{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "This Jupyter Notebook is coming from http://cushychicken.github.io/lock-in-amplifier-simulation/ and used under fair usage. \n", "\n", "# Background\n", "\n", "Lock-in amplifiers are a type of lab equipment used for pulling really weak signals out of overpowering noise. Horowitz and Hill deem it \"a method of considerable subtlety\", which is refined way of saying \"a cool trick of applied mathematics\". A lock-in amplifier relies on the fact that, over a large time interval (much greater than any single period), the average DC value of any given sine wave is zero. " ] }, { "cell_type": "code", "execution_count": 200, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 200, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline\n", "\n", "def sine_wave(freq, phase=0, Fs=10000):\n", " ph_rad = (phase/360.0)*(2.0*np.pi)\n", " return np.array([np.sin(((2 * np.pi * freq * a) / Fs) + ph_rad) for a in range(Fs)])\n", "\n", "sine = sine_wave(100)\n", "mean = np.array([np.mean(sine)] * len(sine))\n", "df = pd.DataFrame({'sine':sine_wave(100), \n", " 'mean':mean})\n", "df[:1000].plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, this ceases to be true when two sinusoids of equal frequency and phase are multiplied together. In this case, instead of averaging out to zero, the product of the two waves have a nonzero mean value." ] }, { "cell_type": "code", "execution_count": 195, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 195, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df['sin_mixed'] = np.multiply(df.sine, df.sine)\n", "df['mean_mixed'] = np.mean(df.sin_mixed)\n", "df[['sin_mixed','mean_mixed']][:1000].plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This DC voltage produced by the product of the two waves is *very* sensitive to changes in frequency. The plots below show that a 101Hz signal has a mean value of zero when multiplied by a 100Hz signal. " ] }, { "cell_type": "code", "execution_count": 192, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 192, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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iIiIKfE13jOOQlJREZGQkaWlpF6YZYwrMCa75AD8/jkNMTAxZWVkcO3aMqCj/Gdc8J8dwLjvHp4uCJ7ni06UDkGyM2WWMOQfMBAYW0X4o8KkL3veS+eIxhvy27DtOk6e+JSvbR7pYebm+ffvyxhtvXPjSsH79eiB3GNCaNWsSFBTEhx9+SHa2Z7oPHzt2jIceeojly5eTnp5+4aB0YTm7d+/Oxx9/DMCWLVvYtGlTqd53wIABzJgxA4AvvviCq666yq+2GEZ/tYnLxn1ndwyf4YrCUBtwvLpUqjXtIiJSD6gPLHGYHCEiCSKySkRucEGeQvniMYbCjJuTqCfDucC4cePIzMykVatWxMXFMW7cOADuu+8+ZsyYQadOndi5cyflynnmelYPP/ww9913H02aNOHdd99l9OjRHDx4sNCcf/vb3zh58iStWrXipZdeKnZQnscff5yYmBhOnz5NTEzMhQPOI0aMID09nUaNGvHqq68yefKfu/9iY2N55JFHeP/994mJiWHr1q2FvLr3yckxPDNnC58npNodxac4PR6DiNwI9DXG3G09vh3oYIx5oIC2TwAxjvNEpJYxJk1EGpBbMK42xvxawHNHAiMB6tat227Pnj2XnHXf0TN0nbyk+IY+ZNa9nWkf632b/IFyfX6VyxvX95FT51izO517P/LsyH3uVD48hM0T3D8egyu2GFKBOg6PY4C0QtoOId9uJGNMmvVzF7CMvMcfHNtNNcbEG2Pio6NL13Uzxx/2JeVz49srOXYm0+4YSnmd69/4ya+Kgie5olfSWqCxiNQH9pH74X9L/kYi0hSoDKx0mFYZOG2MOSsiVYGuwEsuyFQgP9qTlMflExYytENdXvi/lnZHCViDBg1i9+7deaa9+OKL9O1b+m93zujYsSNnz57NM+3DDz+80EPLn506m+VTJ615I6cLgzEmS0RGAQvI7a463RiTKCLPAgnGmLlW06HATJN331Uz4B0RySF362WyY28mV/OnYwz5fbrmN6pGhvFI7yZec9DQGOM1Wdxt9uzZdkfIY/Xq1R57L2/q7ZeQcoTvtx20O4bPc8l5DMaY+cD8fNOezvd4fAHP+xnw2FcY7/nzdY83liTTs2k0LWpVJCI02NYsERERpKenU6VKlYApDoHIGEN6enqe7rx2OXA8g8Fvryy+oSqWnvnsZ/7y1kquvqwa797Z3tYcMTExpKamcujQIVtzKPeLiIi4cMKfXfyxY4mdAqoweNMmrzst3n6QRz7bwAt/aUl4iD1bDqGhodSvr2NaK/f7bst+Pgmg8Zg9IaAKgx92SirUV+v30blhFXo2rUZ0+fDin6CUD1q9y7+6oxbLQ3tlA+q6CgGywXDBY19sosfLS+2OoZRbJB88wc16iQu3CKjCEAjHGPI7fS6byycs1HMdlF95deEObpjys90x/JYWhgBw7EwmsxL2kna06Gv1K+ULfko6zOtLkjmpIxy6TUAVhgCtC0DuZbv7v/6j3TGUcsrqXenc9q7nztEIVFoYAsjR05lc/8ZPpJ88W3xjpbzMG4uTeOTzjXbHCAgBVRgCdVeSo837jjHj5xR+Sz9tdxSlSsQYw8LE3/nnop3s092hHqGFIQC9viSZ7tpbSfmIn5IPM/LDdXbHCCgBVRi0LOR12bhvOXA8w+4YShVq/NxEbn93jd0xAk5gFQbdYsgjIzOHGT+nsP+Ybp4r72KMYW3KEd7/OcXuKAEpoApDIJ35XFL/WfYrV7you5WUd1mQeIAb9YJ4tgmswqCVoUBZOYa7Z6zlsPZWUl5g+k+7mfB1ot0xAlpAFQYtC4X7fttBpi7fxUE95qBsYoxh496jPDtvK/uP6d+hnQKqMGivpKJNXb6LDs8vtjuGClALEg8wcMoKu2N4NU+NbOKSwiAi/URkh4gki8joAubfKSKHRGSDdbvbYd4wEUmybsNckacwWhdKZsT7a/nj1Dm7Y6gA8v6K3Uyc57bBG9UlcrowiEgwMAW4BmgODBWR5gU0/cwY09q6TbOeGwU8A3QEOgDPWONAu4VuMZTM4u0H+c+yZE7ptWiUBxw6cZbxX2/Vk9e8iCu2GDoAycaYXcaYc8BMYGAJn9sXWGSMOWKM+QNYBPRzQaYCaV0ouf/+uJtuL+qIWMq95m/eT/tJ39sdQ+XjisJQG3AcPinVmpbfX0Rkk4h8ISJ1LvG5LqFbDJfmj9OZTP52u16yW7nFvE1p/HPhDrtjqAK4ojAUdDwk/yfw10CsMaYV8D0w4xKem9tQZKSIJIhIQmnHEda6cOne/uFX/rMsmbNZ2XZHUX7k1NksRn2ynl8PnbI7iiqAKwpDKlDH4XEMkObYwBiTbow530n+v0C7kj7X4TWmGmPijTHx0dHRpQqqWwyl884Pu2g27ju7Yyg/sTDxd1o8s8DuGKoIrigMa4HGIlJfRMKAIcBcxwYiUtPh4QBgm3V/AdBHRCpbB537WNPcQutC6eUYeH1xkh6QVk5ZkPg7r32fZHcMVYwQZ1/AGJMlIqPI/UAPBqYbYxJF5FkgwRgzF3hQRAYAWcAR4E7ruUdEZCK5xQXgWWPMEWczFUa3GJzz6qKdHDl1jvEDWtgdRfmoe/QqqT7B6cIAYIyZD8zPN+1ph/tjgDGFPHc6MN0VOYqjV8Rw3vs/p7Bh71H+d39Xu6MoH7J0+0GGv7+2+IbKKwTUmc96UQzX2LD3KF+uSyUjUw9Iq+Kt3pXOpPnbim+ovEZAFQbdYnCdf8zayMsLtKuhKt7NU1eRfPCk3TH8gohnLooRYIVBK4MrvfvTbnrqSHCqEEt3HCR29Dd2x/ArnhpTJsAKg90J/E9K+mnmbNjHmXO6W0n9adWudJ7/Rncf+aqAKgw6gpt7PDRzA0/P2WJ3DOVFhkxdRZLuPnI53ZXkBloX3GfWulTunpFgdwxls2U7DhKnJ6/5vIAqDHqMwb2+33aAxdsOaG+lAPXLb3/w2BebOKknQfq8ACsMdifwfyNmJPDU/3S3UiD6v//8zKETOjysPwiowqDHGDzji3WpdNKR4ALGvE1p2vvIQ7RXkhtoXfCc349nMHt9KkdP60hw/mzxtgOM+XKz3TEChqc+wgKqMOgxBs96+LONjPpkvd0xlBuNmJHACT2m4Dke+ggLsMJgd4LA81PyYR2hyw99uDJFdx/ZwFNfbgOqMBi9VpItDp04y4er9nDgeIbdUZQLzF6fyrg5iXbHCEi6K8kNdIvBPuP+t4URM9ZyPEOHCfVV2TmGY6czefizjXZHCVi6xeAG2ivJXlv2HafV+IV2x1Cl9OzXiVz+rK4/O3nqy22AFQa7EyiARz7fQEKK28ZjUm4w5qtNzFi5x+4YypcKg4j0E5EdIpIsIqMLmP+IiGwVkU0islhE6jnMyxaRDdZtbv7nupL2SvIOX/2yj8Fvr2Tj3qN2R1HFOHYmky37jvHpmr12R1H40K4kEQkGpgDXAM2BoSLSPF+z9UC8MaYV8AXwksO8M8aY1tZtgLN5iqLHGLzLwCkrdPeelxs2fQ3XvfGT3TGUxWcKA9ABSDbG7DLGnANmAgMdGxhjlhpjTlsPVwExLnjfS6YfQt7nyleW8f6K3XbHUPlk5xjaTVzEBt2q8yq+1CupNuC4nZlqTSvMCOBbh8cRIpIgIqtE5IbCniQiI612CYcOHSpVUK0L3icl/TTjv97Kv79PsjuKsmzYe5R/LtxB+ik9a93bGOOZL7ghLniNgi4QXmByEbkNiAd6OEyua4xJE5EGwBIR2WyM+fWiFzRmKjAVID4+vlS/GT3G4L1e+34nXRpVoVF0JJXLhdkdJ2CtTTnCjW+vtDuGKoIx4O5hGVyxxZAK1HF4HAOk5W8kIr2AscAAY8yFSzAaY9Ksn7uAZUAbF2QqkB5j8G43vr2Sv7z1s+7ys8mx05laFHyAJ/47XFEY1gKNRaS+iIQBQ4A8vYtEpA3wDrlF4aDD9MoiEm7drwp0Bba6IFOBdIvB++06fIr6Y+ZzNkvHdPCk0V9u0nMUfIQnPsecLgzGmCxgFLAA2AZ8boxJFJFnReR8L6OXgUhgVr5uqc2ABBHZCCwFJhtj3FYYlO94bNYmlu04WHxD5ZTM7Bwe/mwDM9dqd1Rf4Ynvt644xoAxZj4wP9+0px3u9yrkeT8DLV2RoSRydF+Sz5i7MY25G9N4+rrm3NWtvt1x/NKWfcf4bsvvzF6/z+4o6hJ4YovBJYXBV2hd8D3PzttK9QoRxMdWpnqFCLvj+I0fdh5i2PQ1dsdQpeAzWwy+Qo8x+Kb7P/mFiNAgfnjsSi0OTsrIzCYx7bgWBR/miatEB9i1krQw+KqMzBw6Pr+YgycydD2WkjGGW6et5i9v/Wx3FOUET+z5CKjCkK0fKD6v8wtLGPOVDiV5qfYfO0P9MfNZt+cPu6MoJ/lEryRfoscYfF92jmHm2r3Ejv6GI3pmbomM+WoznV9YYncM5SKe+H4bYIVBK4M/aTtxES/M32Z3DK91+ORZGj05n0/X/GZ3FOVCntiVGliFQTcZ/M47y3fxf/9ZwUkdkD6PKUuT6fPacrL0b97v6DEGF9P/Ef/0y29HGTRlBR+v1oFkjpw6x53vreHlBTt0V5uf0i0GF9NdSf4r6eBJxs7ewmXjvuXgiQy749hi/NxE2k5cxLIdpbv6sPINnviCG1jnMegmg9/LyMyhw6TF9GwazbvD2hMc5ObLUNrMGEPywZP0fm253VGUh+h5DC6mdSFwLNtxiIZPzmdtyhFO+enxh9+PZdDtxaVaFAKMnvnsYnoeQ+C58e2VVC4byoSBcVzXsiZBfrAFkZh2jGU7DvHygh12R1E20GsluZieMRuY/jidyYOfrmfmmt+4MT6GQW1sGVnWacdOZzL5u+3a/TTA6RaDi+Xk2J1A2ennX9P5+dd0Hv5sI7Pu7UyDquWoEhlud6wi5eQY9hw5zZivNrFq1xG74ygvoFsMLqa7ktR550cqu7tbfR64ujHlw0O8ajdTTo5h9vp9LN5+gPmbf7c7jvIiPrPFICL9gH8DwcA0Y8zkfPPDgQ+AdkA6cLMxJsWaNwYYAWQDDxpjFrgiU0G0u6rKb9pPu5n2026CBJ67oSUDW9eiXLh935d+SjrMmt3pvL4k2bYMyrv5RGEQkWBgCtCb3PGf14rI3HwjsY0A/jDGNBKRIcCLwM0i0pzcoUBbALWA70WkiTHGLeM6al1Qhckx8OTszTw5ezN9mlenfWwUA9vUIjwkmIplQt3znjmGI6fPsXrXEfYdPc2shFSSDp50y3sp/+Eru5I6AMnGmF0AIjITGEjesZsHAuOt+18Ab4qIWNNnGmPOArtFJNl6PbeMSK6XB1AlsXDrARZuPcAk6zpMfVtU56b4OpQJC6ZelXLUqBBRqvMjDh7PINsYEvcdZ8mOg6xL+YMdB064Or7yc75SGGoDjgPGpgIdC2tjjMkSkWNAFWv6qnzPre2CTAW66uAHXBO6xV0vr/zVTji7E84CR4GN1uQq5cKILh+ee+KkCJHhwZw+l40BwkOCOH02m2NnMsnKyeGP05l5XrKbdcM9GyPKjwWdbALRjd36Hq4oDAV9dcpf0gprU5Ln5r6AyEhgJEDdunUvJd8FtYKOUDv8AIgQHhJEVnYOxzP88+Qn5QGnIfP0nw+POcw6/1dVwfoZ5T3HtZUPKRMWTBAQEhxEkEBocBDB4b6xxZAK1HF4HAOkFdImVURCgIrAkRI+FwBjzFRgKkB8fHypfjMdH5hx0bSawJlz2ZzLzmFT6lEAUtJPM+5/umWhlHK/iNAgBreLoWbFMnRvHE10+XCCgqBaefuGsXVFYVgLNBaR+sA+cg8m35KvzVxgGLnHDgYDS4wxRkTmAp+IyKvkHnxuDHh8MNoyYcGUIZgrGkcDcEVjuL1TPdJPnuXQybN8tGoPO34/wS+/HSVbj1MopZx0T48GdGlYlYplQmldp5LdcS7idGGwjhmMAhaQ2111ujEmUUSeBRKMMXOBd4EPrYPLR8gtHljtPif3QHUWcL+7eiSVRpXIcKpEhvPcDS3JyTFk5RjeXJLEl7/sY9/RM3bHU0r5kId7NaFH02ia16xAWIh3X6ZOfPEyEfHx8SYhIcG298/IzObIqXNMmr+N+Zv3azdYpVScw3fwAAAWIklEQVSBejWrxk3xdWhRuyK1K5WxOw4iss4YE19cu4A689lVIkKDqVWpDFNuacuRU+fYvv84t0xbbXcspZSXuK1TXa5rVYtODarYHaVUtDA4KapcGF0aVWXnc9ewZPtB3lyaxJZ9x+2OpZSyQcf6Ucy4qwPhIUHknqrlm7QwuEhYSBD94mrQL64GH6/ew3srUkjWs1iVCghj+zfj2lY1qeUFu4tcQQuDG9zasR43tK5NYtpxbnrHLSdxK6W8wNAOdbilQz1axlS0O4pLaWFwk3LhIXSoH8XqJ69m+ordvPPDLrsjKaVc6MfHr6RGxQhCg727h1Fp+N8SeZnqFSJ4ou9lbBrfx+4oSikXeH5QSxIn9KVOVFm/LAqgWwweERQkVIgIZfcL/Vm49QDPfr1Vz4NQyse0qVuJ2fd1tTuGR/hnufNSIkLfFjVYMfoqt13KWSnlejPu6hAwRQG0MNhm4zN9eO3my+2OoZQqRsrka+nRJNruGB6lhcFGg9rEsPuF/nbHUEoV4N9DWgfs/6cWBpuJCNsn9mPCgBZ2R1FKWRIn9GVg69o+fZKaM7QweIGI0GCGdYllzdir7Y6iVEAb278Zm8b3sXXcb2+ghcGLVCsfwfeP9GBg61p2R1Eq4Hz6107c1a0+FSK0Y4gWBi/TqFokL/xfS8Zcc5ndUZQKCPH1KvPRiI50blilVGN5+6PA3l7yUmXDQrinR0MiQoP51/c7LxovWCnlGtdfXotnB7Sgcrkwu6N4Fd1i8GLDusTy4YiO1KtS1u4oSvmdwe1ieGNoGy0KBXCqMIhIlIgsEpEk62flAtq0FpGVIpIoIptE5GaHee+LyG4R2WDdWjuTxx/F1a7ID49daXcMpfzKJ3d35JUb9Tyiwji7xTAaWGyMaQwsth7ndxq4wxjTAugH/EtEHAc5fcwY09q6bXAyj9/a+EwfHuvb1O4YSvm8n564ki6Nqtodw6s5WxgGAjOs+zOAG/I3MMbsNMYkWffTgINAYJ1G6AIVy4QysnsDxl3X3O4oSvmka+Jq8OXfOhNTWXfNFsfZwlDdGLMfwPpZrajGItIBCAN+dZg8ydrF9JqIhDuZx6+FBgcxolt9Hu7VhPIB3s9aqUvRqFokE2+Io129KLuj+IRiC4OIfC8iWwq4DbyUNxKRmsCHwHBjTI41eQxwGdAeiAKeKOL5I0UkQUQSDh06dClv7Xce6tWY94a3tzuGUj6hcbVIvn+kB1Uj9XtnSYkxpvRPFtkB9DTG7Lc++JcZYy7aES4iFYBlwAvGmFmFvFZP4FFjzHXFvW98fLxJSEgodW5/cepsFi2eWWB3DKW81tTb29GzaTXCQrQDJoCIrDPGxBfXztnf1lxgmHV/GDCngCBhwGzgg/xFwSomSO4FSW4AtjiZJ6CUCw9hzv1dGdqhrt1RlPI6Ewe2oFez6loUSsHZ39hkoLeIJAG9rceISLyITLPa3AR0B+4soFvqxyKyGdgMVAWeczJPwLm8TiUeurqx3TGU8iq3dqzL7Z1jCdIzmUvFqV1JdtFdSQWLHf2N3RGUst3cUV1pFVOp+IYByFO7kpQXWTP2ap66tpndMZSyzez7umhRcAHt8+hHqpWP4NaO9dh9+BQfr/7N7jhKeUyvZtUY0r4ubepedPEFVQq6xeBnyoQFM2lQS5pUj7Q7ilIeM/GGOHo1r253DL+hhcFPff1ANz3XQQWEX8b1pmbFMnbH8CtaGPxUeEgw3RtHc0/3BnZHUcothnaow2cjOxGlV0d1OS0Mfiw4SBjTvxldG1WxO4pSLvdon6Z0bKB/2+6ghSEAzBjegf/d39XuGEq5zNZn+1JFL3HhNloYAkBIcBCtalfUK7Mqn/f3Xo359qErKBumHSrdSQtDgAgKEkZ0q881cTXsjqJUqf31igY0q1nB7hh+TwtDgPnPrW1ZriPCKR+UPOkayunl5j1CC0OAERHqRJXh0T5N7I6iVIn8vVdj5j3QjZBg/bjyFP1NByARYdRVjenfUncrKe93b4+GxNWuaHeMgKKFIYC9PqQNPz6uu5WUdwoJErZM6EtEaLDdUQKOFoYAFhIcREzlMjzW96KxlZSy1T96N+HrB7oRqccUbKGFIcCJCPdf2Yh+LXS3kvIe913ZSHsf2UgLgwLgjVvakPBUL7tjKMX6cb0J1gF2bOVUYRCRKBFZJCJJ1s8Cr3krItkOo7fNdZheX0RWW8//zBoGVNkgNDiIKuXCGNa5nt1RVIAa1rkeX9zbmcp67SPbObvFMBpYbIxpDCy2HhfkjDGmtXUb4DD9ReA16/l/ACOczKOcICJMGBjH1ZdVszuKCkATBsYRHxtldwyF84VhIDDDuj8DuKGkTxQRAa4CvijN85X7vHFLG75/pLvdMVSACA4Slj7a0+4YyoGzhaG6MWY/gPWzsK+aESKSICKrROT8h38V4KgxJst6nArUdjKPcoGyYSE0jI7k5vg6dkdRfu6G1rX4bGQn6lctZ3cU5aDYvmAi8j1QUJeVsZfwPnWNMWki0gBYIiKbgeMFtDNF5BgJjASoW7fuJby1Kg0R4cXBrdh/PIPlOw/ZHUf5qX8NaWN3BFWAYguDMabQrioickBEahpj9otITeBgIa+RZv3cJSLLgDbAl0AlEQmxthpigLQickwFpgLEx8cXWkCUa/3n1rakHD7FdW/8ZHcU5UciQoP48m9d7I6hCuHsrqS5wDDr/jBgTv4GIlJZRMKt+1WBrsBWY4wBlgKDi3q+sldkeAhxtStSu5IOnahco2xYMC8NvpwWtfQyF97K2cIwGegtIklAb+sxIhIvItOsNs2ABBHZSG4hmGyM2WrNewJ4RESSyT3m8K6TeZSbrBh9FT2aRNsdQ/mBrc/2Y8DlteyOoYoguV/cfUt8fLxJSEiwO0bAOXr6HKt2HeHej9bZHUX5oLJhwUy7I54ujaraHSVgicg6Y0x8ce30zGdVYpXKhtEvrgYNorUHibo01cqH88qNl2tR8BFaGNQlW/KPnnTX3UrqEqwZ24v+LWvaHUOVkBYGVSr/vrk1/x7S2u4YysuVjwjhveHt7Y6hLpEWBlUqlcuFMbC1no+oivbUtc24sqleYsXXaGFQTkmZfK2OBKcKlDL5Wm5uryej+iItDMppz93QkqeubWZ3DOUlKpcN5e3b2tkdQzlBC4NyWlS5MO6+ogGVyobaHUV5gUmDWtIvTrcifZkWBuUy68f1ZlAbPe4QyHa/0F97H/kBLQzKZXLHc2jBxBvi7I6iPCymchneG96e3KvpK1+nhUG5VIWIUG7vVI/wEP3TCiRPX9dcex/5Ef3vVW6x47lr+OsV9e2OoTwgZfK19GmhxxT8iRYG5TaP9G6qu5X8WMvaFfn0r53sjqHcQAuDcpsyYcHc3qkevZtXtzuKcrEaFSKYNCiOzg2r2B1FuYEWBuV2/70jnjHXXGZ3DOVCq568mlYxleyOodxEC4PyiLuvaMAnf+1odwzlpL4tqrPkHz3sjqHcTAuD8ojgIKFLw6rc17MhocHapdEXxdWuwNPXt6BBdKTdUZSbOVUYRCRKRBaJSJL1s3IBba4UkQ0OtwwRucGa976I7HaYp5fr9HOP97uMKbe0tTuGKoV5D1yhQ7wGCGe3GEYDi40xjYHF1uM8jDFLjTGtjTGtgauA08BChyaPnZ9vjNngZB7lA/q0qMGK0VfZHUOV0D96N2HT+D52x1Ae5GxhGAjMsO7PAG4opv1g4FtjzGkn31f5uNqVyvDJXzvSuYH2avFmT13bjJE9GlAhQq+DFUicLQzVjTH7AayfxZ36OAT4NN+0SSKySUReE5Hwwp4oIiNFJEFEEg4dOuRcauUVujSsyot/aUWVcmF2R1EF+Huvxtx9RQPCQ4LtjqI8TIwxRTcQ+R4o6LTGscAMY0wlh7Z/GGMuOs5gzasJbAJqGWMyHab9DoQBU4FfjTHPFhc6Pj7eJCQkFNdM+ZDY0d/YHUE5mHFXB3ro8K1+R0TWGWPii2sXUlwDY0yvIt7kgIjUNMbstz7kDxbxUjcBs88XBeu191t3z4rIe8CjxeVR/umXcb353/p9PDtvq91RAt6ih7vTuHp5u2MoGzm7K2kuMMy6PwyYU0TboeTbjWQVEyT3kow3AFuczKN8VFS5MO7oXI/ReiKcbQZcXosv/9ZFi4IqfouhGJOBz0VkBPAbcCOAiMQD9xpj7rYexwJ1gB/yPf9jEYkGBNgA3OtkHuXDQoKDuLdHQ8pHhPDuj7vZdfiU3ZECRp/m1Zk4MI6KOtiSogTHGLyRHmPwf78eOsnV/8z/PUK5w1/axvDPmy63O4bygJIeY9Azn5VXahgdScrkawkO0rOk3WneA920KKiLaGFQXm3Nk1fz7yF6Qrw7zHugG3G1K9odQ3khZ48xKOVWVSLDGXB5LTKzDY/O2mh3HL/wSO8m9G9Zg0bV9CCzKpgWBuX1RITB7WKoX7Usn69N5bOEvXZH8llP9LuMkd0b6C46VSQtDMpntKsXRauYSgQHC5+s/s3uOD7l2lY1GdwuRsdlViWihUH5lNDgIJ4f1JLLapTno1V72HngpN2RvF7bupX4542XExGql7ZQJaMHn5VPuqNzLHPu70bVSL3OUmGiy4fzZP/L+Oq+rloU1CXRLQbls8qEBZPwVG8+XLWHWQl72ZR6zO5IXuOyGuX5+oFuhAbrdz916bQwKJ93e6d63BQfw01vr2RjgBeH9rGVuatrfa5pWdPuKMqHaWFQfiE8JJg5o7oxe30qn67ey5qUI3ZH8rhujaoy464O2uNIOU0Lg/Irg9rEcEPr2jwzN5EPVu6xO45HDO8aS/+WNWkfG2V3FOUntDAovyMiPDswjru61ufnX9N5cvZmuyO5RcPoctzboyE3xtexO4ryM1oYlN+KrVqO2KrlaFw9kjeWJLN8p/+M/Dfr3s40io6kso5+p9xAC4Pye+1jo/jvHe04djqTq/75AyfPZtkdqdSeHdiCfi1qUK1ChN1RlB/TwqACQnhIMNUqBLNlQl/2HjnNgsTfee6bbXbHKpErGlfl2pY1GdKhrt1RVIBwqpOziNwoIokikmMNzlNYu34iskNEkkVktMP0+iKyWkSSROQzEdHtYuV2daLKcvcVDfjx8St55cbLKR/und+PLo+pyNJHezJtWLwWBeVRzv5HbAH+D3insAYiEgxMAXoDqcBaEZlrjNkKvAi8ZoyZKSJvAyOAt5zMpFSJ1IkqS52osgxuF8MPOw+xff9xXvh2u62ZGkaX48GrG9OzaTUqltHR1JQ9nCoMxphtkNsLpAgdgGRjzC6r7UxgoIhsA64CbrHazQDGo4VB2aBHk2h6NInmnh4NWZtyhN2HTjH+60ROn8t2+3t3bxLNrR3r0rVRVSK9dOtFBRZP/BXWBhyvk5wKdASqAEeNMVkO02t7II9SRWofG0X72Chual+HvUdOYwzM25zGtv0nSEw7xq5DpR+LukaFCP7WsyG1KpWhZsUImtesQJCekKa8TLGFQUS+B2oUMGusMWZOCd6joL96U8T0wnKMBEYC1K2r+1uVZ9SJKgvAfT0bAWCM4diZTP44nUlIkLB+71GiyoZhMPyUdJiWMRUJFmHf0TN0qB9FcJBw/EwWbepWIscYyobpFoHyfsX+lRpjejn5HqmA4xk4MUAacBioJCIh1lbD+emF5ZgKTAWIj48vtIAo5U4iQqWyYVQqm9tP4nzhALiicbRdsZRyKU9cenEt0NjqgRQGDAHmGmMMsBQYbLUbBpRkC0QppZQbOdtddZCIpAKdgW9EZIE1vZaIzAewtgZGAQuAbcDnxphE6yWeAB4RkWRyjzm860wepZRSzpPcL+6+JT4+3iQkJNgdQymlfIqIrDPGFHrO2Xk6iodSSqk8tDAopZTKQwuDUkqpPLQwKKWUykMLg1JKqTx8sleSiBwCSjtuY1VyT64LJLrMgUGX2f85u7z1jDHFnonpk4XBGSKSUJLuWv5Elzkw6DL7P08tr+5KUkoplYcWBqWUUnkEYmGYancAG+gyBwZdZv/nkeUNuGMMSimlihaIWwxKKaWKEFCFQUT6icgOEUkWkdF25yktEakjIktFZJuIJIrIQ9b0KBFZJCJJ1s/K1nQRkdet5d4kIm0dXmuY1T5JRIbZtUwlJSLBIrJeROZZj+uLyGor/2fWpd0RkXDrcbI1P9bhNcZY03eISF97lqRkRKSSiHwhItut9d3Z39eziDxs/V1vEZFPRSTC39aziEwXkYMissVhmsvWq4i0E5HN1nNeFyl6/OWLGGMC4gYEA78CDYAwYCPQ3O5cpVyWmkBb6355YCfQHHgJGG1NHw28aN3vD3xL7qh5nYDV1vQoYJf1s7J1v7Ldy1fMsj8CfALMsx5/Dgyx7r8N/M26fx/wtnV/CPCZdb+5te7DgfrW30Sw3ctVxPLOAO627ocBlfx5PZM7vO9uoIzD+r3T39Yz0B1oC2xxmOay9QqsIXc4BLGee80l5bP7F+TBFdEZWODweAwwxu5cLlq2OUBvYAdQ05pWE9hh3X8HGOrQfoc1fyjwjsP0PO287UbuKH+LgauAedYf/WEgJP86Jnf8j87W/RCrneRf747tvO0GVLA+JCXfdL9dz/w5RnyUtd7mAX39cT0DsfkKg0vWqzVvu8P0PO1KcgukXUnn/+DOS7Wm+TRr07kNsBqobozZD2D9rGY1K2zZfe138i/gcSDHelwFOGpyB4OCvPkvLJs1/5jV3peWuQFwCHjP2n02TUTK4cfr2RizD3gF+A3YT+56W4d/r+fzXLVea1v3808vsUAqDAXtY/PpLlkiEgl8CfzdGHO8qKYFTDNFTPc6InIdcNAYs85xcgFNTTHzfGaZyf0G3BZ4yxjTBjhF7i6Gwvj8Mlv71QeSu/unFlAOuKaApv60notzqcvo9LIHUmFIBeo4PI4B0mzK4jQRCSW3KHxsjPnKmnxARGpa82sCB63phS27L/1OugIDRCQFmEnu7qR/AZVEJMRq45j/wrJZ8ysCR/CtZU4FUo0xq63HX5BbKPx5PfcCdhtjDhljMoGvgC7493o+z1XrNdW6n396iQVSYVgLNLZ6N4SRe6Bqrs2ZSsXqYfAusM0Y86rDrLnA+Z4Jw8g99nB++h1W74ZOwDFrU3UB0EdEKlvf1PpY07yOMWaMMSbGGBNL7rpbYoy5FVgKDLaa5V/m87+LwVZ7Y00fYvVmqQ80JvdAndcxxvwO7BWRptakq4Gt+PF6JncXUicRKWv9nZ9fZr9dzw5csl6teSdEpJP1O7zD4bVKxu4DMB4+2NOf3B48vwJj7c7jxHJ0I3fTcBOwwbr1J3ff6mIgyfoZZbUXYIq13JuBeIfXugtItm7D7V62Ei5/T/7sldSA3H/4ZGAWEG5Nj7AeJ1vzGzg8f6z1u9jBJfbWsGFZWwMJ1rr+H7m9T/x6PQMTgO3AFuBDcnsW+dV6Bj4l9xhKJrnf8Ee4cr0C8dbv71fgTfJ1YCjupmc+K6WUyiOQdiUppZQqAS0MSiml8tDCoJRSKg8tDEoppfLQwqCUUioPLQxKKaXy0MKglFIqDy0MSiml8vh/zm7KfKhldp0AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df['sin_mixed_101'] = np.multiply(df.sine, sine_wave(101))\n", "df['mean_mixed_101'] = np.mean(df.sin_mixed_101)\n", "df[['sin_mixed_101','mean_mixed_101']].plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is really useful in situations where you have a signal of a known frequency. With the proper equipment, you can \"lock in\" to your known-frequency signal, and track changes to the amplitude and phase of that signal - *even in the presence of overwhelming noise.* \n", "\n", "You can show this pretty easily by just scaling down one of the waves in our prior example, and burying it in noise. (This signal is about 20dB below the noise floor in this case.)" ] }, { "cell_type": "code", "execution_count": 209, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 209, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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G9cf3C/5ATEwM9uzZg6SDB/DcI/chLjoS2Tm5KFGmHK5dvYLLly/jzjvvBAA89thjWLZsmcf3N+VShv1EpWhsFGqVdf3NeSLs/7vu4+YmnkSzKiXQoEJx3euz7VK9LYGXlWvCG/N34fWeDVCppOvx2/Z9+PXfU5hwX1Ov1u2tSzeycfjsNdRVXGm9ciMHby/YgxplCuPJtjUxZtFefD+oFTrUK6u+jvRslCgU7XLsMJsllu45jbub5PUwP//Tv3jijhoY28fyG912/CJKF4lFzXh9Pdc2Z65k4pqbtI9un6xzeI1a7e78kWPhhsW7UlG9dBE0rVLCft+N7FzsP30VLauX9qqN/jKqx3kGgJ5uHr8LQF3rv8EAvjZou5qc89YavL0cT0xXz7v1tySds/5TNqHrx3lfDne/XeUXLDPHhCNOZ1kms1TNnd2XehWvzbUMfhi9cC+mafSUKgfdKAfX/H3kgsuyB89ew9ytJ/HV2iT7fZdv5HjMmb7spod29pYTLvmmy/dYUly+XX8UADSrQrjLPbx13Ep7XrZzbtb2E5dUn3PgtPYAJAD2HtOlu8+oBsFHzqdj5K+7sfPkZRxW5F3Z3uO3rakAegl74Oz4OudvS0GDt5fj6PnrePaHRPyx7ywuZ+gfHW5fn3BM0Wg5fhW+XnsE/b/d5NOgWC2ejk1agaptxL/WwDzb41PWHbXfN3W9ZYChc7qIGq1eq588DLr5fddpbDl20es8y4JICDFNCHFOCKHaRSYsPhNCJAkhdgkhblU8NlAIcdj6b2D+tVpbyqUMzYOtlnr16mHbtm1o2rQpRo4cicmfvu/weHRUNCQsB/HUK1lIz3D8PmbnmnA1Iwd7U68iPTMXsTGx9sds3zE9edWPPPIIFi1ahEKFCqFHjx5Ys2YNAGDAwCcxffp0TJ8+HYMGDXK7jtjYvG1HREQgIjIKmTkmREREIDfXsh90/jnu3r0bxYqXwMXz5+xtrV2vAeauWI9/t2/H7BUb8M2sXyGlb7WWleNzPOWr55rN+HRV3pgVCc/v2+vzd+HuSeu9apNiF+iVNfvPYcGOVLzz+z7M2nwCbSeucXjclp6RkWNCkzErvFy7d05fyXQIMoG8ffvljBx7x8XJS+pjaM5cyUSLcSvx5Z9JLo/NSTyJl2Ztx4+bj2P7ybzj5Yx/ku23H/h6Izp9uFZ13TVHLsGbv7mmeAJ56RW+SLuehUvp2arfo5dmbcc9XzgWfnhtzk488PXGfB/cbUjgLKVcB8BdTbW+AL6XFpsAlBRCGJNMo2HqhqMu921Icg0W3fFU6WJXivplBncjxJWcB5kMn78LXT76yyFo+2JNEvp++Tf+dQoGbUHFOcUXZvZW/YOrnAcj2rz+yy68v/yg7vW489KsfzHi1914+vtE1W1fuO7hAOhhr7c1+RL2nLqCxmNWYPGuVPv9j09zrNLx3rL9Xqfs7D+dFxjbehn+t/yAV+vwxNYJ4PxR/GEdKHPobN5J1I6TlzDOTSUTwNKzu2rf2bzeFgjsU5ws2AYIKgcKZpvMDt83k1l6PSjVRs9BEACG/LwdcxNP+lSNRtkD6Cn41yo5tu6wa/69MvD5OZ8G5eSTGfChU0MIURrAGACtAbQCMEYIUSqgLQ2Q1NRUFC5cGAMGDMCwYcNwYLdrpYVzV7Nw8uINmKW0pujl7XwOnb2OZGs6lVqaDwB06NABc+bMgclkwvnz57Fu3Tq0atXKYZmjR4+iVq1aGDJkCDp1vwvL122GySzR5I6uWLx0GbZu3YoePXp49dqS027gkLVyxtXMHOvYk7y2r1r2O9LS0jBt/hJMHDMCly9fRv369XEp7QJ2brPsJ3NycpB0cD+KlyiBEiVKYMMGS3Dy008/edUWJa2UvYvXs/HpqsMuYy5s8Xpeqoal99d29cy2j3S+6mXjvO+xp2qoHEOyc814b+l+vDTrXzz23WZM/su1AAAAvPnbbpy6nKG5P7QFd6v2ncXJi+rBqzcW7jjldiDcnlNX3KZ3Ojt9xbJ//GjlIZe0B1ugee5qFs76MIBSSsvgxZ0nL+MRa0fMzpOXXdLmvLE39Qpajl+FFuM8V6KyDWrfk2qJwTLzuexifg0OrAxAGdWlWO/TrmvlJyPqdHoK7NYfdh+IewojVjr1xG609gKPXZQXIO225gCd9TAYz2seGmdEpYfFu1w/XlsFCj0EgPQs9z+IvdYfjrKWtvMJyTd/uZ5E2Slep3Kgn3KHq9WD7Qvlem1VOvS814NmWE4+HmldDeMX78M/R9JwcPxdDss8830itiZfwsi7GgCwBMWe3D1pPbJyzSgaG4WdY7rjwW82Yttxx9fr6WzednlV71dm0c5Ur74HWlbvd19K8LsNx/B270Yu90dHhvXQDgdSynVCiBpuFrF3agDYJISwdWp0BLBSSnkRAIQQK2EJwH8ObIuNcTE9G7kmiRrxRbB7924MHz4cERERiI6Oxmtj38fH4992WD7XzSBfrTEuSvfddx82btyIW265BUIIvP/++6hQoQKSk5Pty8yZMwc//vgjoqOjUaRkPCa+OAxSSkTHxCDh9vaoVbkcIiM9p565a42ySs6li2mY9N7/Ye2a1bgWVQIPP/EMhg4dipkzZ+LDb2bif6PfwIejh+N6ZjYGPPUc6tRvaO/1Lly4sNdBvI1tgGaVUoXtg9MBy4l9tnWf9+u/p3Bvi8r2APq37afsg+pt/jt3p8MxJNdkRo9PHXtgtSg7D5zd99XfDp1b6w9fQI/GFTRTEnLNZsRY+xjVAnFbx5A3A9jmbj2JrFwT+txSGSUKWwax2tIZf39JfVCmuzK7atIU8Uvnj/5yaJ/tZailyaVn5WoO1HVmy9f+Yk2SyxgYPWyfz9zEkw5X+Nz95FbvP4unZiZixpO3eb09o+RX4KzWd+jy1gghBsPS64Fq1TyPnvfFpXRL75q7S0qbjqahSeW8PJq1B89jzKK12PxmF/vZvTO1D9pk8m2Awi//5qVGrPIQHHhyPSuvN9G5Hdcyc1TzawNpmxeTvUQIYe9VPHDmKqqXKYwPVhzEa918q97g6aV+tz6vzvB/JlsGxxwY1xNXVcpPeXNesflYXr3k9KxcFI+z7Ci/sF5CO+fFGf/lGzn4U6NiSbK1d8bWQ/K7juDUlr9+PSsXGTkml6BZSasMV8Bm0vXiTc41mVFn1DK809c1hxZwvHrkKXBW9tIfT0vXPTo9RGl1amjdHzJsebc9evRA09YdcOF6FppUKoE9qVfw3bzF9uX+PZIXnHXr1Rfde/XVXOe4T75CheJx9vEpmw5a9tVCCHzwwQf44IMPHJavUaMG9uyxZMmMHDkSI0eOxJWMHPvAYMAyKHDXv1sxdpT7snUdO3ZEx44dsd/6/fz8p4UOj31RpzkAYNTbo+0pf7+vS4TtiPXooGfteeQNGjfF9F+WoknlEg4DtFq2bImdO/N65MeOHeu2TWoyrYPmr2flOgTOJxS9sl/8mYQv/kxCMWuAtumo63Fh3SHH/Zxz2VIl5wBZ5kXOLtSuCOs5OTKSbazRhqQLeKpdLTz4jf7BmM60mr5ax8RXau9F4zEr8r2KxUxFigjgPu7ZYU1d1brinx/yK3BOAaAcZVMFgMtRXUo5BcAUAEhISPDrm6xVZsvWC7dge16NWuWPbl7iSQyfv8shGBizyJK72vrd1Sgc475HQLkuWy9GerYJuSYzojwcsLXSJ9RstQagnkYx23oqAdf8taZj/9C9PaMoLwtFCPWBccrHbdKzTJi47ABm/JOMuGjjegxzzBKfrT6MwR1qqeZOalVm8MaHf+SlvqRcynAZNOrN7FZavb/5Uef6sIf3QtmCK17kZG9NVg/WvckZz7SeAExc5phOc/LiDQiRNxATAGI8/A6VbT99JTPcA2etTg1dnR1A/nR46ObUQrNZYu/pq/bfh1aA5NIz6cPJ4OFz12AySRQrFI2KJeIcvnM2uSazQ9C8bEMinn/8QXTu0Ru5RcsDsOwPoiMECsUUzGqx2bkmCCGQY7KUCHROy/BnV2RP1dCZ9qVGSmk/GdD7MTq32VZXOtAu3cixDzI32pHz2tWaAtbZYRBfZry8fCMbZgmHk7VAya9f5iIALwkhZsOSM3dFShmwNA0AWKKY3Wyeh4kVlD/S4dbLBVo//hsaAwnVeuPOKwa9rU+6gE71y7lth7tBdoClBmrFEnEY3KG2PUA462NlDudBiM70BPGDFJOcuOsNUFLOvhchhNszfedA3zZwYd0h73LV7etT3P50lWUGpHmJJ3Hhejayc82qOxNbz7OzfzRm3buUno01B8451BjVU6Ytx2SGySxdqoQ4vwfPaUzU8dVa33PLbHwNvm0tVD5/4DRjZoN0ppUeZWuD8++z/fuWSgP/jOict6zK55ysMUnNTUCrUyMFlnQN5f1r1VZgZIeHXlduZCMmKhKFPHRk5JjMur7Xzt+JDya+hzlz5zrso7r16otnhgzTXIdtkHna9SwUjY1CCWsdaSXnllSvXQ9L/3Ysgbhy/RaMeuU5h31BbGwsNm/ejILAUxpkim2wmg/fBLXUCj2Ux/AfNh3HhKX7AUD15MX9evzz3YZjqF++mMf6xEbyNgjONZndVr3IT0JYKlXpHRemRUrYZ+nNj95yo8rR/QzLTjZeCJECy6CSaACQUk4GsBSWUnRJsJSje9KI7TrTCiKH58PoeLUzVD2Xym3avOt+JOrOlCuY/ncyAKiW3tJDeQD5wUNlAT2VRtYoZkTMK8mm/wdp2am5u/ymbreb2o/esp0gaPWQap35ag3Ue/nn7diQdEFzWmoBy841obrjOKv7vvobe05dRfLEXjjrwwjhP/adtV990HsS42xeomv1FD1TwduCe+XVjx0asyjOMHDa7Q8Ug1g9nQiSJtVODSHECgDvKgYEdgcwMliNdGabEVOrhJ0Wvb+M4SNG4oGnXkaRmCik6/gNODt3NROFoyMR7aFUo5q6DRtj7or1Xr025b7dyN7EvEF2vq0012RGRo4JxeJcTyIA7c/D115rAeEwsFvZ7OtZuW6uNhlzvmc7LugO3qTrwDbn3vZ6o5Zh19juXrdF6xPr/+0mzat8vvP9/VObgE1vJ06wes4NCZyllP09PC4BvGjEttx54SffS0M/PXOrx8F+3tL67NU+a62ebBtl1Qglb0bEurt048zXn8GbKj8CJYfeVw9feuUBK02jZJ1WTu57y/bjjR4NPNY+ttX29iZNxh1b5ZbVbqZZVwu6beXVpFQvP6iHrVrGTz5WhdimMgjSVjrQmXLHZhsv4G5KbZuxOpbRS9lrolVs30aZD1fQL1MayddODSnlRSHEOAC2y0rv2AYKBo3K52Yym5GeZal5btQscZ72BM517S9cz0J80ViH+zKspUUbVNRfe9jZnlNXUL98MV3Bt5GdCTYmsxl7U6+iQvE4lCvu2zwHRy+kIzPHhKaKMUPu5KVq+MY56BTCUl3i9vcsZeVureb+ZETrK5SZY4KUQEQAxhU7p1vmmBz/zjaZNUu22py7lomMbJNDWtnmY+o/Vz1B8xKVgf2Up2AmUfnoqhd5lcofmIDAqv3agY6vnHtf/0664HGyiPziKVB3TtbXy5saq57Knq3YmzdAIFNjlsa5Kr2kgKWSxi1VSuJuj1OIWnaVs7eeQJNK+nbu/lAL2pT3TbNeVbBwf/j4RaO+tjf5xZ68Nte1dBdgydt3ZkSunqc6sL5Sprj4ejk4FPnTqSGlnAZgWiDapeVqRg7MUqJIbJSu6icnLmY4lFOsrDJphZJaalhWrgkyU3+o5ryPS72cgZKFXXtU9VS1cccsJa5m5aBMVKznhQ0ipcTuU1dQuWQhe2WFizeyfQ6cszzkqipPwHNNZp9/mbbfdMrFDIerhAICmxUDD/89od4p4amDs/W7q3ElIwcHx7ur7GiMB77+x+MyyvZKCbSaYLlivf8dY9r34ixvOyG1P7lL6dkoEhuFGJXYR2sQoN4r1yaTMR1e3ioYUZxBfH0LfZ06W41ttCzglA4hgUenbka/yRt9upTuabYzb3kqMTbDx8A5UGPUfAl2XvjpX826n86k1O7VNtJUReUONc690cqay86cp50tqLZo9HyocVfVwyg3U49zqElOS8f392RyAAAgAElEQVSJizew//RVzZrJSs77bk+7H639gfNJvKeAz0Wgjt+K9ebqzdf2Y3O2E4tTlzPsFaSU743zZFN66ZlwSTmhhq/jLZbsPu2QQgj4NtBMSUAY2hlhFLX9mJ7UukA452asVYtxK/Hyz+qB+HSHjqI836xzU0JWIdVapnd9Ul4Flp+3nAh4XefwCpy9+LEpF9VzhucvZeUEXyeYsNEqLl8QBOf8T5vnup95LU41ula2imUaqQ9+M+CMJVCX597xMHGL0hEDqph4ojWwkwoWb2cIBHwfLO3MyJk1jZBrMmPf6av2MnjB4utYAncdADZzE1PsV6283ZtpVeEQAvjoD88Tekmn//OL3uohzrt3IQLXSeWL7R7SC5VXj33xj4fJ65Q1q0f+utulupLRwixw9u15anV6jWabXtoIdUYtM2xd3uqnUWWCfKfVm66VXxzOPE3vnt8K0sHpZnPdul+2fQZ6ejs9lecMJWv/WIpJH1nqQps8DGJW8pSG587gZ57BkUP+Bx0L587C22+85nE550/Ll+pAmTkmhwGBzvS8Z5+uOoSrmTlen6xpXSGTUmL5njMw58P3MVSuoHk7e6/SI1PdV5RxfgvSdJyo+SOscpy9+YoaUb7LG8pJLtarTPkbLvKjnrCvCmrLlmhU4Fiww7fZ9UJkP6oqOU3/AFa6OdhSNtQuv3r6rh/UmLAqFHTsfrc9Z9s2xiM71+wx99uf3vJJX07G0Quuv0E98xA4y8o1BXSfW2vkEuwe2wPD5u3UvJKntxrI0t1nUDwuGrO3ui9d60zravVdk9bjwJlrGHNPIzzZtqZX6/RWoA+51zJzPM75oOeKQiDl98lDeAXOBThoO6fIKfb3skVBdslDLWpfGfHDUCt7E9phZvAcD1CA609vGYWAZSOAM46/w1q2nuTYqLzbACIjBBAdiTK5JhTXGAQUIYD00o1w+vYxbjd76uQJvPBYP7S4rQ12/bsV9Rs1Qd8HH8XXH7+Hixcu4N3PpqB2/QaY+PYbSDqwD7mmXDz/6gj0uqcPTp08gVFDn0VGhqUE3shx76N5Qmts3bgBkz+eiJKly+B40gHUbdQM7342RTNYq1GjBgY89jh+WbAQuTk5+HDyDNSsUw9XLl3CmGEvIeVEMkqXKIZh4z5EvYZNsHDuLBw/uBtTv/kas+fMwwfvjUdkZCSKFS+OafOX4on778KIce+jQeOmAICB9/XAqHc/Qr2GTVy2/fXHE3Hq5HFkXknDoUOHMGTUOOz+dysSN/yJ4mXK47PpPyM6OhqdOnXCa2+NQ6kyZfBs//vw/cI/UKJkKbS5ox3eHTcWFRq1wuJf52DWtCnIzclGkxYtMWrCR4iMjMSCOT/huy8/Qdly5VG9Vh1ExwR2IgqzBE5euoFEN+MiBFyrVGjRkwvtLsS4/6u8yj62WtdnApT+J6X6MbHl+FVun+dpTgs1Jy86noj503NspI9XHrLf9rVcoq/CK1Uj2A0gn6V66CVheOuespyec7msQOj12YaAb4PISCeTj+LRQc9i/sq/cezIYSxdMB8zfl2O194ah++++BhTP/sIrdq2x6wlazB1zu/4eMJo3EhPR+n4eHwz6zfMWfYX3v9qGv43eoR9nQf27sLrY9/F3JUbkXLiOLZv3eSwzXPXHAOn+Ph4zFn2Fx58bBBmfvMFAOCrj99DgybNMH/l33j33Xfx1ivPu7T90/ffw9c//oJ5f2zAp9/9DAC4v//jWDRvFgAg+WgSsrOyVYNm++s/fgxLlizBwoULMWrIs7jtjvbYuWsXYuPisH61Y49ipSrV8OQLQzF+5Gv4fsoXqFG3Hrp3746jhw9ixe+/YeZvyzF3xXpERkRi6W/zcP7sGXz98XuY+dtyfDPrNxw97H+6h0sax5/eXyXOz3hKrWKHp5gkv/v68mNOC3d2pfhWatVbge5EDbMe52C3gHx1x8Q1QdpyeHxp/J15iShf3DXR5a6j1oNpsyol7bcBoGhsFOKiIz3WsNWrctXqqNuwMQCgdr0GaN2uA4QQqNugEVJTTuDs6VSsXbkM31sD2uysTKSeOolipcvivbdfx8G9uxEZGYnjR/MCuCbNW6J8xcoAgPqNmiA15QRubXW7/fEzVzJRrlheKbd777sPVwE0bNYcq5cvBgBs37oJH3/zPQCgc+fOuHzpIq5dtdRltu2dElq3wej/vojuve9Fl7vuAQB0690XUyZ9gFdHvYMFc35EnwfdVh5Eu45dER0djaZNm8JkNqFtx64AYH/9zu7v/zj+WLwQ836Yjrkr1sEsJTb//Rf279qJR3tbZuLMzMxE6fiy2L19GxJub4fSZSwz5nW/534cP5rk4RPRphbvTlp9WHVZdxWivJ05ULUtfqxiyrqj+HHTcezTKBOXePwS+ngooajVJneVLNQkeOiN1uLP9OfOPNXbDxXhFTiHSRBEKkJlBAQRGcaooBmAQ+pAhIhATIylPrKIiEBubi4iIiPx8ZTvUaN2XftyhWOi8NHE8SgTXw7z/tgAs9mMVnUqqK8zMhImD6VNY2NjgRwgMiISplxrWopKj4/zpef/ffI51qz/G+tX/4EHe7TH3BXrUbJUabRp3xFr/1iKPxYvwM+L/3S7bdvrjYiIQFRUtH0bEREReW1RyMi4gbNnLOMsbqSn49j5dEgJ3POfhzF0hGNqzJrlSwy/XF4Q9/h7U72faMaI9DNlVS4AuHwjxz73xOkr+nLajfwtBVN6luv7+dWfjidpge5EDatUDXPBrdJGBdSF68Ed1EBE6vK7QMYdHTpj1vQp9su8+/dYLmtfv3oV8eXKIyIiAot/mQOTyfdASC0l7dbWd2DJb/MAAKvXrEHJ0mVQtJjjjIPJx46iWYsEvDjsTZQsXQZnUi1l2+7v/zj+N3oEGje7FSVKlXJZtzNv6jB/+u5Y9Lq3H14YNhL/98ZQpGfnonXbDli1ZBHSLlgGuF+5dAmpKSfQtEVLJG7cgMuXLiInJwcrFy/QvR01R86n66p2ld9XmX29svfnQf8mWBv12x7Nx4ya9TZUZKv8/pwn5NIacG+UsAqc+zavFOwmEFEY6f/tJkz/2/2kNRQeBg8djtzcHPTr1hb3d7kdX344AQDw4MCn8Pv8nzGgTzccP5aEQoWLeFiTOrOUqjNjPv/qCOzbtR39urXFq8PewPhPvnJZZvzoN/FA1ztwf5fb0bL1HajfyJLL3KhZcxQpVgz3PviIrjYcOX/doWTfJY1qCIkb/8bendvx5AuvoNd9DyI6OgYL5vyE2vUa4MXho/D8o/ejX7e2ePbR+3Dh3FmULV8Bz706Ao/17Y5n+9+Lhk1v0dUefwPfyX8ZVx1r3SH1aldLDQjCnpy+1fNCbrgtkxfguHn2Fu8HFIY7UVArUSQkJMjExESvnvPDpuN4e4H2mRmFriFd6uIzjRw3okCqFV8Ea4Z19Pp5QohtUsoE41tUcKntt/fv34+GDRtqPmeXIsdZOXiocExU0GZCM7INzaqUBGCZmdTbUnGVShZCfNFYpF7OUL3Ufu7MaTz14D1YuHYLIiIKfj/Y2RNH8cyivEC0UHSk3zP7udOlQTmsPuBfb+/A26tj5kbLLMDv9G2M0Qv3+rSe5Im9VCtS9LmlEhbtdF96tFrpwjhx8YbqY892qKV7pr38pvWa/TGgTTX8uMk1J19t297Su88u+L80L2w+yhnBiIio4LiRlYvz1zINn43w9/mzMaBPV7z8+lshETQHg9FBeQHtZ6R8FlaDA3N11muk0HPoTOhOZEBEN49Xnh6A1JPH7X9HR0bghddHo23HLl6vK/VyBorERKo+dk+/h3FPv4cd7lsw5yfMmjbZ4b7mCa3x5oQPvd52fgj0gP5/jvjfmWbUoMe0AA3OY9ST/8IqcGbhhfC1fO/NN/00FRDcr/hNSpnvkxQEy6dTf3T4291ldj0On7uue9l7H3oU9z70qM/bCiQpZchXvvp+Y7LPz9WanETPz8LdMgU13TZQrusYNBpovL5DREQBExcXh7S0NK8P8MHOby4obQgHUkrk3riK45cDM7Nsfjly3vgZU/X8LI6n+X7iFW62JmvPFJlfwqrHmYiICpYqVaogJSUF58+rVy04e8mS+7v/WiH77XCSkxaNi+mhHTD6S0Li+OUcfL7ZMei5yTpLVfn7Fny7vuBW/QnXikQMnImI3AjlBAMhRE8AkwBEApgqpZzo9PgnADpZ/ywMoJyUsqT1MROA3dbHTkgp+/jShujoaNSsWVPz8buso+7/Gt4Rz8xc68smCrTXe9bH+8s9VwEgCjf/9/u+YDchIMIqcObZKxGRhRAiEsCXALoBSAGwVQixSEppP5pJKV9VLP8ygBaKVWRIKZvnV3vv/GBtfm2KCggesslbRlen8QVznImIwlMrAElSyqNSymwAswH0dbN8fwA/50vLiIhCFANnIqLwVBmActqvFOt9LoQQ1QHUBLBGcXecECJRCLFJCHFv4JoZ3t5ffjDYTSi4QqDLOdDFYH73MPkJFTxhlapxk1Q7IiLSQ22PqBWqPAxgvpRSOWNENSllqhCiFoA1QojdUkqXOY6FEIMBDAaAatWq+dtmogJFhPQoBwoE9jgTEYWnFABVFX9XAaDVvfUwnNI0pJSp1v+PAlgLx/xn5XJTpJQJUsqEsmXL+ttmogLFzMFT5CSsAmd+v4nIaCE8ccdWAHWFEDWFEDGwBMeLnBcSQtQHUArARsV9pYQQsdbb8QDaAgjPIfIUNKEwIcqMf5KD3QQqYMIqVYOIiCyklLlCiJcArIClHN00KeVeIcQ7ABKllLYguj+A2dJxhpKGAL4RQphh6WCZqKzGQUR0s2LgTETkRpIXUx4XNFLKpQCWOt032unvsSrP+wdA04A2jm56OaaC3+NM5CysUjWIiIiIiAKFgTMRERERkQ4MnImIiIiIdGDgTERERESkAwNnIiIiIiIdGDgTEREREenAwJmIiIiISIewCpxDd4IvIiIiIirowipwJiIiIiIKFAbOREREREQ6GBI4CyF6CiEOCiGShBAjVB5/QghxXgixw/rvaSO2S0RERESUX6L8XYEQIhLAlwC6AUgBsFUIsUhKuc9p0TlSypf83R4RERERUTAY0ePcCkCSlPKolDIbwGwAfQ1YLxERERFRgWFE4FwZwEnF3ynW+5w9IITYJYSYL4SoasB2iYiIiIjyjRGBs1oROOn09+8AakgpmwFYBWCm6oqEGCyESBRCJJ4/f96AphERERERGcOIwDkFgLIHuQqAVOUCUso0KWWW9c9vAbRUW5GUcoqUMkFKmVC2bFmvGyKdw3UiIiIiIoMYEThvBVBXCFFTCBED4GEAi5QLCCEqKv7sA2C/AdslIiI3/Kl4JIQYKIQ4bP03MH9bTkRUMPldVUNKmSuEeAnACgCRAKZJKfcKId4BkCilXARgiBCiD4BcABcBPOHvdtVw5kAiIgt/Kh4JIUoDGAMgAZbUu23W517Kh6YTERVYfgfOACClXApgqdN9oxW3RwIYacS2iIhIF3vFIwAQQtgqHjkHzmp6AFgppbxofe5KAD0B/BygthIRhQTOHEhEFJ78qXik97kc1E1ENxUGzkRE4cmfikd6nmu5089B3UREoSSsAmdW1SAisvOn4pHH5xIR3YzCKnAmIiI7fyoerQDQXQhRSghRCkB3631ERDc1QwYHEhFRweJPxSMp5UUhxDhYgm8AeMc2UJCI6GYWVoEzy9EREeXxp+KRlHIagGkBbSARUYgJq1QNM5OciYiIiChAwipwXrH3bLCbQERERERhKqwCZyIiIiKiQGHgTERERESkAwNnIiIiIiIdGDgTEREREenAwJmIiIiISAcGzkREREREOjBwJiIiIiLSgYEzEREREZEODJyJiIiIiHRg4ExEREREpAMDZyIiIiIiHRg4ExERERHpwMCZiIiIiEgHBs5ERGFKCNFTCHFQCJEkhBih8vhrQoh9QohdQojVQojqisdMQogd1n+L8rflREQFU1SwG0BERMYTQkQC+BJANwApALYKIRZJKfcpFtsOIEFKeUMI8TyA9wE8ZH0sQ0rZPF8bTURUwLHHmYgoPLUCkCSlPCqlzAYwG0Bf5QJSyj+llDesf24CUCWf20hEFFIYOBMRhafKAE4q/k6x3qflKQDLFH/HCSEShRCbhBD3BqKBREShhqkaREThSajcJ1UXFGIAgAQAdyrurialTBVC1AKwRgixW0p5ROW5gwEMBoBq1ar532oiogKMPc5EROEpBUBVxd9VAKQ6LySE6ApgFIA+Usos2/1SylTr/0cBrAXQQm0jUsopUsoEKWVC2bJljWs9EVEBxMCZiCg8bQVQVwhRUwgRA+BhAA7VMYQQLQB8A0vQfE5xfykhRKz1djyAtgCUgwqJiG5KTNUgIgpDUspcIcRLAFYAiAQwTUq5VwjxDoBEKeUiAB8AKApgnhACAE5IKfsAaAjgGyGEGZYOlolO1TiIiG5KDJyJiMKUlHIpgKVO941W3O6q8bx/ADQNbOuIiEIPUzWIiIiIiHRg4ExEREREpAMDZyIiIiIiHRg4ExERERHpwMCZiIiIiEgHBs5ERERERDoYEjgLIXoKIQ4KIZKEECNUHo8VQsyxPr5ZCFHDiO0SEREREeUXvwNnIUQkgC8B3AWgEYD+QohGTos9BeCSlLIOgE8A/M/f7RIRUWjLNZmD3QQiIq8Y0ePcCkCSlPKolDIbwGwAfZ2W6QtgpvX2fABdhHWaKiIiujmt2Hs22E0gIvKKEYFzZQAnFX+nWO9TXUZKmQvgCoAyBmybiIhCVK6ZPc5EFFqMCJzVeo6lD8tACDFYCJEohEg8f/68AU0jIiIiIjKGEYFzCoCqir+rAEjVWkYIEQWgBICLziuSUk6RUiZIKRPKli1rQNOIiIiIiIxhROC8FUBdIURNIUQMgIcBLHJaZhGAgdbb/QCskVK69DgTEdHNg0NdiCjURPm7AillrhDiJQArAEQCmCal3CuEeAdAopRyEYDvAPwghEiCpaf5YX+3S0REoU2Ys1EWl4LdDCIi3fwOnAFASrkUwFKn+0YrbmcC+I8R2yIiovBQ6tIebI17MdjNIKIwkimjAQwI2PoNCZyJiIi8lV6kKt7MeSrYzSCiMGJCREAnC2HgTEQUpoQQPQFMgiWNbqqUcqLT47EAvgfQEkAagIeklMnWx0bCMnmVCcAQKeUKo9uXFVcWs0xdjF4tEd3kAhk4GzLlNhERFSz+zOpqXe5hAI0B9ATwlXV9REQ3NQbOREThyZ9ZXfsCmC2lzJJSHgOQZF0fEdFNjYEzEVF48mdWVz3P9dve1CtGr5KIKKAYOBMRhSd/ZnXVNdsr4N+Mr1k5nHKbiEILA2ciovDkz6yuep4LwL8ZXzn/CRGFGgbOREThyZ9ZXRcBeFgIESuEqAmgLoAtRjcwgpEzEYUYlqMjIgpD/szqal1uLoB9AHIBvCilNBndxtgo9t0QUWhh4ExEFKb8mdVVSjkBwIRAtu+BllXw1dojgdwEEZGheLpPRERBERPJQxARhRbutYiIiIiIdGDgTERERESkAwNnIiIKChbVIKJQw8CZiIiIiEgHBs5ERBQUgl3ORBRiGDgTEVFQMGwmolDDwJmIiIKCHc5EFGoYOBMRUVAI9jkTUYhh4ExEREHBHmciCjUMnImIKCgYNxNRqGHgTEREwcHImYhCDANnIiIKCuY4E1GoYeBMRERERKQDA2ciIgoKDg4kolDDwJmIiIKCcTMRhRoGzkREYUYIUVoIsVIIcdj6fymVZZoLITYKIfYKIXYJIR5SPDZDCHFMCLHD+q95gNoZiNUSEQUMA2ciovAzAsBqKWVdAKutfzu7AeBxKWVjAD0BfCqEKKl4fLiUsrn1345ANJJhMxGFGgbOREThpy+AmdbbMwHc67yAlPKQlPKw9XYqgHMAyuZbC8EcZyIKPQyciYjCT3kp5WkAsP5fzt3CQohWAGIAHFHcPcGawvGJECI2EI1kOToiCjVRwW4AERF5TwixCkAFlYdGebmeigB+ADBQSmm23j0SwBlYgukpAN4A8I7G8wcDGAwA1apV82bTzNUgopDDwJmIKARJKbtqPSaEOCuEqCilPG0NjM9pLFccwBIAb0kpNynWfdp6M0sIMR3AMDftmAJLcI2EhATpzWtgqgYRhRqmahARhZ9FAAZabw8EsNB5ASFEDIDfAHwvpZzn9FhF6/8ClvzoPYFoJONmIgo1DJyJiMLPRADdhBCHAXSz/g0hRIIQYqp1mQcBdADwhErZuZ+EELsB7AYQD2B8IBrJcnREFGqYqkFEFGaklGkAuqjcnwjgaevtHwH8qPH8zgFtoFUE42YiCjHscSYioqBgVQ0iCjV+Bc56ZqeyLmdSXApc5M82iYiIiIiCwd8eZz2zUwFAhmIGqj5+bpOIiMIAU5yJKNT4Gzh7nJ2KiIiIiCgc+Bs4652dKk4IkSiE2CSEYHBNRERERCHHY1UNg2anqialTBVC1AKwRgixW0p5xHkhv2agIiKikMJUDSIKNR4DZyNmp5JSplr/PyqEWAugBQCXwNmfGaiIiCi0sKoGEYUaf1M19MxOVUoIEWu9HQ+gLYB9fm6XiIhCXHQkA2ciCi3+Bs56ZqdqCCBRCLETwJ8AJkopGTgTEd3kOHMgEYUav2YO1Dk71T8AmvqzHSIiIiKiYOPMgUREREREOjBwJiIiIiLSgYEzEREREZEODJyJiIiIiHRg4ExEREREpAMDZyIiIiIiHRg4ExGFGSFEaSHESiHEYev/pTSWMwkhdlj/LVLcX1MIsdn6/DlCiJj8az0RUcHFwJmIKPyMALBaSlkXwGrr32oypJTNrf/6KO7/H4BPrM+/BOCpwDaXiCg0MHAmIgo/fQHMtN6eCeBevU8Ulun8OgOY78vziYjCGQNnIqLwU15KeRoArP+X01guTgiRKITYJISwBcdlAFyWUuZa/04BUFlrQ0KIwdZ1JJ4/f96o9hMRFUh+TblNRETBIYRYBaCCykOjvFhNNSllqhCiFoA1QojdAK6qLCe1ViClnAJgCgAkJCRoLkdEFA4YOBMRhSApZVetx4QQZ4UQFaWUp4UQFQGc01hHqvX/o0KItQBaAPgFQEkhRJS117kKgFTDXwARUQhiqgYRUfhZBGCg9fZAAAudFxBClBJCxFpvxwNoC2CflFIC+BNAP3fPJyK6GTFwJiIKPxMBdBNCHAbQzfo3hBAJQoip1mUaAkgUQuyEJVCeKKXcZ33sDQCvCSGSYMl5/i5fW09EVEAxVYOIKMxIKdMAdFG5PxHA09bb/wBoqvH8owBaBbKNREShiD3ORERulCgUHewmEBFRAcHAmYjIjeplCge7CUQ3jZgohiVUsIXVN7RT/bLBbgIRERH5qH2d+GA3wWe9mlYMdhMIQPu6gf0OhVXgbJnwioiIiGz6Nq8U7CboVjQudIde3cnOOxd1yhXN920+075WQNcfVoEzERFRoE16uHmwm+CVlzvXDXYTdDOi+ytY6R753XX3VLua+bxFAsIscA6ls2oiIgpNfZtrzkDulec71jZkPZ4Eo9fPV0ZcOW5YoZgBLfFefl/1vrVaKdX7ixWgXvtwzAMIq8D5buYXEZHBzJKzSFN46t+qarCb4CIcA6381rlBOQxoUy3YzQhbYRU4R0eG1cshIqIwFuwgsVyxuCC3wFXZ4rH+ryRI452C/XkqFZTPVgjgthrqPeMAEF/UgM87n4V1pMkRrkREN4/JA1oGuwnkp8faVPd/JTf5VaLqZYp4/ZzSRWI8LjOkcx2v1ysg8NjtNQAA7/dr5vL4LVVKeL3OYAu7wLla6byaqxI394+HiPwnClQ/ErnTtWG5YDeBPPisfwu3j1cp5X/d9EAd+e+s575qhq8d3dOeSPDtiSo61CvrU4ArdZxsRET49gL73FIJyRN74cGE/EkNCvQFh7ALnNvUKh3sJhARURCxMqnxlg5p7/Nzd47pbr/d5xbfBvE/0z74FSRmDgrMLPSdG5T36Xlq3/OO9coiKoTSVkPxtxo67y4REYW9Bn5URGAtf+MkT+zl8HejSsV9XpcR09YbVckkkIz4+kVHBuc77Km/uVRh/z9DNRPua4ooH3uygyWsA+dQTnNqXZM950Z5+LaCN3KciNTdUbvgzBzXtWF5dPBweT6UVS3tPi3i04cKXr3qRhWLo2yx4A0o69xAOx3IiLSu1a919HsdgWZkfFK+eBzevb+p5uOv96xv2LaMEtaBcyi7pWrJYDeBAuj2WmWC3QTSiWMl8legerYKoiKx/tXbnffc7X49v5N1pjut9/zeFr718jaqWNzvtrnjKTwNZAnJaU/cpvmYEMFPPdC7/R2ju3m1Xom8EwOjAuemlT0PDCwcHWnItozEwJkoCJ5qVxOj7m5oyLrKG1G+iaiAePbO2hjXt3Gwm2GIu5tWcPt4Fz8GM8577nbcVsOYAEYIgaJ+BvFKS4e296ptRs+Al19Xmw+O7+lyX8147ytauOOcMmOUkoU9V9EIpMkDWmL6k9aTkBDrm2DgTCHJm2Ax2D0AaqKjIvBMh1qIi/b/J9ikUuiV8yHSEhMVgUda55Uk++IR91UY1HgbOJUMUC+3Vjv63FIJQzrXQf3yxs1w95+WVXQvW65YLB64tQqKxVle97Du9R0qUuW3J9vWcPj7jZ4NgtMQL8VGOfaGNq5UPF9q8MQXjcXyV3wfrKkmvw+TPZtUcKnh7M13OJjCLnAuE4LFtNXU8KEOYzh5tkMtt48neNGb0aKqdvH1YDMiVy/ETtYLnCqlCrl9PBTL0QkhSgshVgohDlv/d/kRCCE6CSF2KP5lCiHutT42QwhxTPFYviS72g6ktnc8oXopr95/5ZL3eZFm8N1A7cvv3nqxk+dptCuXKoTXutc3dDBjUS+mWf7+qVb46MFbEBMVgeSJvfBI68DPMrd0SHsM78d9/pkAACAASURBVKEvX/X5jrXdnlR4etvevS8vZ7Zl9fzZ/x8afxfqlMufqb7b1imDBhXUB2uG3t4qT6gcy8IucH6la91gNwHxRX2/BLL45XZ49s5amj0gZXQUKderY33fBr14c0AKlHIaAef9t7q2TWsn+6jKweJzDzVGjVLcepD7b7eCN/AhVBWO0Z8LV7lkXrAcpvnmIwCsllLWBbDa+rcDKeWfUsrmUsrmADoDuAHgD8Uiw22PSyl35EurrSIiBH5/qR2mPWlcQOsrT4HIoLaOaQbDe+T1lsZGOR5iY6K0D7m3VvNvXIta7/Z/u9VD90aupc6CcTLYqFJxvNhJf31hrf22nuCqQom8WfPy65XaPtuRd2mn4BXz4uTGX95WMnmla72AtEPXuaEXH9KrAWqnN8IucFZeOrmjdsE6IGoVfi+iOOA3qVwCI+9qqPk9MjJovbuJbzMr9m8V+N4JT+IMGDDQSmWAQ6C/M72aVcTUxxPQopqlF8SbHWnvZr59XlonGUaa+rhxBfzzW6j0cnipL4CZ1tszAdzrYfl+AJZJKW8EtFVeaFqlBIrH5R38a5TJSyWYrzLwTLlvVB6s65UvGpgG6uC8rxzaRbtjx59yb1pe7lIXU0L4t6nkTed8MCtqdW1UHr887/r97FS/LBa91M7Qbbl7SwZ4OQNjMwNn8AtkeqSe9MaKJQI73XjYBc5KzaroP4NvVNG4nZbWmZ4yQO6m6AVQu8TWrm5eSaZh3fPOsF7tFvyzLVuwVzyfzp57NPatOLxNhBe/YiPqjdrMGdzGfrtn4wpIntgLXz5yK7oqPntvdvBar8PTjE/KnUhMgArjd1Xp1coPvtY8VY7mjvbwngSz9JUfykspTwOA9X9Po9AeBvCz030ThBC7hBCfCCE03wQhxGAhRKIQIvH8+fP+tdoNZWDpfPn96XY1HabzVf4knrvTc+pEoLSuVcbQwV0VimsHBP4GKwX5BLJp5RIOn6mnHnPbFduX3cygVzO+SL7+th9tXV3XwEF/qvh0bVge91vzhCMVtZHv8XHSGS3uWrj45XY49l5gBjTqsfjldgFPmQnrwFlLK5X8WCMHh2gNslDu2O5q4n60dTFFT0tzRY6uv+WLjFA0NgqNKxXHRw/mT43PYd39S2dQvu/P3uk+d9rTjEve9Ky2VqQA3FHHu55stbNqXw+Mtt5tAHinb2M8frt3PREFVcvqpfDe/c08L6iiTrmi2DW2O3594Q6Pvf5GpkcZSQixSgixR+VfXy/XUxFAUwArFHePBNAAwG0ASgN4Q+v5UsopUsoEKWVC2bKBq3nsEDg5/RhKF41BdGSEz7+RxpWKo4VGqkR3P0/c9dKTPlGqSAwq+dib9uF/bsnbVgglwi4b2h6/v5zXU6un6XHRkUie2Av/dTp2GFXJyJNg9HjPero1pg5McLhKY3Nvc2MC54B9bwx8v2oYXNVEjV+BsxDiP0KIvUIIsxBCM6IQQvQUQhwUQiQJIVxy7QJF67MYoDNwCPQlPlvvgaez3rZeBF35MeV4ZITAkiHtHXrNtagdjDwNxnJWyIvc1eiIvK+0LYdb2VP7mOLylfL+P17tgG8ea+lVu4yg9R2d+aTr1K6+7rOUr7Nc8Vi81asR5j6rXmN185tdfNxK/qtXvpjD90vP91GpeFw0bq1Wyt5j36l+WZec1IJMStlVStlE5d9CAGetAbEtMD7nZlUPAvhNSpmjWPdpaZEFYDqAwMw1rEN+BHlx0ZH47YW2qo890qoaRvduZMh2BrSpju6NyuOZ9u5P4N2pVNK7/adNv5ZVULec9jHN05WrQArUlTAg7/haLC4Kz3gYdK7XE3fUsN8ed28TrHrtTo/PCeT3uGfjCrijjvbEQbZtd3Ia15T4VlePM3W+52ZykoLmiTtqOFzZDxR/v617ANwPYJ3WAkKISABfArgLQCMA/YUQxuyFPNDaEej9/vozgEL5w9Ja38aRnfHhf25xO5gA8G4a2WIqZ5t6GFmK6KVOdewBvNrAq1u8SKHxRvu68ShZxPL6X+9ZH4WsedDKt0+5g1Z+O+qVL4Yejd1fBdBLmT6gNlhRSzuVHZ/ypMrXEfjK3msBgZioCNX8bsAyi5ONu6swtfLhrB6wfKbOGlYsjjmD22Bsn0aoXTYvEPAmGFF7K2+vXSZfB+8E2CIAA623BwJY6GbZ/nBK01AE3QKW/Og9AWijioKXMCCEMKzqRIlC0ZjyeAJK+3EVw593yJYW6E36WqB99eitKKeSguIujnfXfGXPOpC3D33NwDTHsX0a21NwHmtTHXWcTkjcfUazB7fxezZbvZ/frGdaY+WrHTQfjy8ai1jFeKF2deJdYoGeXh4XPTWtstqJn0Ffx7F9GhtaqUaLX4GzlHK/lPKgh8VaAUiSUh6VUmYDmA3LwJWQNVCjx1o5Pamnyhp1yxWDEAL9WlbRlezu73fB+UwTcBwcp5Z7paeMTyGVQXpRkcJtKaGn2usodq94vYVj9AUzHeuXczg5se148+OHpPTcnbXtO9UiHtruqZenpqIsodarcLeGqAiBUopC93reir+Gd8TvL7XLl0GFnijzj7s1Ko+fnm6NJS+3Q+taZVxqqDbRMQuVXsuGGlsjNQgmAugmhDgMoJv1bwghEoQQU20LCSFqAKgK4C+n5/8khNgNYDeAeADj86HNbgVzwFdBvBLh6aesdvXo60dbYuRdDVC7bHDLnc4clHcB4+6m7gc9e7v77qdRCzjYJwu2fVmbWmUw8QHXFLNfX7gD3w/yfGHnsTbV8VYvfSknd9SOR10vaoX/+HRrrHu9E3aO7q77Od767cU78PMzbTwv6MHgDrVUK2Plh/zYG1QGcFLxd4r1voDT2s+q3S+Ea++W1u+suUYuXPFC6kGSWpmspl6OYF07rCO+G+jd6Gjl4L1vHnN87gf9mjnkAinfE1tvufKy3uQB6mkMyoFnyvfPtj61NBRvd196e2cEHAdW2KZdjY7I3x2mr1tTtl3tO1rGizKHvZtVxI7R3fCv07Sqek4iqpcp4vH7aVRlFU81b5WtfatXQ7StE48IN5/nwfE9cWj8XR63qwzCghmQBYqUMk1K2UVKWdf6/0Xr/YlSyqcVyyVLKStLKc1Oz+8spWxqTf0YIKW8Hqi2LnixrdtUCNun7TxoasubXTTTc5w7N9QOsEbn+jerUiIo6V5qkif2crh6ZFOhRByevbO2V50J61/vhD+HdQQAzNBRHnDSw57HvtxZryx2jO6GLaPyPzXM9t1o7GUVk2lP6D/+Ou9ThnWvp3pFUenWaqXQoZ7nMQLj7m3i9XwVUdYURr1pjyUMHPPl/F0rVywOt3tRvcp5XFdFa4+1tymfRvIYOBswAEXtF6p6qDJ6dLYy31VJrUqDlEBjnTOw3dNMf6L9i51q50096kNEZeu5rV6mCLo0dGy3su6n2g67uqK3Ulk/NHliL/wnQftSUX1FzpNt5xIVIVRLvIy/r4n9tlqQHCGEYbW1lZUQ4qLc7wAEhP1L5i7QckeZB+xNnrmvcVjVUirpMoqm39dC/6xKNeOLoGThGJeBIkacRCRP7IVnOtTC6z19G7SprFyi9zcHOH6ftcRGRSImKgJD3Iymd6diCcvO2Ihyh6RP86ol0fsW7V5H23HXORgpVzzOIVXHsqxA0oS7MLaP45TdE+5r6jKt80CVdDp/9Lmlkk/pXhtHdg5KAKlX1dKF7VckO9b3PEV43+b6+sVKFo5BuWK+DXTU2ou5q6JhM7RrPVQtXUi1NKDWldKoCIHODfSPoYhyqvbzUue6uo9D3qRb2lJcPI3HalcnHkO71MX4e5uiSwN907w/2roapj6eYA+2725a0X51wJsqHVFeHnOc647ff2sVhxPre5pVxIwnb8OA1sae+HrDY+DsYQCKHimwXAq0qQIgVWNbho7OVjupblvH9RKvjacaySte6YAto7o4VF4opqPKha+B1NphHTFfpR6kzeeP3Oq6LWk541//eievBtVppQzYZvKK1PjyF1W8/ioag1aeu7M23ry7AZpUdn+G7y6p/49XO+CnZ1rb/1ZWx1A2rXsjy4GrQ714+2vSTHHQeM22z7RBxbydqKdA3durAfY2KG43r+o+91vjPFC1x1TrNbdRyTnX08uhRjXQ10Erv1qNr1dXI1XeLK2yhsptTHviNnzWvwVqxhexL+/ruAHSz/14krzH5j93u8fZ56IiI3T1qHo7rsPbwad6VSxRyOcAUqlWfBFMf+I2fPWo63FBDyOuvARzArKD43vqymMuXSQG61/v7FUKg7daVC2JEXfpmzZ8rbU336Z0kRiX+zrUK4uisVG43ylGaVm9FOY/dzuGuKkPDlg6j17tVg+li8RgyuMJODCup8d2TbivKbo2Ko+46Ej8+3Y3vNOnMeqUK4rkib1QT8d7ZysDqWd/b8t7rluuqMs+PzJCYJDipFcIgY71y/ncIWaE/EjV2AqgrhCiphAiBpZ6oYvyYbuqnHfQyrMb21mibQCZc23n+hWKue7gvPjstAM4y/+1nPLOasQXUT1o17dWE6ikMTtS3+aVUbV0YfuBQc+IcGXJMltqRMUShezpDlpfUtv72aRycYcIRLkTjouOxOAOtVWDGWUVEHcBXL3yxRx6T5U9gspKGS2rl0LyxF5oXKmExxxndzVRveV8NcBI05+4TbMKhrMHbrX2Smu8ZrXPsb2HS4je6NygnMPJlI3z7GpqZj1tOTEyIrfauccHyOtNdqdssVj0sfamfP1oS7zVq6HuaYLJd7avq1anBmA5yUyoUdph9rkO9Szf3dY1jZm4KGmCepqPEALfPp6AlzvX0VWLF3Ddn3tybwvtXryJbiob2I5h3RpVQKcG5TzmDAfCsqHtkTyxV8Bmn9MjNiry/9s78+iqqnOB/74kJJiEQEICJAQTQgBNmBMjAUFBZHTCgalWxFpblYVi+xQf+qxDcbWrDuWVV3VpfbZ1fCjWgRa1z6et1gEcUQYBqyBOVBTrUKf9/jj73Jw7nDskN7kD32+tu3LPPvve7O9+5+z73b2/IeJc72beGRxjVTaZgcEiEnf+8Ejp00Lbfnt6Cxsvm8Y1c8PdYJpry2KmUfWSmyNB35/uDmC0fPZlRflR/0evwm5h2TnKbKB+PPbt+Ppy7jmrle9PqOPcI4ckNVlBZ9DRdHSzRWQX0Ao8JCLrbHuViKwFMMZ8DSzGyRG6CbjbGPNqx4adOG4eQzeJvruS6t2ucy+gU8bWsPqHraw4YXigXyiuce1XMMONsh3cp0fcaX68QVzRWLd0YlDqpFiGRqQCK6F4s19MbejL9aeM4ZxJg9oM53b+uPNb+HGjim9eeEjMvrGYMNgxuEN9zwOuGj7ve7C9FiIZeqEsPWoIA8uLaElyur94Lo1JB/UJ+9X+0BInr2loAZD+1u/L23psknJ4xmLzFdO58btNEbdLDyxrM1oPqW37kea97urstrv3OujXzpy1biDQmT7pp771fPB+OsjJEc6YUJfQzo3SPnoX5fPjqUP4/RmHhp3zc9UAJ/hp+4qZcQUy++nZe72FGgdzQ7If/Gjq0IC/75LJ9dy/eDw/OLyOcYN6BwWlbb1yBg+f15bNoLWut2/lWJemmjLfYikzrDG8aHxt2Llr547iju+Pbfe9EsohtaUx892HcnASC4j54cYK9S89ICEf7dmjq/nrhZMYNyh8gcAt33z9KU386Tz/7BOdRWem4YuXa+eM5JKjGxL2+XZZNL6W2zz3bXuzkTXVlJGTIzRUlfDEBZO47YxDw1beo9Fe18H20KGfWMaYNcCaCO27gZme47XA2o78r/YwsLyIvBzh6jkjOXZkFQvH1QYi759cNgljYMObewP9y4sLeHLZZPr2KAhMoJccfTDn3vli2HufM6meax/dytEjqrj+8e0AAX+7oxr6MX1YJQ8tOYyGyhLueX4XkPzsDiLCdXNH0Vxbymu798Xsf2prTdQ8nt73nW7LcX9rQ4Zy4xj7yU3V3Pb0m5w4ppobn9gRdn5kdU9e2vkRpYX5rJg9nJ8c20j3brn8dPYwlq8JznY1t3kANzwe/h4bLp7CtyFfgFMa+vLa5dPCsm+4xlGkL8aRHreIeLQyrH/PwBdmLNqzcjG1oW+Q24ZrzHtT97gBHi21ZYFrzRspvnL+aLa990lYe6QgoXiIlEjf+7mFZhpwVzH8ViaOGVnFAy/tDhpPYYHzmvzcnEB2mcaqnry3z0k7vHxmA79/+q12jR+CdT++vpyPPvuS+17czTcRrKiOpJ9UOoaIsHhy5O1m9zr0K6Pr50YWC/cS8Mu2EKvi3/me4hq3h2QJyA+5N+44M/EsApce08BlD7wGOAs07nj+tPFdoO0+KyrISyjYyo9r547iV4+9zsp5oxNawYzGlIP78uim95LyXnUVxaxaMIYJQ8qZtfIvAKxaMIantu/ho8++ivraah+3sgWHHpi0VIOJcvlxjRHTtXY1vYsLwvz/E+HSYxojtnfU9Wd8AjuhVxw/LGjnubPJmqSlXlzH9aKCPLatCNjvQe4IfluCoTkG/SI33W242t5tN2RN7yJeu3xaIEWbG/jkHsdjfCbK8dbnKZLh3FrXm9UbdgUCHi4/blhYHxeDobGqhD3//FdQe7ldzS70WZWt6uV8mZ04ppoBZYVsuOSoiP0ALp7VwJzmAYFtqO45zudSZbfQex7QtuJeV1HMwtaasCAtv2jiSCnrIrlqlBXls2rBGMbWlQX8lue1dCynpsu2n87g9mffCso44V4nVT5uAjX2+gldUR7WvyerFowJFHEBGFRRxKXHNDBrRGUg4GLhuFoaq0p4fOsHNNeUsvVdx3AOvdRWLRgTtdBOSfc89n3xdVDbOZPrWXTLcxx5UB+ef2svez/7iltOa9shmOLjnjKwvO2e6JYrfPWNYeaISt7Z9wXgBAVFoldhPvec1cpB/UpovNQpYhfPau9p42p58OXgsAl3O72+opgrjx/GxfdtpKW2jGH9S3hq+z+Yf0hqviyVxBlbV8bK+aPDgoZi4W7NuyuxofeEm6WjM+blZLBo/MCA4ezl6pNHcu8LbzMywcxMsWioKuG/vhN/VpDbzziUBTc9E7XPTQnEfkwaWsFjW9qSApw/dQjn3PZ80Lb9rBHOgs4tp7Vw9/qdzBzeL9CWDJYcOZhzbn8+ae8XjVNba7vk/6SazkwH6+74F3ZxMHdWGs7/GWNLLBGaasr4+UkjGB0SuHX0iEr69CigZWAZ9X2KA1/wkQy4q04YzkGVJYxLwqqAH+Pry2muKWXZjLZVkBObqjl8aIWvuwnAtXNHsvSul6ivKOahJeG5a1fMHsaEweW+gWu9iwvYvmJmmDvE4UMq+N3TbwYVO8nPy4mYa/eIoRVcdmwjJzVVM62xL1vtqullUQz9ePjWExz4y3mj2Pe5syrhnWi3XDk9LPvKiU3V/PdTf/fN3drzgG58/PlXnH/UEK55ZGugPS83J2wyXNhaS0NlSVD5bS8HV5bw1wsn0b/XAeza+3nQudAvBBFhkcdXeMeKmYg47W4ku2sMhE5Vsb5c1p47IezH1+GDKzj3yMGc2lrDZ19+w4Y39walBszJES6YPpQJ9cG+6Q2Vjo779Cjg2eVTAu0/Omooo6p7MTFCUROXppq2HxBuLvRbT2/xdYkCJ+l9aBaF6cP68cDiwxjWvwQR4RS7GtGTbkFjgrbJNx3K2SvhiEjA7zwRfjhxEIcOLAtcU+4P6SF9i/nJsY0Bg3nm8OQUPuosQoPWS4vyO7RCmCzG1ZdzzZyRAffHjvLrU5r4x6dfBo6nNfYLWvjyUt+nmH/vhPLZs0ZUMmvELGqXPQTALYsOYdEtz0UMqla6lkeWTgxbSFty5GB6FxcEFhC7iv3+m8L164nmyD8nQuo2EQkYQ8210f1eexcXBKJ9pzb07VDVKD+KCvJYfda4sPZoRjM4/l/R0pz16N4tIP9VJwznqrWbw1YuI22VTmnoy+YrpseV1ktEAr7mRwztE1fKI3ACZg6K4lu3YvZwrn54C+MGlYdtnbpE2nn4j6MbuGD6UN9diTVnj+PJbXv4bmttkOEciZwc8TWaXdxtxAEJBkRECvSb33Ig97+0mxN9igB4ueqE4Vx07yuMqSmlurQwbDvTjcQG6O0zvrOP8E//FLrQkJ+XE/DVdHHdT05sCp74vLmYD29n1o94c6X/4PBB9OieF+bPqmQ2OTkS9EPMZU7zgIC/63PLp4RVyFx33kR2fNBpaasTYvMV06MGbaWCuooidnzwKeCkCksW3bvlRq4qlwL+dtFkCrvl0bOwGw8vnZg240pn+pR0Z/O7n/h+13aUSFlQunfLTcmPyP3ecO5VmB/Tly2Z3Hhq+NaVa1xWJJjUvKtJxKiFzs+FOy9GEY4BZYVcNy/x3YecHAnsHDyw+DD+tmNP0Pm6iuJAINsv543i6R0fJvw//Pjt6S2BAL/2UF1ayF8umBxX3/ktBzJ7dP+k66nURlP/27TY6Zhyc4SNl00Lq0DZWZNvJPLzcjgtjqwfSmbTMrCM3zz5RlA++EjuS0P79QjKZd/VlBXl86FdeU3HfOL3Lz6MT76I7lOc6Xgz8MSTei0asRav/Pi/Hx/BZ19+06H/3ZWsnDeKRze9H0iMMK2xH1f9cXPMNL+ZiMSb8aGraW5uNuvXr0/1MLqMu9fvZFpjv6hb0oqSLdz93E4G9SmKuCKYLYjIBmNM+xJ8ZyjpPm9/+OmXnbLjl0z+9fU3GJOeRrOSGBvf/ph+Pbu323hOZ154ay+b3vkkZcGVnUG8c/Z+v+KcLkRyB1GUbGWOukUoKSDdjWaInstaySwixfRkC6MPLA1KuLA/kV7OU4qiKIqiKIqSpqjhrCiKoiiKoihxoIazoiiKoiiKosSBGs6KoiiKoiiKEgdqOCuKomQZInKyiLwqIt+KiG+UuIhMF5EtIrJNRJZ52geKyDMi8rqI3CUi6R9VpyiK0gWo4awoipJ9bAROAJ7w6yAiucAqYAbQAMwXkQZ7+mfAtcaYwcBe4HudO1xFUZTMQA1nRVGULMMYs8kYsyVGtxZgmzFmhzHmS+BO4DgREWAysNr2uxU4vvNGqyiKkjmo4awoirJ/0h/Y6TneZdt6Ax8ZY74OaVcURdnvSdsCKBs2bNgjIm+246XlwJ6YvTKXbJZPZctcslm+9spWk+yBeBGRR4F+EU4tN8b8IZ63iNBmorT7jeNM4Ex7+E8RibXSHQm9fjKTbJYNsls+lS2cuObstDWcjTEV7XmdiKzP5jK32Syfypa5ZLN86SqbMWZKB99iF+At4VgN7Mb5wuklInl21dlt9xvHjcCNHRlIun7GyUBly1yyWT6Vrf2oq4aiKMr+yXPAYJtBIx+YB9xvjDHAY8BJtt9CIJ4VbEVRlKxHDWdFUZQsQ0Rmi8guoBV4SETW2fYqEVkLYFeTFwPrgE3A3caYV+1bXAicLyLbcHyeb+5qGRRFUdKRtHXV6AAd2jLMALJZPpUtc8lm+TJONmPMGmBNhPbdwEzP8VpgbYR+O3CybnQVGfcZJ4DKlrlks3wqWzsRZ1dOURRFURRFUZRoqKuGoiiKoiiKosRBVhnOfuVj0xkRGSAij4nIJlsi91zbXiYij9iSt4+ISKltFxFZaWV8WUTGeN5roe3/uogsTJVMoYhIroi8ICIP2uOI5XxFpMAeb7Pnaz3vcZFt3yIi01IjSTgi0ktEVovIZqvD1mzRnYgstdfkRhG5Q0S6Z6ruROQ3IvK+iGz0tCVNTyLSJCKv2NesFJFIKd2UEHTOTr/7HnTOzlTdZdOcbceRnvO2MSYrHkAusB2oA/KBl4CGVI8rjnFXAmPs8x7AVpzytz8Hltn2ZcDP7POZwB9xcq2OBZ6x7WXADvu31D4vTbV8dmznA7cDD9rju4F59vn1wFn2+dnA9fb5POAu+7zB6rMAGGj1nJtquezYbgXOsM/zgV7ZoDucghdvAAd4dHZapuoOmAiMATZ62pKmJ+BZnEA8sa+dkeprM90f6Jyddve9R0adszNMd2TZnG3Hkpbzdsov4iR+wK3AOs/xRcBFqR5XO+T4A3AUsAWotG2VwBb7/AZgvqf/Fnt+PnCDpz2oXwrlqQb+jFPC90F7ge4B8kL1hhPd32qf59l+EqpLb78Uy1ZiJyoJac943dFWVa7M6uJBYFom6w6oDZmAk6Ine26zpz2onz589aFzdprd93YcOmdnoO6ycc62/z/t5u1sctXwKx+bMditktHAM0BfY8w7APZvH9vNT850lf864ALgW3scrZxvQAZ7/mPbP11lqwM+AG6x25o3iUgRWaA7Y8zbwC+At4B3cHSxgezRHSRPT/3t89B2JTrpfG3Ehc7ZGXff65ydubpzSfm8nU2Gc0JlYtMNESkG7gHOM8bsi9Y1QpuJ0p4yRORo4H1jzAZvc4SuJsa5tJPNkoezjfRrY8xo4FOcrSM/MkY+6zd2HM5WXRVQBMyI0DVTdReNRGXJRBnTgYz+3HTOjnou7WSz6JydubqLRZfN29lkOPuVj017RKQbzgR8mzHmXtv8nohU2vOVwPu23U/OdJR/PHCsiPwduBNn6+86bDlf28c7zoAM9nxP4EPSUzZwxrXLGPOMPV6NMylng+6mAG8YYz4wxnwF3AuMI3t0B8nT0y77PLRdiU46XxtR0Tk7Y+97nbMzV3cuKZ+3s8lwjlg+NsVjiomN4rwZ2GSMucZz6n6cUrcQXPL2fuBUG0E6FvjYblesA6aKSKn95TnVtqUMY8xFxphqY0wtjj7+1xjzHfzL+XplPsn2N7Z9no0CHggMxnHqTynGmHeBnSIy1DYdCbxGFugOZ7tvrIgU2mvUlS0rdGdJip7suU9EZKz9rE5FS1THg87ZaXbf65wNZKju2D/mbEiHeTtVDt+d8cCJqtyKEwW6PNXjiXPMh+FsD7wMvGgfM3F8jf4MvG7/IvAGNQAAAPBJREFUltn+AqyyMr4CNHve63Rgm30sSrVsIXIeQVuEdh3OjbgN+B+gwLZ3t8fb7Pk6z+uXW5m3kEYZC4BRwHqrv/twonazQnfAZcBmYCPwO5wo64zUHXAHjt/fVzgrDd9Lpp6AZvs5bQd+RUjwkT589aJzdprd956x6ZydYbrLpjnbjiMt522tHKgoiqIoiqIocZBNrhqKoiiKoiiK0mmo4awoiqIoiqIocaCGs6IoiqIoiqLEgRrOiqIoiqIoihIHajgriqIoiqIoShyo4awoiqIoiqIocaCGs6IoiqIoiqLEgRrOiqIoiqIoihIH/w9U4mldEX7nnAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "noise_fl = np.array([(2 * np.random.random() - 1) for a in range(10000)])\n", "df['sine_noisy'] = np.add(noise_fl, 0.1*df['sine'])\n", "\n", "df['sin_noisy_mixed'] = np.multiply(df.sine_noisy, df.sine)\n", "df['mean_noisy_mixed'] = df['sin_noisy_mixed'].mean()\n", "\n", "fig, axes = plt.subplots(nrows=1, ncols=2)\n", "fig.set_size_inches(12,4)\n", "\n", "df['sine_noisy'].plot(ax=axes[0])\n", "df[['sin_noisy_mixed', 'mean_noisy_mixed']].plot(ax=axes[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It doesn't look like much at the prior altitude, but it's definitely the signal we're looking for. That's because the lock-in output scales with the amplitude of both the input signal and the reference waveform:\n", "\n", "$$U_{out}=\\frac{1}{2}V_{sig}V_{ref}cos(\\theta)$$\n", "\n", "As a result, the lock-in amp has a small (but meaningful) amplitude:" ] }, { "cell_type": "code", "execution_count": 210, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 210, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df['mean_noisy_mixed'].plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Great! We can pull really weak signals out of seemingly endless noise. So, why haven't we used this technology to revolutionize all communications with infite signal-to-noise ratio? \n", "\n", "Like all real systems, there's a tradeoff, and for a lock-in amplifier, that tradeoff is *time*. Lock-in amps rely on a persistent periodic signal - without one, there isn't anything to lock on to! That's the catch of multiplying two signals of identical frequencies together: it takes time for that DC offset component to form. \n", "\n", "A second tradeoff of the averaging method becomes obvious when you consider how to implement the averaging in a practical manner. Since we're talking about this in the context of electronics: one of the simplest ways to average, electronically, is to just filter by frequency, and it doesn't get much simpler than a single pole lowpass filter for a nice gentle average. The result looks pretty good when applied to the product of two sine waves:" ] }, { "cell_type": "code", "execution_count": 184, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 184, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def lowpass(x, alpha=0.001):\n", " data = [x[0]]\n", " for a in x[1:]:\n", " data.append(data[-1] + (alpha*(a-data[-1])))\n", " return np.array(data)\n", "\n", "df['sin_mixed_lp'] = lowpass(df.sin_mixed)\n", "df['sin_mixed_lp'].plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "...but it starts to break down when you filter the noisy signals, which can contain large fluctuations that aren't necessarily real:" ] }, { "cell_type": "code", "execution_count": 211, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 211, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df['sin_noisy_mixed_lp'] = lowpass(df.sin_noisy_mixed)\n", "df['sin_noisy_mixed_lp'].plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can clean get rid of some of that statistical noise junk by rerunning the filter, of course, but that takes time, and also robs the lock-in of a bit of responsiveness. " ] }, { "cell_type": "code", "execution_count": 212, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 212, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df['sin_noisy_mixed_lp2'] = lowpass(df.sin_noisy_mixed_lp)\n", "df['sin_noisy_mixed_lp2'].plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On top of all this, lock-in amps are highly sensitive to phase differences between reference and signal tones. Take a look at the plots below, where our noisy signal is mixed with waves 45 and 90 degrees offset from it." ] }, { "cell_type": "code", "execution_count": 247, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 247, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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AcJdJEF4jD2fdPHXKlfVQQprh+JEIP4PF2JTGni481bUZdhqF86nZvP2/Y/hP24gQgrMpWQCE+aqW75hyqlIu3HHWzEXkTqZWVb7TE+gZKBVjiUQikUgk5RIVf41uc/4g28SF4dCF60xccdhQgc7NyZ7WjT0qnKP4sU5q6FVAfTeLvrHd/A3H/UMb8vaDavGbyxl5FmNNeWNwaxb/S40N+2xU+wrJ4WCnoVgr+GL7Wb77Kx6A7IJidp5SC4j0aXkXABN0Ja0BzqZkGXyqAeb9epI5m08w5PPdFVrTGkIIlu2JJ9UG2TSqm1qpGAd4BnAu/RxaIUsiSiQSiUQiKZ0RC/dw8XquWdsvh81zCOQUFOHmWH46vaOz1AIyy/ddICu/iOu6QiALR3fg5xe68fML3XjrgVACdQqzvUZDv9aqcvrZY0Zl9/f/68UPz3TmwxFh1HG25+x7gxjXI5B+rRsSP2cwd3lUPItEq0bmFuhjF9N5f8sJAIaG++jeXzFjvtuHEIJ+H+2g70d/AqpC+9kfZwzXRider/C6ppxNyebNX47x0vJDAJxKzsR/2kbWHkws58qaR+1UjD0CyC3K5UqOzNEnkUgkEomkdPRuEnoejfAzO7+alU9WXhGuTuXnI6jjbMxz/OX2M+w+o1pmB7ZpRLifl6EgyCVdlbolf8fjW9eV+DmDebCdMfdz8wbudA+qz8gIP47OGnDD1fQA1ky4x+z80a/3Go4DGxjdP/48mcIn29QgQ71Cn1vCF/nGy1+rvtkX0lQXkv4f7wTglVVHKuRTXZOolYpxM89mAJzPqHweZImkuhg3bhyxsbZLm7NkyRJefPFFm81XGvv378fOzo41a9YY2uzs7AgPDyc8PJwHH3zwptdISkpixIgRNz0PQO/evSmZb9cUf39/rl69apO1JDUTuddK507ca6lZBWbnkcPamJ1HvLuNM1ey8HQxL+5RHmUV4ainS7VmzTfY1rhXQKHX86ku+waomSyy8s1LjWfmlV0yvTSy8lUF21rQ4aJdtcv1tVYqxgEeak3w02mnyxkpkdQcFi1aREhISPkDaxDFxcW89tprFlHrLi4uHD58mMOHD7N+/fqbXsfHx8dMGZBIbga510rnTttrl9JzzdKoAdjbWao+2QXFeFVSMV4VVbqbwLM9VD3lk1HhlZrzRvGxkqotolldAKYOaGn1ml4f/snu0+oPl84B9QztJZVlaxQUac2C9TJyVQt0YbHgx3/O42SvMVT/C6jvxrAv/2LBn2c5mJDG6+uOWi2RXVOo+M+MGkRDt4b4uPlwOOUwoxld3eJIajKbp8Hlo7ads1FbuH9OmUOys7N55JFHSExMpLi4mJkzZ7JgwQLmzp1LREQE7u7uTJw4kQ0bNuDi4sIvv/xCw4YNrc41ZswYnJ2dOXbsGMnJycybN48hQ4YAqvVn4MCBnD17lmHDhvHBBx8AMGHCBPbv309ubi4jRozg7bffBmDatGmsX78ee3t7+vfvz9y5c0lJSWH8+PEkJKglST/55BO6desGwOeff87w4cPZv3//DX9c/v7+PP7442zfvp3CwkK+/vprpk+fzpkzZ5g6dSrjx48nPj6eIUOGEBMTw7x584iJieHbb7/l6NGjPPbYY+zbp/rGvfTSSxw9epSioiJmzZrF0KFDyc3NZezYscTGxtK6dWtyc3PLFwqIj49n4MCBdO7cmUOHDhEcHMyyZctwdbUeZS4pB7nX5F4rhercawmpOWbnK5/rAsD/3ReMi6Md7248bhx7zXxsRZnzcFuLttFdmtExoB6hPpb5kKsCfdW7jv512R+vZrRYrnuv43oE8OFW6xXzftb5Wo/tFkCYryff7IojNSu/XCv0kM93cSo5i/UvdiPM14uMPFUxzsgtZMa6GAD6tGzAqqhE/rNZ9Xc+lGD0X57Sv6XBql7TqJUWY4DgusGcSTtT/kCJpBrYsmULPj4+HDlyhJiYGAYOHGjWn52dTZcuXThy5Ag9e/bkm2++KXO++Ph4duzYwcaNGxk/fjx5ear/2uHDh1m5ciVHjx5l5cqVXLigphCKjIwkKiqK6OhoduzYQXR0NNeuXWPdunUcO3aM6Oho3njjDQAmTpzI5MmT2b9/Pz/99BPjxo0D4OLFi6xbt47x48dbyJOXl0dERARdunTh559/Lvfz8PPzY8+ePfTo0YMxY8awZs0a9u7dy5tvvmkxdtKkSZw5c4Z169YxduxYvvrqK1xdXYmMjKRv377s37+f7du3M3XqVLKzs1mwYAGurq5ER0czY8YMDhw4YEUC65w8eZLnnnuO6OhoPDw8+PLLLyt8raRmIPeaOXKvmZOm86V9vHNTzr43yJDr96V+QTzdLcBsbEVtmFFv3Mv/XuxuODf149Vjb6e5ZUoxwNZJPRka7sPK57qy7t/38OGIMBx0lnEnezvi5wzm3HuDLK7Tp6tzd7KnQzPValxWFT09p5LVdHBxV7MBiLmopoMzLVjSoE7peZNTKrBGdVErLcYAzb2asztpN4XaQhw0lXv8IbmDKMfaVFW0bduWKVOm8NprrzFkyBB69Ohh1u/o6GiwRHXo0IHffvutzPkeeeQRNBoNQUFBBAYGcuKE+gu8X79+eHqqX74hISGcP38ePz8/Vq1axddff01RURGXLl0iNjaWkJAQnJ2dGTduHIMHDzasv23bNjN/zIyMDDIzM5k0aRLvv/8+dnaWkdoJCQn4+Phw7tw5+vbtS9u2bWnevPRKlHrfyLZt25KVlUWdOnWoU6cOzs7OXL9uHgWt0WhYsmQJYWFhPP/88waL2q+//sr69euZO3cuoCoMCQkJ7Ny5k5dffhmAsLAwwsLCyvwsTfHz8zPMP3r0aD777DOmTJlS4eslJsi9JvdaGVTXXhuvS1M2MLSRRYCbRqPw97S+7I+/xsQVh5mtS6tWHvXdnajv7sTIDr6sPpBoyBVcnbg52fOpLsVb+6Z1ad+0rsUYTRkBfu7O9py/piq5Ty7+hxPv3G913J6zqTz2jTG4b82BRIaGN2HhDstKfymZ+dRxsifTimuGmtat/HzO1UGtVoyLtEVcyLhAoFdgdYsjkZgRHBzMgQMH2LRpE9OnT6d///5m/Q4ODii6ZPN2dnYUFZXt06UoitVzJyfjL3L9PHFxccydO5f9+/dTt25dxowZQ15eHvb29uzbt4/ff/+dFStWMH/+fP744w+0Wi179uzBxcU8SCQqKopRo0YBcPXqVTZt2oS9vT0PPfQQPj5qdHVgYCC9e/fm0KFDZd6s9XJqNBozmTUajdX3fvr0adzd3UlKMqZUEkLw008/0bKlpb9cyc+nopT2uUpqD3KvmSP3mnVKZl/Q4+PlwtDwJgxu29iq73FZfDiyHR+ObGcL8W4ZB964lzHf7edoiWIeTvYaBoQ2Ysa6GPIKrafCjbuabaYUA+w6fZXiUqoFNqjjxPAOviz5O96iL13nk1wTqbWuFM291C+G09dlAJ6k5pGUlISrqyujR49mypQpHDx48KbmW716NVqtlrNnz3Lu3DmrNyw9GRkZuLm54enpSXJyMps3bwYgKyuL9PR0Bg0axCeffGIoS9u/f3/mz59vuF7fHhcXR3x8PPHx8YwYMYIvv/yShx56iLS0NPLz1cdgV69e5a+//rJpoFN6ejoTJ05k586dpKamGgKFBgwYwOeff24I2jh0SM2X2bNnT3788UcAYmJiiI6OrvBaCQkJ7NmzB4Dly5fTvXv3cq6Q1DTkXrtx7oS9Zq+zkgbdZenuYDaukkpxbcXb3Ym6Ot9eU1eHem6O1HMt2+f3dLL1tGtXMo2FS755KsJw3MTLlcQ0637oE368uX1aldRai3GAZwAKCmevW5rvJZLq5ujRo0ydOhWNRoODgwMLFiy4qceGLVu2pFevXiQnJ7Nw4UKcnUtP/t6uXTvat29PaGgogYGBhseXmZmZDB06lLy8PIQQfPzxxwB89tlnvPDCC4SFhVFUVETPnj1ZuHBhqfMfP36c559/Ho1Gg1arZdq0aTa9WU+ePJl///vfBAcHs3jxYvr06UPPnj2ZOXMmkyZNIiwsDCEE/v7+bNiwgQkTJjB27FjCwsIIDw+nU6dOFV6rdevWLF26lOeff56goCAmTJhgs/chuTXIvXbj3Al7rUdQfS6l51n1A75TcdT9CJj3SDsupefRvIEbDUspKJKVX4Srgx0ajYLGxMp/Vx0ngy/yrPXHCG7oTvMG7twX0pCz7w3if0eSeLCdD6+vKz0g94UfD/LpqPAa96NEqa6UGREREaKs/IcVYdDaQbSq14p5vefZSCrJ7cDx48dp3bp1dYthM8aMGcOQIUNslntUomIanV8W1v6fFEU5IISIKOWS2xJr39lyr0kqQkX3Gtj+f2rkwr+x12gMGRokcDk9j8/+OM1bD4TgZG/u1/7Gz0fZdPQyB2fex5krWdw7bwdNvFz4a1pf3t9yggV/nuXnF7oR7ueF/7SNAHg42+PuZM89Leozt4RryXPLovg1NhmAgzPvY++5VP5tYi3+dFQ4Q8ObVPE7Vqno93attRgDtPBqIS3GEonkjkVRlIHAp4AdsEgIMadEvxOwDOgApAKPCiHidX1hwFeAB6AFOgoh8pBIbgP8p23Ey9XBUOFNYqSRpzPvDbNMMQdqZb9r2QV89vtpvN1V1wp9Oe0Ff6r6lr4QShMvFy5ezyWvSEtGXh7JGZZfH9MHtebX2GRCGntQz82RQW0b42ivMRQC0dTAuI5arxjvStxFYXEhDnYyM4WkdhMZGcnq1avN2kaOHMmSJUuqR6BKMmzYMOLizCscvf/++xYFC24VnTt3Nvhn6vn+++9p21a9Ifj7+1fIglVTURTFDvgCuA9IBPYrirJeCGFa8u0ZIE0I0UJRlFHA+8CjiqLYAz8ATwohjiiK4g3cMRqE3Gu2pby91qiJH3/vP3TL5Pl+r1oVVyrFlSdTl4943m+nWPa00VUm/mo29dwcuZZdQCOd28Xu1/owaeVhftHlQt512rLKob+3KxP7BTGig6+h7cib/Tl/LZuBn+yqkUF4tVoxbu7VnCJRRHxGPEF1g6pbHInkppgxYwYzZsyobjFumHXr1lW3CGb8888/1S1CVdMJOCOEOAegKMoKYChgqhgPBWbpjtcA8xU1HUB/IFoIcQRACJF6q4SuCci9ZlvK22undEFbbZt42iwbxYVrOaRmFxDu52XWvvv0VWb+XHt/8FY3SdeNVl/Tghy95/4JqBX2XBxV9wtFUXh9UGuDYmwNRVGYfF+wWZuLox0B9d0AuJ5TYO0yC7RawYGENDr61yt/8E1SszyeK0kLrxYA0p1CIpHciTQBLpicJ+rarI4RQhQB6YA3EAwIRVG2KopyUFGUV2+BvJI7nMtWHrXfKD0+2M5DX/xFZl4h/tM2Ejh9I0IIRi+2VNJNrZWSsnl1oDELy8fbTln0u5aoiGcatLfq+a4VXsfJ3g5XRztDARZrXErPRatLBbd8fwIjF+7hl8MXK7zGjVKrFWN/T380ikambJNIJHci1kxvJaOpSxtjD3QHntC9DlMUpZ/FAorynKIoUYqiRKWkpNysvJI7nKqodrZyv/rbUCsgYPomrNWweLCdj83XvV1p1ciDe1vfVWq/vZUP+J/X+7Fzah86BVTOmlvX1ZG0UizGl9Pz6PqfP/h42ymKirWGMtMTVxyu1Bo3Qq1WjJ3snGhap6m0GEskkjuRRMDP5NwXKPlM0zBG51fsCVzTte8QQlwVQuQAm4C7Sy4ghPhaCBEhhIho0KBBFbwFyZ2GrTNhvbvxuNm5aa2Jk+8O5NfJPekZLP93K8PXT0ZYlHMObKC6Ppy4bJnLuKGHM029XSu9jperA2sPXuSL7Wcs+q5mqT+ith2/Qp+P/qz03DdDrVaMQfUzloqxpDYwbtw4s3KwN8uSJUt48cUXbTZfSdLS0hg2bBhhYWF06tTJLFBty5YttGzZkhYtWjBnzs2XAk5KSrJZiqzevXtTVipIf39/rl61DBKphewHghRFCVAUxREYBawvMWY98C/d8QjgD6FqJluBMEVRXHUKcy/MfZNrNXKvlU517DXTlGDnU3NssnZFcLK3I7hhzSw7XJPRaBRWm7hFxP1nEIPbNrZ56jY1AAAgAElEQVT5Onm6aoQfbj1paPstNpkrGXmGanrFWm2plfiqilqvGAd6BnIh8wKFxTUvslEiMWXRokU2Tc5f1bz33nuEh4cTHR3NsmXLmDhxIgDFxcW88MILbN68mdjYWJYvX37TSoiPj4+h6pakYuh8hl9EVXKPA6uEEMcURZmtKMqDumGLAW9FUc4ArwDTdNemAfNQlevDwEEhxMZb/R6qCrnXSqc69ppWCENRiYw829yrfeu6lNn/47jONlnnTsXUd1hRlCr5gXE2JdvsPDu/iGeXRfHssiiy89Xy5UVaYRFgqe+rKmq/YuwVSLEo5nzG+eoWRSIxkJ2dzeDBg2nXrh1t2rRh5cqVZtYVd3d3ZsyYQbt27ejSpQvJycmlzjVmzBjGjx9Pjx49CA4OZsOGDYa+pKQkBg4cSFBQEK++aoyfmjBhAhEREYSGhvLWW28Z2vWVs8LCwgzVwVJSUhg+fDgdO3akY8eO/PXXXwDExsbSr5/qdtqqVSvi4+NJTk5m3759tGjRgsDAQBwdHRk1ahS//PJLqfL7+/vz+uuv07VrVyIiIjh48CADBgygefPmhqpf8fHxtGnTBoB58+bx9NNPA2pVszZt2pCTk0N2djZPP/00HTt2pH379oY1c3NzGTVqFGFhYTz66KPk5lovQVqS+Ph4WrVqxb/+9S/CwsIYMWIEOTm3zpplC4QQm4QQwUKI5kKISF3bm0KI9brjPCHESCFECyFEJ30GC13fD0KIUCFEGyFErQ2+k3vNSE3dawnn4xnSqyPvTH2REfd1Y/jw4Te914qKBfe2bmjW5uygqjRO9hq6tah/U/Pf6egzT+gZEtaYj0a248Q7A222Ru+WRhcXIQQjF6olw09cziRLp/yeS8nmt1jzPfvdX+apCm1NrU7XBtDcszkAp6+fpkXdFtUsjaSm8f6+9zlx7YRN52xVrxWvdXqtzDFbtmzBx8eHjRtVI1x6ejoLFiww9GdnZ9OlSxciIyN59dVX+eabb3jjjTdKnS8+Pp4dO3Zw9uxZ+vTpw5kzqk/W4cOHOXToEE5OTrRs2ZKXXnoJPz8/IiMjqVevHsXFxfTr14/o6Gh8fX1Zt24dJ06cQFEUrl9XU/FMnDiRyZMn0717dxISEhgwYADHjx+nXbt2rF27lu7du7Nv3z7Onz9PYmIiFy9exM/P6Nrq6+tbbromPz8/9uzZw+TJkxkzZgx//fUXeXl5hIaGMn78eLOxkyZNonfv3qxbt47IyEi++uorXF1def311+nbty/ffvst169fp1OnTtx7772G/ujoaKKjo7n7bgtX2VI5efIkixcvplu3bjz99NN8+eWXN1VO+E5G7jW516whhEAr4OzpU3z+5Vc0aRXOB69PKnWvCSH435Ek+oc2tKjKZkpmXiHNvF2JeuNeMnILCWzgTl5hMa+vO8rUAS1LvU5ScT4cEUaIjwegWo2H2zi7R8tGdfjzpBrU+3+rjhB7KQNQnzDoj/X0CKrPF0/cTdisXzmZnGVTOUpyW1iMneycOHyl6iMVJZKK0rZtW7Zt28Zrr73Grl278PT0NOt3dHRkyJAhAHTo0IH4+Pgy53vkkUfQaDQEBQURGBjIiROqAtKvXz88PT1xdnYmJCSE8+fVJyerVq3i7rvvpn379hw7dozY2Fg8PDxwdnZm3LhxrF27FldXNVhi27ZtvPjii4SHh/Pggw+SkZFBZmYm06ZNIy0tjfDwcD7//HPat2+Pvb291eCZ8nKTPvjgg4bPpXPnztSpU4cGDRrg7OxsUBr0aDQalixZwpNPPkmvXr3o1q0bAL/++itz5swhPDyc3r17k5eXR0JCAjt37mT06NEAhIWFERYWVqYspvj5+RnmHz16NLt3767wtZKagdxr5lTXXisq1pKv8xk1Rat7D018fQ3z9xr8cKl7LS2nkJeWH+KdDeYuI0IIouKvIYSgWCvILijG3cme+u5OBDZwB8DZwY55j4TT2LNsNwtJxRgZ4Ueoj2f5A2+QVo2M7hlHL6YbjguLBZ9sM8829uaQEDycHdj1ah8+fTS8ymSC28Bi7GTnRMt6LTmVZplvTyIpz9pUVQQHB3PgwAE2bdrE9OnT6d+/v1m/g4OD4QZnZ2dHUVHZPlMlb4b6cycnY+Swfp64uDjmzp3L/v37qVu3LmPGjCEvLw97e3v27dvH77//zooVK5g/fz5//PEHWq2WPXv24OJieTP57rvvAPWmFBAQQEBAADk5OVy4YEyfm5iYiI9P2emQ9HJqNBozmTUajdX3fvr0adzd3UlKMiZZEELw008/0bKlpTXoRosGlPa5SiqP3Gt39l47m5JNflExrRp5YKdROJaUTrFWGLIYKIqCm0kOXP08hcVacgqK8HRRyw/rg65+2JvArAdCsdf5Jv8Td41RX+/l1YEtDenX9CWLJbWTh8KbcCjhOsv2nKeZtxunr1i3BG+Z1IMgnY+zX73KZ7+oLLXeYgxqoQ+ZmUJSk0hKSsLV1ZXRo0czZcoUDh48eFPzrV69Gq1Wy9mzZzl37pzVG5aejIwM3Nzc8PT0JDk5mc2bNwOQlZVFeno6gwYN4pNPPuHwYfUpS//+/Zk/f77hen379evXKShQc0wuWrSInj174uHhQceOHTl9+jRxcXEUFBSwYsUKg5XKFqSnpzNx4kR27txJamqqIVBowIABfP755wYr2qFDaonZnj178uOPPwIQExNDdHR0hddKSEhgzx7Vr2358uV0797dZu9DcmuQe+3GseVeyy9SrcXnr2WTW6Aq4FoTi3fihQvs+2cvAFt++Ymu96jW41PJmZxPzaGgSM08YJonN9kk73Fatvr5HEq4bij1bBogJql9KIrC7KGqv/u246X7/re8xZlFar3FGFTFeO3ptaTmpuLt4l3d4kgkHD16lKlTp6LRaHBwcGDBggU35bvasmVLevXqRXJyMgsXLsTZufQbQrt27Wjfvj2hoaEEBgYaHl9mZmYydOhQ8vLyEELw8ccfA/DZZ5/xwgsvEBYWRlFRET179mThwoUcP36cp556Cjs7O0JCQli8eDEA9vb2zJ8/nwEDBlBcXMzTTz9NaGjoDb+3kkyePJl///vfBAcHs3jxYvr06UPPnj2ZOXMmkyZNIiwsDCEE/v7+bNiwgQkTJjB27FjCwsIIDw+nU6dOFV6rdevWLF26lOeff56goCAmTJhgs/chuTXIvXbjlLbXpr8+g1demXxDey23oJiCYsv0Wi1btWLp0qX8sWMXTQOa0+uhxwGjhTgxLYdm3q5kFxjdMRKv5dDES7WuF+uU7KJirSGzhaeLg80+C0nN5KW+LW75kzzF1sm2K0pERIQoK/9hZfg76W+e/+15FvVfROfGMkXLnc7x48dp3bp1dYthM8aMGcOQIUNslntUohIfH8+QIUPMcsZaw9r/k6IoB4QQEVUpX03D2ne23Gu1FyEEeYVai+wDAMeSVH/P8vxLhRBcyczHw9mB01csCz/oKUpP5qlHh6tW5kSjn3OLu9w5U+LxeXLCOZ5dfwmAeY+04+G71YCvVfsv8OpP0XRvUZ/RXZoy/oeDbHq5hyE4TFJ7yc4vIvStrQBMvjeYnsH1Gfbl38wY1JpnewbabJ2Kfm/fFq4UwXWDATidJktDSyQSieT2JTu/iOSMvJuuIHfmShanr2RyvURJ3rzCYoq1wmDJLYvCYkFyRh6nr2TiaG9dnQhp7EE9N6Ovc11X1S/YzcmerLyy/b1fWXWEnIIiMvMKyda5ZxQWa8nIVY89XG6Lh953PG5O9sweqj4JCfPzpH3TusTPGWxTpbgy3Bb/Vd7OqvvEoqOLGB0yupqlkUhujMjISFavXm3WNnLkSJYsWVI9AlWSYcOGERdnnl/y/fffZ8CAAdUiT+fOncnPzzdr+/7772nbti2g5nwtz1osuT2prXutqFjL2ZQsJo0bzZWkC2b+uJXda3q9N+FaDl6uxiC25Iw8s/X0wW+gKs1aIXB1VFUHfa7ZJx64l8IC870W+clC7u/VGXs7jdlea1LXhbScArLzi0ot1PD7//Wi30c7ABj19V6iE40ZC4q0wuBK4SFdKW4bnurqT/+QRjTyrH6/8dtCMdb7n6TmpVazJBLJjTNjxgxmzJhR3WLcMOvWratuEcwoL9+r5M6lNu61wmIt+boAtU8W/YC9RlNhNwKtLsWZg4mS6+ygMQTMCSHILSjmTIq5W8OVzHx8vIwZNE4lq+4SYb5eBpkAfvzfNqvr6hVoUzSl+Is29HA2KOXNdenXADOlGODA+TSCG9ZBUcDdyvyS2ktNUIrhNnGlAHgk+BHcHNzQiltbU1tSM6ku33nJ7YX8Pyof+RlVPYXFWo5fyuCcieJapK34vS7mYjrHL2WY/a1MA+QupedZKMUAV7Pyrbo76LNNmFqXAbzdjJZnR7vKqRcOdhqEEAjUud96oPSS3sv3JSAEaDQyvaLE9tw2inGIdwjZhdkkZCRUtyiSasbZ2ZnU1FR5w5bcFEIIUlNTy8xKcKcj99qt4XiJKmB6TAPZSqLVCou/y/Vc1QUhI7eQXJPsD1ezzN0gTDl3NYvoxOtmSrDe/7hkZTp7Ow2+dVULc4M6TpSG3jJ4Vx311U6jgBAU5WRw/roqY11XmaNYUj3cNs8hWnm3AtTS0P6e/tUrjKRa8fX1JTExkZSUlOoWRVLLcXZ2xtfXtmVQbyfkXqs8RVotWi2lBquVpFgrSE7PK7U/+rqTmYvExbRc7O0UCosF9hqFRp7OJKflApCcAL51XUjJzDe4ZZRGY09nLpmsa5ZlVrdmom5ePWn2CnfVcaa4sJjkDDuulGHQdQDSMqG4sBjFTuFimsLB8xl8/k8azw4CL1ej/3CngHrsi7tGn5YN2H5S/q9JqpbbRjFu7tkcjaLhVNop7mt2X3WLI6lGHBwcCAgIqG4xJJLbHrnXKk/vD7cTn5qDi4MdxVrBqcj7yxw/5rt9/KlTBrsE1mPvuWvE/WcQAdM3GcbEzxlsOL5/2kaz64/O6s/9S381G3tg73neWB9Dz+AG7DxlVDTdHO0MeYTj5wxmSIm59Kx6vithAfUs1hrbzZ+3Ot14+r4HvjfOZ2ox3hd3DYA6zg6cjryffh/t4IdnZGpWSdVw27hSONs707ROU5myTSKRSCQ1lvjUHAByC60XwijJnyYW0m/HdGTXq31QFIVvnlLTsQ4Ja2zo//vsVYvr28761ez8SkYeeYWq8vvJo+E8fHcTQ9/MIaX79ZpyLbuAyzprckhjD+Y8rGZ6mTHo5nJaRw5rw4cjwgBzi3GXwHoAFBRpcbDTsPPVPjT1rvrSwJI7k9tGMQY1n/GptFPVLYZEIpFIJBaY+vVWBH0WCIAx9/jj6miPXz1VIby39V3YaRSamSiIj39TfiaWp77dR4YuoM7TxYEH2/kY+gJ12SAimtUFYLCJ0g0wooPqVjT+hwN8sf0MALGXMhjVqSnxcwabpXa7EZ7o3IyREX4AZink7gtpBMCWY5dvan6JpCLcVopxUN0gLmReIKcwp7pFkUgkEonEjMQ0y3tTgc7Xd/m+BEZ9vYcTlzPYfPQSaw4k0v/jnYZxnQPqmV2nKArFWsEX28+WW4xjYr8gjrzVH1AtsZl5hdRxssdOo9C1uVoH4N2H2hhKLAc2cAPg4fZGa3L8nMHMHdnOcP793vMADG5rrjzbCg9n1dOzQR0nXBwsq/NJJFVFhXyMFUUZCHwK2AGLhBBzrIx5BJgFCOCIEOJxG8pZIfQV8M5cP0NYg7BbvbxEIpFISkEIQX6RFudaouT8FptM1+beuDvZLhTnMSsW3es5BVzJzGf62qMADPxkl9VrB7ZpVOq8v8Um42QSzPfr5J7M2XyCP05cAWDyfcGGvr3nruFkb0cdneLpZG9n5qP83ZiOdAlUleXeLe8CYMETdxv667o6kJZTaDg3VZZtiaIofDe2Iy0b1qGxpzPXsvN5pnv1VEKT3FmUazFWFMUO+AK4HwgBHlMUJaTEmCBgOtBNCBEKTKoCWctFrxhLdwqJRCKpWXz3VzytZm7hSmbpGRZqCuOWRvHssijavLXVpvNaS4vW6b3fGfL57nKvVUopjAHg4mjH2CX7Dee+dV3K9BfecSqFOs7Wq8b1aXUXLo7qjxc7jUL8nMHcb2IVPvRmf9o39TJbu6ro0/IufLxcUBSFF/sGVelaEomeirhSdALOCCHOCSEKgBXA0BJjngW+EEKkAQghrthWzIrh4+6Dq72rVIwlEomkhjF7QywAnSJ/59NtNTNIOnJjLP7TNrLteHL5gyvIgfPXGPDxToqKtXTyV90hlj3dyWbzA6zYZ56/39XRnoD6bhbjzr03yHB8wYpbR0UZc4//DV8rkdR0KqIYNwEumJwn6tpMCQaCFUX5S1GUvTrXi1uORtEQVDdIZqaQSCSSGkRJH9iPt1WP8SK/qJilf8eX6pP7za44m6yjz/qQV1jM8AV7OJmcyQv/PYiLox3+3q70DG7AiXcsb5P/HdcZ/0pkW9j9Wh8ANscYg9IeMAmme6yTHy/2aWE4N60Ul1PJQEBThoaXVAEkktuHijhPWXt+U/JbxR4IAnoDvsAuRVHaCCHMyvIoivIc8BxA06ZNKy0sWi0UZoNTnVKHBNcNZmv8VoQQZT56kkgkEsmt4Vp2QXWLAMCiXXF8uPUkTvYaRnUyvwf9fOiixfgmXi6VXmNbbDLjlkXx2WPtiYq/Zmjfeky1QusrwzmVKPDx7ZgI7mlRnzUT7iHi3W1mffMfb291Ld+6lkr0yA7GgjT/ebjqYm1iZw9AFjys4ZzcDMtHwYsHoH6L8sdLgIpZjBMBP5NzXyDJyphfhBCFQog44CSqomyGEOJrIUSEECKiQYMGlZd2fgRsmlrmkOC6wWQUZJCUXVJEiUQikVQHmXlqsNZHukCtvq3uqvI1hRD8958Exi01+t5+uPUkAKk6RV2rFWTnq6nLJq08DMDdTb2YdG8Q/+rajJSs/HLLXb+zIZbpa6MN5+OWRQHw8vJDrDmQaDE+1McDUH2G4+cM5vjsgRx5sz99WzUEoL67E8feHkBAfTeOvNVfLbQR5mMxT0ka1HHi+OyB9Awu+976gS5PsD4P8o3i6miPmw0DEyVVwPJR6uv8DtUrRy2jIorxfiBIUZQARVEcgVHA+hJjfgb6ACiKUh/VteKcLQUFwL0hxP5S5pC2DdRE4ytPrLT58hKJRCKpPJm6vLl13dSArz9OXCk3xdjNELkxloDpm3h93VG2Hb/Cq2uOmPWn6RTjyE3HCX1rqyFlGkByRj6T7g2msZcLBUVaqy4H22KT+fnQRTLzClm8O47l+1Rvw+hEs4ekVq8Nusv8iaeLox2eruaBcG5O9myf0tuQPq0s9N4R+2fcW6HgtEci/Ij7zyDuC2lY7lhJLebiweqWoNZSrmIshCgCXgS2AseBVUKIY4qizFYU5UHdsK1AqqIoscB2YKoQItXm0gotFOZAYelRzSH11EjcwymHbb68RCKRSCpPhs5ibJoJIUunLNuaYq2w8BVeFZVIToFxvUW71X590JpePoCL13N1sqrW0NC3tuI/bSOvrDLeU8Yti2LSysMWVeWum6QxM+X1Qa0Mx8kZts3Kceztgfzzer9KXSPdDG9zCnLgmz7mbUU1w52pNlChAh9CiE1CiGAhRHMhRKSu7U0hxHrdsRBCvCKECBFCtBVCrKgSae9+Sn29WnrghqIoNHJrRHZhdpWIIJFIJJLKoXcp8HB2MOS93RxzqUrWyi20HlQW8qZl6jWNTkHMNFHSl+oyRuw5a27bWXvwYpluFf7TNvLUt/us9j3bw5h/t1Vjj1LnuBFcHO1o6OFs0zkltZwME3/5oAHq6+Vo62NrC8VFcHwDt8KxvXZVvvMJV1/LUIwB+jfrz/mM8xRrbzzqViKRSCS24ZfDasxHXVcHQ0WzabqCFrYmJ9+o5E6+N7iMkaA3nJ69kgWoAXG9dD66ptkd9Px+vOKZSB115ZHnjmyHoiiGIhlPdL6BwHOJpDLkGIM+0VcCTtxvfWxtIOkQvOMNK5+AuUEQt7P8a26C2qUYe7cAjQMkx5Q5rIVXC/KL87mQeaHMcRKJRCKpWtJzCg0lfe/ycK6Q3+zNoPfrfayTHxPvDSKwRD7fPi1VxXfoF3+RobMU6wPmHr7bmNGhZ5BlENuZlCxDhTqAJ7s0syrDhpe68+vkngwJa8yQMLU4xv1tGxM/Z3CtqfwnqUXkpcO68UaFOEf3tKPPDBj6hXpcaJK3evUY2Lvg1shmCwPl172Nx9kpsPX1m5+zDGqXYmzvBI3D4ELZv3yC68kKeBKJRFLdJGfk0W72r2buDaaBZuVlfLgRsnW+xL2C1cwXE3o3B+DQzPuInzOY7SdTADhy4brFtctNCmW4ONoxe2goXz1pjOh3c7QzjHm5bwveeagNU/pbWqWbeLngX9+N+Y/fLRVhSdVzeDkcWQ4fBELseljxmNre7jFw0VUp/H22cfyxdbBlWtXLdeUEzK6nukDcDHp3ED0N297cfOVQuxRjAN9OcPEAFFsPcgDVYgywI3HHrZJKIpFIJCV4efkhizZne6OiWJo/8M2gtxi7OanrjIzwI37OYOq6OZZ7rUsJJfaprv4MCG3E8dlqMQ7T4DoPneX7uZ6q4h05rA2juzTVrS3TmEluJcL4uupJY7OrNziYPDHZ8wWc31P14uycC5dj4KL6JIbj/7u5+Vy9jcevnIBhVWvtrn2KsV8nKMqFy6X7pznZOeGgceDvpL9voWASiUQiMWX6oNaGY0ddQQt9gQtQA+IOJaTZdE29YuxaSuqy3a/14V9djS4Qpu4Q347paPUaZwdV9o9+Mz6F1Cu/jvYa4ucM5onOzXj7wTYceau/4b1KJDZFCEg5adlemvXX0RXsTH6kbX0dfptZ+ty2oCAb/ngHFnaDC7pg1JvNgpKrcxGZFAMejW9urgpQ+3avX2f1tRxH8geaP8DV3KvkFuXeAqEkEolEUpJwPy86+dcDMOQKtrfT8H/3Gd0P/j5rm8yeOQVF5BcVG4LvXB2tW21967ry9tA2LH+2C6fevZ93HmrDgifu5vlegXRt7m31GmvpzfabVLXTY6dRqtyHWlKLEUKt4HujRC2GLzpB3C51nlme8Edk5eYoqTtpi9V53vaCovwbl01Pfpbx+OBS9bX4JlPF5aZBQC/w8it/rA2ofYqxZxPwaAIX/ilzWB8/NYefdKeQSCSS6uPjUWo2ofruRleGf/dpwdBwNetDdOJ1PthyAm0lC34Mnb+bx77eC6ip1ULe3ErLN7bw9S61tlR5Vtuuzb0NY+5v25jp97cuc3xJ+oc0qtR4SS2hKvP9vu0Fs+veuHX2iC4T7tIhkJ+uHu/8wPrYZ7cbj8dusT4mOVYN3NPz7k1WpMy4BBsmW7bX9Tcex/8Fv7xYuc8gNw1c6t6cbJWg9inGAL4dy7UYd/Pphr3GnhOpJ26RUBKJRCIpSX13R9o28eTdh9oY2uw0Cp88qirMW48l8+WfZ/lfdFKZ83y7O47WM7cghEAIwZHEdPacS0UIwWPf7DWMO5SgBtXVdS3fp7gy9NZlszgTeT+/Tu7JwDY6xTg9EdLO23QtSTXxw3B4t4HqI2trTBXuH4arAXCVISvFXO9Z+oD1cWM2wqx0aHK3sa1ZV7XNvUS1wwVdYf1L5m2FN/iUvTAP5rWCkxst+0zlXjIIDn0Pp39VLdVXT1ufTwj175BxSSrGFaLJ3XA9wTxXXwkc7Bxo7tmcE2lSMZZIJLcniqIMVBTlpKIoZxRFsXA0VBTFSVGUlbr+fxRF8S/R31RRlCxFUaZUlYxO9nb876XuDGxj7htY0j0hs5xKeLM3xJJbWEx+kZaYixmG9vRc64HY9SoQbFcZloztRPycwdjbaQhuqCvrnHEJPg6FT8NsupakmjizTX394x3bzz3fmN2Es7+rKdMqg6llFyzjrO7/EGamgn/30ucYt82y7USJjBE3msbt1Gbzcw9feEOX91ufd9jUSvzHu+rryU3W57t6Wv07rB4jFeMK4aP7JVSOO0XLei05ec2Ko7pEIpHUchRFsQO+AO4HQoDHFEUJKTHsGSBNCNEC+Bh4v0T/x0CJO1r1kHS9YpaqjLxCPvzV+L1uKx/lG2JXFVgWJdWDqW8swMWDtp3/ekLpfflZsPND1epaGgVZpfdNjIbOz5kH2lnDy6S4jFOJCowdxqqvv79d9hylUVLRH/2TmmJXz/m/VVcSPfpKfPalVG3Ux4elngZtEbjWuzG5boDaqRjrA/C2TC9zWKt6rbiae5WLWRfLHCeRSCS1kE7AGSHEOSFEAbACGFpizFBAFwHDGqCfojPVKoryEHAOOHaL5LXgr2l9Dcdf/nm2QtcM/GQXyelGBeLfPxoVGL27ww2hLbZUjsoj++qNryepWcTvNj9PtvG2aNBKfXVws+z7TxPVgqoPVgNjkN7Fg7DmGcjT5d2OeBrG/WEcF9AT6lovNFMmr5Vw/wl7pPJzlMVduvfbWufy8d391sc5uFhvz9M9FdIXK5EW43KwdwSNPaTFlenAHeKtGk/Wna6kL49EIpHUfJoApuU9E3VtVscIIYqAdMBbURQ34DWgTPOQoijPKYoSpShKVEpKis0ENwjn5cKbQ4xGbn3mCj1nrmSSVyLX8bXsAjr4W94knR00LBnbiQ9HhPHF43db9JfLpimqgqIthpNbVP/HL7qUfU3sz8bjvQtUxfqLzmqAUWJU1QZySWzL8kfVV70frp0Ns4vkZah+6E0iIPyx0sflZ6q+xxv/Tw3SuxQNK0dDzBr1/wmg/ZPga+KWMeyrysnSdyb0+D/QaIxWYjAPkLsR6gbAXSUfWOnay0KY7PnCXMjV/QDIzzAfJxXjCtBD5xJ37VypQzo07ICTnRMJGWU8wpBIJJLaibXkoCUtBaWNeRv4WAhRpolUCPG1ECJCCBHRoO2nIDEAACAASURBVMFNWGPL4Onuxhtn8BtGr46cgiLunbeT4QvUfPSdAoyPUv/7j/qdPu3+Voa2Mfeo84yM8GNw2A3kOo36Vn2dXc+oJKUcL318SaPMlmmw431IOaEGGC3qB8sehO+HQUGO9TkkNYfGajAoz+v8YXMtKyNaJf0i/Pm+9VRn5/+Gr3rBHD+ja4ApJdfQ+9TuX6Se/zBcNQLq+wCcdP7tb1yB8bvBw6dicurpOQX6vaket+invrrWN5+nou9dj7ZYNVQ2aAkPfArPmli0Y36yHP/0VuOx6d5YdC+83wxi1kL0KvNrpGJcAdqOUF/jd5U5rHuT7sRei70FAkkkEsktJREwTezpC5RM7WAYoyiKPeAJXAM6Ax8oihIPTAJeVxTlxaoWuDRiZxtLvoa+uYXEtByydPmIjyVlkJyRZ9UHeXyv5uyY2puPRrbj1QEtb5m8XNgHJ0yi7xvoUr39/Zn5uIQ9cPYPtbBCFZS/ltiQuv7gHQRuuh+AuRUsPLNtFvz5HiwZbNn33f1w6bDxPPMSOHsaz7OSy547+wpcL+HyoLdk2ztBo5ssjazRzdX+CfU1sLf6mlMJv30h1B+ToFq7O4yBJiYW7QwrrqyevmpeYoBCE8U4OUZ9XTPW/GkMSMW4Qni3UD+oM1aiLE0I9Q7lfMZ5MgoyyhwnkUgktYz9QJCiKAGKojgCo4D1JcasB/6lOx4B/CFUeggh/IUQ/sAnwHtCiPm3SvCSuDra4+GsWsayC4rp/v52LqYZFeEjF66TmGY9OK+ZtxvDO/ii0VSwuta1uMoJd/2C+XnCXlh8H6zUKRMD58DgcoLwDnwH68ZXbl3JrSU/Q1VaNXbgUg8O/xe+7mPMqFAaxTpLceJ+c+vnLE/LsRkXodskcNPlCy7IqnzBjzqVtBCXRfAAeGgB9Jmhnkc8o76WzIBRFldPld0/9EvLNqc68NQv5muVtqaDq/rqbOXzrCJqr2KsKKrvyvH/lfmPFVo/FIDYVGk1lkgktw86n+EXga3AcWCVEOKYoiizFUV5UDdsMapP8RngFaCU2rHVT0n3h2Ff/m04XrjDGJinL8rxfM/Ayi8SvQo+C4czv1f8mpLGl28HmJ8X5Vv6Vk62ErgVvaLia0puDbO8YOWT6nFeulH5cmsA6QmQdFDNF6xX2hL2wtrnza3/diaZF7ZHqgrxr6WUXW45CJw9YOR36vk3fVXXAQCvCgbQ2dswDaGiQPjjxuwR2bo4gv8+Wv61p7dBpA+kmgTNDv3CclzbkdCsO4zdDDOvqnvD2dNYJlr/lOWnZy2vrR+sFirp8gK437qCOrVXMQYI6KG+lvGFE1JP/cI6mGzj1CsSiURSzQghNgkhgoUQzYUQkbq2N4UQ63XHeUKIkUKIFkKITkIIi6AMIcQsIUS15x3r07L0qlsHdUU7xvdqzql372ffjH5m/sWlkp2qBjDpWau7+Z7/y3Ksq7fRYgbQUFeQZMMkVdnZ9431NRq0skwl5ehuPO7/rvG4uOxczZIqJvUs/PMVXDmus+gKOL5ezUd9LU5VWgGulkjzmnpGHf/tAFXf+H22se+Uib/sHt1DF1OXmub9jMcP6vpN3TT0QWb5mTByibG97UhzGV6Ng9fLLoJz0zTtqr5mXyl/7I/DoTAbVpgEE7YfbTnO3hHGboRm96huIJ6+5v16d47TWy2vFULNbjHwPTVY8BZRuxXjeyaqr/FWvuR0eDmrefOWHFtyCwSSSCQSyY1QmquEKRN6NQfgrjrOFgVCzLh4QA0g+qYPfNXDsn/XR+bncTtVv8oL+6CrztX6kWXmYzaVUgMlWGdBnnEZggeCbyc1R2yYzurW7B7j2Ksny7xf3fZseR22zqi+9b8fBptfhXXPm7fPawW51ywf1zvqAt2+6WvevnueMedwfjluB94t1FdnL3DzVo9NfXD1dPgXhA4znhebZDRpEqH++HK0kurNljSowI/N0hi+uPLXNO8LjduZt/U2ScObWkpVvCqmdivGbt7Q+kGI21FmYEOgZyBu1nIHSiQSiaRG8FRXy0fJwQ3daeJlzHPq4VJOAQNQI+T1j6j1gUtzgy1Tp5neM+J0QdzJR+HeWfDSQfBubjl3grH0NN0mwQv7jY+EHVzg8ZUw7jfVujXkExjxrbkStOAeNWPFlTKyXdzO7P3CaFWtDvTW2UtHrPfb6/7X9K4xL0WVPtdXPSu25vm/YNRyeG67sc3DB3w7mo/rPMH8PHQYNNQF1w2ZV7G1bpaKWmVN9wGAT3tjQoTK4FIXLkapAao1iNqtGAME9oL0C2WmbRsYMJDU3FQyCzJvoWASiUQiqSj2dhri/5+98w6votr68Ds56ZWSQgk9dELvXTqoIEUpgqAoXCmfBRULCoIoWPB6RRRRBEGkKQqidEIXCDX0ltBbSO9tvj/26SU56STs93nyzJ49e2bWSTlZZ81avzXncSLmGKr7L9xN4PcJIuI67fH62UeJdVgr4km4C4fM9F7/elVIbZ1YiV7lzqeKeNyrc4rNo2BrXzC9pl8d23Y4u0OjwWLcbZrpsSu7cnwZpQ7jWiDjlJKE+0K/9txGOGNeO1oApMQJybSdH+esNHFihdg+/7eQbfMwS+95fpNhnBoPd7QqCjpVEh3GBWd3T0G9flDOLCd+zEZ454Zh30WbftNnLrR6UTjGg76HxsOs6wMXFi21v+P/TLW9xjzPXlcgl1vSEsV2mVGkvEw16P2JGPcrngwvOz5+P+RU1T6m2vdf6P+11SVN/ZqionLk7hG6VuladLZJJBKJJNf8PqE9gxbsx9fTmQBvVxNnOUdSbGiwbtE6p+0miahl5CWhE2usVTxmo+k5uq5dOoylp3rNtt+mdpNFZzNr13kUuHsazv9t2E+JAQ9fEalf+oTp2hm5UESwhwVtxffbWDZN42JQkygfJHKIwfAzdStrKQ/W+xOo1s6w718fvusgxl3eEhJjOpo9C39O0B6z4WA6uoivl/eL9BpdmkRbI/WSgAYwKJcNPPKLTlnj4HfiNecURfZvCAPy+BTgwibLuSbDxLbhQPDOgx55AVDyI8a6nJhzG20uaezXGIAvQr+wuUYikUgkDwfNq5YlYs7jhE7rmfuTc2pO0GykKIi6uteygYd5a11HF1H0VKWtaQevuv0M+aL24ORqup+Tfm1p49v2ph8Mrh8U2xuHCv/e5h9CAhrB+0bFZeONeiFY0wV+KxxGb4B2Wkd3uvb367KRsomHL/T9TIx1xXa6QrY6fbK3L6AhtBmX/ZqixDjAGGbWZCMpylSG7qlvYcJ+y2i4vbSdYLo/aJFITVKUYnOKoTQ4xg4OULu3yB/LyrS6xMPJAy8nLyLiIorWNolEIpEUDPfOwgErmqjm6FIpAoycHB+jPihOblCmqv33dS8HYzeLNro6Bn5n//nmePhB/J28n18aWDlCbEOXWB7LSCvYZih1+pru65pI/GcvvHpKpLy8cUlEi80LwUD8/GsY5RNbS+fxriyc2xmxMOp3MTdmI0wKhcp5aE9enDg6G5z8qHD49zuRjnL9MPzX7INDYOv83cvPrCmPte9/MVDyHWMQSd9p8XAnzOaSUQ2EVuHF6OKpcpRIJBJJPvipL2x+x6AGYIubR8R20EKRI/rk/6DDK4bjZatDmSqm53SZal2D1ZgAozzPvDQbmHYfJvwLVdo8ehFjazmyt08IrWBzPvKDObn44GJOUhRsnyXymDNS4cI/1tdVCDb8Hnj6QftJ1p1eazy71nTfWqGmgwZ8a9tv98NEE62iyq45sGmqaGn9Yw/RkERHu0ngG5S/+zQbJVpIv3YaBv1g6SgXE6XDMa6mzfOxpTMJ9KjWA4ADtw4UhUUSiUQiATj1G+z6VDyCPfZL3q+jK5wKW5P9uh2zxNbZE968KGSwmmq71Oke+RpHkJ/8Hzz2rnUNVmMqNYfHpsFreWwW5egs8lK9Kj56EeOMFKj7OEw6YpgzVnUwV2hIjTPVCs6OrCzRUCNSmye8uA/s+RxmlYePrGhjm0eQ80LtntBIq8JgXlhZGnDxznmNrnAuPzhoRAtpn0Bo/HSOy4uK0uEY+1QW2+PLbS6pXbY2VbyqcPjO4SIySiKRSB5xsjKFksNObVHTnxNyjvjmxPpJ4lF79FWI1Vb1n14nHG/j/EfjfGFndxGRek6reqBryBEQLBxne1AU6PKm4f9NXvH0F8Vn5vJxpZmkKPF9sxVhfG499DRzhM21ps25tB3+/VYUcO3/H8xvIaLEthSqOr4mtoEtc2e7LXp+CPWegDalsNW3PZHz2r0K345ionQ4xgC+2hB8qm1JttYVWhNyIwS1IPOXJBKJRGKd3620eT3xa96uVbOrYXz0Z/iqMXzZUHQzWzMm5/MbP214dK5oxNa9rO31hYWuK156AUTcSgKZGeKDgJv2w4hxJziAt6+JDy7uVooZjSXezFk+CDa9bdp5bVZ50SnNnE5ToOlIoVNs3EQjP/gEwrBfwMWrYK5XknjvrpCgK6WUHse41Ytiq6t2tYKDIl6uTKeQSCSSIsBa9O7Mn7kvrsrKhCshhn3jx+xf56G4qWIT4RwbF9QVFTpZroJ4FF0S+Lm/2Orysp9ZCg2eMhzXzVvTGM6uq1x5G/m71mqNFAcRrZ52x3o+sCR3mKuslDJKj2PcdIR4ozPvyGLE2OCxAGwMty3tJpFIJJICwprzcmUn/JjLx7AXt5ruJ0Vmv961TPbH3cvB9CjTKHRRURyOcdztwmmeYQ9XtS2wdWohLl7Wew4EP2MY6yTOkqJsXzen3wFj2v+f/WsllgxfZRhXLqBUlIeY0uMYu3hCxcbZ9qGv7Clywy5EXygqqyQSieTR5akFonodoFpHw3xu9WvjbxvGujQIcxwcofsH0GQ4TI3I3fWLEl07aOOUkvRkoaaRkwZzXplXD1aPyn9+d34IMkqhcPUWRfOtxxvmvALE1sHJ0H3NVqe61ATLY8aFfQB95og2yzNixf0kucNYiq1uH/ggSrQ4H7vV9jmlhNLjGIOoGr57KtvHdC8Fv8TF6IskGMuOSCQSiaTg0ThB79mitfLTS/J+nb9eFdsXtpjmorZ52TB+fJ5IjRj4nf2yW8VBPW0XP2NljNkVYFE3mFvNph5/gbDx9cK7tjUS7hvGVcw0b5//G/p9ajr3Vji8ecnQdc6WYxwdbjlnXNhX7wlo+zL0nZN7myWCkb+Z7jtoRIvznDrhlQJK1yssHyRkXrLRM25TsQ2ZaiZH7h6xuUYikUgkBUjwEKEV2/uT/F2nXA1QjRxH4wKg5s/l79pFRdnqYht3E2KuWUq3fVpTNFQoDI7/krPaQ0GiC0DZ2wjCvRy4lTEU6tlKpYi7JbbPbxJOtK6gUUdAw9zbKjHlEY6yly7HuFIzsf3Jtk5hU/+muGhc+Pe27VxkiUQikRQC7YxawKYmZK86YA3XMpD0wLBfrQNU7wQv7Xi4o8TG6IrN9nwhOollmKU3pMSIhgrbPsz7PdJThHTd1y0sn6Bunymaa8zwEU74pnfzfh9bZGWJCPiZP8V+uwnZrzfH009sjVNojNF9cPDwFWkz72rbPvf7HPzqQee3cm2yxAoefo9kfnbpcoyrthXbbNIkXDQutKrQiuVnl0vZNolEIilqumodsVNrYWbZbOtC9JStIVLlHJ0Nc/4NxOPdMX9B5RaFY2th4GCWIx26WGwrNjWd3zsv9x8cdJz5Q2wfXIL0JMvjq7TNTJIewL85dPzLC+c2iJzpbdPFvnFKhT3oPjzozjcn1aiQz5jWL8HEg6BxzN39JNZ58xL0mlXcVhQ5pcsxVhTo/KYYZ/OH2Mi3EQBnHuSxg5FEIpFI8kaNTmK7Qdum2VbLXh1ZWSKnNFn7WF2ndFFQjRqKm31fia15Di5AxG7tdl/uCvM8jTq+6ZqgtJsEXd8R4xizVswZqfZf2x5Wm6W15NRVMLfoIsb2dGiTSHJJ6XKMAepq0yhCPra5ZEht0cpR5hlLJBJJEeNdyXTflsqEDl2hVXSE2A7/VRTdPfFVgZtWrLSdAM+aFTz9Ph6OLIEl/URhXlqSiPZm1y45KwuWGTWx+E77QaRSM1GQBkLBw/j7nk1jrFxjrWDO2T3v17Mma5caJ16Dk1veryuR2KD0OcaVtGLvusdTVgjwCKCKVxXpGEskEklRU6aaIZ0Ccs4N3mfmAPvWFmoDpa06vlwNqN0DeswwzCXcMUTWARa0gbMbRH6yeQtsgL1fwrpxpnOZ2miwohiK1LIyRP5ogwFiPyWbRhrG/PS45T3NWdjFMFY0woHNC921aRR3wuDbDnDrGPz8FJxYJV5nVkbJySuXlCjsemdRFKWPoijnFUW5pCjK29msG6IoiqooSvE941IU8KsvxtnkELcIaMHRe0fJUvOYwyWRSCSS3KMo0HWqYV8XCTYnKwvWvQxo38df2FLYlhU9zUeLra5zK0CHV2HyUegy1XK9eQoEmOYhb5sBYWuMDho5jqpqmt/sXg4aDxPjbAJJJlzdK7bZpV7EXDWMp0fBBw9sr82OCsFiu7i3kGFdM0Y0hzF3/CWSAiZHx1hRFA3wDdAXaAAMVxSlgZV1XsD/AbZ7MhcVbbR/OLbecIHm/s2JSY3h6N2jRWOTRCKRSAx4aPNgT6+DpU9C2FrT40kP4MQKOPqz2PevV7T2FSbvR4puYk9+JRpQPG4koaYoom2xrkNeTuhaLluL5I763TA2lzC7d8YgyXVgfs73idhrGEdftb1OR5mqOa/JDuM8acj2/7lEUpDYEzFuDVxSVfWKqqppwEpggJV1s4BPgWJsraOlWgexvWg7wtC2olCwCL0bWhQWSSQSicSYl3YYxuG74bexppq+J1aYrnfN4RF+SULjJLqJ5TUV4HmjgsWIPdbXTLsPtboZ9v3rW67RNdIASLiX/T3PbjCM/3nTMI67DZe2iXSMk6sN8+WNGm7kBQ//nNdIJIWAPY5xZeC60f4N7ZweRVGaAVVUVf2rAG3LO751xPaft2z+sVf0rEgz/2ZsjthchIZJJBKJBIAyVSznvqhrGG/9oOhseRipY1uPn8otoKe2AK/ps6bH6vcXUWhjaTtrOHuBV0XD/ue14f4F2+sPfmcYXwmBG6Fw/bBoN718MKwaBb+/ZFhjLj+XWzx8rc8rWrdlvI0PBBJJPrHHMbb2kVafvKsoigPwJTAlxwspyjhFUUIVRQm9fz+Xuoa5QVFAo31T2P2ZzWWdAztzKeYS1+Ks5G1JJBKJpHB5W/veq8t1tcbko8LRe9TwqyNaG+t495Zh7OgCHV4BJw8R9c1IMxwzd5TfChdfOoYuF9txO00jxiD+X6Yni3zklc9C5EVLu3Q/qx+6w489DPPhu0zXdXwt+9eXExon6P4BjN0KdR83zL//AKbdg4qN83d9icQG9jjGNwDjj/aBgNFfKF5AIyBEUZQIoC2w3loBnqqq36uq2lJV1ZZ+fn55t9oeJh4S2weXbS7R6Rk/vu5xm2skEolEUki4+gind9BC0/ljWuetUnORb/uo4lvbMHb2gA+iRX6yjvREkR+cqA009fhQpGgY415OfOmo/6T4nvvWFkGkp741HAtbDbMrwIdl4NxfMF/7b9y4kL1DDp3QOr8Jb1wsmJbCnaYIfec4rRZznb5CjcTRJf/XlkhsYI9jfBiorShKDUVRnIFhwHrdQVVVY1VV9VVVtbqqqtWBf4H+qqoWb/JuuRrQejxc3g7xd60uaRXQSj9Oz0wvKsskEolEYovoq/DnRDF2dC1eW4obnZyaLrLr4CAiqeac0uof20o/yI6mI0Q+sneg9eOpCaD7/9jmZVHEp7GRpuHfALpNsyycyy+3T2gHslutpPDJ0TFWVTUDmARsBs4Cq1VVPa0oykxFUfoXtoH5QtdJaMXTVg9rHDR80UVUAx+9J9UpJBKJpNj5yugR+bX9xWfHw0ClZjBmI0zJJvcXYOv7YusZkLf7ODrbzkleNdJQ4HdOW0aUaZS6MckoBnZPdpOVlHzs0jFWVfVvVVXrqKpaS1XV2dq5D1RVXW9lbddijxbraDRYbPWfNi3pWLkjAC9uedHmGolEIpEUMn1t14M80lTvaNtpfXGH6X5+WiTbigJf2WloslK9o+Vx43SPFmPyfv/seHye2F7YVDjXl0iMKGWtg8xQFAjSFgdYE0YH3J0MrSpjUnLRi14ikUgkBYd3Rcu51uOL3o6SRGALqNresO/ilfdrtZ9suu9jVFqkK6zrMUNsdV3pzPGskPf7Z0diIRbrSyRmlG7HGKDPXLE16QZkyqJeiwDYc1PKv0gkEkmxYNzA4cXtosis36fFZk6J4bk/DWN7m4JYo+mzMMJIh3iilV5dXlrHt90ksTXXKr5YSPKnrbQycON2Zb9OIikASr9jrKto3j7T5pLWFVrj5+bHnhvSMZZIJJJiQRcd7vURBLa0XmQmscTRGRoPFWNz+bXcoCiGVIzA1pZOdqc3TO85IxYmHzFdU6+QFJ48yov7VcqnNrJEYgel3zE27iyUmWF1iYPiQFP/puy9tZeMLOtrJBKJ5GFDUZQ+iqKcVxTlkqIob1s57qIoyirt8YOKolTXzvdUFOWIoihh2m0383OLHJ2zZf5IX5IzAxYUjESaTgbNw4qcardpOZ/fdkL+7i+RPASUfscYDH+sl7bZXFK3bF3i0+KZvEO+KUskkocfRVE0wDdAX6ABMFxRlAZmy8YC0aqqBiEaMWlzy4gEnlRVNRgYDSwrGqslhYLGsWAk0io1E0WQA+aL/RmxMHChaBCSXfvqt6/D6+fyl8ohkTwkPBqOcffpQkj++C82l/Ss1hOAvTf3ciE6B2kciUQiKX5aA5dUVb2iqmoasBIYYLZmALBUO14LdFcURVFV9ZiqqrpGTacBV0VRZNeERx1FgTbjTBuCNBlmum8NV2/rxZMSSQnk0XCMnVyFvuPZ9RB1xeqSmmVqMr+b+JQ8eP3gorROIpFI8kJl4LrR/g3tnNU1Wk36WKC82ZrBwDFVVVMLyU6JRCIpMTwajjEYqlo3vmFzSZcqXfTj+LT4wrZIIpFI8oO1Z9vmrcGyXaMoSkNEeoVVXTRFUcYpihKqKEro/ftSMksikZR+Hh3HuM04cPaE++dM+76bsbDnQgBCrocUkWESiUSSJ24ARmKzBAK3bK1RFMUR8AGitPuBwDrgOVVVL1u7gaqq36uq2lJV1ZZ+flYKsiQSiaSU8eg4xgB950LcTTi52uaSthXbEuAewJarW4rQMIlEIsk1h4HaiqLUUBTFGRgGmHcjXY8orgMYAuxQVVVVFKUMsBF4R1XVfUVmsUQikTzkPFqOcf0nxXbdOJtLHBQHelbryf6b+0lISygiwyQSiSR3aHOGJwGbgbPAalVVTyuKMlNRlP7aZT8C5RVFuQS8Dugk3SYBQcD7iqIc134VgKyBRCKRlGweLcfY1ccwTrCdL9erei/SstLYdUN22ZFIJA8vqqr+rapqHVVVa6mqOls794Gqquu14xRVVZ9WVTVIVdXWqqpe0c5/pKqqh6qqTY2+7hXna5FIJJKHgUfLMQYYs1FsT6+zuaSJXxP83fzZenVrERklkUgkEolEIiluHj3HuHpHsf3nTchIs7rEQXGgR7UebL+2nbi0uCI0TiKRSCQSiURSXDx6jrExIR/bPKSTbuvwa4eiskYikUgkEolEUow8mo7xe3fE9qLtFtHtKrbTj6/HX7e5TiKRSCQSiURSOng0HWMnN+j8JtwNg9gbVpcoisKmwZsAmLZ3WlFaJ5FIJBKJRCIpBh5NxxighrbL3ZcNbS6p7Cm6qx69d5TdN3YXhVUSiUQikUgkkmLi0XWMq7Q2jGf42Fy24+kdAEzcPpHMrMzCtkoikUgkEolEUkw8uo6xowu8e9uwH7bW6jI/d0Mb1L039xa2VRKJRCKRSCSSYuLRdYwBnN3hpZ1i/NtYyMqyuizkmRCxvRFSNHZJJBKJRCKRSIqcR9sxBqjcHGp2FeMt71ldUt6tPE8FPcXfV/4mKT2pyEyTSCQSiUQikRQd0jEGGLpcbP9dYDPfuHf13iRlJPHL2V+K0DCJRCKRSCQSSVEhHWMAFy9oNtKwf+AbiyXN/JsB8L9j/ysqqyQSiUTyEHP4zmGClwbTa20vbiXcKm5zJBJJASAdYx1dpkK9J8R487uQEmty2MPJg06VOwFw8PbBorZOIpFIJA8ZL2x+AYDbibfp/VvvYrZGIpEUBNIx1lGmKgz7BQIaif0dsy2WzOwwE4AFxxcUpWUSiUQiKQFISU+JpOQjHWNzxu8R20MLITXB5JCvmy91y9bl6L2jpGemF4NxEolEInlYiU+LL24TJBJJPpGOsTkODtD7EzHe+r7F4X41+wHw7Ylvi9IqiUQikTxEZKkGec9ZHWYBcObBGa7FXSsukyQSSQEgHWNrtH1ZbC/vtMg1Hl5vOACLwhaRkpFS1JZJJBKJpBjZErGF5WeWk5yRDMDg2oMp61IWgPHbxvP4usf59PCnrD6/mri0uOI0VSKR5AHpGFtDUaDXbIgOhzlVIc7QIc/N0Y2ugV0BOHbvWDEZKJFIJJKCZN/NfQQvDSb0TigAqqry0b8fWbzPT9k1hbmH5xKTGgNAQ9+GeLt4m6xZdmYZs/6dxeTtk4vGeIlEUmBIx9gWLV8wjOfVg4tb9bsfd/oYkEV4EolEUpRsv7adzw9/XijX/s+2/wCw/KzQtY9JjWHV+VWM3TzW6vo+v/UBhAOdlplmdc3Re0fZfWM3qZmphWCxRCIpDKRjbAtnd5gRC1Xbi/1fhoCqAuDl7EUFjwocv39c5pNJJBJJEfHh/g9ZemapTUc0r0SnROvHiemJAMw7Mg+A9CxDofX5qPMW595Pvk9z/+b6/UDPQJPjE7dP5IVNL5ifJpFIHlKkY5wTL/wDtbX6lF8b3vxW9FsBwOPrHud2wm1rZ0okEomkAIlOFQ7srhu78nyN1edX3oLRYQAAIABJREFUE7w0GFUb6ACRN6zj39v/suPaDn3Qo07ZOgC0/qU1QzYMsbhey4CWOGmcGNd4HPO7zee3/r9ZrDkZeTLP9kokkqJFOsb2MORHsY26Askir8zP3U9/ePCGwcVhlUQikTwydF7ZWT82dmRzy6x/hYLEi1te1M+lZJoWUr+y8xWO3jsKwIXoC7y1+y19sR1AY7/G+nGbim0AmNxsMl2qdMHdyZ11/dfRo2qPPNsokUiKD+kY24OLFwxZLMaL++inw0aH4eXkRXxaPPeT7heTcRKJRFK6ORV5Sh8tBmjk2yjf1zx05xAgcoQ/DxV5y2MbWc8n/if8H5P9Tzp+ku21g8oG8eVjX3JwxEF6VxdPHP+68ld+TZZIJEWAdIztpZE2Knz/LNw7p5+e1GwSABO2TzDRtZRIJBJJwTD/2HwAulftDoBG0QCw/Mxy9t7ca7H+VOQpqylug9YP0o9r+NQA4EHKA/3chKYT7LKnqndVFnRfkON6dyd3NkdsBuCdPe/YdW2JRGKbZzY8w/+O/q9Q7yEd49wwaJHYnlylnxpRfwR+bn6cizrHaztfKybDJBKJpPSy79Y+AN5s9SYA8emiw9zcw3N5eZvQnY9JiSF4aTDBS4MZvnE4vX7rReidUFacXUFCWgJZahYXoy/qr1nNuxqAiQPtrHE2ua+rxlU/Ni6wA+gU2ImXm7xcUC9RIpHkQExKDGejzuqlEgsLuxxjRVH6KIpyXlGUS4qivG3l+OuKopxRFOWkoijbFUWpVvCmPgQ0fgZqdIG98+DiNv30ol7CYd5xfYdsCSqRSCSFhL+7P26ObiSkJXAr4ZZ+/nr8dcZtHWex/vnNz/PJoU9o92s7Oq3spJ9vEdCCkOshLD+znBF/jwDgw/Yfmpz7nyb/YWaHmfr9cY0tr28P77V5Tz9OSk/K0zUkEgl0WiX+htdcWFOo98nRMVYURQN8A/QFGgDDFUVpYLbsGNBSVdXGwFrg04I29KGhdi+x/WUwZAhtylplajGj3QwA2v/ansjkyGIyTiKRSEofQWWC6BzYGScHJzydPLmTeIfev/XWH+/3ez/ORp3N9hq6LnTzus4jPVNIsM09PFd/vFc18d4+tO5QQHS061a1GwODBrLj6R00KC/+7c3tNJfcMKzeMP04Ii4iV+dKJBJIz0zniXVP6PentZlWqPezJ2LcGrikquoVVVXTgJXAAOMFqqruVFVV91H4XyCQ0krbCVBP+wM69bt+enAdgzLFopOLitoqiUQiKZWoqsqlmEt6rWFPZ0+2XM1elWJY3WE2j1X1qkrnwM4W857OngC81eot1vVfRwWPCrhoXJjZYSZ+7n6UdS1L2Ogw+tXsl+fXMuvArDyfK5E8qkzZNYWrcVf1+8/UfaZQ72ePY1wZuG60f0M7Z4uxwD/ZHC/ZODjA00vF+I//6OXbAEJHhlLduzorzq0gIyujmAyUSCSS0oMunzgsMgyA8NjwHM95t827No9V96lOebfyJnN7hxkK+Jw1zgSVDcqLqTYJeSYEgFMPTrH2wtoCvbZEUtoxz/1XFKVQ72ePY2zNAtXKHIqijARaAp/ZOD5OUZRQRVFC798vwfJmGkfDeG41CBGP1lw0Lni7eAPQbFkzEwF5iUQieRS5GH3RpLNcbvnj4h82j73R8g39+MRzJ1jUaxHL+y23+Mc5qekk/dhF44Knk4gO96zWk+OjjuPj4pNn++zB2BFffX51od5LIiltuDu6E+AewLK+yzgw/ECh388ex/gGUMVoPxC4Zb5IUZQewHtAf1VVrTaGV1X1e1VVW6qq2tLPz8/akpLDNCPHPuRjuHsGgJ96/6Sfzulxn0QikZRmkjOSGbR+EJ1XWaYu2EtCegIAfWv0NZlvU6GNPiWibtm6OCgOtK3YliZ+TQCY0mIKAK82f5UAjwCTc10dhdpESkYKGgdNnm3LDcdHHcfPzY+zUWf1baclEknOJKQn4OnkSVP/pvqUp8LEHsf4MFBbUZQaiqI4A8OA9cYLFEVpBixEOMX3Ct7MhxBHZ5h8FFqPF/vftoPkGJw1zmwcuBGAN3a9kc0FJBKJpHQzfd90/fj1kNfzdI2q3lUB9NJoOu3gTzp9Qg2fGqx9ci2/PvGrxXljGo0hbHQYY4PH0qe6aMxUzrUcAE39muLm6MbzjZ7Pk015QeOg4X6yCKjIIjyJxH4S0hKKxCHWkaNjrKpqBjAJ2AycBVarqnpaUZSZiqL01y77DPAE1iiKclxRlPU2Lle6KF8L+hkJcMytBr8Op6qbv36qsIWoJRKJ5GHlTNQZ/Xjr1a0mbZXtJS5VqEl4O4s0tfGNx7N32F783MVTx7rl6uLk4JTtNVwdXZnaaipL+iwBoIxrGQ49e4hWFVrl2p788H7b9wH0qhgSiSRndBHjosIuHWNVVf9WVbWOqqq1VFWdrZ37QFXV9dpxD1VVA1RVbar96p/9FUsZ043Eps//DaufY//w/QAsCltERGxE8dglkUhKNXZozLsoirJKe/ygoijVjY69o50/ryhKb/NzCwIfZ9PcXWvd6HJCpw2vc4wdFIc85QSPbDBS3+2uuKhfrj5gkI6TSCQ5E58W/3BFjCV2oCgwNQK6aiuhL27GK9HQZvTJP56Uwu4SiaRAsVNjfiwQrapqEPAlMFd7bgNEWlxDoA+wQHu9AmVhz4W80vwVFvZYCJi2X7aXO0l30CganDTZR4VLAl7OXoB0jCWS3BCfFv/wRYwlduBWFrpOhV4fif2vmhA2OowAd1H08dbut4rROIlEUgrJUWNeu6/Vl2Qt0F0Rkg0DgJWqqqaqqhoOXNJer0DxdPbkxeAX9WkPeXGM115YS6aaWdCmFQs61SJdeohEIsmeLDWLmNQYfX1AUSAd44Km/WTD+O4ZVj2xCoBdN3aRniXzyiQSSYFhj8a8fo22XiQWKG/nuQWGTq4sKjkqV+elZKQUhjnFhi5irEsPkUgktvkh7Af6/d6PTDVTn0pVFEjHuDCYcl5sv21HeUd3nqkjurT8E156+55IJJIixx6NeVtr7NKnLyjteR9nHxwUB6JS7HeM49PiafVL0RbHFTZODk64ObrJVAqJxAYbr2wkeGkwCWkJfHX0K24m3AQMHyqLAukYFwZeFQzj2RWY1vJNAN7b+14xGSSRSEoh9mjM69coiuII+ABRdp5bYNrzGgcNWWoW269tt2v9/aT7tP+1vX4/uxbPJQ1vZ2/pGEskNnh7j6ghXnBigcm8dIxLA0ZKFcrsACq6iX8qv56z1NuUSCSSPJCjxrx2f7R2PATYoYqWnOuBYVrVihpAbeBQYRt8KeaSfpylZrH+8nrSMtMIjw3nyN0j+mM91vYwOW9MozGFbVqR4eXsJVMpJIVKSkYKwUuDCV4azO4bu0tMSlJkcqR+vOzMMpNjUpWiNKAoMMnwRr/xjBh/fPBjUjOtNgaUSCQSu7FTY/5HoLyiKJeA14G3teeeBlYDZ4BNwERVLdwKt+b+zQFITE/k2L1jNPm5Ce/tfY9fz/1K/z/6M2bTGP3aLDVLP/6h1w9U9iy09Ocix9vZWzrGkkLlRvwN/Xji9okM++vhf+Ky/+Z+Hlv9mM3jXk4yYlw68A2CGbEAOAEv1R0OQMvlLVlzYU0xGiaRSEoDdmjMp6iq+rSqqkGqqrZWVfWK0bmztefVVVW10Asgjt47CsC6i+v45tg3+vlbCYYMjpkHZiIC2gbaVGxT2KYVKW5ObnlqdCKR2Mu9ZNMGxJdjLxeTJfbz/r73LeY6Vu6oH8tUitLGoB8AGL/lM/3UzAMzeZCce+kiiUQiKcnEp8cT7Bes38/IytCP11xYk6sCvZKIu6O7dIwlhUZEbATjt463mM/MergkD5MzkllwfAFpmWmApTMPsPfmXgI9AwHRvbKokI5xUdD4aShXC5esLMKqPcvUlkLTuOvqrlLCTSKRPBL0qd4HgAXHF/BD2A/6+dUXVpusm3torn58fNTxojGuCHFzdJMNnySFxsKTC63OR6dG68dJ6UmF6nt8eeRL/r39L6qq8vvF362mjy45vYRvT3zL2gtrTeZntp9psj+/+3xG1h+Jv7t/odlrjnSMi4r/7BXbkE8YuWaSfrr5suYELw2WEQSJRFKqmdZ2ml3r/okwZHVoHAq8GV+x4+YoUymssf/mfvbc2FPcZpRYLkWLwlbjyKqfm0FJZsmpJQCoqkqbFW1ovqw556POF7gd6ZnpLD61mJe2vMQPYT8wff90k9QpHbomN+lZ6SbR7KeCntKPxzceT60ytZjaeioOStG5q9IxLiqc3WG84Y/+s3uRJocn75hsfoZEIpGUGnKbI/h8w+cLyZLiRTrGBq7HXafzys4sObWE8dvGM2H7hOI2qUSy7+Y+Bq4fyAubXzCJwK4bsI6PO34MiLSE2NRYlpxeoj8+ZMOQArVj+7XtNF/eXL//0+mfALibdNdkXeidUP649AcAGkVj0hFTURS6BHbB392fl5u8XKD22Yt0jIuSio1FMV7t3vRJTCIs/BoHIkTzqYO3D3I/Ke8C+hKJRPIw46A4sKTPEip5VNIX1TT1a8quobvoW70vr7d43WT9i41fLA4zCx03RzdSMlNMlDceRVRVpd+6fkSnRvPFkS+K25wSjU6F4vCdw/q5rlW64uPiQ6/qvQBRgNdxZUfmHZlXaHa8uvNVk32d+orx77qqqjy/+XkS0hMA8b6QkCbG5V1Fh8z53eez/entxfbESDrGxcGzq2GI+CTlqaq89UDk/nRb0407iXeK0zKJRCIpNFoEtGDzkM182+NbwkaHsazfMsq5luPTLp/StUpX/bqNAzcWaQvYosTN0Q0wbXd9KvIU847MY/eN3cVlVpGz56ZMmygonDROFnOfdRbF/i4al2zP3XV9V6HYZIxxPvM3x03TKlIyU9h/az8AH3X8qNBtsQfpGBcXjQaJ6PH4PYxyKKuf7rm2p0mVtkQikTwK1PCpQdjoMMJGh1HVu2pxm1NouDu6A5CUIQrwktKTGL5xOD+d+omJ2ydy4v6J4jSvyLAVBDKX65PkzM5rOy3mjHONVz+xmg6VOpgcL+si/I5JOyYRvDSYvTf35vn+SelJBC8Ntnlc1/EyPSvdojgwMjmSuYdFwa3ub6O4kY5xcVOxMTy3nsMR12mbLPLO2i1v9cg/ZpNIJJLSiJuTiBjr8oxjUmNMjhsrdhQ0USlRRKdE57ywkJi6eyq91vbiWtw1Nl7ZCMBXj31lUiQ2ZdcUTt4/WVwmlkhCboQAcHDEQaa1mcaEpqa52vXL1+e7nt8RVCZIP9eqQiuTNS9ve5nw2PBc3zs1M5U2Kyy1xnW5zTpC74TSfJnIP9Y55WDa4c7JwTLyXRxIx/hhoFwNXKfH8F0rUbWdomYwdevEYjZKIpFIJAWN7ong1birgNC0B5FmAhByPaTQnhp2WdWFzqs6F8q17eHv8L+5nXibAX8M0Dd8aVOxDZ92/lS/ZuvVrTz797PFZWKJxt3JnaH1htosWlvce7F+bK0Y1jhH2V6ux123Ol/Bo4LJ/vObDcW0X3T9gure1S3OqV22dq7vXxhIx/ghQtNiDCcjRBL9ptt7yciUGscSiURSmrgeLxyJ9ZfXA7Dv1j4Amvk3069ptqwZwUuD+fTwp5YXKAVkqAbH393RnZYVWnJwxMFitKhkU9OnJj2r9cxxXVlXQ6RWURSL47P+nZXrexvrI+uo4FGB+uXq2zzHx8WHDQM36NvE6yjKJh7ZIR3jhwxlejRdksQjtgmrehSzNRKJRCIpSIbXGw5Ay4CWNPvZ4AxPbGr5lND4MXNBEnontFCumxd0Dpq7kztho8PoU70P1byrFbNVJYvkjGS783P3DtvLrqG7aF+pvX6ubcW2+nFuO+Tp0i9GNxitn1v1xCo8nT0JGx3G1iFbLc7R2Wrc+KNH1YfH35GO8UPIp4OEvt+B9Ciibh4pZmskEolEUlD4uPgAIpXCOHLq6OBosVYnX5VfLkZfpO0Kg/Pz4YEPC+S6ucFYhSM7fN18iUyOzHmhRM/txNt2R1t9XHwo51qOntV6smXwFtpXas8HbT/QH9dpD9uLLso8tN5QAF5r8RrlXMvpj1fwqMC2IdtMzgnwCABEasfg2oP5ue/PzOtaeDJyuUU6xg8h7gGNeK/GQAC6bBtD5gwf2D4TsmRBnkQikZRkdPJZP5/5Odt1joqlo5xbTt4/ydW4qwxaP4jE9ET9fP9a/fN97dyic3YnNJ1gUgRmTjnXciSmJ3Il9kpRmVaiiU2NBWDV+VW5PreiZ0UW9lxIFe8q+rmvjn6VJzsCPQM5MPyA1cY85d3EBzyNouHA8AP6Ijt3J3dmtJ9BM/9mVlM7igvpGD+kDO1k+ETftEZVgm+sQZ1ZFmb4wJk/xVb3tfYFkBI3EolEUiLpXrU7AF0CuwAQNjqMDDVD3wQhrzz797M8se4Ji/niiMhuitgEQKPyjVg3YB0r+q2w+phd93j9pc0vFal9JZWolCgA+lbvm6/r/DHgD/34XNQ5fjplX+S4uX9zgsoEoSgKns6eVh1cRwdH/nzqTzYN3oSns2e+7CwKpGP8kKIoikUxwlJvbRXp6udMF5/6DT4sA3+9Dgu7QC5zhCQSiURS9HSs3JEugV34oJ14lD2/+3xOPiekygbUGkAZlzJ5um6WmmWiK+vl5MXTdZ4mbHQYACvOreDwncMkpSfl8xXYjy4SqYseBvsFWygXAPrXfC/5XpHZVpLROcZP1X4qX9epVaaWfvz0hqeZd2SeXbKxqZmpBLgH5Liupk9Nqz/vhxHpGD/EuDu5c/jZw/o3zS/KlyW4RlViHBzIBNSGg6C5IeGd0B/h9nGYWQ7Sk61fVFXFV1rRvSFKHj3m77jID3uusCb0OrsuWG91rqoqVx8kEptkUF9Jz8wiMiGV+JR0ElNloxtJ6WZo3aHM7z7fJCdTF3HzcPLIs+Nq3qwhIT3B5B4AL2x+gf/b+X95un5u+fXcr/pxTnnT/YMMaR6y2VX2JKYncjnmMlAw+ei9qvWyuH5OJKQnWJV+K8nkP4lJUqi4OrrydJ2n8XTy5K3dbwHQqVqgOJgUCkkwoMdkPtq3HJKNZFNmG30ym3oVnNzgI3/rN/kgGhzkZyRJ3lFVlddXn6B3wwACy7rz+ZYLJsfLeziz9IXWPL/kMPfjU21cxTo/jWlFlXLuTFlzgg+eaECLakJyKCoxDW9XRxw18ndXUrL49fFfiUuNo33l9jbXeDh5EJ8ez8YrG3m85uN2XTc5I5molCj+Cf/HZF5FxdPJ8hF2fFp87gzPA1+EfsGS00v0+8aSYdYwbgUemxqrjzBLBPFp8Ry6c4iugV1NCioL4vs0NngsW65u0e8vP7Ocl5ta10QG8YHnatxVapd5OPSHCwrpGJcQ+tboS71y9ej/h2XRxJ+X/+TPCl4cGXkBZ8URZpq98czNQfrmzB/QcCA8RMnvkpJDXEo6jWeIN9N1x25aXfMgMY0nvs5by9HnlxhE5wd/u9/i+PmP+uDiqOHI1WgGf7ufsR1r8ONe0w5Ovp7O7H+7O86O0omWFD+NfBvluMbdSUhavb3nbWJSY+hcubNJkZQ5T/3xFJdjL5vM9aneR5/bq1PDaOrXlOP3jwOYdJwrLIydYn83f5w1znafG5MaU2oc4xVnV/DJoU8Akc9rnLpgLwdvH+TFLS8CQhLNGN3PNz80KN+Ar7t9zeQdkwEIiwyzufZO4h0+Pii62227ts3mupKIdIxLEDV8arCo1yJm/zubMQ3HULNMTU7eP8nnoZ8D0GJ5C14MfpH/mx6DcmUnXPsXds01uUb9lMXMG9EOVycHulZIRfmqMax9XnwBvHICylYvMJt/2rgHv8RzXPZpx0uP1cPdOftfudkbz3D5fiKLx7TiyNVoavl5MOefczzTqgrNq2YfaZAUDGtCr3P8egyzBwZbPR6VmMa3IZf48/gtutcP4NdD16yui5gjoly3YpJpP2cHAP5eLnSr58+lewl0qu3H0FZV2HrmDhlZKhoHheZVy9Kwkrf+cfKfx2/yysrj2dpbd9omk31zpxggMiGNOtP+4czM3rg5aTgUHsXVB0mkZGTyXLvq2V5fIikOnB0MDuScQ3OYwxx9jrA1zJ1iwEQPWEUUaC/tu5T4tHim7pnK4TuHCbsfRrCf9b/1/GKco7qo1yIalG9g13nf9/yecVvHWbTLLkzi0uI4FXmKdhXbFYpCgq6hC8CWq1t4uYztSKw1VFXVO8UAQ/8aqh87OTgVWDvlrlW6svLxlQzbOMzkQ0x4bDi3E27rn3L0XGtoKKJTWiktSMe4hNG2Yls2DNyg32/m34zh9YbTYrloJ/pD2A/8EPYDx0Ydw7FWN3jsXQDu377GoP9tIxlXXl5xTH/+IqcW9NQYaSV/1YQUnLnY9TtqtR+QoyNrjcivuuAbLZwZE+GWAxA3YiPeSjJqzHWUVi8AkJKeyYD5+zh/1/BYr/rbG02uufLwdTa/2pkq5dxwUBRcnTTciklm7qZzfDakiYwEIt44wXpHI1VVSUzLxNPFkYjIRMp5OuPtKt5IMzKz2Hb2Lm+uPUl8iiGn7/j1GGr5eZKSnsmpm7EsfaE1Z+/Es2DnJc7dET8rY6c4/JN+KIpCWkaWycOHSmXciJjzOBmZWVbTHkZl45gOaFqZAU0rm8xtOX2HlYev07J6WT7ddN7muXUDvHiQmEqWKpx5gAYfbLZYV8nHjR4Nci4ekUiKEp0ja0x4bDg1fGpYrrWhSmQcmfZw8gDAQXEQWrYu5UjKSGLE3yOydbjzg64wDEybSOSErgAvJsW2Y/wg+QFdV3dlbqe59KvZj5P3T3L07lFGNxxNyPUQapapmatGIZ8d/ow/Lv3BrA6zeCoof4Vs5uy6vovTD07r9xeHLbZo2xybGouzxhk3Rzer17ideNvq/Pc9v6d1hdYFZyyG1szbr20nIyuD0LuhvLRFqISEjQ6zyGH/pd8vBXr/4kY6xqUAZ40zx0cdp+mypvq5ZsuaUcWrChOb/h91PTvS46swwPKf/0vpU/BJTyAdRzY4v0cth9u4kkZwyAsQAufbfUbd3uNyNiItkZhrpyizvBe+2SzzXiGiiArAxtcAmJY+Hk1WNRSq0tfhEE0cLrMssxd7XV5hZUZX3s4Q9+/9391Gr9mBtEwRjXB11DB3SOOcbcwnN6KT+GFPOM+1q0ZNv+KRnEnLyGJByCUCvF0Z1ko8Vr0fn0rrj7fr1yx4tjkZWSo/7QvnelQSkQlp2V7T19OFyATLvN/Tt+I4fStOv9/zy90WawB+eK4lner46h1yWx9SCioXuFfDCvRqKHLoX+pUkzfXnKCMuzMRDxL5aUwrVBUcHEw/HKSkZ1Lv/U3WLkfV8vZ1jJJIihJrzq5Os1ZVVRLTE0nOSMbP3Y+0LPE33rVKV0KuhwCwrO8y7iUZlB26Ve1mcq1M1aBepKqq3VFSndqFPc60rnhwUtNJdl1bR2Uv8WF4yq4pHH/O8olReGy4Pq1w6p6pLD61mPPR4kNyfHo835/83m4bZx2YRdtKbTnz4AwAS08vzbVjvO7iOmr41KCpf1OrxyftMH39KZmmzU4uRl9k0PpB2dps3CXOGD83PzQOmlzZmxPGkeL3973PX1f+0u+vPLeS2Qdn6/fHNR5H3XJ1C/T+xY10jHNBSnomrk6mv4CnbsZS088DjYPCl1sv8t0u8Thr7X/a0bJ6OWuXsUpWloqiWI/2mfP70Ru4O2u4Epmoj5h5OGtITJuNoknBs47oRHM9/jpv73mT1PvdAFFteuXjfiZOQ5fPdnL1ATzTMpCENv/yR8jPPHX5ff3xugfepMVOTxJwY0DLmsx6qhEujmZ/hOnJ8HEljIWF/i9gKWO6NcbH1ZFa1aqS8SCCO1/3IpC7Fq/nc6eFFnPjHUXEeJhjCMMcQ5hc9ls23DbkUOmcYoBVodcJvRrFtte7kJmlcuZ2HMGVfez6XqZlZDF68SGyVJWPnmpEkL8nUYlpHI6Iok+jigCERkQxY8NpTt0UTuKS/RF0DPJl6QutuXI/gaUHImhQ0Yd314XxVNNK/HdYs2zuCNvO3GX7ubtU8nHji60X2PpaZ45fj+HNtUKm6T9davFGrzocvx7D3kuRtKpejtdXH+dunOkb4zu/W38DnfDL0RxftzHmTvEPz7Wklr8nj30eYvOcWn4ebJ/SNVf3yRf3z8M/U6Hjq1DTcF8njYPF99vaj93VSUP4J/3YfvYevl4ulPdwpkpZN0hPAmePwrVdIskDuhxjY85FnaOpf1Ma/2wIBBwddZT7SUL5pVVAK71jXM61nIk8lvmj9r/D/9aPo1OjLVQrrGHcLjg9Kz3Hx/c3Em4AWI1yZ4euAC9TzSQxPVEf7dZh7KgBeqcY0DvFACHXQ2jm34zj947TpUoXi/skpSex+sJqVl9YrZ+r7l09V7YmpSfxwX6hHGXs1O6+sZt65erh62Y9VLT96na6VxP61cYpEjbvkyE+ZExoOoEFxxfo5/OSq5wbzL/Xxk7xh+0/ZFDtQYV6/+JAOsY5cORqFIO/PWD12DcjmjNxhXUnZMh3B3ixYw2yVFiyP5x9b3ejoo8bN2OSiU5M405sCi/+bLtfve6xNAjnLTIhVZ+naY3EtExAg5rpQfzZj3Cr+iOOHiLX0sVvBy5+O9g+6F8cHBTe3vM2h28fZlSDUex4/Tk0RpG8JqP+DxASPpfnD6RW5A6OuGof+ZwSXx1Tv2JEYCQBkf/SV92NO6aO1ZDyv/HLS4+ZONCO5asTOOMCSWkZDFuwi7m9A6jkoXB99xIaXfqenPg6cCezXvoGHzcnbsem6L8XY9pXZ8n+CC7fT6TGO3+bnPPp4MZcjkxg/fFbbJjcEV9PkQc17udQtpyxdNDNI6JuThqS061rQu+9FEmtd/+2mP/j+C38vFx4t199/c/vZkwyyWmZpKRnMuuvMxwO53qSAAAgAElEQVQMjzI5x/y+3+26rP+AVZY4vsIT1Q5lxfBP+vHhhjMs2R8BCAdRVaFbPX92nLvHl0Ob4OvpgrPGARWISUpn29m7rD1yg/WTOtA40FQzVZcjnJmlkpGVxb9XosjKUulSx88iImtB/B1wKwuO2eSeJUbCqd+hyTBw9TY9dmABZKQIje67pwzzV3aKbZU2UKsbNBkOZa08Lr2wBVY8LcavnISbR1CqtqNHA/Fhhzth8GFHMR78IwQPyf71SCRFzMCggUSnRHP47mGG1xvOqztfZfbB2TxT9xmTdc2XNdeP/d0NykNlXctmK6P1VNBT/HFJNHWIS42zyzG+FHNJP94asZV+NfvZXGtcbJafXOG2K9rqHc77SffptqZbDmcY0BWRASzts5TmAeJ7lZ6ZzrpL6zhx/4TFORFxEbmyr82KNhZz6ZnpTNw+EYCKHhX18xObTuSb498A8GrIq/rXpUs5UVA4/eA01b2rW3wY0EXfm/s358jII/x85me6BHYp1o5xJUWXOLcotnKTCpuWLVuqoaG2HcPi4MutF/hq+0UAJj5Wi+PXY9h36UGurtGnYQU2nb5TIPaUcXciKS2TtAzbIttta5bDQVHYf/kBzaqWYd2EDizeG872c3cZ2CyQL47MJcElJNv7hDwTYrPyV/20JkqSfd+DBc7P89wzw/AMsj+XTE9aIhz4RkTwuk+HmKtw5xR4BsCPPQzrAhpBv8/AJxA0LvBDd1L7L6TuosIt0nDSKKRnqpyY3ouj16J5/qfDFmt83JyITU63crYl3iSQijODNHv4NbMbz2q2M9tpMQA/ZvRlRWY3tru8aXHevjL98Rz0P5pkU4iYmJqBh0s+P/OmJYFzLlMM4m5D1BW4dgB2iKcWdJkK7r7gWxvibkF0uJAO3D4zf/YZ894dcU2Asxtg1Ujbays1h1tmH2annAev3L3BK4pyRFXVlrm0tETzML5nPypEJkfy2OrHcly3sOdCxm8dDxiily2WtUBF5ego09/7hLQEHlv9GCmZKbzR8g1GNxxtcT1jstQsmvzcxGTO2mP/G/E3+CL0CxOlgj1D91DGNXfNSjKyMmi2zPA0aHm/5byw6QV92khuebv12zxb/1kAFp9azJdHvrS59p3W7zCi/ogcr2n8PXHRuBA6Uvx9HLl7hDGbxlisPzbqmMlrChsdRlJ6koVz3apCK2JTY+lQqQOvt3wdEBHoidsnsqLfikIrljTGuEGMjgblG+hTTlw0Lhx+9vBD1co5J+x935aOsRHmBV86Fo5qwU/7whnTvgYVfFz5cW84F+7Ec/5uPPUrevPX5I5cuZ9AakYWjSr7kJWl8unm8/qony0aB/rQJLAMZT2cKefuRMfavvSYZz2PU4cuipcb4tPiaf+rqV6mq8ZVn+dU2bMyGwdutJ6npKoQeQE0TuAdSNYXdXFINkQ8M1QHdrh2p/7YRVTxLyTViN9ehLA12S7JeD+aG9HJlPd0xiv9Aat+WcTUiGZos5mtUq+CiKasGt8OHzcn0jKyyFJVXBwduBuXSttPRN7uby+3F9q5KbEGhzEtiVtZZfBw0uBzYwcJV4/i2WIoe6K8GfXjIf09HMhihGY72zKbE487dZQbrHOZnv/vydvXwDX/8jxW2fUZ7PzIdO6x96DDq+DoDFlZ8OAS3DgsosL7voLr/xaOLQAvHxCOtcYJHlyG7zqBufB842FwcmXuruvoBu/ehDzk50nHWFLUWHNUzFnebzmVPCoB4OcupNh0kUZrqRlh98MY8bdwAAM9A/mt/29W1wH87+j/WBS2yPR8K45xy+UtLfJhj486nqc82HFbxnHgtnhiO6bhGBPpN3O+6f6NPkob7BtsVWpMZ++0vdP48/Kf2d7bnvzkpaeX6lWhAHY+sxNfN1+2RGxhyq4pVq/Ze21vbiXeAuDkcydN0mKscfK5k8w9PJd9N/cRERfBuv7rCCoblKNt+cXa79vyfssZ+bcIPAwMGsjMDgUY4CgC7H3ffuRTKZLSMnji671cuS/+0QaWdeNGtKFr3Jr/tKNV9XL0bmiIKH093DKHtHaA4ZGVg4PC233r8XbfeoChsMGeAged47v/UiQjfhAtoT8ZFIzGQeGJxhWzO9UmXs5ehI0OY8PlDbhoXOhWtRuODo5kqVkM+GMAEXER+sK9Q88eMq2KVRTwMyTWO0wV6RmxMVG4pdzFOaAevQr7E+PA78Wj85BPwEb02nFWWaq/egoWPQUPLjEUGOoKMUEDKXNpHZf6/MLSiDL8cjyakzN64+niZEhGvbgVytXE2bsyOLmCqlKBSCKmtYZNU+HoBrgaZIiCaqlkNPYE2D+XTh5+hL+7m2G/XuVgeBQrnWfR2uE8HznZ13eeZiPh2HLD/n/2wqVtIq/2/nlYJ6JBzKlqWNNzFtR7HLwrgcbZ4OidWAl/TAA1E3p/DElR0PUd0Nj4s09NgE8qWz+2czYcmC8c8sOL4J+3sn8dDQbAreMi8m8NxQEenyde729jwdEVXMsIh9fBCfrMET8Lc8rXgvfEPxVUVbRCB1OnuHwQPL8JPP2EE68oovnNp0Z5js1GwpNfy8Y2khJJvxr9THKEdXg4eugdYh22HF3ApOX0jYQbLDi+gDdavWF1rc4pXtJniT4a2ue3PrzS/BX61uirX2etSCyvxWGdAjvpHePlZ5abHPu2x7e8vE2k+fm4+NA5sLP+2Ptt3+eZv0xTToJ9DY5egId1FRpfN18ikyMBoYiRXZRbVVUTpxhg3819DAgaYNUp1tG2Ult+v/g7AO/sfUc/X927utU0jgO3DvDLWYPqg6ujlffFQqCJXxOLVJMmfk14vtHz/HTqJzydi6cAvSh4pB3jwxFRPP2daf7wHxM74Ovpkq30VW7RXSM312of5Jun6HB2PFnrSZN9B8WB3/r/ppd6A2j9S2v2D9+fY4tHnzLlAENOWlJ6Es4aZ24n3GbwhsEkZyTj7ODMyAYjCfYNpktgF2LTYrkYfZG3dr9FOddyrHlyjX1i7w4O0Pol8WXMpW3g4Q8LO4n9/1qK5pe5tA6AoE3PMguY5QrM0R6s+ZghZ7WgSLyPMq8+qxzdwNVGW26A9yO1bbtVoTddp7fh2IBvTNdW0L6hV2oGjYbALLO0l63vi6/s2Cxk+9jzOdR7QqQORIXD5e3CSVXN0nWGLIbwPeLeJ1fB9YMiYj7DRpR6+ErwqQIVbDQuyMqE5BjwsJKy88zP2dtuC0URaRTGXR7fuCQcYh06x9e9HMyIzdt9JJKHjDmd5jC381xSMlL47eJvzDkk3tSyc4KtYe74nYs6l+M5jX0NEc6bCTd5a/dbJo6xjqAyQSY5yXlhWN1hfHr4UwAyVNP20B0qddCPv+xqmhZRv3x9/fjoqKMM/HMglT3Fh/5TkadMCvR6VuvJ1qtbWdx7Mb+e+5WtV7cCsDF8oz71QkdSehK3Em4RVDaI1r8YJNI+6/IZb+56E09nTxOJOoDRDUaz9MxS/b7xU/qNVwxPqae3m87zm00ETgEYv228yX5RaQZ/3/N7Ju+YzMDaA+lTvQ9pmSKFxfjDVGnlkXOMVVUlOT2TOf+c4+cDhmjWB080YESbqnrViZKUN5MfnDXOhI0OE/qPm0SOmXHaxZQWUxjTaIzVc1VVJSMrg7+u/KWvyjUmLSuNxacWWz03JjVG75B/2fVLulftnvvveZA293h6jCFyCPDcevCrB1/UEft1+sKFfyzPz4tTPCNWOHmKg4hY3gwVDqvGCWJvwJcNxboMI6d47DahfBBgJm6v0VZ0GzvFOaFxNKQNdHsfru4Xzm12ePhDokG2iXOmVcYWTvHL+yGgITQaLPZbjRVFcGtfMKxp9RI8bhotyRYHjXWnOL84uUmHV/JI8V2P7/Tvla6OrgwMGqh3jG1p4NrCy9mL+d3mk5aVxushr9uUGzN25pw0Trg7uutVEozROU8AQ+oMobp3dSp65u1Jp+5exng7exOXFsfuobtRFIXDzx7m0J1DtKrQChDd4HQRX/01HJwo61KWTRGbcNG4mKRQzGw/kx7VejCkzhBaVWhFI99GesfYUbF0j8ZtHceJ+yfoGtjVRHKtYTnxvr/i7Ape3fmqyTkjG4xk6ZmlBJUR6Q+2gkE67WAdCopVLWvzJwKFhbuTOz/2/lG/7+ggvh86x9z4Z13aKNWOsXGr2uw4N6uPhQzbo0bzgObsHbaXjis7msx/ceQLmgU043bibd7c9SYdKnVgfJPxTN8/nfBYyw5jIJqOnH1w1kKr0RavhQg946Mjj5q8Ec4/Np/I5EhmtJ+R/QUUxbpzZDyXngz3zorisKxMEQG9uBXqPwkd/k9EUFVVtMe+fgg6vm4aeTRG91hQUaCKkbC6T6C4Z+ID+KymmBv1B1RplcN3IJcMWii+dCRFCYUHvzoQfRW+agz1+8PQZabnqSr8PADCdxnmBnwDf04EFx9oPxm6WBb8AcJJrt0L9v4XOr4GLqX3MZpE8jBycMRBolKiCPQKNJl3d3Jn3/B9nH1wlrKuua/z0MmY2XJ2QUizAUxuJlQeNg7aSM+1PfF18+VOoqHYfNV5Q5viEfVGFHiAKS4tjhH1Ruhfp6ujq0kKha3OeronoOZ5xQNrDwSgfSURDHJzdOPpOk+z5sIaiwg1oE8tCLkRop/7oN0HeGglHw/dOWSyfsvgLVTwqMDv/X/XK4ZU8RL689PbTee/R/+r16b2dPKkR9Ue+qLFWmVq5TviXhjoJPp0vxOlEbscY0VR+gBfARrgB1VV55gddwF+BloAD4ChqqpGFKypOXMzJpmXloZSt4IXU3rVoePcnCOC217v8sg7xTp8XHz0BQdbr25lzfk1HLh9QJ9sD7Dv1j723dpncW4NnxpU8apCY9/GjA0eq/90qSMjK4Nd13fRtUpXNA4aolOiuRZ/jd03dusfazVf3pyZ7WdaRJ+bBzSnf63++XtxTm5Qubn4Amgy1HKNokDDgeIrP3iUL5AoZkZWBtP3T2dys8nZy+K4lxNfIKTLbN1bUWD0esv5ZtmoOBjj4gXdc0jZkEgkhYK7k7vNVAlvZ2/aVLSUDcsNHk4e+kI9c0LviKLLVedWMa7xOHzdfDk26hjfn/yer499TfDSYMJGh3E30SCDWVhPXfPikFnLh32vzXtW177X5j1+v/g780LnceTuEeZ1nQfA+SjrXTY1isaq1N3EphP10XLjaPDI+iMJcA+gV/VeDKkzhMsxl/F390fjoGF2x9mMjh5NRY+K/B3+N/OOiHvr0j0eBnTR+V7VehWzJYVHjo6xoiga4BugJ3ADOKwoynpVVc8YLRsLRKuqGqQoyjBgLmDF8yh4Xlt1nHXHbprMnbkdZzL3ao/aDG9dlYwslUo+ro9MmkR+6FmtJz2r9aT9r+2JTxPtf3WPsYz572P/5bEqj+GgZF/E5OjgqBczB6GxWda1LE38mvByk5f1EjbWUjLe2/sejX3/v71zjZKquhLwt5tukIc8I0jAFlrF6BhBeSiiLBUQBJSHIOhEmEQGA+OMJjEGB5kwgUwSTRzjyizFgBgxCkgCLaygIJIYlSbybJBngyAvaaShAXk0XbXnxz1dVFVXdTdtddWtZn9r1ap7zz331t73nHvurvPY+3raNWn3NbVKPkENMiVvCr2ze9OjTY9yx1fsX0FOkxxezn+Zudvm0u3SbgQ0wL4T+0I9MW/vOGfMzrtnXq2LMpQqVJWjZ45Wq5fNMGob9TPrs3zPcsaeGEurBq0Y/c5oHrn+EW5re1soUEfPy3pGnBPuo/fk2ZMs3LkQOP8gGRUxZ+Acxrw7huNnvffQ8A7Dq3Re7qDc0Dk7jpb3EBUv6EidjDoENEBAAyzdvZRjJcdoXLcxK/bHjmcQ691XkUeLOhl16Ne+X2g/PEBHg6wGoeksA3MGhgzj8wltXdO0b9K+xkKI+4Wq9Bh3AwpUdSeAiMwGBgHhhvEgYLLbngf8TkREa9gXXGkgWM4oDqdpgyxWTeydsFC0FyIfP/BxTG8aqsqe43vIbpwd58yqk5mRydqH1nLTH2+iJFjCjzr/iD7t+nDy7EnmF8xn1qZZLN+znNGNR1dqgJfJtuvYLrIysvhmo2+Gzik4UsClDS9N+Gra3cd2s+/EPrq37l7uPn33ne+ypnAN87bNq9K1oofiohm2cBjTek/jlja3VJjPqJizwbM89v5j/H3f3yP8mxrGhUqdjDoUnS6i75/68kb/N1h/aD3jl41nw+gNTN8wHYBBVwyKOCd8TvOJsye46/K7mL11NrmDK3aFdj5c2+Ja5t4zl3vm38Nrd78WsbCuInKa5oS2tx3ZFtru2bYnj3Z6tMrX6fFmDzaM3hAxzS9/VD4f7f+Ice+N44aWkV6qZvatogeiSrikwSVMunkSr376Kv3a9WP6hulM6TGl8hONr01VDOM2wJ6w/b1A9JhNKI+qlopIMdAC+JIEMmnBRt5ev5/iU2fp0KoR2w6eAKBj2ya8+J3O1MvMoHnDupw+G2Tj/mK6nkdIZiM+sXrYRSQhRnEZmRmZrPrOKkq1NCLM6JNdn2TWplk8t/q50L/naB678TGGXDmEFvVbsOPoDgbnVhznflqfaaE5ZfEoDZZSEijhyQ+eZPCVg+l9+bkgI8Vnihm5aGSoF6WMwVcOZuz1Y8nKyOLiuhfzcv7LrCk8v/DM0XoNaD+A1o1ac7r0NOPeG8eqg6t49P1H+XDkh+e9Aj2d2X9iP1uKttCjTY+vtSq76HQRs7fM5sX1L4bSemX3quAMfyIizYE5QDtgF3C/qh6JkW808LTbnaqqfxCRBsBbwBVAAFioqhOSIbfhX8LXjJT5NgY4fOowVzS9ggNfHYhweQaEPD2A59N3+9HtNK3XtEodGOdD24vbsnbU2mqfHz4VIVMyKzWKp/SYwqSPzk0bO3zqMPtOeJ1wCwYtQES4tc2tET2nbRq1Yd+JfXRs2bHc9arL/VffH4p0uPLBlee9uNKoHpUG+BCR4UBfVR3j9h8Cuqnqv4fl+dTl2ev2d7g8h6OuNRYYC5Cdnd159+44Pk5jEAwqN0xZGjOy2Nap/SLCDxu1i6o4tq8O79z3DqsPrqZDsw7k7c/jVOkp7sy+k4AGGLEocTOBxncczzUtruG6b1xHk3pNyMrIYmfxTkoCJbRq0IojZ46Q0ySn8gsBy3Yv4/G/Ps7MvjNZcWAFt7a5tVyPRTSBYIAMyTivKUQnSk6w8fBG/nWJ5yKvzHF9sll5YCVjlowpl54pmSwYvCDmEGPhyUJ6vXXO2A13/B9N3oN55UKvVoVUB/gQkWeAIlX9pYhMAJqp6k+i8jQHVgFdAAVW460DOQPcpKrLRaQusAz4H1WN4brlHBbgo3ZTlXY2egi9+ExxaMF2w6yGfOUC7/htqH1X8S7uWeC5K60o0ms4JYGSkOekmX1nhlypLRu+LCL0dhmFJwvZfHhzaDGj4T8SFvlORLoDk1W1r9t/CkBVfxGW512XZ4WIZAJfAJdUNJWiOo1sMKhMXLCBJvXr8tLfdvCr+77NiK6J67U0/ElQg+QW5NKhWQdyd+SSfXE2d2TfweLPFnO69DTT8qeVO+e3d/yWO7PvZEGBZzyVLY4YOH9gwuSa0G0Cv/zHL/n9Xb9nW9E2nl31bFw5EkW00VdGtOFaGixlfsF88vbnsWS355nlgxEfVGk+7Vvb3uJnK8pHNFo0ZFFC57oFggGCGiznkqmMM4EzdHm9cttz7PVjQ6vl9xzfQ/8/96/S7w/vMJz/6l5+TntV8IFhvBW4XVUPiEhr4K+qenVUngdcnkfc/jSX782ofL8FNqpqZFizKMwwrt1UxzCODtscL1+qCWqQX6z8BQ9864GIKRaVEeue+E03o+ok0jDOBLYBvYB9wCfAg6r6aViefwO+rarfd4vvhqrq/TEv6LBG1kgkQQ2y/PPldG7VmUZ1G5XzilFGIBig8GQhd/2p8hW1+aPyAUIhO5fct4Rdx3Zx/SXX0yCzQYU9sEENJnw4Ebz505WFEK2I8Z3GM66jFy1q+5HtDH17KEOvGsqkmyex4+gOhi0cFpF/YM5AFu085/f46ZueZurKqHDReOFBJ3SbwA//9kM+2ud5LQn3gR3UIK9vep3NRZsZcuUQHl7ycOjcfu36senwJg6dOsSAnAH0ubwPjyyNdGo/6+5ZdGrZiZ3FO5maN5VPvvikUl0fvu5hZmycUS49ES82HxjGR1W1adj+EVVtFpXnCeAiVZ3q9icBp1T112F5mgJrgN5l60jiYW127WbEohFsOryJrIysmJ4fBCF/dH659HWF63ho8UOh/V7ZvXj+judrVNZkMSR3SDmXaWYYpy8JM4zdxfoDz+O5a3tFVX8uIj8DVqnq2yJyETALuAEoAkZaI2ukA8VnitlStCXC1dGag2voeEnHaocxrWkOfnUQEaFlg5YRw33xuP2y28nbn1dlv9IAo64dxY+7nvNp3Gdenwh/pclk8dDF5Xy3gvcnYezSseQdyCt3LH9Ufo16n0mGYSwi7wGx/PRNBP5QBcP4x0C9KMP4pKr+xu1nAguBd1U1piXzdaa/GenF86ufZ8bGGbx737v84K8/4MtTX3K85DinwoIVxTMKy3pW773iXiZ3nxx3FCjdOHn2JDe94b0bnujyBF0v7RrXV7LhfxJqGNcEZhgbRuL4cN+HTPxwIj/t/lPmbJ3D0KuG0ufyPsA5d0K5Bbk8/dHTEec1rdeUo2eORqQ90eUJRv/T6HK/0WtuLwpPeRH0XrjjBRpmNWTlFyvZcGgDKw6cc2V0W5vbWFO4JjTfMB4jrh5Bs4ua8dL6l8jMyKQ0GOlQv6rG7fzt8zlVeoqgBgloIKbsicYHPcZfeyqFiLwCnFDV/6jKb1qbXbspCZSw98RecprkcDZwlpJgCQ2zGrLh0AYe/MuDtGvcjoVDFsY8t8wwXvvQ2rijdelKmW7rHlrn284So2qYYWwYRjn+svMv5O7I5eP9H1M/sz4rHljBV6VfMfnjyWRmZPJMz2eqdd0jp49wuvR0RPjX4yXHueXNWxjXcRzjO40HPDdpmZKZ9r7EfWAYPwscDlt811xVn4zK0xxvwZ2LasMaoLOqFonIVOAaYLhqdEzw2FibfWGiqkzLn8aAnAGhqG3RnAmcoSRQEoowZxh+xAxjwzCMGsIHhnELYC6QDXyOZ+AWiUgX4PthXoS+B/ynO+3nqjpTRNriudfcguehAuB3qjq9ot+0NtswjHSmqu127RrzMAzDuABwrjDLuSdR1VXAmLD9V4BXovLsBdK7y94wDKOGsJBwhmEYhmEYhoEZxoZhGIZhGIYBmGFsGIZhGIZhGIAZxoZhGIZhGIYBmGFsGIZhGIZhGIAZxoZhGIZhGIYBmGFsGIZhGIZhGEAKA3yIyCFgdzVO/QbwZYLF8Qu1WTeo3fqZbulLdfS7XFUvqQlh/EotabP9Iotf5ACTJRZ+kQP8I4tf5IDqy1KldjtlhnF1EZFVqYw4VZPUZt2gdutnuqUvtV2/VOOn++sXWfwiB5gsfpYD/COLX+SAmpfFplIYhmEYhmEYBmYYG4ZhGIZhGAaQnobxy6kWoAapzbpB7dbPdEtfart+qcZP99cvsvhFDjBZYuEXOcA/svhFDqhhWdJujrFhGIZhGIZh1ATp2GNsGIZhGIZhGAknbQxjEeknIltFpEBEJqRanqogIpeJyHIR2Swin4rIYy69uYgsFZHt7ruZSxcRecHpmC8iN4Zda7TLv11ERqdKp1iISB0RWSsii9x+exFZ6WSdIyJ1XXo9t1/gjrcLu8ZTLn2riPRNjSaRiEhTEZknIltcGXavLWUnIj9wdXKjiLwpIhelc7mJyCsiUigiG8PSElZWItJZRDa4c14QEUmuhv7CT89GHFkmi8g+EVnnPv3D8sess/I13zEicnXY760TkWMi8niy70sFciT9nrhr+KKtiSPHqyLyWdg96eTy1nSdfczJ8amIPO7Skv78xJEjKfVE/Nxmq6rvP0AdYAeQA9QF1gPXplquKsjdGrjRbV8MbAOuBZ4BJrj0CcCv3HZ/YDEgwM3ASpfeHNjpvpu57Wap1i9Mzx8CbwCL3P5cYKTbfgkY57bHAy+57ZHAHLd9rSvTekB7V9Z1fKDXH4Axbrsu0LQ2lB3QBvgMqB9WXv+SzuUG9ARuBDaGpSWsrIB/AN3dOYuBu1NdP1Nch3zzbMSRZTLwRIy8MessCX7HuOt9AVyeyjYjSo6k3xN80tZUIMerwLAY+WusbIDrgI1AAyATeA+4Ktn1pAI5klJP8HGbnS49xt2AAlXdqaolwGxgUIplqhRVPaCqa9z2cWAz3gM6CK8xx30PdtuDgNfUIw9oKiKtgb7AUlUtUtUjwFKgXxJViYuItAUGANPdvgB3AvNclmj9yvSeB/Ry+QcBs1X1jKp+BhTglXnKEJHGeA/uDABVLVHVo9SesssE6otIJl7DeIA0LjdV/QAoikpOSFm5Y41VdYV6Le5rYde64PDTs1GBLPGIV2cT/Y7pBexQ1d2kts0IlyMeNX1P/NLWRMuxv4K8NVk21wB5qnpSVUuBvwFDSH49iSdHPBJaT/zcZqeLYdwG2BO2v9elpQ1uSOgGYCXQSlUPgGc8Ay1dtnh6+ln/54EngaDbbwEcdQ8aRMoa0sMdL3b5/ahfDnAImCneNJHpItKQWlB2qroP+DXwOd5LqhhYTe0ot3ASVVZt3HZ0+oWKn56NeLIAPOqGXV8pG5KtYVnCGQm86bZT2WaEywFJvid+aWtiyaGqS9zhn7t78r8iUi9ajqjfS0TZbAR6ikgLEWmA1xt6GcmvJ/HkgNQ9O75os9PFMI41NyRt3GmISCPgT8Djqnqsoqwx0rSC9JQiIgOBQlVdHZ4cI6tWcsyP+mXiDfO8qKo3AF/hDe3EI210cw3dILzhsG8CDYG7Y2RNx3KrCuerT7rqWVP46dmIJ8uLwEWW6QUAAAM2SURBVBVAJzxD6DdJkMX7AW++7L3AW5VlrUlZYsiR9Hvil7Ymlhwi8h3gKeBbQFe84fif1KQcAKq6GfgVXu/mO3hTD0orOKVGZKlAjpQ9OxWQ1DY7XQzjvZz7JwPQloqHQXyDiGThGcV/VNU/u+SDrqsf913o0uPp6Vf9ewD3isguvOGTO/F6kJu64SqIlDWkhzveBG8oxY/67QX2qupKtz8P7wVcG8quN/CZqh5S1bPAn4FbqB3lFk6iymqv245Ov1Dx07MRUxZVPaiqAVUNAr/n3LB7Mp7Tu4E1qnrQ7aeqzYiQI0X3xC9tTUw51JvuqKp6BphJkuqJqs5Q1RtVtSeefttJQT2JJUeKnx1ftNnpYhh/Alwl3krWunjDQ2+nWKZKcXOjZgCbVfW5sENvA2WrJ0cDuWHpo9wKzJvxhnsOAO8Cd4lIM/fP9y6XllJU9SlVbauq7fDK5H1V/WdgOTDMZYvWr0zvYS6/uvSR4q1Ibo+3AOAfSVIjJqr6BbBHRK52Sb2ATdSOsvscuFlEGrg6WqZb2pdbFAkpK3fsuIjc7O7XqLBrXXD46dmIJ0vZy9UxBG/YuEyWWHU2ke+YB4icvpCqNiNCjhTdE7+0NbHk2BxmhAneHNTwe1JjZSMiLd13NjAUr5ySXk9iyZHiZ8cfbbZWc9Vtsj9481+24a1+nJhqeaoo86143ff5wDr36Y83Z2oZ3r/EZUBzl1+A/3M6bgC6hF3re3iT3QuA76Zatxi63s45rxQ5eA9MAd4wXj2XfpHbL3DHc8LOn+j03opPVvzjDSWtcuW3AG/Va60oO+C/gS14jd4svJXGaVtueC+WA8BZvN6ChxNZVkAXd692AL/DBUe6UD9+ejbiyDLL/VY+3ku1dWV1lgS8Y/AWdR0GmoSlJf2+xJEjVffEF21NHDned/dkI/A60ChJdfbveH8Q1gO9UlhPYsmRlHqCj9tsi3xnGIZhGIZhGKTPVArDMAzDMAzDqFHMMDYMwzAMwzAMzDA2DMMwDMMwDMAMY8MwDMMwDMMAzDA2DMMwDMMwDMAMY8MwDMMwDMMAzDA2DMMwDMMwDMAMY8MwDMMwDMMA4P8BiAd6E55th/EAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df['sin_phase45_mixed'] = np.multiply(df.sine_noisy, sine_wave(100, phase=45))\n", "df['sin_phase90_mixed'] = np.multiply(df.sine_noisy, sine_wave(100, phase=90))\n", "df['sin_phase45_mixed_lp'] = lowpass(df['sin_phase45_mixed'])\n", "df['sin_phase90_mixed_lp'] = lowpass(df['sin_phase90_mixed'])\n", "\n", "fig, axes = plt.subplots(nrows=1, ncols=2)\n", "fig.set_size_inches(12,4)\n", "\n", "df[['sin_noisy_mixed_lp','sin_phase45_mixed_lp','sin_phase90_mixed_lp']].plot(ax=axes[0])\n", "df[['sin_noisy_mixed_lp','sin_phase45_mixed_lp','sin_phase90_mixed_lp']][6000:].plot(ax=axes[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These plots illustrate that there's a component of phase sensitivity. As the phase of signal moves farther and farther out of phase with the reference, the lock-in output starts to trend downwards, closer to zero. You can see, too, why lock-ins require time to settle out to a final value - the left plot shows how signals that are greatly out of phase with one another can produce an initial signal value where none should exist! The right plot, however, shows how the filtered, 90-degree offset signal (green trace) declines over time to the correct average value of approximately zero. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Quadrature Output\n", "\n", "Like all lab equipment, lock-in amplifiers were originally analog devices. Analog lock-ins required a bit of tedious work to get optimum performance from amplifier - typically adjusting the phase of the reference so as to be in-phase with the target signal. This could prove time consuming given the time delay required for the output to stabilize! However, advances in digital technology have since yielded some nice improvements for lock-in amplifiers: \n", "\n", "* digitally generated, near-perfect reference signals,\n", "* simultaneous sine and cosine mixing,\n", "* DSP based output filter - easily and accurately change filter order and corner!\n", "\n", "This easy access to both sine-mixed and cosine-mixed signals allow us to plot the output of a digital lock-in amplifier as a quadrature modulated signal, which shows changes in both the magnitude and phase of the lock-in vector:" ] }, { "cell_type": "code", "execution_count": 258, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 258, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def cosine_wave(freq, phase=0, Fs=10000):\n", " ph_rad = (phase/360.0)*(2.0*np.pi)\n", " return np.array([np.cos(((2 * np.pi * freq * a) / Fs) + ph_rad) for a in range(Fs)])\n", "\n", "df['cos_noisy_mixed'] = np.multiply(df.sine_noisy, cosine_wave(100))\n", "df['cos_noisy_mixed_lp'] = lowpass(df['cos_noisy_mixed'])\n", "\n", "df['noisy_quad_mag'] = np.sqrt(np.add(np.square(df['cos_noisy_mixed_lp']),\n", " np.square(df['sin_noisy_mixed_lp'])))\n", "df['noisy_quad_pha'] = np.arctan2(df['cos_noisy_mixed_lp'], df['sin_noisy_mixed_lp'])\n", "\n", "fig, axes = plt.subplots(nrows=1, ncols=2)\n", "fig.set_size_inches(12,4)\n", "axes[0].set_title('Magnitude')\n", "axes[1].set_title('Phase (radians)')\n", "df['noisy_quad_mag'][8000:].plot(ax=axes[0])\n", "df['noisy_quad_pha'][8000:].plot(ax=axes[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Bonus Material\n", "\n", "If you've got a copy of *The Art of Electronics, 3rd Edition* handy, you can read Horowitz and Hill's description of lock-in amplifiers in section 8.14.1. *AoE*'s description focuses more heavily on analog lock-in techniques, and touches a bit on the phase detectors, which form the circuit basis for analog lock-in amplifiers. It starts on page 575. \n", "\n", "Zurich Instruments, a prominent vendor of lock-in amplifiers, has [a great overview of the state of the art on their website](https://www.zhinst.com/applications/principles-of-lock-in-detection). They also have some great, mathematically formal descriptions of what's happening in the time and frequency domains during the process of lock-in amplification. (With nice pretty pictures, too!) \n", "\n", "Also - this is my first time writing a blog post as a Jupyter notebook. If you want to pull down a copy to tool around with, grab it [here](/assets/)!" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }