn21Q7E5EoQBrSaYfBERmVpUMu90NBcmXwWw19jDp5IPzt86r3YoNkcjdLL+Yeft+WLZ\nkYjI1KJTornfy0yYfD0HS4+mIv4pJepHsuNpRyIic+B+L/Nh8vUc3HRvGhLEP1cG6TmeZUciIrNg\n8mU+TL6eg8mXaWiETtbKl8Zek3dCkoiITIptJsyHpx2fg2VHU5Hf54unHYmITCslMwU5uhy4Obqp\nHUqxwJWv5/Cp5IOE9AQ8yHmgdig2RQOd/LIjN9wTEZnUo5IjTzqaB5Ov53Cwc4C3kzcu3L6gdig2\nRRLccE9EZGlYcjQvJl+FCHAOYOlRcQZcL8Tki4jIpKJSohBQJUDtMIoNJl+F4KZ75RlSduSGeyIi\n02KPL/Ni8lUIbrpXniSzz5fGnmVHIiJTY5sJ8+Jpx0Jw5Ut5kpB/vRBPOxIRmU5yZjK0Oi1cHV3V\nDqXY4MpXIXwr++La3WvIys1SOxSbIUEne88Xy45ERKbzaLM9TzqaD5OvQpSwK4GaFWvi/G3e8agU\nCQKSHcuORESWgiVH82PyVQSWHpUl8bQjEZFFYfJlfky+ilC3al0mXwrSgNcLERFZkqjkKAQ4s82E\nOTH5KkJAFfb6UpIkuPJFRGQphBBsM6ECnnYsAsuOypKgk33akckXEZFpJGUmAQBcyrqoHEnxwpWv\nItSuXBtxaXHI1marHYpNkLvh/tEqmdAxASMiUtrZ5LOoV7UeTzqaGZOvIpS0L4kaFWrwjkeFyN1w\nDwA6SEy+iIhMICo5CvWq1lM7jGKHyZceuOleORqZfb4AQECCLpeb7omIlHY25SxPOqqAyZceeMG2\ncuReLwQAOmi48kVEZAKPyo5kXky+9BBQhZvulWJI2VGw7EhEpDghxOPu9mReTL70wLKjclh2JCKy\nDPHp8XAs4YhKpSupHUqxw+RLD7Ur18bl1Ms88agAlh2JiCwDS47qYfKlh1L2peBZ3hMX71xUOxSr\nx5UvIiLLwJOO6mHypSeWHpXBlS8iIsvAk47qYfKlpwDnAEQl88SjsTTccE9EZBFYdlQPky891XWu\ni+hbXPkyxqMEimVHIiJ1aXVanLt1jhdqq4TJl5648mU8w5MvDSC48kVEpJQraVfgXMYZ5UqWUzuU\nYokXa+upTuU6uJR6CTnaHDjYOZj9+aeTTuNo4lFkabNQy6kW2tZoizIOZcwehzGETkAHSXbGLyQJ\nYNmRiGzAzXs3ERYXhpTMFLg4uuCF6i/ArZyb2eNgyVFdXPnSU2mH0vAo74HYO7FmfW54Qjia/9gc\nIWtCsP/qfpxJPoNpB6fB8xtPfBb2GR7kPDBrPMbQ5eogIP/yVpYdicjaXU69jP6/9of/d/5YF7UO\n52+fx5qza1B3YV0M2jQIyZnJZo2HyZe6uPIlQ32X+jiTdMZsNfKv//oas/+ajW+6fIN+dfvBTmP3\n+GuXUy9j8u7JCFoShI39NsKvip9ZYjJG3sqXBnZFD81HBw1XvojIaq09uxZv/fEW3mnxDn4M+RGO\nJRwffy09Kx3TDk5Dgx8a4LfXfkMLjxZmiSkqJQrdfbqb5Vn0LKNXvkJDQ+Hn5wdfX1/MnDnzma+v\nWrUKDRo0QP369dG6dWucPn3a2EeqJrBqIM4knzHLs6aGTcXSk0txdORRDAgckC/xAoBaTrWw7tV1\neKfFOwj+KRgRiRFmicsYQicMXvniaUciskZzw+fi/V3vY/fg3fjwhQ/zJV4AUL5keczoOANLQ5ai\n55qeOHj1oFni4sqXuoxKvrRaLcaPH4/Q0FBER0djzZo1iImJyTemVq1aOHDgAE6fPo1PPvkEo0aN\nMipgNQVWDcTpJNMnjysjV2JF5AqEDQ2DZwXP546TJAkjGo/A4p6L0XNNT4vvQ6bL1eWtYskkoIHQ\nsuxIRNZlyfElmHdkHg69eQgNXBsUOra7b3esfmU1+m7oa/KG3jnaHFy8c9EqKia2yqjkKyIiAj4+\nPvDy8oKDgwP69++PLVu25BvTsmVLVKhQAQDQvHlzJCQkGPNIVdV3qW/yla/olGhM2jkJ2wduR9Wy\nVfV6TUidEMzpNAc9VvfA7fu3TRqfMQxe+ZK48kVE1mX35d34NOxT7By0E9UrVNfrNZ28O+Hjth+j\n34Z+Jr3J6AiPAAAgAElEQVTOLvZOLDzLe6K0Q2mTPYMKZ9Ser8TERHh6/rsy4+HhgSNHjjx3/NKl\nS9G9+7M15ilTpjz+dXBwMIKDg40Jy2RqOdVCSmYK0rPSUb5kecXnz9HmYPBvgzGtwzTZ+8oGNxiM\n08mnMXDTQPzx+h/QSJZ3lkKXq4PG0LIjN9wTkZWIvxuPQZsGYU2fNfCt7CvrteOajkPoxVB8vv9z\nfNn+S5PEx5KjPGFhYQgLC1N0TqOSL0nS/xvpvn37sGzZMhw+fPiZrz2ZfFkyO40dApwDcDb5LFp5\ntlJ8/u+OfodKpSthZOORBr1+eofpaLu8Lb4/+j3GNRuncHTGe7ThXi5uuCciayGEwIhtIzCu6Ti0\nq9lO9uslScKPIT8i8PtADKo/yCSlQSZf8jy9KDR16lSj5zRqecTd3R3x8fGPP46Pj4eHh8cz406f\nPo2RI0di69atcHJyMuaRqgt0CcSZJOVLj8mZyfjq4FeY13WerKT2SfYaeywNWYrPwj7D1bSrCkdo\nPEPLjoDEJqtEZBVWRK5AcmYyJreZbPAcro6u+LDNh3g79G0IE/zfdzaZdzqqzajkKygoCLGxsYiL\ni0N2djbWrVuHkJCQfGOuXbuGV155Bb/88gt8fHyMCtYS1K9aH6eTld90/9XBrzAwcCD8nf2Nmsff\n2R/vtnwXo7aPMsk/WmMIrYF9viT2+SIiy3cj4wbe3/U+lvdabnQz7vHNxuNK6hXsvbJXoej+FZkU\nWeQBADIto5Ive3t7LFiwAF26dEFAQABee+01+Pv7Y9GiRVi0aBEA4PPPP0dqairGjh2LRo0aoVmz\nZooErhZTrHwlpCfg58if8UGbDxSZ771W7yElMwU/n/5ZkfmUkrfyZVjZkRvuicjSTQidgFFNRqGh\na0Oj53Kwc8BnL36GT/Z9ougP0hlZGbh57yZ8K8nbi0bKkoTKyyOSJFncCk1hUjJTUHtBbdx5/47B\n5cGnTfhjAkrYlcCcznMUmQ8AIhIj8Mq6V3B+/HmULVFWsXmNkXrpDiRfb1TUpcp6XYK9FxAWBo82\nXiaJi4jIWAevHsTg3wbj3PhzKGVfSpE5tTotAr8PxNyuc9HZu7Mic/4V/xfeDn0bR0ceVWS+4kiJ\nvMXyjsRZOOeyzihlXwoJ6cq0zLjz4A5+Of0LJrWcpMh8jzRzb4Y21dtgbvhcRec1hsHXC7HsSEQW\nTAiB93a9h6/af6VY4gXkHfJ6v/X7+PrvrxWb83TSaTRwYclRbUy+DKBkp/tFxxYhpE4IqpWrpsh8\nT5rWYRq+Cf/G7HeGPY8xpx1ZdiQiS7UhegNydbkYEDhA8bkH1BuAM0lncDb5rCLzRSZFor5LfUXm\nIsMx+TJAfZf6inS6z9Xl4ruj3+GdFu8oENWzajnVwuAGgzF1v/HHYpXA045EZGuycrPwwZ4PMLvT\nbJP0VyxpXxL/afofzDsyT5H5Im9GcuXLAjD5MoBSK1+/X/gdNSrWMOmpk49f+Bjrzq7DldQrJnuG\nvvJOOxqw8iVpWHYkIou07OQy+FbyRfua7U32jBGNR2BD9AakZ6UbNY9O6HAm+QxXviwAky8DKLXy\ntej4IoxuMlqBiJ6vcpnKGB00GrP+mmXS5+hD6ASEAYcUBKzrUAYRFQ852hzMODwDn734mUmf4+ro\nig41O2D1mdVGzXMl9QqcSjnBqbR199u0BUy+DODv7I+Ldy4adfdWQnoCjiQeQd+AvgpGVrCJzSdi\n3dl1SExPNPmzCmPohntIvF6IiCzPz6d/hm8lX7T0bGnyZ41sPBI/nvjRqDlOJ53mqpeFYPJlgFL2\npeBV0Qvnb503eI51Z9eht19vs1xs6lzWGcMaDcPsv2ab/FmFEkZsuOfKFxFZkFxdLqYfmo5P2n5i\nlud1rNURCekJiL0da/AcbK5qOZh8GcjY0uOas2swoJ7yJ2Oe572W72Fl5Eok3Usy2zOflndi8d+V\nLyEEEtMTEZ4QjvCEcFzPuF5wkiVJvNuRqJjJ1eUi9nYsDl87jGPXj+Huw7tqh5TP+qj1cHV0Rdsa\nbc3yPDuNHfrV7Yc1Z9cYPMfppNOoX5UrX5bAqIu1izNjNt3H3o5FQnoC2nnJv3TVUG7l3DAgcAC+\nPfItpnWYZrbnPkmXq4NGknA17SrmRczD+qj1yMrNgldFLwgIxKXFwbGEI/oG9MV/mv4HXhW9APyz\n50vLsiNRcXDg6gF8f+x7/BH7B5xKO8HV0RUPcx8i9nYs/J398Ub9NzC88XCUcSijWoxCCEw/NB1z\nOs1RrNm2PgbUG4A3t76JT9p+YtBzI5MiVfv/n/LjypeBjFn5WnN2DfrV7Qc7jZ3CURVuUotJWHJi\nCTKzM8363Eeych8it0Q6Gi9uDI2kwZ+D/kTyf5MRMTICR0ceRfJ7ydjafyt0Qocmi5vg3T/fRWZ2\nJoSk4coXkY2LvR2Lzj93xvCtw9HaszXOjz+PK29fwd/D/8bJ0SeRNjkNMzrMwL64ffCd74tfo39V\nLdY9V/ZACKFY13l9tfBogYe5DxGZFCn7tY+uFfKpZP13LNsCJl8Gqu9S36B/AEIIs5ccH/Gu5I0X\nqr+AFZErzP7sK6lX8J99r0DY5eLs2LOY3Wn2M5eIS5KEQJdAzOk8B9H/iUZyZjIaLmoIrV0Wm6wS\n2bAVp1ag1bJW6O7bHdH/icb4ZuPh4uiSb4y9xh4danXAptc2Yd2r6/DR3o8wcttIZOVmmT3eueFz\nMbHFRLOuegF5/0f2r9ffoNLjmeQzCHAOgL2GBS9LwOTLQDUq1MD9nPtIyUyR9brIpEg8yHmAFh4t\nTBRZ4Sa1nIRvwr+BTpivjBd5MxJtlrdBF/eXoXlYFW7l3Ip8jYujC35++Wd82e5LZJW9hKNJe80Q\nKRGZkxACn+z7BJ8f+BwHhh7AxBYT4WDnUOTr2lRvg2Mjj+H2/dvosboHMrIyzBBtngu3L+Do9aN4\nPfB1sz3zSQPqDcDas2tl/x/Ok46WhcmXgSRJQkPXhjh185Ss162PWo/+9fqb/SemR1p7toZTKSds\nv7DdLM87k3QGXX7pgm+6fIM+tYbKPu34Wr3X4HDfB0vPf6FqmYGIlKXVafHG5jew+/JuhA8Pf2Yl\nvCjlSpbDhr4bUNOpJnqs7oH7OfdNFGl+847Mw6gmo8xyUr0ggVUDUdahLI4kHJH1usgkdra3JEy+\njNDQtSFO3jwp6zXbLmxDb7/eJoqoaJIkYVLLSYpe1Po81+5eQ7dV3fBNl2/Qr26/f7rUy086Ndqy\neD9gPsbvGI+1Z9cqHygRmZUQAmN+H4MbGTew9429cC7rbNA8dho7LHppEbwqeqH/r/1NvqKf+iAV\nq8+sxtigsSZ9TmEkSUJvv97YHivvB2heK2RZmHwZoZFrI1krX1fTriLpXhKaVmtqwqiK1se/Dy7d\nuaRIl/7nyczORK+1vfB287cfXzYrhIDOgLvPdJIG1cvWxq7Bu/B26NvYd2Wf0uEqJu1hGg5fO4zN\n5zZj+4XtOHHjBB7kPFA7LLJxKZkpOHj1ILac24LtF7bj5I2TRjWBNrWP9n6EyJuR+O2134xeQdJI\nGiwNWYo7D+7gywNfKhRhwZaeXIoetXugWrlqJn1OUXr49pBVveC1QpaHO++M0NC1IaYfmq73+N9j\nf0c3325mP+X4NAc7B4xqMgoLjy7EDy/9YJJnTPpzEgKcA/Beq/f+/aShF2v/0+cr0CUQq19Zjf4b\n++PQsEPwreyrXMBGSH2QiqUnl2LN2TW4cPsCApwD4FLWBVqhRUJ6Ai7duYQWHi3wRoM38Frd11DS\nvqTaIZMNuHnvJn488SPWRa1D/N14BDgHoHKZytDqtLh29xqupF1BO692GNpwKHr79baYjdY/HPsB\nm2I24dCbh1CuZDlF5nSwc8CGvhsQtCQITas1RTffborM+6RcXS7mR8zHpn6bFJ9brhYeLZCYnoj4\nu/HwrOBZ5HheK2SBhMosIASDZedmi9Jflhb3su7pNb7bL93EurPrTByVfq6nXxcVZ1QUaQ/SFJ97\nc8xmUXNuTXH34d18n4/dGiUulagje74zZZuJM0v+fvzxD0d/EHXm1xGpD1KNjtUYD3IeiC/3fykq\nzawkBm0aJPZd2SdytDnPjMvIyhAbojaIzj93Fh7/5yF+ifxF6HQ6FSImW5D6IFW8E/qOcJrhJEZv\nGy0OXzsscrW5z4xLe5Amfon8RbRa2krUnl9bbDm3RYVo8wuPDxfOs5zFhVsXTDL/wasHRdXZVcXV\ntKuKz70haoNos6yN4vMa6vWNr4vvj36v19hN0ZtEj1U9TBxR8aFE3mIZPwpZKQc7B/g7++NM8pki\nTy9mZmfi0LVDWN3HuItRleJWzg2dvTtjZeRKvNX8LcXmvXnvJkZvH42N/TaifMny+b+oM+x6oaf7\nfI0OGo0zyWcwYusIbOi7QZXDC5E3IzFw00D4VvJFxIgIeFfyfu5YxxKOeDXgVbwa8CrCE8Ixevto\nrDy9Ej/0+AE1nWqaMWp5UjJTsOvyLkQkRuBK2hXcz7mPMg5l4FneE03cmqCzd2e4l3dXO0y9CSFw\n6uYp7L2yF2dTzuLmvZvQ6rRwKu2EOpXroLVnawR7BVv0yuTeK3vxxm9voLtvd8SMi3mmHcOTKpSq\ngNfrv47X67+OnRd3YkLoBKw+sxqLXlqECqUqmDHqPCmZKej3az8s6bnEZKvWbaq3wVvN3sKY7WPw\n+8DfFf2/4buj3+GtZsr9X2msl2q/hFVnVmFM0Jgix568eRKN3BqZISrSF/d8GUnfE497r+xFk2pN\nULFURTNEpZ9xTcdh4bGFit2bKITAyG0jMarJKLSu3vrZr+tEXglRNgl4KsY5nefg4p2LWHx8sYHR\nGm7zuc3o+HNHfNDmA/z22m+FJl5Pa+HRAsdGHkN7r/Zo/mNz/HnpTxNGapijiUfRe23vx40s3cu5\nY0iDIfhvq/9iaIOh8Hbyxs5LO1H/h/rosLIDdl7cadF3b97PuY/Fxxcj8PtA9N3QF5fTLqOVRyuM\nbzoe77Z8FyG1Q6ATOnxx4Au4fe2Gt/54C3FpcWqHnU+uLhcf7/0YgzYNwvJey7G45+JCE6+ndfHp\nglOjT8GptBNaLm2JS3cumTDaZ+mEDq9veh0DAweil18vkz7r/dbvIzEjEavPKPeDbkxKDM7dOqfq\nYamndfHugv1x+/U65Xnixgk0dm1shqhIb0avnRnJAkIwyvwj88WobaOKHDdq2ygx5/AcM0SkP51O\nJ+p+V1fsubxHkfm2nNsi/Bb4iazcrAK/fn5DpLhQsq7seSPLtRKR3x185vMxKTGiyqwq4mzSWdlz\nGkKn04kZB2cIj//zEEcTjxo93/64/cJ1jquY+/dciyhDXrx9UXRf1V24f+0u5h+ZX2Q5/WHOQ7Hq\n9CpRZ34dEfxTsIhIiDBTpPrR6XRi9enVwm2Om+i5uqfYfWl3kb/P19Kuicm7J4vKMyuLT/d9KjKz\nM80U7fPdz74veq3pJdqvaC9uZtw0er4FRxYIl9ku4kDcAQWi08+34d+Klj+2LLAsbwpHE48Kl9ku\nIvlesiLzvf3H2+KjPR8pMpeS2i5vK7af317kOLc5biIuNc4MERUPSuQtqmc+1p58Hbx6UDRb0qzQ\nMTqdTrh/7S7OpZwzU1T6WxixULyy7hWj57mffV/UnFtT7Lq067ljzq07Jc6XCpQ996nybcSp+QV/\no1h6YqkIXBj43IRPSV/s/0LU/a6uSLiboNicV1KviLrf1RUf7/1YtQRMp9OJH47+IKrMqiJmH54t\nHuY8lPX6HG2OWHJ8iXCZ7SI+2/eZ2b7BFib+brzo8nMXUf/7+uLv+L+LfsFTrqVdE/029BNec70M\ner1S0h6kibbL24r+v/ZX9O/4zos7RZVZVcShq4cUm/N5opOjRZVZVUTs7ViTP+tJ7/35nhi8abDR\n82RmZ4rKMytbZPIy69AsMXb72ELHXE+/LirNrGQRP+DZCiZfFiD9Yboo81WZQr/hRCVHiRrf1LDI\nv/zpD9OF0wwnEX833qh5Ptv3mXh1/auFjjm39qQ4V6q+7LlPlX9BnJq3v8Cv6XQ68dLql8Rn+z6T\nPa8cX//1tfCd5ytuZNxQfO7ke8kicGGgKgnYvax74uW1L4smi5qI6ORoo+ZKTE8UHVd2FK2WtlI0\nQZXr4NWDwm2Om/hi/xciOzfbqLk2x2wWzrOcxXcR35n9z+buw7siaHGQGPf7OKHVaRWfPzQ2VDjP\nclZkFfd5snOzRdDiIL03hispIytDuM1xM3pFdtmJZeKl1S8pFJWyTt88Lby/9S50zO8XfhcdV3Y0\nU0TFgxJ5C/d8GalcyXKoVq4aLty+8Nwxe6/sRYdaHVTral+YciXLYWDgQCw6vsjgOeLS4rAgYgH+\nr/P/FTrO0CarQpIgtAU3T5QkCT/0+AELjy40Wd+y5SeXY37EfOx5Yw9cHV0Vn9+5rDP2vLEHW85t\nwef7P1d8/udJupeEdivaoVzJcvhr+F+yO4w/rVq5atg5aCe6+3RHq2WtEJUcpVCk+lt8fDH6rO+D\n5b2W4+O2H+t1VU1hevn1wuE3D+P7Y99jzO9joNVpFYq0cA9zH6L32t5o4tYE87vNh8aA/nhF6eLT\nBUt6LsFLq18q9P8vY8z+azYql66M0U1Gm2T+wjiWcMTn7T7Hu3++a9SexB+O/4AxTYre1K6GulXr\nIj0rHVfTrj53zIkbJ9DYjfu9LA2TLwU0cm2EEzdOPPfre6/sRXuv9maMSJ6xQWOx9MRS5GhzDHr9\nZ2GfYVyzcUX3mzGwyaqQNIVerO1e3h0zOs7Am1veRK4uV/b8hTl87TD+t/t/+OP1P/Tqp2Mo57LO\n2P3Gbqw8vRLLTy432XMeiUuLe3yR8U+9fkIJuxKKzKuRNPio7Uf4qv1XaL+yPQ5cPaDIvPqYeWgm\nZh6eiUPDDqGLTxfF5vWt7Iu/h/+NC7cv4I3Nbyj+d+xpubpcDNg4AFXLVsV33b8z6Q9tvfx64Yt2\nXyBkTQjuPryr6Nyxt2Pxf3//Hxa9tEi1HzyHNRyGtIdp2Hxus0GvP3HjBJLuJaGrT1eFI1OGRtKg\nXc122Bf3/MbT3GxvmZh8KSCoWhCO3zhe4Ne0Oi3C4sLQrmY7M0elv7pV68Knkg+2nt8q+7VRyVEI\nvRiKd1u+W+RYndawlS/g+StfjwxrOAxOpZ0w78g8A+YvWPzdePTd0Bc/9f4JflX8FJv3eaqWrYod\nA3fggz0fYPfl3SZ7TvzdeLRf0R7vtHgHU4KnmOQb46D6g7DqlVXos74PDl49qPj8TxJCYErYFCw/\ntRwHhh4wSRsDxxKO2DFwB1IfpKLfhn4G/6Cij//u+i8ysjKw8uWVZmnIPLLJSHSo1QGvb3pdsZU9\n8c/1QR+98BFqVKyhyJyGsNPYYU7nOXh/9/sGdfz/4dgPGNVklOqNsQvT3qs99l7Z+9yvc+XLMjH5\nUkBQtSAcu36swK9FJkXCxdFF9esoijImaAx+OC6/2/0n+z7B+63ef7anV0F0hq98Pd1q4mmSJGFh\n94WYfmg6EtMTZT/jaVm5WXhl/St4u/nb6O7b3ej59FWnSh2s77seAzcOxLlb5xSf/0bGDXRY2QHj\nmo7D+GbjFZ//SR1rdcSaPmvQZ30f2ZcAyzHt4DRsjNmI/UP3m7TvWGmH0tjcfzOytdkYvnW4Se4R\nXHZyGX6/8Ds29N2g2GqkPuZ2mYuM7AxM2T9FkflWRq5E2sM0RXsIGqqzd2fUrFgTP536Sdbr7j68\niw3RG/BmozdNE5hC2tfMS74KKq3evn8bdx7ckdUOh8yDyZcCGrs1xqmbpwr8qXHvlb3oULODClHJ\n08e/DyJvRiL2dqzer4lIjEBEYgT+0/Q/eo0XwrA+X0KSCi07PuJb2Rdjgsbg3T+LXoUrysf7Pka1\nctXwfuv3jZ5LrrY12mJ6h+l4ed3LyMjKUGzee9n30G1VNwyuPxjvtjL+90gfHWt1xPJeyxGyNgRn\nks4oPv+PJ37E0pNL8eegP2X1vTJUCbsSWN93PS7euYjJuycrOvdf8X9h8u7J2NJ/i9mvgXGwc8D6\nV9dj6YmlCIsLM2qu1AepeH/3+1j80mKLudJoSvAUTDs4Tdbq1y+nf0GnWp1Mss9TST6VfKCRNIi9\n8+z/3Y+aq5pizyAZh38iCqhYqiLcHN0KXKnYc2UP2te03P1ej5S0L4mhDYdi8Qn9m5Z+su8TfNL2\nE70vxhW5OsPudtSj7PjIB20+wJHEI9hzeY8Bz8mz69IurDmzBktDlqq2V2V44+FoU70N3tz6piIN\nTLU6LQZsHICm7k3xcduPFYhQfz1q98A3Xb5BzzU9cSPjhmLzbj2/FZ/u+xQ7B+2EWzk3xeYtShmH\nMtg2YBu2X9iuWJk7JTMF/Tb0w/Jey40++GAoF0cXLOu1DIN/G4w7D+4YPM/U/VPxst/LaFKtiYLR\nGaeVZyvUrlwbK06t0Gu8EALfH/seY4PGmjgy40mShPY12xf4fx5LjpaLyZdCCio9ZmuzcfjaYbxY\n40WVopJnVJNR+OnUT3iY+7DIsceuH0N0SjSGNRqm/wOEyCshyqRP2fGRMg5l8G3XbzFuxzhk5WbJ\nflZKZgqGbhmKFb1XoEqZKrJfr6T53eYjLi0O34R/Y/Rc7+16D/dz7mNh94WqJJQDAwdieKPhCFkb\ngszsTKPnO510GiO2jsDWAVtVuWC9cpnK2PH6Dkw7OM2oRB/I6/4+ZPMQDKo/CD1q91AoQsN09emK\nPv59MHLbSIOS/uiUaKw6swpftPvCBNEZ57MXP8O0Q/qtfh2OP4xcXS6CvYJNH5gC2tdsj71xz+77\n4mZ7y8XkSyFB1YJw7Eb+5Oto4lH4VPJB5TKVVYpKHp9KPmjk2ggbozcWOXb6oel4r+V7sval5JUO\nDSw7yvhG0LN2T/hU8jEoaZkQOgED6g1Ah1rql4pL2ZfCr31/xYxDM3D8esEHOvTxc+TP+P3C7/i1\n769Gt14wxsdtP0aAcwCGbB5i1Gre7fu30Xttb3zb9VsEVQtSMEJ5vCp6YU2fNXh90+u4nHrZ4Hm+\n/utrpD1Ms5iEZUbHGbhw+4Ls63mEEJgYOhEfv/AxnMs6myg6w7Wu3hq+lXyxMnJlkWO/P/Y9RjcZ\nbZHtgQrSzqsd9l3Z98w+xOM3jnPly0Ix+VJIE7cmz6x87YvbZ9GnHAsyJmhMkT2/YlJicOjaIYxo\nPELW3EKrgzDkP7NC+nwVPFzCvG7zMPuv2UhIT9D7ddsvbMfRxKP4vJ35em0VpUbFGpjXbR4GbByA\ne9n3ZL8+KjkKk/6chI39Npp9H9HTJEnC4pcW49rda5jz1xyD5sjV5aL/xv54NeBVDAgcoHCE8rWr\n2Q4fvvAheq/trdcde08LTwjHnL/nYE2fNaomxk8qZV8Ky0KWYdKfk5B0L0nv1227sA0J6Ql67wFV\nwydtP8HMwzMLPdWZkpmC3y/8jiENh5gxMuN4VvBEpdKV8u2rvPPgDpLuJZnlpDbJx+RLIY3cGuF0\n0ul8R9APXTuEttXbqhiVfD1r98TFOxcLbZA58/BMTGg2AWVLlJU3uTFlRz023D+pllMtjA0aq/em\n6PSsdIz9fSwW91yMMg5lZMdoSv3r9Ufr6q0xMXSirNfdy76Hvhv6YlbHWQh0CTRRdPKUtC+JX/v9\niq///tqgjd2Td0+GRtJgeofpygdnoLeavYVAl0C8s/MdWa9LfZCKARsHYNFLi1Rtx1CQpu5NMaTB\nELz1h36nFbNyszBp5yTM7TrXYpLIgrSp3gaVS1fGlvNbnjvmp1M/obdfb1QqXcmMkRnvhRov4HD8\n4ccfH7t+DE2qNbHoNhnFGZMvhZQvWR7VK1RHdEo0gLwNzn8n/I1Wnq1UjkweBzsHjGg84rmrX1fT\nrmLbhW0Y12yc7LkNLTsCkt57vp40uc1khMWFITwhvMixH+75EJ29O1vs4Yh5Xedh/9X92BC1Qa/x\nQgiM2T4GLTxayNuXZwbVK1THzy//jIEbB8pqC7LmzBpsPrcZa/qssahvKJIk4fse32PP5T1YH7Ve\n79eN2zEOPXx7oLdfbxNGZ7ipwVNx6uYp/BbzW5Fj54bPRd2qddHZu7MZIjOcJEn4b6v/YvZfswss\nfeuEDouOL7KKjfZPa+3ZGoeuHXr8cURiBJq5N1MxIioMky8FPbnp/mzyWbg6ulrk3oeijGg8AqvO\nrCpwY/SCowswpMEQVCxVUfa8eWVHA1a+NBpZZcdHHEs4YlqHaXg79O1CezIdvnYYm2I2YU4nw0ph\n5lCuZDmsfmU1xu0Yh2t3rxU5fsmJJTiddBoLui8wQ3TydfLuhHFNx6Hfr/302gB96c4lTAidgF/7\n/WqRKxLlS5bH2lfXYvyO8biSeqXI8euj1uP4jeOY1WmWGaIzTGmH0ljScwkmhE4otOR9I+MGZv81\nG193/tqM0Rmut19v3Lp/K98q0SO7L+9GuZLlrDJpae3ZOt97ikiMQLNq1vc+igsmXwoKcvt30/3h\n+MNo7dla5YgMU71CdbT2bI11Uevyff5e9j0sP7kcbzUzsHGiEIbt+TJw5QvI67QOAKtOryrw61m5\nWRixbQTmdZun+p6oojR1b4qJLSZi2JZhhSaT526dw0d7P8KGvhssroT6pA9e+ACVSlfCh3s+LHRc\ntjYb/Tf2x6dtP0VD14Zmik6+oGpB+KDNB+i/sX+hHfBvZNzAW3+8hZ9f/tmi/3wA4EWvFxHsFYwv\nDjz/MMAHez7AiMYj4FPJx4yRGc5OY4dJLSZh9l+zn/naD8fy7nG0lo32T6pduTbu59xHQnoChBBc\n+bJwTL4UFFQtCEcTjwLIS77aVG+jckSGGxM0Bj8cy9/xfmXkSrxQ4wXUdKpp0JzCwOuFCrtYuyga\nSYO5Xebigz0fFPjT+9zwufB28kYf/z4GzW9u77d+P69lxNGFBX49R5uDQZsG4Yt2X6BOlTpmjk4e\njV4GGvEAAA+eSURBVKTB8l7LsS5qHXZe3PnccR/t/Qhujm4m78ivhIktJsK5jDM+3ldwLzUhBEZu\nG4lRTUZZzTfG2Z1mY9nJZY+3VDwpIjECuy7vwkcvfKRCZIYb2nAowhPC810onpieiLC4MAwMHKhi\nZIaTJClv9evaYcSnx0OSJHiU91A7LHoOJl8KauTWCNEp0XiY+xCHr1nvyhcAdPHuguTM5MctDnRC\nh3lH5mFic3mbvp8kdIZvuDemNUFLz5Z40etFzDw8M9/nE9MTMeuvWZjbda7V/KRrr7HHit4rMCVs\nSoG3EXxx4AtULVsVo5uMViE6+aqUqYKVvVdi2JZhBZ6s23lxJ9aeXYtlvZZZxZ+RJElY3ms5fo78\nucBLxZeeXIrrGdfxSdtPVIjOMK6Orvik7ScYv2N8vn+HOqHDhD8mYFr7aShXspyKEcpX2qE0RjQe\ngQUR/5blfzzxI/rX62917+VJrT1b41D8ocerXtbwb6a4Mir5Cg0NhZ+fH3x9fTFz5swCx0yYMAG+\nvr5o0KABTp48aczjLF4ZhzLwq+KHbee3ITMnE7Ur11Y7JIPZaewwqsmoxxvvd17ciVL2pdC2hhGn\nNw0tO0qS7NOOT5vRYQYWHl2Iq2lXH3/uv7v+i7FBY62mXPJI7cq18emLn2LI5iH5jsyHJ4Rj8fHF\nqnbmN0S7mu0wrNEwDN0yNF859ea9mxi2ZRh+fvln1RveyuFc1hmLXlqEoZuH5rse6krqFXyw5wOs\nfHmlWe9tVMJ/mv4HqQ9Tsfbs2sefW3V6FQQEBjcYrGJkhhsbNBa/nP4F6VnpyNXlYsmJJRgTNEbt\nsIzSunreyhf3e1k+g5MvrVaL8ePHIzQ0FNHR0VizZg1iYmLyjdmxYwcuXryI2NhYLF68GGPHWt8J\nErlaeLTAN+HfoJVnK6v6BliQ4Y2GY0P0Btx9eBffHvkWE1tMNOo9GVp2BCQInXGXGHtW8MSEZhPw\nv93/AwAcuHoAh64dwgdtPjBqXrWMbzYepexLPe6XlZmdicG/DcbCHgvNetWOUqa8OAWpD1Lxbfi3\nAPJWVd747Q0MbzzcarqMP6lnnZ5oX7M9Jv05CUDe+xm6ZSjeb/U+6lWtp3J08tlr7LGw+0K8t+s9\npGelIyMrA5P3TMa8rvOs9t5Aj/Ie6OTdCT+d+gnbL2xHjYo1UN+lvtphGaWJWxOcv30ee67ssZqy\ndnFl8K2nERER8PHxgZeXFwCgf//+2LJlC/z9/72XbOvWrRgyJK9RXfPmzZGWloakpCS4uJj+Aly1\nNHdvju+PfY9ZHS33FJO+XBxd0Nm7Mz7e9zFO3jyJzf03GzVf3sXahp12NHblCwD+2/q/8Fvgh/1x\n+/HWH29hTuc58nuVWQiNpMGyXsvQdElTdPftjoXHFqK1Z2u84v+K2qEZxMHOAav7rEbzH5sj2CsY\nuy7vwv2c+/jsxc/UDs1g33T5Bg1+aIBt57ch9k4sdEKHSS0nqR2WwVp6tkQX7y744sAXcNA4oGOt\njmju0VztsIwyodkEDN0yFDUr1sSYJta96gXk9dFr7NYYh64dUvX2ByqawclXYmIiPD09H3/s4eGB\nI0eOFDkmISHhmeRr/Cv/7k9p6t8Ezfwt50JWuTzuO6LxdaD2qcqIuWL4lTCWol9ae0w7MwZvVR+B\nK2uf33hVH/dPxaKMgacds2MuIeYX438/p4jR+GhWdzRwDEA9x1qIOWndf0afS2Pw7pcdIUkaTGu8\nVpHfIzXNtJuIydO7I0eXhekNVyJ2daTaIRnla/sPMXfBUGiFDl80+AkXVp9SOySjjMx6DZNPvAYA\nmG4Df9+cREnUj7PHrYdHUF83BTFnrPv9AED7BG9USL2Gmxsv46bawSigop8r3ILcVY0hLCwMYWFh\nis4pCQN3Mm/cuBGhoaFYsmQJAOCXX37BkSNHMH/+/MdjevbsicmTJ6N167yN5x07dsSsWbPQuPG/\nd01JkoTo0rZz95QAkF3mCko88IIkrLvsCDx6P1dR4qE7JJ3BufpjSc1DELxP3mpGWMjXcNkt7565\n5xEAcspcg31WVWi0pRSZU00CQE7peNjlOMEu11HtcBSRXToRdrmOsMupoHYoisgpmQRJlIB9tmW3\nMtFXbonbAATss61nH15htA7p0Gmy4JBlfT0ZC6K1z4TO/h4cHtpGhSml1wi0XWNZW5YkmfcNF8Tg\n76bu7u6Ij49//HF8fDw8PDwKHZOQkAB392czWP/71v/TBunHv+ghzwje+i6Ad5UOhYiILJwh3zOs\ngcE7JYOCghAbG4u4uDhkZ2dj3bp1CAkJyTcmJCQEK1fm3SAfHh6OihUr2vR+LyIiIqKiGLzyZW9v\njwULFqBLly7QarUYPnw4/P39sWhRXmuC0aNHo3v37tixYwd8fHxQtmxZLF++XLHAiYiIiKyRwXu+\nFAtAgdopERERkTkokbdYZ4MWIiIiIivF5IuIiIjIjJh8EREREZkRky8iIiIiM2LyRURERGRGTL6I\niIiIzIjJFxEREZEZMfkiIiIiMiMmX0RERERmxOSLiIiIyIyYfBERERGZEZMvIiIiIjNi8kVERERk\nRky+iIiIiMyIyRcRERGRGTH5IiIiIjIjJl9EREREZsTki4iIiMiMmHwRERERmRGTLyIiIiIzYvJF\nREREZEZMvoiIiIjMiMkXERERkRkx+SIiIiIyIyZfRERERGbE5IuIiIjIjJh8EREREZkRky8iIiIi\nM2LyRURERGRGTL6IiIiIzIjJFxEREZEZMfkiIiIiMiMmX0RERERmxOSLiIiIyIyYfBERERGZEZMv\nIiIiIjNi8kVERERkRky+VBIWFqZ2CKrg+y5e+L6LF77v4qW4vm8lGJx83blzB506dULt2rXRuXNn\npKWlPTMmPj4e7dq1Q926dVGvXj3MmzfPqGBtSXH9S8v3XbzwfRcvfN/FS3F930owOPmaMWMGOnXq\nhAsXLqBDhw6YMWPGM2McHBzwzTffICoqCuHh4fjuu+8QExNjVMBERERE1szg5Gvr1q0YMmQIAGDI\nkCHYvHnzM2NcXV3RsGFDAICjoyP8/f1x/fp1Qx9JREREZPUkIYQw5IVOTk5ITU0FAAghUKlSpccf\nFyQuLg4vvvgioqKi4Ojo+G8AkmTI44mIiIhUYWDq9Jh9YV/s1KkTbt68+cznv/rqq3wfS5JUaBJ1\n7949vPrqq/j222/zJV6A8W+AiIiIyJoUmnzt2rXruV9zcXHBzZs34erqihs3bqBq1aoFjsvJyUGf\nPn0waNAg9O7d27hoiYiIiKycwXu+QkJCsGLFCgDAihUrCkyshBAYPnw4AgICMHHiRMOjJCIiIrIR\nBu/5unPnDvr164dr167By8vr/9u7g5Ao2jAO4P8V9hJEGuiyucHGuirV7uyAtB2qQyUEoRFeNNoO\nZYeOIhHdvKRZeAjpFHWoi3UJQ3dljRRXOyzVLEEeEhphV01IPJgZU+vT4cP5Wpuxvhx3Pt95fied\nmcP7978uLzvMs3jy5AlKS0sxOzuLy5cvY3BwEOPj4zh27BjC4bB+W7KrqwunTp2yNARjjDHG2Hbx\n15987d69G8+fP8f79++RTCZRWloKANizZw8GBwcBAEeOHMHq6ioymQwURYGiKAUbr6GhIdTW1iIY\nDKK7u3uTUf7f/H4/wuEwZFnGoUOHAPzZrLTt5uLFi/B4PAiFQvqxjXJ2dXUhGAyitrYWyWTSjiVb\nwih3R0cHfD4fZFmGLMtIJBL6OVFym83yE71zs9yid/7161dEo1FEIhHs378f169fByB+32a5Re97\nTT6fhyzLaGhoACB+32vW57a0b7LJ9+/fKRAIkKqqpGkaSZJEk5OTdi1ny/n9flpYWCg4dvXqVeru\n7iYiops3b9K1a9fsWJqlxsbG6M2bN3Tw4EH9mFnOd+/ekSRJpGkaqapKgUCA8vm8LeveLKPcHR0d\n1NPT88u1IuWem5sjRVGIiGhpaYmqq6tpcnJS+M7Ncjuh8+XlZSIi+vbtG0WjUUqlUsL3TWSc2wl9\nExH19PTQuXPnqKGhgYic8Z5O9GtuK/u27euF0uk0qqqq4Pf74Xa70dzcjP7+fruWUxS07g7vn8xK\n226OHj2KsrKygmNmOfv7+9HS0gK32w2/34+qqiqk0+mir9kKRrkB46d5RcptNMtvZmZG+M7NcgPi\nd75jxw4AgKZpyOfzKCsrE75vwDg3IH7fuVwO8Xgcra2telYn9G2Um4gs69u2zdfMzAz27t2r/+7z\n+fQ3LxG5XC6cPHkSdXV1uHfvHgBgfn4eHo8HwD9Pj87Pz9u5xC1jlnN2dhY+n0+/TsTXQG9vLyRJ\nwqVLl/SP5kXNPT09DUVREI1GHdX5Wu7Dhw8DEL/z1dVVRCIReDwe/darE/o2yg2I33dbWxtu376N\nkpJ/twtO6Nsot8vlsqxv2zZfThuuOjExAUVRkEgkcPfuXaRSqYLzv5uVJorf5RTpb3DlyhWoqopM\nJgOv14v29nbTa7d77s+fP6OpqQl37tzBzp07C86J3Pn6GYZO6LykpASZTAa5XA5jY2MYGRkpOC9q\n3+tzj46OCt/3wMAAKioqIMuy6UxOEfs2y21l37ZtviorK5HNZvXfs9lswc5RNF6vFwBQXl6Os2fP\nIp1O67PSAGw4K227M8u5/jWQy+VQWVlpyxq3QkVFhf7G1Nraqn8MLVrutVl+sVhMHznjhM6NZhg6\npXMA2LVrF06fPo3Xr187ou81a7lfvXolfN8vX77Es2fPsG/fPrS0tODFixeIxWLC922U+8KFC5b2\nbdvmq66uDlNTU5ienoamaXj8+DEaGxvtWs6W+vLlC5aWlgAAy8vLSCaTCIVCfzQrTQRmORsbG9HX\n1wdN06CqKqampvQnQUUwNzen//z06VP9SUiRcpPJLD/ROzfLLXrnnz590m+1rKysYHh4GLIsC9+3\nWe6fvwFGxL47OzuRzWahqir6+vpw/PhxPHr0SPi+jXI/fPjQ2v9vyx4L+AvxeJyqq6spEAhQZ2en\nnUvZUh8+fCBJkkiSJDpw4ICedWFhgU6cOEHBYJDq6+tpcXHR5pVuXnNzM3m9XnK73eTz+ejBgwcb\n5rxx4wYFAgGqqamhoaEhG1e+Oetz379/n2KxGIVCIQqHw3TmzBn6+PGjfr0ouVOpFLlcLpIkiSKR\nCEUiEUokEsJ3bpQ7Ho8L3/nbt29JlmWSJIlCoRDdunWLiDZ+LxM5t+h9/2x0dFR/6k/0vn82MjKi\n5z5//rxlff/1kFXGGGOMMfbf2XbbkTHGGGPMiXjzxRhjjDFWRLz5YowxxhgrIt58McYYY4wVEW++\nGGOMMcaKiDdfjDHGGGNF9AN+R/gD83brQwAAAABJRU5ErkJggg==\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": "b90b7174", "metadata": {}, "source": [ "What happens if we apply the Fourier transform matrix $F$ twice?" ] }, { "cell_type": "code", "execution_count": 592, "id": "e09958a8", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 592, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl8AAAE1CAYAAADZOIW8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUECELwAAgAIifAEAABTQ/wPSBcNDHPbbFwAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "double = dot(F,transform)\n", "plot(max1(double))" ] }, { "cell_type": "code", "execution_count": 593, "id": "b6a710e7", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAATsAAAE1CAYAAACY1ke3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imshow(abs(dot(F,F))); gray()" ] }, { "cell_type": "markdown", "id": "c1498934", "metadata": {}, "source": [ "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.\n", "\n", "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": "ee0954b0", "metadata": {}, "source": [ "Fast Fourier Transform\n", "=======================\n", "\n", "\n" ] }, { "cell_type": "markdown", "id": "cd64cdcc", "metadata": {}, "source": [ "Thomasson-Lanczos-Cooley-Tukey-Gauss Lemma\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", "$$ b^{(k)}_n = e^{-\\frac{2 \\pi i}{N} k n} $$\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 $\\log N$.\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": 647, "id": "a7ffc257", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 647, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjwAAAGwCAYAAACtlb+kAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQgi/JwGPEEIIIfyeBDxCCCGE8Hv/HyU8lizhjNO7AAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,10); xticks([]); yticks([])\n", "imshow(imread(\"fft-image.png\"))" ] }, { "cell_type": "markdown", "id": "1d93cefa", "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": 649, "id": "77225d9d", "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": 649, "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": 651, "id": "3b9332eb", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 651, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlcAAAJMCAYAAADXKoPcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nwiFUXFEoFAqFQqFwyP8Dr9h6431P5dsAAAAASUVORK5CYII=\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": "7984e2e3", "metadata": {}, "source": [ "Fourier-Based Filtering\n", "=======================" ] }, { "cell_type": "code", "execution_count": 595, "id": "849349f4", "metadata": { "collapsed": true }, "outputs": [], "source": [ "mix = data32+data128\n", "play(mix,r=10)" ] }, { "cell_type": "code", "execution_count": 596, "id": "40a9402b", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 596, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlcAAAE1CAYAAADK78VIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAFpJJREFUeJzt3X1sleXdwPHfmbAsGb7gAi1SDARhvFXohjMxI6u6srkE\ngmKMsCkRNIvLljmN0f2xDP5Q8TFkU7c/zIKKsuDMEpEs2jFiuhk2IQ5INjXqTEkQS+fG6iPqxov3\n84c5fURZseU67XWf8/kkTerdnsOPq7fcX67zQqUoiiIAAEjiUyM9AABAPRFXAAAJiSsAgITEFQBA\nQuIKACAhcQUAkNCAcbVv3764+OKLY/bs2TFnzpy47777IiJi9erV0dLSEm1tbdHW1hadnZ3DMiwA\nQO4qA73P1YEDB+LAgQMxb968OHToUHzxi1+MzZs3x+OPPx6nn3563HzzzcM5KwBA9kYN9MXm5uZo\nbm6OiIgxY8bEzJkzY//+/RER4b1HAQA+bsCdqw/bu3dvfOUrX4kXXngh1q1bFw899FCceeaZMX/+\n/Fi3bl2cddZZ/3+nlUrNBgYASC3lptEnekL7oUOH4sorr4x77703xowZEzfeeGN0d3fHnj17YsKE\nCXHLLbeccEgfw/fx4x//eMRnaLQPa27NG+HDmlvzRvhI7aRxdeTIkVi6dGl861vfiiVLlkRExPjx\n46NSqUSlUonrr78+du7cmXwwAIAyGjCuiqKIVatWxaxZs+Kmm27qP97T09P/+RNPPBGtra21mxAA\noEQGfEL79u3bY+PGjXH++edHW1tbRETceeedsWnTptizZ09UKpWYMmVKPPDAA8MyLP9de3v7SI/Q\ncKz58LPmw8+aDz9rXn6f+Antg7rTSqUmj2ECAKSWulu8QzsAQELiCgAgIXEFAJCQuAIASEhcAQAk\nJK4AABISVwAACYkrAICExBUAQELiCgAgIXEFAJCQuAIASEhcAQAkJK4AABISVwAACYkrAICExBUA\nQELiCgAgIXEFAJCQuAIASCi7uCqKiAMHRnqKwfnf/414552RngKAiIj33ovo6xvpKQantzfi/fdH\negpSyS6utm6NmDBhpKcYnBkzIi65ZKSnACAiYtmyiLFjR3qKwWlujnjkkZGeglRGjfQAH3Xw4EhP\nMHg9PR/8TQmAkffaayM9wdC8+eZIT0Aq2e1cAQCUmbgCAEhIXAEAJCSuAAASElcAAAmJKwCAhMQV\nAEBC4goAICFxBQCQkLgCAEhIXCVSFCM9AQCQA3EFAJCQuEqkUhnpCQCAHIgrAICExBUAQELiCgAg\nIXEFAJCQuAIASEhcAQAkJK4AABISVwAACYkrAICExBUAQELiCgAgoQHjat++fXHxxRfH7NmzY86c\nOXHfffdFRMTBgwejo6Mjpk+fHgsXLoy+vr5hGRYAIHcDxtXo0aPjJz/5Sbzwwgvx3HPPxc9//vN4\n6aWXYu3atdHR0RGvvPJKXHrppbF27drhmjdbRTHSEwAAORgwrpqbm2PevHkRETFmzJiYOXNm7N+/\nP7Zs2RIrVqyIiIgVK1bE5s2baz8pAEAJjPqk37h3797YvXt3XHjhhdHb2xtNTU0REdHU1BS9vb0f\n+/7Vq1f3f97e3h7t7e2nPCwAwKnq6uqKrq6umt3/J4qrQ4cOxdKlS+Pee++N008//bivVSqVqFQq\nH7vNh+MKACAXH930WbNmTdL7P+mrBY8cORJLly6Na665JpYsWRIRH+xWHThwICIienp6Yvz48UmH\nKqMT9CUA0IAGjKuiKGLVqlUxa9asuOmmm/qPL168ODZs2BARERs2bOiPLgCARjfgw4Lbt2+PjRs3\nxvnnnx9tbW0REXHXXXfF7bffHldddVWsX78+Jk+eHI8//viwDAsAkLsB4+rLX/5yvP/++yf82rZt\n22oyEABAmXmHdgCAhMQVAEBC4goAICFxBQCQkLgCAEhIXAEAJCSuAAASElcAAAmJKwCAhMRVIkUx\n0hMAADkQVwAACYkrAICExBUAQELiCgAgIXEFAJCQuEqkUhnpCQCAHIgrAICExBUAQELiCgAgIXEF\nAJCQuAIASEhcAQAkJK4AABISVwAACYmrRIpipCcAAHIgrgAAEhJXAAAJiSsAgITEFQBAQuIKACAh\ncQUAkJC4AgBISFwBACQkrgAAEhJXiVQqIz0BAJADcQUAkJC4AgBISFwBACQkrgAAEhJXAAAJiSsA\ngITEVSJFMdITAAA5EFcAAAmJKwCAhMQVAEBC4goAIKEB42rlypXR1NQUra2t/cdWr14dLS0t0dbW\nFm1tbdHZ2VnzIQEAymLAuLruuus+Fk+VSiVuvvnm2L17d+zevTu+/vWv13RAAIAyGTCuFixYEGPH\njv3Y8cL7DgAAnNCoodzo/vvvj0ceeSTmz58f69ati7POOutj37N69er+z9vb26O9vX2oMwIAJNPV\n1RVdXV01u/9KcZJtqL1798aiRYviL3/5S0RE/P3vf49x48ZFRMSPfvSj6OnpifXr1x9/p5XKkHe3\nNm2KWL68XG/KWalEnHlmRF/fSE8CQGtrxF//Wr7ryP/8T8Stt470JI3pVLrlRAb9asHx48dHpVKJ\nSqUS119/fezcuTPZMGVWqYz0BABADgYdVz09Pf2fP/HEE8e9khAAoNEN+JyrZcuWxe9///v4xz/+\nEZMmTYo1a9ZEV1dX7NmzJyqVSkyZMiUeeOCB4ZoVACB7A8bVpk2bPnZs5cqVNRsGAKDsvEM7AEBC\n4iqRMr0qBQCoHXEFAJCQuAIASEhcAQAklG1ceQ4TAFBG2cWVqAIAyiy7uKoSWQBAGWUXV6IKACiz\n7OKqSmQBAGWUXVyJKgCgzLKLqyqRBQCUUXZxJaoAgDLLLq6qRBYAUEbZxZWoAgDKLLu4KqtKZaQn\nAABykF1cVXeu7GABAGWUXVwBAJRZtnFVtp2rss0LANRGdnElUgCAMssurqpEFgBQRtnFlagCAMos\nu7iqElkAQBllF1eiCgAos+ziqkpkAQBllF1ciSoAoMyyi6sqkQUAlFF2cSWqAIAyyy6uqkQWAFBG\n2cWVqAIAyiy7uKoSWQBAGWUXV6IKACiz7OKqSmQBAGWUbVwBAJRRdnFlxwoAKLPs4qpKZAHQCKrX\nO9e9+pFdXDm5AIAyyy6uqkQWAI3AzlX9yS6unFwAQJllF1dVIguARmDnqv5kF1dOLgCgzLKLqyqR\nBUAjsHNVf7KLKycXAFBm2cVVlcgCoBHYuao/2cWVkwsAKLPs4qpKZAHQCOxc1Z/s4srJBQCU2YBx\ntXLlymhqaorW1tb+YwcPHoyOjo6YPn16LFy4MPr6+moymMgCoBHYuao/A8bVddddF52dnccdW7t2\nbXR0dMQrr7wSl156aaxduzbpQE4uAKDMBoyrBQsWxNixY487tmXLllixYkVERKxYsSI2b95ck8FE\nFgCNwM5V/Rk12Bv09vZGU1NTREQ0NTVFb2/vCb9v9erV/Z+3t7dHe3v7kAYEAEipq6srurq6anb/\ng46rD6tUKlGpVE74tQ/H1WAodwCglj666bNmzZqk9z/oVws2NTXFgQMHIiKip6cnxo8fn3SgKpEF\nQCPwsGD9GXRcLV68ODZs2BARERs2bIglS5YkHcjJBQCU2YBxtWzZsrjooovi5ZdfjkmTJsVDDz0U\nt99+e/zud7+L6dOnxzPPPBO33357TQYTWQA0AjtX9WfA51xt2rTphMe3bdtWk2EinFwAQLll9w7t\nVSILgEZg56r+ZBdXTi4AoMyyi6sqkQVAI7BzVX+yiysnFwBQZtnFVZXIAqAR2LmqP9nFlZMLACiz\n7OKqSmQB0AjsXNWf7OLKyQUAlFl2cVUlsgBoBHau6k+2cQUAUEbZxZWCB6CRuO7Vn+ziCgCgzLKL\nKwUPQCNx3as/2cUVAECZZRdXyh0AKLPs4qpKZAHQCDwsWH+yiysnFwBQZtnFVZXIAqAR2LmqP9nF\nlZMLACiz7OKqSmQB0AjsXNWf7OLKyQUAlFl2cVUlsgBoBHau6k92ceXkAgDKLLu4qhJZADQCO1f1\nJ7u4cnIBAGWWXVxViSwAGoGdq/qTbVwBAJRRdnGl4AFoJK579Se7uAIAKLPs4krBA9BIXPfqT3Zx\nBQBQZtnFlYIHoJG47tWf7OIKAKDMsosr5Q4AlFl2cVUlsgBoBB4WrD/ZxZWTCwAos+ziqkpkAdAI\n7FzVn+ziyskFAJRZdnFVJbIAaAR2rupPdnHl5AIAyiy7uKoSWQA0AjtX9SfbuAIAKKPs4krBA9BI\nXPfqT3ZxBQBQZtnFlYIHoJG47tWf7OIKAKDMsosrBQ9AI3Hdqz+jhnrDyZMnxxlnnBGnnXZajB49\nOnbu3JlyLgCAUhpyXFUqlejq6oqzzz475TwKHoCG4rpXf07pYcHCmQAAcJxT2rn66le/Gqeddlp8\n+9vfjhtuuOG4r69evbr/8/b29mhvb/9E96vXAIBa6urqiq6urprd/5Djavv27TFhwoR48803o6Oj\nI2bMmBELFizo//qH42ooRBYAjcDDgsPvo5s+a9asSXr/Q35YcMKECRERMW7cuLj88suTPaHdyQUA\nlNmQ4urdd9+Nt99+OyIi3nnnndi6dWu0trYmHUxkAdAI7FzVnyE9LNjb2xuXX355REQcPXo0vvnN\nb8bChQuTDOTkAgDKbEhxNWXKlNizZ0/qWY4jsgBoBHau6k+279AOAFBG2cVVlcgCoBHYuao/2cYV\nAEAZZRdXCh6ARuK6V3+yiysAgDLLLq4UPACNxHWv/mQXVwAAZZZdXCl4ABqJ6179yS6uAADKLLu4\nUvAANBLXvfqTXVwBAJRZdnGl4AFoJK579Se7uAIAKLPs4kq5AwBlll1cVYksABqBhwXrT3Zx5eQC\nAMosu7iqElkANAI7V/Un27gCACij7OJKwQPQSFz36k92cQUAUGbZxZWCB6CRuO7Vn+ziCgCgzLKL\nKwUPwKko23WkbPNyctnFFQBAmWUXVwoegFNRtutI2ebl5LKLKwCAMssurhQ8AKeibNeRss3LyWUX\nVwAAZZZdXCl4AE5F2a4jZZuXk8surgAAyiy7uFLwAJyKsl1HyjYvJ5ddXAEAlFl2caXcAYAyyy6u\nqkQWAENRtofZyjYvJ5dtXAEAlFF2caXgATgVZbuOlG1eTi67uAIAKLPs4krBA3AqynYdKdu8nFx2\ncQUAUGbZxZWCB+BUlO06UrZ5Obns4goAoMyyiysFD8CpKNt1pGzzcnLZxRUAQJllF1cKHoBTUbbr\nSNnm5eSyiysAgDLLLq4UPACnomzXkbLNy8llF1cMTVdX10iP0HCs+fCz5sPPmg8/a15+Q46rzs7O\nmDFjRkybNi3uvvvuZAMp+KHxP+Pws+bDz5oPvzKuedmuIx+dt4xrzvGGFFfHjh2L7373u9HZ2Rkv\nvvhibNq0KV566aXUswEAlM6Q4mrnzp1x3nnnxeTJk2P06NFx9dVXx5NPPpl0sLL8jaOqbPMC1Luy\n/blctnn57ypFMfgf569//ev47W9/G7/4xS8iImLjxo2xY8eOuP/++z+400ol7ZQAADU0hBz6r0YN\n5UYni6eUAwIAlMmQHhacOHFi7Nu3r/+/9+3bFy0tLcmGAgAoqyHF1fz58+PVV1+NvXv3xuHDh+NX\nv/pVLF68OPVsAAClM6SHBUeNGhU/+9nP4mtf+1ocO3YsVq1aFTNnzkw9GwBA6Qz5fa4uu+yyePnl\nl+Nvf/tb/PCHP+w/Xqv3v2p0+/bti4svvjhmz54dc+bMifvuuy8iIg4ePBgdHR0xffr0WLhwYfT1\n9fXf5q677opp06bFjBkzYuvWrSM1eukdO3Ys2traYtGiRRFhzWutr68vrrzyypg5c2bMmjUrduzY\nYc1r7K677orZs2dHa2trLF++PP7zn/9Y88RWrlwZTU1N0dra2n9sKGv85z//OVpbW2PatGnx/e9/\nf1h/D2VzojW/9dZbY+bMmTF37ty44oor4q233ur/WtI1LxI6evRoMXXq1KK7u7s4fPhwMXfu3OLF\nF19M+Us0rJ6enmL37t1FURTF22+/XUyfPr148cUXi1tvvbW4++67i6IoirVr1xa33XZbURRF8cIL\nLxRz584tDh8+XHR3dxdTp04tjh07NmLzl9m6deuK5cuXF4sWLSqKorDmNXbttdcW69evL4qiKI4c\nOVL09fVZ8xrq7u4upkyZUvz73/8uiqIorrrqquLhhx+25on94Q9/KHbt2lXMmTOn/9hg1vj9998v\niqIoLrjggmLHjh1FURTFZZddVjz99NPD/DspjxOt+datW/vP19tuu61ma570n78Zjve/alTNzc0x\nb968iIgYM2ZMzJw5M/bv3x9btmyJFStWRETEihUrYvPmzRER8eSTT8ayZcti9OjRMXny5DjvvPNi\n586dIzZ/Wb3++uvx1FNPxfXXX9//KlhrXjtvvfVWPPvss7Fy5cqI+OApCGeeeaY1r6EzzjgjRo8e\nHe+++24cPXo03n333TjnnHOseWILFiyIsWPHHndsMGu8Y8eO6Onpibfffju+9KUvRUTEtdde238b\nPu5Ea97R0RGf+tQH6XPhhRfG66+/HhHp1zxpXO3fvz8mTZrU/98tLS2xf//+lL8EEbF3797YvXt3\nXHjhhdHb2xtNTU0REdHU1BS9vb0REfHGG28c9wpOP4uh+cEPfhD33HNP//+MEWHNa6i7uzvGjRsX\n1113XXzhC1+IG264Id555x1rXkNnn3123HLLLXHuuefGOeecE2eddVZ0dHRY82Ew2DX+6PGJEyda\n+1Pw4IMPxje+8Y2ISL/mSePKm4fW3qFDh2Lp0qVx7733xumnn37c1yqVyoA/Az+fwfnNb34T48eP\nj7a2tv/63m3WPK2jR4/Grl274jvf+U7s2rUrPvvZz8batWuP+x5rntZrr70WP/3pT2Pv3r3xxhtv\nxKFDh2Ljxo3HfY81r72TrTFp3XHHHfHpT386li9fXpP7TxpX3v+qto4cORJLly6Na665JpYsWRIR\nH/xt58CBAxER0dPTE+PHj4+Ij/8sXn/99Zg4ceLwD11if/zjH2PLli0xZcqUWLZsWTzzzDNxzTXX\nWPMaamlpiZaWlrjgggsiIuLKK6+MXbt2RXNzszWvkeeffz4uuuii+NznPhejRo2KK664Iv70pz9Z\n82EwmD9LWlpaYuLEif0PY1WPW/vBe/jhh+Opp56KX/7yl/3HUq950rjy/le1UxRFrFq1KmbNmhU3\n3XRT//HFixfHhg0bIiJiw4YN/dG1ePHieOyxx+Lw4cPR3d0dr776av9jxnwyd955Z+zbty+6u7vj\nsccei0suuSQeffRRa15Dzc3NMWnSpHjllVciImLbtm0xe/bsWLRokTWvkRkzZsRzzz0X7733XhRF\nEdu2bYtZs2ZZ82Ew2D9Lmpub44wzzogdO3ZEURTx6KOP9t+GT6azszPuueeeePLJJ+Mzn/lM//Hk\na57uefkfeOqpp4rp06cXU6dOLe68887Ud9+wnn322aJSqRRz584t5s2bV8ybN694+umni3/+85/F\npZdeWkybNq3o6Ogo/vWvf/Xf5o477iimTp1afP7zny86OztHcPry6+rq6n+1oDWvrT179hTz588v\nzj///OLyyy8v+vr6rHmN3X333cWsWbOKOXPmFNdee21x+PBha57Y1VdfXUyYMKEYPXp00dLSUjz4\n4INDWuPnn3++mDNnTjF16tTie9/73kj8Vkrjo2u+fv364rzzzivOPffc/uvojTfe2P/9Kdd8SP9w\nMwAAJ5b0YUEAgEYnrgAAEhJXAAAJiSsAgITEFQBAQuIKACCh/wNuD2PxzM2yVgAAAABJRU5ErkJg\ngg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(abs(fft(mix)))" ] }, { "cell_type": "code", "execution_count": 597, "id": "2cbdd298", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 597, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlQAAAE1CAYAAAAh2H5LAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAF19JREFUeJzt3V2Ilde9BvD/TvRcaRsLOkoURow2fow6VBoolY6Ysc1F\nrSKESCsStZRCD0hKqIUGxosm5kJKtLkIxQaLYBMKGi+qtaFn2iC0HqhC0ZCkVMHamUkb60ETDprx\nPRceJ36M43L2ftdk6e8HG8Y9M9t1sXh89nrf/7ZRVVUVAACM2gNjvQAAgNIpVAAATVKoAACapFAB\nADRJoQIAaJJCBQDQpBEL1ZkzZ2LZsmUxf/78WLBgQezYsSMiInp6emL69OnR2dkZnZ2dcejQoSyL\nBQD4NGqM9DlU/f390d/fH4sXL46LFy/GF77whdi/f3+8/vrrMXHixHjmmWdyrhUA4FNp3EjfnDp1\nakydOjUiIiZMmBBz586Ns2fPRkSEzwMFALhqxBOq650+fTq+8pWvxIkTJ2L79u3x6quvxmc/+9lY\nsmRJbN++PR566KFPXrTRqG3BAACt1uxBUVKhunjxYnR1dcWPfvSjWLVqVbz//vsxefLkiIh47rnn\noq+vL3bt2vXJizYaTrBI1tPTEz09PWO9DApgr3A37BdStaK33HHK7/Lly7FmzZr41re+FatWrYqI\niClTpkSj0YhGoxGbNm2Ko0ePNrUIAICSjVioqqqKjRs3xrx582Lz5s1Dz/f19Q19vW/fvujo6Khv\nhQAAn3Ij3pR+5MiR2LNnTyxcuDA6OzsjIuL555+PvXv3xvHjx6PRaMTMmTPjlVdeybJY7k1dXV1j\nvQQKYa9wN+wXckq+Kf2uXtQ9VABAIbLcQwUAwMgUKgCAJilUAABNUqgAAJqkUAEANEmhAgBokkIF\nANAkhQoAoEkKFQBAkxQqAIAmKVQAAE1SqAAAmqRQAQA0SaECAGiSQgUA0CSFCgCgSQoVAECTFCoA\ngCYpVAAATVKoAACapFAVbGAgoqrGehVACfr7x3oFcG9TqAr25JMR//3fY70KoASLF0f8z/+M9Srg\n3qVQFex///fqA+BOPvoo4tKlsV4F3LsUqoINDl59ANyJvIB6KVQFE5BAKnkB9VKoCiYggVTyAuql\nUBVMQAKp5AXUS6EqmIAEUlTV1Ye8gPooVAW7cuXqA2Ak13JCXkB9FKqCOaECUlzLCXkB9VGoCqZQ\nASkUKqifQlUwhQpIoVBB/RSqgilUQAqFCuqnUBXMTelACjelQ/0UqoI5oQJSOKGC+ilUBVOogBQK\nFdRPoSqYQgWkUKigfgpVwRQqIIVCBfVTqAqmUAEpFCqon0JVMFN+QApTflA/hapgTqiAFE6ooH4K\nVcEUKiCFQgX1U6gKde3oXkACd6JQQf0UqkIJSCCVvID6KVSFEpBAKnkB9VOoCmVqB0glL6B+ClWh\nvOMEUskLqN+IherMmTOxbNmymD9/fixYsCB27NgRERHnzp2L7u7umDNnTqxYsSLOnz+fZbF8QkAC\nqeQF1G/EQjV+/Pj4yU9+EidOnIg//vGP8fLLL8fbb78d27Zti+7u7nj33Xdj+fLlsW3btlzr5f8J\nSCCVvID6jViopk6dGosXL46IiAkTJsTcuXPj7NmzceDAgVi/fn1ERKxfvz72799f/0q5gYAEUskL\nqN+41B88ffp0HDt2LB577LEYGBiItra2iIhoa2uLgYGBW36+p6dn6Ouurq7o6upqerF8QkACqeQF\n3Ki3tzd6e3tb+ppJherixYuxZs2aeOmll2LixIk3fK/RaESj0bjld64vVLSeqR0glbyAG9180LN1\n69amX/OOU36XL1+ONWvWxLp162LVqlURcfVUqr+/PyIi+vr6YsqUKU0vhLvjHSeQSl5A/UYsVFVV\nxcaNG2PevHmxefPmoedXrlwZu3fvjoiI3bt3DxUt8hGQQCp5AfUb8ZLfkSNHYs+ePbFw4cLo7OyM\niIgXXnghtmzZEk8++WTs2rUr2tvb4/XXX8+yWD4hIIFU8gLqN2Kh+vKXvxxXbnPR/c0336xlQaQR\nkEAqeQH180nphRKQQCp5AfVTqAplagdIJS+gfgpVobzjBFLJC6ifQlUoAQmkkhdQP4WqUAISSCUv\noH4KVaEEJJBKXkD9FKpCCUgglbyA+ilUhTK1A6SSF1A/hapQ3nECqeQF1E+hKpSABFLJC6ifQlUo\nAQmkkhdQP4WqUIODEePHC0jgzuQF1E+hKtSVK1cD0k2mwJ3IC6ifQlUo7ziBVPIC6qdQFWpwMOI/\n/kNAAncmL6B+ClWhBCSQSl5A/RSqQglIIJW8gPopVIUSkEAqeQH1U6gKZWoHSCUvoH4KVaFM7QCp\n5AXUT6EqlCN8IJW8gPopVIUSkEAqeQH1U6gKJSCBVPIC6qdQFUpAAqnkBdRPoSqUqR0glbyA+ilU\nhTK1A6SSF1A/hapQjvCBVPIC6qdQFUpAAqnkBdRPoSqUgARSyQuon0JVKAEJpJIXUD+FqlCmdoBU\n8gLqp1AVytQOkEpeQP0UqkI5wgdSyQuon0JVKAEJpJIXUD+FqlACEkglL6B+ClWhBgcjxo27+rUb\nTYGRKFRQP4WqUFeuRDz44NWHQgWMxJQf1E+hKtTgYMQDD1x9eNcJjMSUH9RPoSrU4OAnJ1RCEhiJ\nS35QP4WqUAoVkEqhgvopVIVSqIBUChXUT6EqlEIFpFKooH4KVaFM+QGpTPlB/RSqQpnyA1KZ8oP6\nKVSFcskPSOWSH9RPoSqUQgWkUqigfiMWqg0bNkRbW1t0dHQMPdfT0xPTp0+Pzs7O6OzsjEOHDtW+\nSG6lUAGpFCqo34iF6umnn76lMDUajXjmmWfi2LFjcezYsfja175W6wIZnpvSgVRuSof6jVioli5d\nGpMmTbrl+aqqalsQadyUDqRyUzrUb9xofmnnzp3xi1/8IpYsWRLbt2+Phx566Jaf6enpGfq6q6sr\nurq6RrtGhuGSH5DqWqG6ciWiqiIajbFeEYyt3t7e6O3tbelrNqo7HDedPn06vv71r8df/vKXiIh4\n//33Y/LkyRER8dxzz0VfX1/s2rXrxhdtNJxi1eyJJyL+8z8jnn024rXXIhYsGOsVAZ9W7e0R//Vf\nEbNmRVy+fPWNGPCJVvSWu57ymzJlSjQajWg0GrFp06Y4evRoUwtgdJxQAankBdTvrgtVX1/f0Nf7\n9u27YQKQfAQkkEpeQP1GvIdq7dq18fvf/z7+9a9/xYwZM2Lr1q3R29sbx48fj0ajETNnzoxXXnkl\n11q5jik/IJW8gPqNWKj27t17y3MbNmyobTGkM+UHpJIXUD+flF4oR/hAKnkB9VOoCiUggVTyAuqn\nUBVKQAKp5AXUT6EqlIAEUskLqJ9CVShTO0AqeQH1U6gKZWoHSCUvoH4KVaEc4QOp5AXUT6EqlIAE\nUly7xPfAA/IC6qRQFUqhAlJcy4oIeQF1UqgKpVABKRQqyEOhKpSpHSDFtayIkBdQJ4WqUKZ2gBTX\nsiJCXkCdFKpCueQHpHDJD/JQqAqlUAEpFCrIQ6EqlEIFpFCoIA+FqlAKFZBCoYI8FKpCmfIDUpjy\ngzwUqkKZ8gNSmPKDPBSqQrnkB6RwyQ/yUKgKpVABKRQqyEOhKpRCBaRQqCAPhapAVXX14X+PB+5E\noYI8FKoCXblytUw1GqZ2gJGZ8oM8FKoCmdoBUskLyEOhKpAjfCCVvIA8FKoCCUgglbyAPBSqAglI\nIJW8gDwUqgK5yRRIJS8gD4WqQG4yBVLJC8hDoSqQI3wglbyAPBSqAglIIJW8gDwUqgIJSCCVvIA8\nFKoCCUgglbyAPBSqApnaAVLJC8hDoSqQqR0glbyAPBSqAjnCB1LJC8hDoSqQgARSyQvIQ6EqkIAE\nUskLyEOhKpCABFLJC8hDoSqQqR0glbyAPBSqApnaAVLJC8hDoSqQI3wglbyAPBSqAglIIJW8gDwU\nqgIJSCCVvIA8FKoCCUgglbyAPBSqApnaAVLJC8hDoSqQqR0glbyAPEYsVBs2bIi2trbo6OgYeu7c\nuXPR3d0dc+bMiRUrVsT58+drXyQ3coQPpJIXkMeIherpp5+OQ4cO3fDctm3boru7O959991Yvnx5\nbNu2rdYFcisBCaSSF5DHiIVq6dKlMWnSpBueO3DgQKxfvz4iItavXx/79++vb3UMS0ACqeQF5DHu\nbn9hYGAg2traIiKira0tBgYGhv25np6eoa+7urqiq6trVAvkVgISSCUv4Fa9vb3R29vb0te860J1\nvUajEY1GY9jvXV+oaC1TO0AqeQG3uvmgZ+vWrU2/5l1P+bW1tUV/f39ERPT19cWUKVOaXgR3x9QO\nkEpeQB53XahWrlwZu3fvjoiI3bt3x6pVq1q+KEbmCB9IJS8gjxEL1dq1a+NLX/pSvPPOOzFjxox4\n9dVXY8uWLfHb3/425syZE7/73e9iy5YtudbK/xOQQCp5AXmMeA/V3r17h33+zTffrGUxpBGQQCp5\nAXn4pPQCCUgglbyAPBSqApnaAVLJC8hDoSqQqR0glbyAPBSqAjnCB1LJC8hDoSqQgARSyQvIQ6Eq\nkIAEUskLyEOhKpCbTIFU8gLyUKgK5CZTIJW8gDwUqgI5wgdSyQvIQ6EqkIAEUskLyEOhKpCABFLJ\nC8hDoSqQgARSyQvIQ6EqkKkdIJW8gDwUqgKZ2gFSyQvIQ6Eq0M1H+FeuRFTV2K4J+HRyyQ/yUKgK\ndH1ANhpXH47xgeEoVJCHQlWg6wMyQkgCt6dQQR4KVYEUKiCVQgV5KFQFun5qJ8LkDnB7pvwgD4Wq\nQNdP7USY3AFuz5Qf5KFQFcglPyCVS36Qh0JVIIUKSKVQQR4KVYEUKiCVQgV5KFQFUqiAVAoV5KFQ\nFciUH5DKlB/koVAVyJQfkMqUH+ShUBXIJT8glUt+kIdCVSCFCkilUEEeClWBFCoglUIFeShUBVKo\ngFTX58W1e6ncmA6tp1AVyJQfkEpeQB4KVYFM+QGp5AXkoVAVyCU/IJW8gDwUqgIJSCCVvIA8FKoC\nCUgglbyAPBSqAglIIJW8gDwUqgKZ2gFSyQvIQ6EqkKkdIJW8gDwUqgI5wgdSyQvIQ6EqkIAEUskL\nyEOhKpCABFLJC8hDoSqQm0yBFFV19XH9PVTyAuqhUBXITaZAiitXIhqNq49r5AXUQ6EqkCN8IMXN\nWREhL6AuClWBFCoghUIF+ShUBVKogBQKFeSjUBVIoQJSKFSQz7jR/mJ7e3t85jOfiQcffDDGjx8f\nR48ebeW6GIEpPyDFzVkRIS+gLqMuVI1GI3p7e+Nzn/tcK9dDAlN+QIqbsyJCXkBdmrrkV1VVq9bB\nXXDJD0jhkh/k09QJ1eOPPx4PPvhgfOc734lvf/vbN3y/p6dn6Ouurq7o6uoa7V/FTRQqIIVCBcPr\n7e2N3t7elr7mqAvVkSNHYtq0afHPf/4zuru749FHH42lS5cOff/6QkVrKVRACoUKhnfzQc/WrVub\nfs1RX/KbNm1aRERMnjw5Vq9e7ab0jBQqIIVCBfmMqlB99NFHceHChYiI+PDDD+Pw4cPR0dHR0oVx\ne6b8gBSm/CCfUV3yGxgYiNWrV0dExMcffxzf/OY3Y8WKFS1dGLdnyg9IYcoP8hlVoZo5c2YcP368\n1WshkUt+QAqX/CAfn5RemGtH9de/6xSQwHAUKshHoSqMgARSyQvIR6EqjIAEUskLyEehKoypHSCV\nvIB8FKrCmNoBUskLyEehKowjfCCVvIB8FKrCCEgglbyAfBSqwghIIJW8gHwUqsIISCCVvIB8FKrC\nmNoBUskLyEehKoypHSCVvIB8FKrCOMIHUskLyEehKoyABFLJC8hHoSqMgARSyQvIR6EqjIAEUskL\nyEehKoypHSCVvIB8FKrCmNoBUskLyEehKowjfCCVvIB8FKrCCEgglbyAfBSqwghIIJW8gHwUqsK4\nyRRIJS8gH4WqMG4yBVLJC8hHoSqMI3wglbyAfBSqwghIIJW8gHwUqsIISCCVvIB8FKrCCEgglbyA\nfBSqwpjaAVLJC8hHoSqMqR0glbyAfBSqwjjCB1LJC8hHoSqMgARSyQvIR6EqjIAEUskLyEehKoyA\nBFLJC8hHoSqMqR0glbyAfBSqwpjaAVLJC8hHoSqMI3wglbyAfBSqwghIIJW8gHwUqsIISCCVvIB8\nFKrCCEgglbyAfBSqwpjaAVLJC8hHoSqMqR0glbyAfBSqwjjCB1LJC8hHoSqMgARSyQvIR6EqjIAE\nUskLyEehKoyABFLJC8hHoSqMqR0glbyAfBSqwpjaAVLJC8hHoSrMvXiE39vbO9ZLoBD2yt25F/Pi\nbtgv5DTqQnXo0KF49NFHY/bs2fHiiy+2ck2M4F4MSKFHKnvl7tyLeXE37BdyGlWhGhwcjO9973tx\n6NChOHnyZOzduzfefvvtVq+NYdzvAQmkkxeQz6gK1dGjR+ORRx6J9vb2GD9+fDz11FPxxhtvtHpt\nDGO4m0yv3SPhRlPgere7KV2hgtZrVFVV3e0v/epXv4rf/OY38bOf/SwiIvbs2RN/+tOfYufOnVdf\ntNFo7SoBAGo0ijp0g3Gj+aU7FaZmFwUAUJJRXfJ7+OGH48yZM0N/PnPmTEyfPr1liwIAKMmoCtWS\nJUvivffei9OnT8elS5fitddei5UrV7Z6bQAARRjVJb9x48bFT3/60/jqV78ag4ODsXHjxpg7d26r\n1wYAUIRRfw7VE088Ee+880789a9/jR/+8IdDz/t8Ku6kvb09Fi5cGJ2dnfHFL34xIiLOnTsX3d3d\nMWfOnFixYkWcP39+jFfJWNiwYUO0tbVFR0fH0HMj7Y0XXnghZs+eHY8++mgcPnx4LJbMGBpuv/T0\n9MT06dOjs7MzOjs74+DBg0Pfs1/uX2fOnIlly5bF/PnzY8GCBbFjx46IaHG+VC308ccfV7NmzapO\nnTpVXbp0qVq0aFF18uTJVv4V3APa29urDz744Ibnnn322erFF1+sqqqqtm3bVv3gBz8Yi6Uxxv7w\nhz9Uf/7zn6sFCxYMPXe7vXHixIlq0aJF1aVLl6pTp05Vs2bNqgYHB8dk3YyN4fZLT09PtX379lt+\n1n65v/X19VXHjh2rqqqqLly4UM2ZM6c6efJkS/Olpf/1jM+nIlV10yTogQMHYv369RERsX79+ti/\nf/9YLIsxtnTp0pg0adINz91ub7zxxhuxdu3aGD9+fLS3t8cjjzwSR48ezb5mxs5w+yVi+Elz++X+\nNnXq1Fi8eHFEREyYMCHmzp0bZ8+ebWm+tLRQnT17NmbMmDH05+nTp8fZs2db+VdwD2g0GvH444/H\nkiVLhj7LbGBgINra2iIioq2tLQYGBsZyiXyK3G5v/OMf/7hhuljecM3OnTtj0aJFsXHjxqFLOPYL\n15w+fTqOHTsWjz32WEvzpaWFygd6kuLIkSNx7NixOHjwYLz88svx1ltv3fD9RqNhLzGsO+0N+4bv\nfve7cerUqTh+/HhMmzYtvv/979/2Z+2X+8/FixdjzZo18dJLL8XEiRNv+F6z+dLSQuXzqUgxbdq0\niIiYPHlyrF69Oo4ePRptbW3R398fERF9fX0xZcqUsVwinyK32xs3583f//73ePjhh8dkjXx6TJky\nZegfxk2bNg1dprFfuHz5cqxZsybWrVsXq1atiojW5ktLC5XPp+JOPvroo7hw4UJERHz44Ydx+PDh\n6OjoiJUrV8bu3bsjImL37t1Dmx1utzdWrlwZv/zlL+PSpUtx6tSpeO+994amRrl/9fX1DX29b9++\noQlA++X+VlVVbNy4MebNmxebN28eer6l+dLqO+l//etfV3PmzKlmzZpVPf/8861+eQr3t7/9rVq0\naFG1aNGiav78+UN75IMPPqiWL19ezZ49u+ru7q7+/e9/j/FKGQtPPfVUNW3atGr8+PHV9OnTq5//\n/Ocj7o0f//jH1axZs6rPf/7z1aFDh8Zw5YyFm/fLrl27qnXr1lUdHR3VwoULq2984xtVf3//0M/b\nL/evt956q2o0GtWiRYuqxYsXV4sXL64OHjzY0nwZ1X+ODADAJ1p6yQ8A4H6kUAEANEmhAgBokkIF\nANAkhQoAoEkKFQBAk/4Pw4pkX7r2Oy0AAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(abs(fft(mix))[:200])" ] }, { "cell_type": "code", "execution_count": 600, "id": "2dd90574", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 600, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlEAAAE1CAYAAADH8bUPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAUIUAEAD/g8NCREJxsT8iAAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(abs(fft(mix))[120:140])" ] }, { "cell_type": "code", "execution_count": 601, "id": "9f73e793", "metadata": { "collapsed": true }, "outputs": [], "source": [ "transform = fft(mix)" ] }, { "cell_type": "code", "execution_count": 603, "id": "25391bae", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 603, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlcAAAE1CAYAAADK78VIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCf0fXukJb3D3s7EAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "transform[120:130] = 0\n", "transform[-130:-120] = 0\n", "plot(abs(transform))" ] }, { "cell_type": "code", "execution_count": 608, "id": "c3123b59", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 608, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmUAAAE1CAYAAACm6ZdNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niApQUkYIIYQQogL/D1RCq+IvlN7mAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(real(ifft(transform))[:100])\n", "plot(mix[:100])" ] }, { "cell_type": "code", "execution_count": 613, "id": "65d20a30", "metadata": { "collapsed": true }, "outputs": [], "source": [ "play(mix,r=10)" ] }, { "cell_type": "code", "execution_count": 612, "id": "478ca530", "metadata": { "collapsed": true }, "outputs": [], "source": [ "play(real(ifft(transform)),r=10)" ] }, { "cell_type": "markdown", "id": "54e4b32c", "metadata": {}, "source": [ "Removing Noise in the Fourier Domain\n", "=====================================" ] }, { "cell_type": "code", "execution_count": 620, "id": "103ca01a", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0" ] } ], "source": [ "test = numpy.fromfile(\"test.raw\",\"int32\")[::2]\n", "test = test*1.0/amax(abs(test))\n", "play(test)\n", "print amax(test)" ] }, { "cell_type": "code", "execution_count": 625, "id": "40f34876", "metadata": { "collapsed": false }, "outputs": [], "source": [ "noise = test+sin(arange(len(test))/10.0)\n", "play(noise)" ] }, { "cell_type": "code", "execution_count": 636, "id": "dc7767db", "metadata": { "collapsed": true }, "outputs": [], "source": [ "Noise = fft(noise)" ] }, { "cell_type": "code", "execution_count": 637, "id": "6bf29ad0", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 637, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmAAAAE1CAYAAABAwFwJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(abs(Noise)**.5)" ] }, { "cell_type": "code", "execution_count": 639, "id": "14477c42", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 639, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAloAAAE1CAYAAAA/EU74AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot((abs(Noise)**.5)[400:500])" ] }, { "cell_type": "code", "execution_count": 640, "id": "d6da1a2d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 640, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAloAAAE1CAYAAAA/EU74AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XeYFFXaNvC7CaIsSlAYkGEdJChhgDGAi6DDR1AMhJc1\n4CuimGDVVVERUWFwF0XUZVExrCKiuIQXJaiACDqArMACgyKgIJIZBpAgeWCmvj+ONRW6qrqqu1J3\n37/rmqu7q6pPna6prnr6xIgkSRKIiIiIyHXlgs4AERERUapioEVERETkEQZaRERERB5hoEVERETk\nEQZaRERERB5hoEVERETkEctA68SJE2jTpg1atWqFpk2b4qmnngIA7N+/H507d0bjxo3RpUsXHDx4\n0JfMEhERESWTSKxxtI4dO4bKlSvj9OnTaNeuHV5++WXMmjUL5513HgYNGoQXX3wRBw4cwMiRI/3K\nMxEREVFSiFl1WLlyZQBAcXExSkpKUL16dcyaNQt9+/YFAPTt2xczZszwNpdERERESahCrA1KS0tx\nySWXYNOmTRgwYACaNWuGoqIiZGRkAAAyMjJQVFSkeU8kEvEmt0REREQe8GqinJglWuXKlcPq1aux\nY8cOLFq0CF9//bVmfSQSMQysJEky/Nu1S8KaNcbr+Cf+hg0bFngekvmPx4/Hj8cuOf94/Nw/fvPn\nSygtDT5vYf/zku1eh1WrVsX111+PlStXIiMjA7t37wYAFBYWolatWrZ32LMnkJ3tPKNERETkTKdO\nwHffBZ2L9GYZaO3bt6+sR+Hx48fx5ZdfIicnB926dcOECRMAABMmTECPHj1s7/DkyQRyS0RERI54\nXGBDMVi20SosLETfvn1RWlqK0tJS9OnTBx07dkROTg5uvvlmjBs3DllZWZg6dapf+U0Lubm5QWch\nqfH4JYbHL348donh8UsMj184xRzeIa5EIxHTOs+cHGD1akbYREREXotEgFWrxL1X7dVXgbFjgZ9+\nCiZfYWMVtySKI8MTERGlmS+/BDZsCDoX6cH3QOvAAb/3SERElH5KS83XcRQm//geaG3d6vceiYiI\n0g/vt+HAqkMiIqI0wxIt/zDQIiIiSmFGQRUDLf8w0CIiIiLyiGeB1p/+BBw65FXqREREROHnWaC1\ndCmwZYtXqRMRERGFn6dVhxyUlIiIiNIZ22gRERGlGRaE+IeBFhERUZphoOUfBlpEREQpiEM4hAMD\nLSIiohRmFHCxRMs/bAxPRESUZnh/9g9LtIiIiIg8wkCLiIgohRmVXrFEyz8MtIiIiIg8wkCLiIiI\nyCMMtIiIiNIMqw79w16HREREKUge1oHjaQWLJVpERERphgUh/mGgRURElGYYaPmHVYdEREREHmGJ\nFhERUZphQYh/GGgREREReYSBFhERUZphiZZ/GGgRERGlMA7vECwGWkREREQeYa9DIiKiFGRVksX7\ns39YokVERJRmGGj5h4EWERERkUcYaBEREaUZlmj5h4EWERERkUfYGJ6IiCjN8P7sH5ZoERERpTCj\n3ocMtPzDQIuIiCiFMagKFgMtIiKiFMRxtMLBMtDavn07OnTogGbNmqF58+Z49dVXAQB5eXnIzMxE\nTk4OcnJyMHfuXFcyc/AgcPKkK0kRERGlhf37gVOngs4FmbEMtCpWrIjRo0dj7dq1WLp0KcaOHYv1\n69cjEolg4MCBKCgoQEFBAa699lpXMlO9OtC/vytJERERpYVzzwWGDg06F2SmgtXK2rVro3bt2gCA\nKlWqoEmTJti5cycAQLJR7hhP0eSWLc7fQ0RElM527HC2PasO/WMZaKlt2bIFBQUFuOKKK7BkyRK8\n9tpr+OCDD3DZZZfhlVdeQbVq1XTvyMM77wCzZwO5ubnIzc11N+dEREQEwDhw2rDB/3wki/z8fOTn\n5/uyr4hko2jqyJEjyM3NxTPPPIMePXpgz549qFmzJgDg2WefRWFhIcaNG6ckGokAkLBsGdC6tW6H\nvzfOM9prJALk5gJffx3vxyEiIkovkQhw223ARx9pl7/9tmiO8/33QHa2dt1VVwGLF7NkSxaJRGzV\n1MUjZq/DU6dOoVevXrj99tvRo0cPAECtWrUQiUQQiURwzz33YPny5Z5kjoiIiNzHAMs/loGWJEm4\n++670bRpUzzyyCNlywsLC8ueT58+Hdn6UDkBVt1RiYiIKBoDp/CybKO1ZMkSTJw4ES1atEBOTg4A\n4Pnnn8ekSZOwevVqRCIR1K9fH2+//bbh++P5x/NkISIiShzH0QoHy0CrXbt2KC0tjVretWtXzzJE\nREREzjgNnBho+YcjwxMRESU5Bk7hxUCLiIiIyCOhC7R8GtaCiIgo6R0/Lh6nTAk2H2TO00CLRZlE\nRETe+fHH2NsYNYrn/dk/oSvRIiIiIm8x0PIPAy0iIqIkxbEnw4+BFhERUQriOFrhwDZaRERESYol\nWuEXWIlWz55B7ZmIiCg1WAVa990nHo0KPVgQ4p/AAq0ZM4LaMxERUXpjoOUfttEiIiJKUnaqDlm9\nGCwGWkREREmKQVT4sTE8ERFRmuH92T8s0SIiIkpSLNEKPwZaRERESSreQIslWv5hoEVERETkEQZa\nRERESYolWuHHQIuIiCjNMNDyD3sdEhERpTA2mA8WS7SIiIiSFKsOw4+BFhERUZphoOUfVh0SEREl\nKVYLhl9oSrT27g06B0RERMmFgVb4hSbQ2r8/6BwQERGlnp9/DjoH6S00gRYRERE5Y6dEa8qU6GVs\n2uOfpAm03nkH+PrroHNBRETkvxEjgLVro5fbCbSMtmGg5Z/QBFqx/un33QcMHOhPXoiIiMLkmWeA\nN96I770MqoLFXodERERJiuNohV9oSrSIiIjIfUZBFQMt/7BEi4iIKAkY3VPtlGjxXhwsBlpERERJ\nilWH4ZdUVYccmI2IiIiSCUu0iIiIkhQLIMIvKUq0li4NOgdERETBevNN99JiQYh/kqJEa84cd9Ih\nIiIi8lNSlGgRERFRtHh7HbJEyz9JUaJFRERE0djrMPySokSLjf2IiIgoGVkGWtu3b0eHDh3QrFkz\nNG/eHK+++ioAYP/+/ejcuTMaN26MLl264ODBg4bvZ8RMREQUPrw/+8cy0KpYsSJGjx6NtWvXYunS\npRg7dizWr1+PkSNHonPnztiwYQM6duyIkSNHGr7fyT+S/3QiIiL3TZ8edA7Sm2WgVbt2bbRq1QoA\nUKVKFTRp0gQ7d+7ErFmz0LdvXwBA3759MWPGDO9zSkRERI6dOhW9jIUb/qlgd8MtW7agoKAAbdq0\nQVFRETIyMgAAGRkZKCoqMnhHHj74APjmGyA3Nxe5ublxZ1Juo8W2WkRERIlL90ArPz8f+fn5vuzL\nVqB15MgR9OrVC2PGjMHZZ5+tWReJRBAxjIDy0KcP0LmzG9kUVq1yLy0iIqJ0de21wAUXBJ2L4OgL\ngIYPH+7ZvmL2Ojx16hR69eqFPn36oEePHgBEKdbu3bsBAIWFhahVq5bhe9M9YiYiIgqjSASoWDHo\nXKQHy0BLkiTcfffdaNq0KR555JGy5d26dcOECRMAABMmTCgLwIiIiCj8JInNcfxiWXW4ZMkSTJw4\nES1atEBOTg4A4IUXXsDgwYNx8803Y9y4ccjKysLUqVMN388SLSIionBioOUPy0CrXbt2KC0tNVw3\nf/58TzJERERE3mJBiH9CMwWP1baMuomIiKIlEjDx3uqP0ARaRERE5A/en/2TFHMdEhERkXvYGN4/\noSnRsvqH82QgIiKKtmJF/O/lvdUfoSnRYjEmERGRM2vWxPc+3nP9E5oSLSIiIvIHqw79E5oSLSIi\nIvIPAy1/sESLiIgozfD+7B+WaBERESWpREqlWKLlD5ZoERERJal4gyXen/3DQIuIiCjNsDG8f5Ki\n6nDTpqBzQEREFD6cgif8kqJEq6TEnXSIiIiINU5+Ck2JFieVJiIiciaRNlq8t/ojNCVaY8ear+PJ\nQEREZG37dmfb897qj9CUaL35pvm6I0f8ywcREVGyUBdoFBTE9z7yVmhKtNT0UfYnnySeFyIiolQy\nezaQl6e8dnrPZYmWP0JTokVERET2LVigfV1aav+9LNHyT6AlWr/+6uXeiYiIUsvy5ebr1PfcESOs\n02FjeP8EGmj99puXeyciIkotbdqYr1OXaH31Vey0GGj5g1WHREREIXbggL3tnFQHsurQP4GWaFmt\nt3tiERERpTKz2p+tW7WvnbbRYomWP0JbotWiRdA5ICIiCq+PP9a+Zq/DcArl8A4AsGOHe/kgIiJK\ndex1GE6hLdEiIiIi+9TBk51AiiVa/ghtGy0iIiKyjyVa4cQSLSIiohTgtNchS7T8Edo2WkRERGSf\nkxItgIGWXwINtPhPJiIismb3XslxtMIp0KpD/qOJiIjcwarDcGLVIRERUYjZvZeqqw7tBFEMtPzB\nxvBEREQphr3+w8PTQOvwYev1Xv+jr7oKKC72dh9EREROLFgADBkSbB62bAFOnAg2D+nC00Dr/vu9\nTD22xYs5ZyIREYXLP/4BvPBCsHlYtiz4YC9dsOqQiIgoBUyZ4mx7FkT4I+UDLdZDExFRmDhthG53\n+/nzvc0HxYfDOxAREfmI9770Yhlo9evXDxkZGcjOzi5blpeXh8zMTOTk5CAnJwdz5871PJOJ4AlN\nRETJLJ77mJ33VKrkPF1yzjLQuuuuu6ICqUgkgoEDB6KgoAAFBQW49tprTd///PPWO1+71n5GiYiI\nUsHixd7vIz/fen3dusCrr3qfD4oRaLVv3x7Vq1ePWi7ZDK/PPdd6/Vtv2UomIRzegYiIwiTW0Ed+\naNkSqFEj6FykhwrxvOm1117DBx98gMsuuwyvvPIKqlWrZrBVHj79FNi1C8jNzUVubm5iOSUiIkpD\nXjSBSfcpePLz85Efq9jPJREpRvHUli1bcOONN2LNmjUAgD179qBmzZoAgGeffRaFhYUYN26cNtFI\nBICEN98E+vfX7VD1j+3SBfjii+jlMjln6nVOTrhIRAzKdsEF9t9DRETkJfmeZvd+tmULUL++8tro\n3hhrnX5fXbsCDz0EXHedvTykukgkYru2zinHvQ5r1aqFSCSCSCSCe+65B8uXLzfd1o08szE7ERGl\nMy9KntK9RMtPjgOtwsLCsufTp0/X9EiMRR80MYgiIiKy5tW9koGWPyzbaPXu3RsLFy7Evn37UK9e\nPQwfPhz5+flYvXo1IpEI6tevj7ffftv0/W5MahnvCcYgjoiIyBjvkf6xDLQmTZoUtaxfv362E/fj\nH9m/v/hr1cr/fRMREbnppZeACy8EevXydj+sOvRPXL0O7fIj2Hn7baBq1ehAy888EBERuWHQIKBx\nYwZaqcTTKXjcaJMVbxrydgy0iIgome3e7X6aDLT842ugdeqU9Xo7Vq2Kb99ERETJqHt399NkoOUf\nXyeVdiMqLy1NPA0iIqJksWePN+ky0PKHryVaTtfb3cbqfSzZIiKiZOLHfYv3Rv8E2kbLzj963z7n\n73GyHRERUTJxazBwlmj5I/SN4e+7z/l+1FjVSEREySRWAORGVWJ+PnD6dOLpUGyhL9EqLk5s39Om\nxfd+IiKiIPhVIzNzpj/7SXe+NobXO3QIeP75xNOxmlizfPnE0yciIkoGR44Af/tb0LkgtUAbwxcU\nAE8/bb6+pAT44ovo95iZMSN6VvRygYaSRERE5n77Tdy3Skrsv8dqgpZvvgGGDrWXDu+P/gh1G60T\nJ6KXbdxovn3PntHL2NiPiIjCas0a8XjsmP33zJ5tvu6jj+ynw0DLH54eZi/G/jAK1qyW6QdJJSIi\nChu32mVZFUboMdDyh6eH+aWXtK/9auAXiSj7GjzYn30SERE5sWAB0K6deO7W/dFJOl5M7UPRfI1n\nvQq0WD1IRETJ5ocflOdBjP3IGh9/hKLg0EkPCQ5YSkREqcCLQoLly+1vy6pDf4SiRCvRrqivv25/\nX0RERGGgDrSc3rOseuDbxUDLH6E4zImO3m7UW4OBFhERJQv1PcvOPfHnnxPfJ5vd+CMUgZaT8UOI\niIhSgVmgs2mTP/tniZY/QlF16EUaLNEiIqIwS6Tq0I17HEu0/JGy8exbbwWdAyIiInMPPqg8D6Jw\ngCVa/ki6Ei27OH4WERElCwZaqSupD/M//xl0DoiIiNy3fbv1ejaPSR5JXaKlH3nezMmT0flYvdrd\nvBAREclKS4Hvv49evmGD8fb6++O6de7nSY8lWv5IusMcT7A2bZr2db9+QE6OO/khIiLSmzkTaNky\nernRMsD5vc2NhuwMtPzh+WHWlyYlSn1yxXuiLVniTl6IiIiMmE1vk+i4kbJEaohOnBCPZ53lTl7I\nmueB1plnKs/d6L46fnziI8k7md2ciIjIqQoVxKP+PmZWQGB2f2zb1r08yeQAq0kT99OmaKFuo2U0\ns/ihQ8DQoeK53RItjhVCRER+Kl9ePCYaaH37rXt5omCEOtD68EN39jtlijvpEBER2VGxovFyudpO\nT39/jHW/vPVW53kCtDOxdOoUXxrkjK+B1uTJzrafP9983alTwI4d9tKZNcvZfomIiBIhl1zF25bK\nq57xb76pPK9Xz5t9kJavgdZ33znb3qrR4DvvJJYXIiIiryQaaD31lHt5Ufv1V2/SJXOh7txpdYIe\nPepfPoiIiLzk1wCkbvTcJ2dC3UbL6iR47z1naRk1rDcyeTKQl+csbSIiSk9t2wL790cvNyrRWr7c\nPJ3166OXvfFGYnkzwuDKf74GWk7HD7E6IX780VlaffpELzMK/IYPF39ERESxfPst8NNP0cuPHxeP\n6vtMmzbm6WzdGp3OAw8knj89Blr+C3XVoZtOn45eNmFC9DKehERElKiePZ1tL0n2O3glglWH/gt1\n1aGb9u2LXvb++9HLjIpviYiIzLzwgvk6u/e90lJ/Ah8GV/5Lm0Drhx+C2zcREaWuzz83XzdunL00\ngrg/MujyR9pUHRIREfnNbjsrSfIn2GJw5b+UKdHasMG7tGOZMwfIzQ1u/0RElJhEqu7cmCh6wIDE\n07CDgZb/LAOtfv36ISMjA9nZ2WXL9u/fj86dO6Nx48bo0qULDh48aHtnTk/GX36xv+277zpLG3Av\n8Js+HVi40J20iIjIf+qpaYJi1HvRbWwM7z/LQOuuu+7C3LlzNctGjhyJzp07Y8OGDejYsSNGjhzp\nWeaKiuxv+9JLnmWDiIgoitm8hfHyYjgHCp5loNW+fXtUr15ds2zWrFno27cvAKBv376YMWOGd7kj\nIiIKKaOBSpMJS7T8UcHpG4qKipCRkQEAyMjIQJFpsVNe2bObbsrFu+/mYtWqeLJIRETkD0myH4Cc\neaa3eXHbggXGwxqlo/z8fOTn5/uyL8eBllokEkHE9IzMK3s2bRpw773JH/3PmQM0aQJkZWmXBzls\nBRERucco0JozB7j4YqB+/WDy5JY77/RnUNRkkJubi1xVL7bhHk4J47jXYUZGBnb/PnFgYWEhatWq\n5Xqmwuj4ceC664CHHw46J0RE5Db5B7PRD+frrgMuvNDf/PiBVYf+cBxodevWDRN+n7tmwoQJ6NGj\nh633hbHUx8lJdviweDx6NHpdGD8bERE5x+s5uc0y0Orduzfatm2Ln376CfXq1cP48eMxePBgfPnl\nl2jcuDG++uorDB482NaOJAmoU8eVPAdC/vJt3RpsPoiIyDtOAq1kCspOnYpexhItf1i20Zo0aZLh\n8vnz5zvekSQB1asDhYWO3xoK8hfKaHJqIiJKbskUNMXjt9+CzkH68m1keL+mF3DCKmh69FEY9pLc\nssWz7BARUcDs3qdGjQI++8zbvFBqSKjXoRNhC7IAYMkS83X//KcIxC65RLy2yn8YPxsREdln1Rje\nyJNPAvXq2U9/5UrnefIaqw79kdYlWk5Y5X32bP/yQURE7luzRjw6uU9t325/28mTneWHUkfaBVrF\nxfa3XbbM3na/j3ZBRERJSr6OL17sftqnT4ez9CiMeUpFngVal1+ufR2GIAsAKlWyv+1//6s8D0v+\niYjIfeV+vxseO6ZdXloave22bc7SrlgxHEEN72PB8CzQ0v9Dw1CilciJHnTeiYjIO+VM7obffRe9\n7NAh5+mPGuX8PW4KQ6CXrnyrOgSSO1hJ5rwTEZE1OdCaMSP2trwfkBNp10ZL74UX7G0XZN6/+w74\n5Zfg9k9EFAYLFng3HpQcaG3YoF3u9Np/4oTokRhGO3cGnYP05Gug9fPPfu3NviFD7G2nH2j1m2+A\nq65yPz9GWrUCOnTwZ19ERGHVqRPwyive7qOkRARLlStHr5PHXly3zvz9K1YEX01oZNOmoHOQvnwN\ntMLKzrQ6V1yhff3559G9U4zq8t0S5uNHRJTsRowQj6Wlog3W8ePR2/zrX+JR3VFKr18/9/PmhgUL\ngs5B+vKtMXyvXl7tKXFWI8Tre6BYmTkz8bwQEZE5rxp1L1woHv/7X/MftkePikerqeT27XM3X255\n6qmgc5C+PAu0MjK8Stlfd95pvNzvHhwnTvi7PyIi0gZd8nOTaYABsHcfRfMs0Kpf36uU3dewofmX\nw6zxoN9fpr17/d0fEVG6Mho7y0pGhpjSLRIB9u/3Jk+UvHwd3iEZGRUhjx8PPP+8vW2JiMg9Vk09\n3DJlinhs0EBbFWj2A/ucczgVG5nzrY1WMvjLX+xt949/uL/vq67yJl0iolQiN1rXy8oCpk1zZx8H\nD4rHX34BNm5Ulpvd1yTJ+Mc3EcASLQ25R0ksP/xgvDyR4HLxYuCxx+J/PxFROtu6FbjpJvfTfegh\n99Ok9MISLZWSkqBzEE0uwg674cOBw4eDzgURxWvRouTpOR3UwJtmVYfJeL8j/3gWaDVq5FXK4fXj\nj+6neeut7qdppF8/66rLMWOAl182X5+XJwZxJaLkdMstQI8exutOngSuvx746Sfz9196qX9jNWVm\n+rMfPbOAymyeRCLAw0ArVYpbv/3W3oCmgDLybkkJ8Ouvie134UJ/S9jGjwfeest8/SOPAE88ASxb\nZr4Nf9URJS+r7+8NN4jG3nPnmm+zahUwb577+TKzbVvis43E05vbqC2Wuh0XkZ5ngVYqRfhW0y2o\nyReq0aOB885LbJ+5ueHsxcKuy0Tpx6xdapDatUus5uT4caBWLeN1VsP3vPlm/Puk9JRC4ZB3nHYn\njtV+4N57gV27YqfjdCyXRCVaIsUJS4mSV1GR+bowDsJ58mTsbSZPBiZONF4X7zARLLknpxho2WD3\nCyl/AY22Vy97912lLcOiReaTfbpdehSJWFeDJnoBYfdmovRmFpDl5QHdu7u7r/LljZfPmaNMkdOn\nj/iTqa/DR46Ypx3GwJKSl2eBViqdqE5/+axYoX29fTtQsaLxtldfDdx+u/E6L0aD37bNfF2is7vL\nJXDvvOPtBNtE5A6739VEr+cffQTMmpVYGnpmgdZ11wHPPCOeq388zpqlvQ5/9FF8+02lexv5gyVa\nLlq1SjwuXapdLg9+Z0bd6H34cODUKfHciyJqLy8Scn7vuw8YOtS7/RCRO+x+V+Xrxo4d8e3Hi+uO\nOi+dOhlvo762mv2QXLYM+P57+/tl1SE5FUig9dJLQezVHxMmaF8fOgT83/9Fb1dYqJQAqS8GeXlK\nCZrRF/o//wn2i25U9Si3lfC7TRkRee/YMWUaGqshXgDzgCqRQGvPHtGrz+q6px9W4tgx823Hj9e+\nHjVK/KmlUjD14YdB54ACqTqsVs2rvQbvzju1r997D/jb38Tzq69Wlj/5JPD3v4vn+rYCZuNRbdoE\nXHmlUnIWj0R/WQ4YEP3LUG5LxkCLKPX06RO74XmsYR0Sue506wY0biwmbTYi1wCoTZ4cvWzgQPHY\nr582T5984qwaMdk6/Vx0UdA5IFYdJshqbi39WFqLFmnHF5O/3Bs2aLd75RXxqG8b1rBh7H3GYvRL\nb8wY5XkkIub3snLihPa1HGjJDVCJKHlYNQoHYlcXPvAAcM014vnIkeI6p2c10KmV/fuVsfvatzfe\n5owzYqdjVDVoFRymUonWH/4QdA6IgZYNVgOHWjUknTQpetnrryvPzX7lLVwoHp991nj9yJHm+4zl\n+HHleWmpuKA88oh2G6tu3nL+OnYU75Uk4xHxrQY2JaLw+Oqr6GWSBBQXA5Uri+YPVt54Q/u6Rw/l\n2pCovLzE0wCMpzKLZ3BVu4NXh0miYzpS4hho2dC7t/k6qyLxRx+1TtfsvfoSIyf0JVbjxon9zJgh\nXqsHki1fXilOV2vbVgRh8+cbB3Xjx4uL8113ATVqGF9QObApUfIqVw6YPl38MDMqjereXazTt0kF\nxPWgXDmgc+fodTfeKK5H+uDNrE1VIs0k1D7+2Nn2ZkGiPqhMBuwlGbxAAq1U+sfL7ayMnD4N/Pvf\n1usTUbMm8NRTyutNm6KLid9/XzzOny8e9SP2//OfxmmvWQM895w2fZk8fMWECaJHpbpt1oED4jGV\nit6J0pHVPKuzZokqRX2bVEC5HhjNe/jZZ+JRXWr+2WfR161IRDSh+PZbR1nWUE+Low8W77jD+r1y\nu1oiN7BEK0GxAgr9mFpqic7TtW+f9kJkNL+inL+xY8Xj9dfbC/AOHlQave/ebb3tnj3K85tv1u6X\ntOQqGfKPnRHESRHruxvr+qHvFGPUiF29D3mWDP37Vq5MrINNu3bm69gTj/zEQCvJyRes/fuBNm3s\nvSc/39528gVQ34ZLT93AXy4583NC7GTywANApUpB5yJ97N0LnHkmA38nbrzRer1cam32g0EfHBkF\nPOr/hzzwqNkApPFS/wAkChIDrSS1ZYt4lCRRatakifF2RjcYp70Wp093tj0pjh9Xgs+mTTkhrd/k\nyZCvvFJUk5eWAp9/Hmyewi7W8ZGvKfIwCXpWY1jp0wC0AVZWlhLAyZ2CKDGp1FQnWTHQSlL164tH\nSQIuv9zZrzd9O61YvKrqOnAgdo+mZPfee0qj4PXrg81LOpJv6N9+C8ycKQKvG24INk9+2LbNu1K8\nYcPEY6xhYKyo81ahgvJ861bRyQZQStQpMQy0ghd4Y3h5TiqKj1GgEomI6qktW4wvtn598WJdiLOz\nzas7J0/09t3XAAAgAElEQVQWAxHu3KmMSp2MrG52kQh7Z3rl5ZeBSy7RHv8ffkiNKsT168WPn40b\nzYdRueAC4+Fl1OKde/Ctt8RjIt/LkhIxGnuDBtpJnwHrDkRk7Iorgs4BWQm8ROvpp4POQXIzGwqi\nuFiUesXbayfeYEz9vgYNlGVyVafazp3A5s3G6fTuDXzxBVCvHpCbG19ewmDmTOv1cnsXctfnnwMF\nBdrAat8+5bV+kOBk0rSpGI+vcWPrG6zRufXEE8qPm+7dvcmfHS1aiNkxEikVI3NDhgSdA1ILPNBy\nWo1FWvH8Qj98OPY2ZhOwxmLWoDWeaoCRI8XnS7YpLwBxk5MkpX2WmVQoYQmjWD8UBgwQ7efUA/gm\nk1ijuQPG59bs2cDy5e7nh4KlP9/tjJZP/qkQexNjWVlZOOecc1C+fHlUrFgRy/ntDUQ8Q0R8+KHx\nQINqZg1dY9EHznIPpEQCikQGcA1KjRrsRBBG8nkot22sVEkMI5Bs7IxQbjQ0gnxDjjWtDiUX/mAL\nt7jLkyKRCPLz81FQUMAgKwm5NbWFnv6X1dCh4tHsQlBcLEZtVvealEvc5PdYDRWxaxfw3//Gl1c3\nfPNNdLArT3KrHn/MrNG/0XEpKuL8ZHasWaN0CtGTz0Ordkhr1xqPPD57duxpqLw0a1bsG6d62hy5\ndKu0VHxuubraagyqevUSy6NdiQ7KTPZkZgadA7KSUMWd5EIYrb8xGw26Se577jlv0tUPDjlihHhc\nulQ0Rjbq+j11qjJf4qFDwDnniOf/+Y94lAMXI336AK1bJ5bnRLRvD9xyi3i+a5cYrX/7dvFa/fUw\nG4l69mzxHZDntTx8WMyfaaeLfLpbulS0/du1SznWdeqI4ymXgs6dq32P3Cbo66+VZQsXAs2aKa+v\nvz7YtqPdu8cuqVa3eTz7bPEo/yCRG5OrS++OHRMTK69da5yePEWX20aP9iZdUnz7LfDCC0HngqzE\nXXUYiUTQqVMnlC9fHvfffz/uvfdezfo8TZFJ7u9/8nvN061RI94cUZg98YT4A6J/rU+dqjx3Ooq3\nl1Ugv/2mBH1W5FKR5ctFg2t5dHw1s96FL78sHv/+dzHtR+vWxpN0k7m6dUU1bY8eSimiXCKlnoYF\nMG6Tpe5sIZc8vvce8O675vssKRHBnFclj1Y/LszI3yv19wkQJcY33WT9XvWgw24aNMibdElx7rna\nITLsMht7MV3k5+cj3+7o3QmKO9BasmQJ6tSpg71796Jz5864+OKL0b59+7L1eXl5GD7clTxSitmz\nBygsNF7ntHOEl73HqlYVUxFVrSpeb9oknp93XvS2EycqQZlcKqtuR6P/cbFmjXjUB4oMsuxTH9O9\ne7XrzErG582zTrNaNfGo/zGwZo3oRVu5snj95JNiLj6v2sYMHmxc7emkpHP2bNG7z047TrbZSi3n\nnht7m3TviJabm4tc1a+s4R4GLHEf6jp16gAAatasiZ49e8bVTotTkaSnjAygVavo5XfcIare4jFn\nTmJ5kiTjNi3qEraGDUWpiZE+faIvXC++qDxfvFi7rkWL2Hk6dUoEE4cOAY8+Gnv7VPfrr6JUtG9f\ncVzU/y99O76DB43TiHeOuxYttNXt+kmKjfIQD3lcwU8/NV5/9Kjx8kgEmDJFu2z+fKBTJ+OJ4Sm1\n6AP+AQNiv4cDmfonrkDr2LFjOPx7i+WjR49i3rx5yM7OdpzOwYP8Z5PCzk1w7lzjibqvuy76RmNk\n3z7gk0+AXr3EYI/y+de/v/HQFPoLmNXQGG6fy3IX7WXLxPQx6W7+fFHV+sEH4vX99yvr/JhbM1Zp\nUoUKYly46dOBSy8F/vpXca6984699Nu3V9o0qk2YoLT7szrHzNoBUvopX17bYcII773+iSvQKioq\nQvv27dGqVSu0adMGN9xwA7p06eI4nTPPjGfvlK5KSoCuXUW3fEBUjajJc6P9+qv4O3QIOOsspVTq\nxAngL38RQdYnnyiDPX74IfCvf2nTsuottWeP6G2oJ7fvMRqcNRG8IMbmRu82o7GpPvlE26hc9tln\n2u3kdnoXXijmEl21CnjtNXGu3XefMucioLSZ2rZNBO5yw339OSWft3feCfzxj+Z5JDIiN3mg4MXV\nRqt+/fpYvXp13DvljYOcOnAgej7H66/XvpZHwde3oTrzTBEEXXON6Kmm93//pzxfvVqUmsm90/Ql\nWmvXiqpPILpdUKI9Bc3mq0zk+7Jnj6iCrFs3/jTc9t13YvolN9uIjBkjptxJxJdfRi/r1UtpLG/U\nHmvyZDEKvTw/H2Bc6pmdLc7BSZNE6SmgTO7eqZPxvn/+WdsbEgDGj4/5MSgNxTPVGu/D/gmkOZz6\npLD7z5482Zu8UHKw0xt19ero4Ee2f79513Z1e5icHNGmRa7u0V/A1FVUqr4fABKfTkcO4PRuvDH+\nNP/0J/OxpoLSqlV0iVCiNm8WvTYTIfcAlcnjUVl1TOrdW3SE6NhRWWbWQP70aSW4UvvxR+P5/fTn\nqyR5NywLJYe//MV4eTydMhho+Sdp+h3IYxVR+rJzMZF78+kdPx5fCYq8T6NSCn0PQbN5GxOVyMj4\ne/eKEq2jR4F169zLk1OnT4vqs+Ji8TqezxRr6iijUiEn5HHbZPrpkw4dsldFaRZESpL5Ofy//xu9\nTL+v336LvW9KbWPHOn+PWUDFQMs/SRNoEandcIPxcrNG0XIPvnjZGU/rzTfjT9+pgwedzXdXpUp0\nNZSf3n1XVJ85GbunsFDbs9DvDgGvv659PXEiEhqyxizQMhta4dFHtYPx8saY3tTjvelxCp5wY6BF\nSUM9EOjnnxtvM3Kk8fKWLc27/FsJshRI75FHgJdeEgFd/fqizVksdhtP79ghSpycDhgr27ZNDBaq\nnnZITS6Nktu+ycMYWDn/fFGFe8MNwPr15lW/fkqko8Po0bF7gqnt2aOdXoqNm9ObVaDNNlrhFveA\npYlQ/4P5zya7zKoF1dyeILhz5/D8WhwzRvtaX9WlZzQu2N69wNtvi7ZCcn+Ww4eVue9GjACGDHGe\ntwsuUJ7r22AWFUVPhbNxo9gu1vd/714RVOvbwwXJrNNCLM8/724+iBKR7gOW+ik0h1rdELh58+Dy\nQcnNbPLmRNgZWTtIvXqJoS169hSThT/zjBhTyWgE+2++EYO7fved0l5KPd3L0aMioLPzA+jYMbGd\nWbslOf19+4xLckaPFu/fuFEEep9/DgwcKIbbkN8rB22DB8fOj1/iaSdD5KWsLOfvYSGHfwIp0TJy\n/vnK/GRezR9GFI/HHgs6B+bGjxdjPa1cKab8+eEH68BQXRpTqVJ0u6HS0ujxnHbuVIaHKC4WVbC1\naik94IzaxX38MfDnPytpGpHHlnruOVF1uXChCL5atlSG4YhVaue3H38UbbWI3HLuudopo6pXN+7B\nbBUYVazobHs768k9gZdoyf/sRo2il8VLM581UYKM5pwLi379xKM8r2Ks0jd5DCdZYaG25Ku0NHoI\ngsxMpYTp6aeV0me5/Ze+WvCPf9Tmw2yCZDlAkwOX775Tlr/xhnHaQTOalYAoEfv2aV8//bT29dVX\n20/r1lsTzw+5L/BAy46PPw46B0SpY9Mm5bl+zr5Ro5TngwYpba/koEjuIReJKKVj+vkft29XSqcB\n85568lQ6MnnCZw5jQOnMqHQKUAog7IwpaAdLtPwTykCrWrX435uT414+9IzavBAlG3UQZDUY6ksv\nid6EgFKdqB44WD2ivt7o0cpzeeBPu+R9EqWjWJ1v9OuN5mi1g4GWf3wPtJo2jf4H33239rX8S/fF\nF43TsBq8tIKHrc7C0vuMyC12h38YNMjbfBClO/mHvP4+Izer0d83u3UTjxdeqCwbOFCZ4SBWIHXl\nlfHlk5zzNNAyCkzUA/AB4mR4913tMrlES764yydM9+7iUV9VoU9PPgGNNGxovi6Wp56K/71EySyB\nqU2J0t5HH8XeRq6m19835fHT7r9fPMr3w8zM6DSaNrXXeeell4BXXom9HbnDtxKthx8Wj+PGxZ/G\nhx+KR6tIvWZNUX1oVI/drl1i87516RL/e4mSHasaiOJz223Gyz/5RHku37PMak7kXrzxuOce7Wt+\nl/3leaBVu7Z4lKdMsTNImtmJJncTN2uHtXMnMGmSdRqJVP/x5CQiIrdt3qx0GrF7j4q1nfp+dcYZ\n2nWXXGI/b5Q4zwOtqVPdS0sOtBo3Nl5//vnA2WeL52ZTErCdFRERhUlWlhjXDoi+RyX6A9/o/R06\nJJYmORNIr8N4Txz9wIfque/0HnpIqdNW75eBFhERBa1yZeOJ3u0O2O3kXsb7XrBCObyDWURfvbp2\nMNLLLzef/+6554C33opOx2yU6rDQV63+z/8Ekw8iojCSm6EkA7MxsQAx3ZW6dka+z917r5hEHRD3\nvL/+FfjXvxLLBwOtYHkeaMmjSLsxKWy5csCwYcprSXI2L6K6RMvJaLt+uusu7evq1YFPPw0mL0RE\nYRPE9XDDBvN1V11lvu7BB53vq0IF4OKLxfNIRMwDeu+99t6rn9Bd1qSJeJQ7lJG/PA+0GjcW//xK\nlYATJ+y9x27V4plniscnnrCfrlxiJLflstK1q/Z1uXJijjcvyfX0avw1QkQUnAYNopfZ6QWob4Tu\nlNXg3XbuYbKHHgJOngRuv533kyD4WnVoFEQYOeMMoKDAepuCAqUNltF4ImryFD6RiNJj0c6XRD/y\ndVC9DsNe3UlElMr01/677lLuD/Xqmb9vwIDoZXLpUixbtwJLlkQvlwOl4cPFJOd2RCKJB30Uv9A2\nhm/VKvZ6uyeOXDKlHhaib1/gnXfM33PxxdGNEv0ItPT7GDmSgRYRkdr//m+w+5fHhQSAc8813kaS\njEukWrY03l5/7f/jH5XhkYycdRZw0UXm6zkcUXiEsjG8XiInTG6uEpDZGXBUnr5ArmK86SZlnSR5\nf/Lq0z/vPPGFIyIi4dJL/d2f/rpsFQCZkafKeeghYPBg9/Jidx0FJykCrUR8/bUy6aZ+eAejump5\n3kU50JoyRTulgTzvlJuqVFGeGzXSv/RS4Jdf3N+v2ttve5s+EaU+N8dN1MvNBbZsEc+t2hk9+qj2\ndSLTrhn56Selk5dM3Ttcbjtspm1b4IUX3M0ThVvKB1p6dmdGr15dPEYiwIgRyvrHH4+9j1GjrNcf\nOABs3Ki8VjewN2s7Vr++UtqWTGbNCjoHRKR3zjnxvW/FCnfz4cSsWcp8gHqvv648l4dUGDJEXGf/\n+9/o7eXPf9ttQP/+zvKhHzD7D3/Q3ldatHCWHqW+lAi07PaiiESUAEr/vuxs5fnmzcD06crrChWU\n99uZQuiJJ6x/1VSrpv2VZWfCUcC60aXaAw9ELzO7QMnsFjlff7297WRhHfNGXYpIlG6cjs8nt0Oq\nW9d6u1jX4gULopfF6vgkU/ey0+9HfV1q1048Vq4srrNGY1kNGSIeu3YF/t//s7d/I+vWAc8+a75e\nrk0JAqsRwyMlAi0nBg8GNm2y3iYrS9vAsXx5ID9fNDx0++StUgVo3VoEdiUlyvIrr4w/TaMhKKwG\nzrND7pzgZ4By++3epX3ttd6lTeQH/Zh7Ttj90SZ74w3xaLfnuJnKlaOXnXWW83TUgdall4pr9m+/\nAXPnKj/urII+eZ9OZgspKgLWrtUua9IkOv/qe0SVKs56BlJqCm2vQ1nVqsbTFKjJg7vZccYZSqNE\nJ+OJXH21N1+EqlVFKVmPHtrSMqMelXJ+//Mf6zSNxleJlfdY6+USOPUvNLPjPm+e/XT1qlZVnqtL\nH91mNl9mGEycCIwdG3QuksOKFUCbNkHnIhhOq7zM7NoVexs5ePFi3r1Y1+Heva3fI6d59tnANddE\n78MoOFRvo07Lqkq1Vi2gaVPjdVafwapnoJpZ70W9hx82HjaCwiv0JVoHD8ZuzHjNNYkPwpboBcTu\n/u+7z952RvnJyhKPf/qTvTTioS8N69VLO5qwOl9mbRGcBL56l12mPLd7TC+8UExT4URYe3JOmCC6\nrnfqFHROksOllwKLFgWdC2Oxhqgx89RTzra305tarUkT7fdY37Bbzajqy+q7ZvadlZtfGK2P9T2X\nq/mcvEe9jbxvIPrY6ku0Dh2Kna5XMjPtfa6hQ5USRissIQuP0AdabtKfeL17A+PHa5c5rWJr2lSU\nRpn561/FhUKepuHvf7eXrtGXpE0be1/E88+3tw+j/RUVKcuysoBp04yr8Fat0jZAVVNXgcabDyc2\nbQLGjPF+P24ZOlT7Wl26VqOGeDSqYiFjZ5xhPmOD0YjefqlZ0/l7JMl+lbl8DltdE4xKaCIRe+f/\nd98BhYXR7x0zRjslTSQCfPONdVpt25qvs5pto3x5Mc2a/jM6CbQA4NtvxWOPHqLaVP1j1Sit996L\nnb6aehDSnBzgzTedvd9LDLiCF5pA66abgM6dvd2H/oQ75xzgzjuBr74CJk8Wk3zGaoOkT2PtWm3D\nedngwaJR/JgxotfiZ58Be/dGX3zNvgSxvhylpdo2GoMGiQb9e/cCN98MPP+8WC43gpfTUzf8NGvY\neskl4nHx4uh18kUpJ0cJCr76Stt2wW4ReMeO0cvUn/vxx4HRo+2l5VQkAvz8s/IZYlF3lrCjYUPt\nxfy885Tn11yj3VZ9Y5U/f2ameSBLwt695uvkQHXqVOtgy+yG6mR6EyMbNkTPLGGXnSBi2DB7gZa6\nNEemDrQaNtR+5zZuVOalbdFCuV7J28iPjRop12ujH4/PPKN93aePcV4LC8X14vPPxTkv99geMQJ4\n6y3g1Cnjz+V0EOcrrhCdnFq3BrZtEyXnf/yjKBE1CuKctn/729+A48fFLCRDh7pXresUR38Pp9AE\nWn/+s7Ztj586dBC/SJyUIsTqTTJsmHaYh7PP1t5sY7HTpuq995Ri/BdfBL7/XuwjEgGuu04sX7NG\nTOUgW7BAubA88ojSLqx3b+XGsHKleFRfgNq0EY0+jdpGtG2rtHuTP+vNN8f+jLGqPC64QBnX7MUX\nY6enHoPMTm+fBg2M82k0d+aiRcD+/dHLR45Unp8+rVSnbtignT7DqpRRXYqqbgMST4lIOpCrktTf\nJ/VI3YBynso/GoyUlCg31OXLgX//W1lnNM5RUZHxj4h//St6WVaWtr2hGfX5I/c+tgqc5NLzvDx7\ngZaRSERJR99Qu2FD7XdZT30jl/c7ZIi4Pqh7T/fvL64tV18ttrvnHmXd2rXKtvLAn9ddB2zfrvwQ\nfOIJMcWa2XXQaYkWoDS9kG3dKtpPydsZ9ZC2cx0DxPXmzDNFb846dey9x22SlHinJ/JG6BvDh03z\n5qKou2/fxIcumDwZeP9943V2j5FZo+6WLcUvrLPPFr/c9Olt2yYCLXmE5cqVred/fPxx4Ngx4wuc\nUVVErPkn//1v7cVXZjZL/aBB4lEOII3k5yvPT5+2N1aQ+vPIbQGNxkE744zoxvk1amhLxNTBnfqY\ntG+v7U6v3menTkoPyPvuE+OlyTp0EMucVova5STwD5PHHosucZCDr+bNRRCSl2f83mHDlOfqzif6\nYVu6d49+r1EV16hRxuesne/v/PnAk0+K55mZYkwnwPg71q0b0K+fNlhQB1pGAcGSJWIfRnkzmwbG\niiSZD1tToYLIv/rHTlER8Omn0ds2bSq2PX7cfF+xAoZYgdaIEeIabYfcrMPos91yS3xNMcIgme+z\nqSY0JVrJ4oILxAVk3Djji4iT6s9bbjGuPgPsf0msSuHUFw59evXqiYuj01KT0aPFaPt6+gvjiBFK\nSZp+KIUKFUQJWo0a2nF1LrpIO+URIAYDlKsm9DcUs6BMtn69eSmpvjSga1flgmvEqAv6Z5+Jm9+7\n7yrL9L+a/+d/xM1OXbIiSUqniC+/NG80XbOmGLFfrv5RHys7v+j1x91pBwA7Y8aZkY+D/GPEqIG3\nnV6l6s85d654rFHDvMrvrLNEMPWXvyjL1Od+Xp4onVSXJAHa79HmzSLwUXdIuOUW8aivylanvXq1\nUqIZ6/s7b562Gl8fpMt5lc2cKa45Awcq7UrV1cxTpijbPv64KMlu21Y7v6tMLv376Sex31h5nTQp\n9mjnMvXUNOedZ10Fa5Sm3RIZOw3o9d9FM2ZDXUiS+P7u3GkvHSIzBjX4qcuPCN+NKXrmzBGDmn7x\nRext+/SxN+/XnXcaj+o8bhywY4f9vNWurVxM1e029DflM89Ubuxz5gBPP620G1NfYI0GCxwyRNm2\nXDnxXiP//KfxL3m5Yer555v/GtUHWrNnixK7v/1NvJ45Uxx/uXePvP2tt4q2XR99pJQmduqk3Cgn\nTQJOnFD28/HH4lHdpkSS4hu6wukYRu3bK8HJ0KHi/1G9uiiZ+cc/xA161y4lj3pTp5qXcvbsadw2\nUbZ8uahCefhhcXx69BBVRidPKue1WWmQGTvt6fRtifTPAXFc5HZIgKiykktgzzlHuUF//rn4u+su\n8X8HtNVCI0cqpVA//yyqolevFudsrCBV/4NMXV3XtKkYBd3oR1S9euK7rP5c+umzatUSJXtG1AGK\nvjTcrBex/Nnt+vRT8+9drIGTs7NFR5tY5M+xaJF7VXVWVaZECZE8ECvZiRMlyZs9mwMk6auvvN3H\nb79JUnGxO2kdOyZJ7dq5k1Y8AEnats16m9JSsd2pU8p7rrzSeNunnhLrAUmqUiV6X4Ak3XabeL1t\nmyQ9+qhxOu+/r2xv5PbbJWnuXOP0AUmqVEk8vvuuWDdwoHlaH38s1n3xhfF6J2bNUvLw44+SdOSI\nJK1erc3jvfcav/c//xHrFy7Ufnb15wIk6fRp8ThkiFg/dqx4vWKFeb5OnIhOB5CkZ56RpMOHxfoj\nRySpWTOxfNMmSTp0SLx38WJJ+ugj4/ebOXZM+R+qP/uAAZL0wAPG6cjPd+ywThuQpNatlddLlojH\nfv1i58uu06cl6cEHzdOSvxPqPMU6Pv37S9K0adFpLVhgne+jRyXpjjui9zVqlHY7O/8XQJJycsTz\nO+6wd6w6dfL/Oi5bu1b72RN16JByHfPKhRf6e7x+/FHs78AB//aZzDwKh0TaniQa0kDr66/93Wcy\nsxNoydvJF6jsbEmaMcN4O3Wg1bevdl25cpJ0wQXiJhbLypXOb5qAJBUVSVLDhpK0c6d4PW6cWHf0\nqCRt2GD8PjnQcsPp0yJQKi01z6NZoCXT33j795ekV18Vrz/4QCwrLpakkhLxfNkySTrrrNh5U9+I\n77rL+DMfPixJgwZFL5cDtWHD7N3QJUmSdu3SbiPn+cgRSapRQ6zr31+S/v1vbf7sfA51oCUrLRXH\nf9Gi2GnY8dln1vnRB9CAJL3xhiQ9/rgk3Xqr/XNq40Zn57r8v3jtNe1yO/+XHj0k6R//EM+TIdBK\nRgy0ws3LQCuQqkM20kst8v/z++/Nt5GL+vfsiW4Xtm2baJthp6fgJZfYa5+ktnSpqE5RT+Qt9wir\nXNm8utfpfqyUL2/dBsyO9u1FVbFc/SKP1fPXvyptcdRtXFq3FtWhsWRminZwxcWiWkquPlWrUsW4\n52elSsCWLSJP27aJ6qhYbVrq1NEeWznPf/iDeP/SpdpxiC691P6AtEbXlkhEHH91daGX1A3N69cX\nvRvlkbwPHtQ2yLfSsKGzc7BSJdE2Sz8SuSSJKjZ1Q3U9q2pgIkpMWrXRimdOrSDk5+cjNzc30Dzc\ndJP1QILxMmp8H2uiWqf0x08/RcvmzbHbigDhG5OmYkXggw+M1yXy42X7du3rjRvzUbduru33y8fS\n6SCPdhm1LQySVYNt/bknD5Uiq1ZN/HnFrG1WIrM1mBk2LHpMuESF4drnlYwM4JdfvN1HKh+/ZBZ3\nv6K5c+fi4osvRqNGjfCinUGOArZunfiFnwzy1eMUBGTqVPuNr+3c5P2c8ibW8cvKspfn664TpSt+\nSaQEze4gsXYEef517qwdZdspP0rLO3UyPy/0x656dW/n7LTLyY+Ga66x9z9o1070cHRTGK59Xpk9\n2968kolQHz/WHIVHXIFWSUkJHnzwQcydOxfr1q3DpEmTsH79erfz5ir9/F7kDkmyNwzA/feLapNk\nUr68fxMWv/++8znuZJKk7VafzJ57Tvwoiscnn4jRxL1WrlzyTWRdrRpw4IC9bW+7Lf7/AZmrVi24\nwUwpWHFVHS5fvhwNGzZE1u/9oG+99VbMnDkTTRL5KUoprVw5eyNlpyu7gyuSuZ49g85BuHlZZUlE\n5iK/t7Z3ZNq0afjiiy/wzjvvAAAmTpyIZcuW4bXXXhOJsuiIiIiIkkgc4ZAtcZVoxQqkvMosERER\nUTKJq41W3bp1sV3VVWn79u3IjDW5HREREVGaiSvQuuyyy7Bx40Zs2bIFxcXFmDJlCrp16+Z23oiI\niIiSWlxVhxUqVMDrr7+Oa665BiUlJbj77rvZEJ6IiIhIJ+5xtLp27YqffvoJP//8M55S9UtPtvG1\n/JSVlYUWLVogJycHrX8f1Gv//v3o3LkzGjdujC5duuCgagyEF154AY0aNcLFF1+MefPmlS1fuXIl\nsrOz0ahRIzz88MO+fw4/9OvXDxkZGcjOzi5b5uaxOnnyJG655RY0atQIV1xxBbZu3erPB/OJ0fHL\ny8tDZmYmcnJykJOTgzlz5pSt4/HT2r59Ozp06IBmzZqhefPmePXVVwHwHLTD7Njx/LPnxIkTaNOm\nDVq1aoWmTZuW3V957tljdvwCPf/cnM/n9OnTUoMGDaTNmzdLxcXFUsuWLaV169a5uYuklpWVJf36\n66+aZU888YT04osvSpIkSSNHjpSefPJJSZIkae3atVLLli2l4uJiafPmzVKDBg2k0t8nyrv88sul\nZcuWSZIkSV27dpXmzJnj46fwx6JFi6RVq1ZJzZs3L1vm5rEaO3asNGDAAEmSJGny5MnSLbfc4ttn\n84PR8cvLy5NeeeWVqG15/KIVFhZKBQUFkiRJ0uHDh6XGjRtL69at4zlog9mx4/ln39GjRyVJkqRT\np3h3EPgAAARiSURBVE5Jbdq0kRYvXsxzzwGj4xfk+Rd3iZYR9fhaFStWLBtfixSSrkfmrFmz0Pf3\nQZT69u2LGTNmAABmzpyJ3r17o2LFisjKykLDhg2xbNkyFBYW4vDhw2UlYnfccUfZe1JJ+/btUV03\npLabx0qdVq9evbBgwQK/PpovjI4fYNwjmMcvWu3atdGqVSsAQJUqVdCkSRPs3LmT56ANZscO4Pln\nV+XKlQEAxcXFKCkpQfXq1XnuOWB0/IDgzj9XA62dO3eiXr16Za8zMzPLvmAkhsXo1KkTLrvssrIx\nyIqKipCRkQEAyMjIQFFREQBg165dmp6c8rHUL69bt27aHGM3j5X6XK1QoQKqVq2K/fv3+/VRAvPa\na6+hZcuWuPvuu8uqHnj8rG3ZsgUFBQVo06YNz0GH5GN3xRVXAOD5Z1dpaSlatWqFjIyMsmpYnnv2\nGR0/ILjzz9VAiwOVWluyZAkKCgowZ84cjB07FosXL9asj0QiPIY28Vg5N2DAAGzevBmrV69GnTp1\n8NhjjwWdpdA7cuQIevXqhTFjxuDss8/WrOM5aO3IkSP485//jDFjxqBKlSo8/xwoV64cVq9ejR07\ndmDRokX4+uuvNet57lnTH7/8/PxAzz9XAy2Or2Wtzu8TXdWsWRM9e/bE8uXLkZGRgd27dwMACgsL\nUatWLQDRx3LHjh3IzMxE3bp1sWPHDs3yunXr+vgpguPGsZLPx7p162Lbtm0AgNOnT+PQoUOoUaOG\nXx8lELVq1Sq7QN9zzz1Yvnw5AB4/M6dOnUKvXr3Qp08f9OjRAwDPQbvkY3f77beXHTuef85VrVoV\n119/PVauXMlzLw7y8VuxYkWg55+rgRbH1zJ37NgxHD58GABw9OhRzJs3D9nZ2ejWrRsmTJgAAJgw\nYULZRalbt26YPHkyiouLsXnzZmzcuBGtW7dG7dq1cc4552DZsmWQJAkffvhh2XtSnRvHqnv37lFp\nTZs2DR07dgzmQ/mosLCw7Pn06dPLeiTy+EWTJAl33303mjZtikceeaRsOc/B2MyOHc8/e/bt21dW\nrXX8+HF8+eWXyMnJ4blnk9nxk4NUIIDzL5GW/UZmz54tNW7cWGrQoIH0/PPPu5180vrll1+kli1b\nSi1btpSaNWtWdmx+/fVXqWPHjlKjRo2kzp07SwcOHCh7z4gRI6QGDRpIF110kTR37tyy5StWrJCa\nN28uNWjQQHrooYd8/yx+uPXWW6U6depIFStWlDIzM6X33nvP1WN14sQJ6aabbpIaNmwotWnTRtq8\nebOfH89z+uM3btw4qU+fPlJ2drbUokULqXv37tLu3bvLtufx01q8eLEUiUSkli1bSq1atZJatWol\nzZkzh+egDUbHbvbs2Tz/bPr++++lnJwcqWXLllJ2drY0atQoSZLcvVek4/EL8vyLa1JpIiIiIorN\n1apDIiIiIlIw0CIiIiLyCAMtIiIiIo8w0CIiIiLyCAMtIiIiIo8w0CIiIiLyyP8HkeL93X+WBBUA\nAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Noise[480:500] = 0\n", "Noise[-500:-480] = 0\n", "plot(abs(Noise)**.5)" ] }, { "cell_type": "code", "execution_count": 644, "id": "edb20f62", "metadata": { "collapsed": false }, "outputs": [], "source": [ "denoised = ifft(Noise)\n", "play(real(denoised))" ] }, { "cell_type": "code", "execution_count": 643, "id": "a85dd6fc", "metadata": { "collapsed": true }, "outputs": [], "source": [ "play(noise)" ] }, { "cell_type": "code", "execution_count": null, "id": "ee326b42", "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }