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@joelfrederico
Last active August 10, 2020 20:09
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Fourier Transforms\n",
"\n",
"The Fourier transform and its inverse are defined as:\n",
"\n",
"\\begin{align}\n",
"S(f) &= \\int_{-\\infty}^\\infty s(t) e^{2\\pi i f t} dt \\\\\n",
"s(t) &= \\frac{1}{2\\pi} \\int_{-\\infty}^\\infty S(f) e^{-2\\pi i f t} df\n",
"\\end{align}\n",
"\n",
"Since $e^{i \\omega t} = \\cos{\\left(\\omega t\\right)} + i \\sin{\\left(\\omega t\\right)}$, this $F(\\omega)$ can be understood as the amplitude of the sinusoidal component of $f(t)$ that has frequency $\\omega = 2*pi*f$.\n",
"\n",
"## Demo\n",
"\n",
"A demo helps some. Let's assume a Gaussian envelope of a sine wave:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"def gauss(t, mu, sigma):\n",
" return np.exp(-(t-mu)**2/(2*sigma**2))\n",
"\n",
"freq = 5\n",
"def s(t, freq=5):\n",
" return gauss(t, 5, 1) * np.sin(2*np.pi*freq*t)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"t = np.linspace(0, 10, 201)\n",
"plt.plot(t, s(t))\n",
"plt.title(\"Signal\")\n",
"plt.xlabel(\"Time [s]\")\n",
"_ = plt.ylabel(\"Amplitude [arb.]\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that there is some sinusoidal component in this signal. The gaussian envelope avoids some conceptual issues with long or infinitely long signals.\n",
"\n",
"Next, we can do the Fourier transform of this signal. Since we don't know if it's traveling left or right, we will get both positive and negative components:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x112bf36d0>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"S_f = np.fft.fft(s(t))\n",
"f = np.fft.fftfreq(t.size, t[1])\n",
"power_spectral_density = np.abs(S_f)**2\n",
"\n",
"plt.plot(np.fft.fftshift(f), np.fft.fftshift(power_spectral_density))\n",
"plt.axvline(-freq, color='pink')\n",
"plt.axvline(freq, color='pink', label=f\"Sine component: $\\pm${freq}\")\n",
"plt.xlabel(\"Frequency [Hz]\")\n",
"plt.ylabel(\"Power [arb.]\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can do the inverse and recover the original signal:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"s_recovered = np.fft.ifft(S_f)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are two components, real and imaginary. Since we started with a real component, the imaginary component is nearly zero. It isn't identically zero due to numerical noise:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Amplitude [arb.]')"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t, s_recovered.real)\n",
"plt.title(\"Real Component\")\n",
"plt.xlabel(\"Time [s]\")\n",
"plt.ylabel(\"Amplitude [arb.]\")"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 0, 'Time [s]')"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t, s_recovered.imag)\n",
"plt.title(\"Imaginary Component\")\n",
"plt.xlabel(\"Time [s]\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You'll notice that the y axes have no units. If you want a pset, find the appropriate normalization factors to convert this to real power given the signal amplitude has units of Volts."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Noise\n",
"\n",
"The real significance of the Fourier transform is to reveal a signal even with large amounts of noise:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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EFMxwcadAn81GHUUnSjE3GQIYbCSpJfniCM0YieabaOzU9Nit75S8nagdxQWIKMlwrh1VGr5qjWKnitmKeqo690aopzjNEPoCoV9NbQ2LfHrsOFt4AK4eQZ/dehzF2dUezrcj52ftKMXshHIUgzQWyrBaHKEZI91ioe/BEzvPUdRido0nPeZXewCqDWelRmHE7J2jUSSpiih8chQl5043kB4bpRlC34PvVVNbw4LSY7eihQeQp57W31X2F/6/O/HmD93t/KwTJdgzMVxE0daptEudqO/rykDrVbSit+N27ts19ne7sK2jUGtsD04vK864irOvqqOgh7VqJ7wdrZdpuA1RT2XnNk0BR+we2/A9G7FkEo0Rx5dG+lihN/70WMB1CmTYOtHw51xY7ZlUXoLSKMLCucrQ1hHF+REiCgrefCHQ8L0dt3M3EUU94a7GkxVntKMo22FLKY1hze+gB4nZGylsGxVZZsVsoHyHZ8TsUainRCL0PQTaYG7kvcWaevI8RWWNGlE8PL+KW46dK/1dj6fHxsWsp946IopunBWypNaiFDOtcCg6qE0axQiOwkQUvvpsd9rcB1rfZkeFf/XFY7jj8cVNPeZmoHYUFyDOrCjqqczm8boBwN2Fm4ii5OFIMwl6abyVYrbU9EQf6sk0BRwxoggDe/yqVuZDHSvJTOQT+t7Iu9G3feYofvxdt5Y6rUg3HgRyEYV+7Xqop16SOpXYUkqsRQkmGz5C3xtoJDn1tN6hTxTtUqLCOGpOCO+6+RHcuU7jbPS4Tb7Xf+uT9+GDtz++qcfcDNSO4gLE6T4RBe0SKduEv4aMZFxSkcuF3i1Nj80kPAEEXj/qaXM0CsDmz4+COJXGUTSCwYa2Cp0oxXI3wdefWCr8rpdkJiuJ00xmXGwmh6ZxenHmOJZekiGT6t5o+F7pfcBB1FOcynXPxyCqLPDGTz299ZP34e/+5fi6/oZn0m1Et3KPmaEbZyYS20moHcUFiNPL1WI2PZBlhU60Ay4zcDzbaMvTYxn1VCZ6bqiFB2kUpIGM+N6klCbrCcCGjB8Z/S8ePVv6O6pz4NPo+LqHzXzqxqkjiJOxn2r4CANvYK+qNusrtd4UWbo36bMd5+YjTuW69aKyDdRGsaY/l4324xoHakexA9FLUvzrP/kibj66MJbj94soyAm0SiIKM1C+5KHihmirxWyP1VGUpbDa9Nj1H5+iAEttjfbe6Po0tEMLfc/RE9YD+oxufqh4f0RJZrKSyuoogOHpp17iRhTkeCYbwXARBXMyi2vry3wimpASFcaV9UQOfL2fBb8PNmtt5FhXu7WjqDEEFlYjfPWxRXzgtvFwlfNaoyjj7Gn3PakdBXcAtAMu2wlzQ7QdEYXfp45iPWL2r37k6/ilD9rWJlRH0e/4w4CumdUoxMjHIkd96yPnnJYdgDLuU00fgSdK6ygAt9aiClJK9JIMcWqpKoouJho+wkAMIWZbg7e0TkE74RGFN/hco4LOk7+Og5COYWNE16sd7TxHUZkeK4R43hB/H0sp7x78sic/VnsJQl+gqUc3bgR0w9z0wLwxhJsJkx7bT6MISzSKAWI2YSsL7uj6hH2znopidjdO4QlhqCDCPSeXscxokkgL0P2OPwxo902OwvfE0OJ6u5dgqmkf1TjNEHgC3TjDVx9bxDdcvd9ZbyPwMBH6jkbBd8DDRBS9XJpt6HsmQphqDilmM659vdRTxhxFIxifRmGzwdYbUdjPbrMyn+h67Tbq6SYAvwPgd/v8++i4F7hb8CPv+Are+sn7N+VYbVbRutmpcr0kNXntZYbKaBRhMaIw6bElYTrPdNrS9Fjq9dRPzC5J2/2Jd9+Gt3z4a8XXppmzo6OUVt+j9NiN0UVhwBzFEA718XNreNav/SPuPm6F6yjNcN3hGQDAsYV24TzNwEer4ZfWUQDDzdN20mz164l6mgiDoTSWdi/BbEs5uPWmyPKIYpzUEznwdVNPaXEDBahr9CPv+Aoenl9d91pMRLHLHMWtUsqXSylfVvUPwMMbObkQ4juEEPcLIY4KIX655PevE0LMCyHu0P9+fCPnGydOL3fNTn2j4Duxm+4/synHJJzRQvZ0M6hIr3TTY7nh7ddm3HnddrQZ99YnZj92bg33lAxgipLM4YjVYCSBsE/67TCga0cahSeGiyjOrHSRZhInlzr2WIk0BjhfF9GLUxNRlNVRAMOJ2WVdaMnBTDZUY8OBBXdRgovnJgAAi+uszqZ7M/C8sVJP5MDXSz0lmTRddPm9//i5Dr5wdAF3Hl//Bm/VOIpdlPUkpXz5oD8e5jVVEEL4AP4YwKsAXA/gtUKI60te+gEp5XP0v3eMer5xI06zTbuZ6YaZbQX49GY7Cq1PHNnT6ks9lWsUJGbbG/nkUgcfu+sJ53Xjjijef8tjeO3bv2zO5ek2D1XntvMo+M4vxROLncJro8RNTyTqabM1Ct8TQ2kmvPjRrCnNMEOOImesKbNKUU/FOgpgSOqppGdUnnoatMtv9xLsn26gFXrr1ihs1hO2hnpad9ZTZjZTcdlmaoREBYpk21GyaSm3m4XtFLNfCOColPJhKWUE4P0Avmcb17MhRFr42wxQiP/Cq/bh4fn2gFePduw9E2Ff6qmsjiLfMXNpLcYPv+Mr+On/+VVnFz7uvjx3nVgyO7ZM0uCi6oK4sqaAa70EC6tRYXcdpZnOglE/VwV3Xt/K72FQ5iiGiSjo73g0FCUZppvljqKXqH5SeeppcyIKTT01gqEqy9u9FFONAHMTDZxfb9aTcRRe3+mFG0ViNj/r1ygmSlqgRxtxFHqDIqVNld0pGMlRCCH+ZRPOfQkAntZzXP8sj+8XQtwlhPigEOKyivW8QQhxmxDitvn5+U1Y2vrBs0M2CuIo9001Nn0nxcXqMobIpMeWTBbLd4/9mfd/1TgyioJ8T2x4EtwgdKLUVluTmG00ij5ZT9rYSinNg3gyNyuBHnB6aONU6l5PG9QoysTsIYxfWYv0KM0w0VCZTWVZTyqi8HLT6LiQP/g98NeQYyGHMRlSRDGYeppuBpibDNetURhHQZXZY+qpFI0cUUiTQl5WazRK6jPXJnaaTjGSo5BSDpMRtRn4KIArpZTPAvBPAN5VsZ63SylvlFLeePDgwS1amos4zTbtZl7VRmrvZANxKtfd/qAfyGC1Qq+85iDXwsPNF3erez/3wDz2TzX0mtWN3QqqR5L2Qy9J8ZufuBdLQ2THrEWJMSSpBDyWHltmyK1TUd9348y0G8nTT/QZUoRE6bH9NJBhYDQKPQbVF8M5iqgiomj4HpqB51BEUqrCsaavqacN1FE4WU9RzlE0VWX2ME0BJ5s+9kyEpVlPxxba+I2P3VN6HYyj8AXCLcl66n9N/vgzR/H+Wx4z3yeprKCeqjMDB4E7h52W+TSUoxBCHBFCvEYI8d1CiCObdO4TAHiEcKn+mYGU8qyUsqe/fQeA52/SuTcVWSbX1RphENaiBJ4A6/u/eQ8JHasZ+sgkCk6IdkRlGgV3AJRCenCmCcAa1lbojyRm3/PEMv78cw/js0NoMmtRqntLSaRZBl/ApK/2E7PJifCsphNVjqLHHQVr4TEkBXJqqYsPsbYQeerJ20BEQWtqhr5j0PlnO5GnnrhGMUzWEy+0MxFFotJVfW8o3aAdpZjSEUWZRvGZ+87gnV84hsfOrRV+l/CIYgzU0+Ja5OiKgyKAD99xAh+/+yRbX1Y6fW8jGsUq08Z2XUShM41uAfB9AH4AwJeFEP9hE859K4DrhBBXCSEaAH4IwEdy576IffsaAPduwnk3HXGOu98oVnsJpnT162YeF7COoKXrPfLPXz49Nm+gCLTz3zupIgoyvq3QH6kfEr3HvOEuA+1sM6miBJ+J2WVRUmLSY/XfswcyH1HQhDhyFCRmr7eFxwdufRw//7d3morkKOcofCGGaimSlKT2Uq1EM/Ac6omMU8P30MqL2VyjGCLDpzw9NsVk6EOIwSmrFGGTRlGW9UTnKEsqKFRmbzL19G2/9zm86+ZHhnYUUZJhWW+GskyqnlclEcVGNArecmWnRRTDzKP4TwCeK6U8CwBCiP0Abgbwlxs5sZQyEUL8NIBPAfAB/KWU8utCiF8HcJuU8iMAflYI8RoACYBzAF63kXOOC4Mmv60XVGBldslJBjQ35dDMEdgsIV7QRzc6idlV+eL00OydUlGPoZ5Cz/xulHWdOD+8o0iyzLYZr6CGeNt0Mj5rsV0fN1JE3QBuQ7tGwFp4DPkZz68q7ePkUhdzmkIEXI2ix1pgSCnx9SeW8YxL9jjHofWQU6Ho1TqKrPDaRuBhsuHnWngwjWKoOopi6461XorJpm/eRz9jSNePIorzazGklBDC3mt0jrLPPNXXOaDBRZsYUaSZxMJqD6eXu4aKHZQeGyUZVrpu/VG5jpc5/68Hq45GsfvE7LMAVtj3K/pnG4aU8hNSyqdIKa+RUv4/+mdv0U4CUso3SylvkFI+W9du3LcZ591skPHYtArNKFUpiGOYhJaPGDIp8c4vHMNvfuJe/fvBGgVgqac5iih6LKIYZe4DOYohIgrKvkkzaQYXUVZS/tz8e0o5bDsRhRWzuZNZ6bkaRb8JemVYWFE76FNaLI/Zbh8oitlfOLqAV//RF3DPE25tB52PXsojk2bgOxoFOY1mUNQoKOr1BNAdYrfbddJj1ddrcYrJhtpbNga08KBU2ummj6sOTCFKMjycKw6k9ZZ95vRReJ5Aw9/cOgpycCpT0bIB/e7bXpJhpWvvO8BupvjzuaH02F6CGZ3NttpzqbqbHpgv3BtbiUpHIYT4eSHEzwM4CuArQohfFUL8CoAvA3hgqxa4GxBtYBdRBoooyKiMctNJKc2AIo4o5wjSTOLmowv47P0qWyzfwsPRKJjTWNa7K5p25mgUI1wH2pWtJ6KgFs+eqK7Mduo7KKLQjubwbNOJKPgD3+4lZveuWnisb3DRgh43S1lVRqMgMTuXHvvoWcXT5/n6fIt0o0MEHpphBfUUaOqpJKKYbgZDVmbb15Bj7kSJuS8aA1p40MZhshHgBVftAwDc9og7bImcXKmjyGxEsdnUk3EUudqnfs8ZjyjsM1LMtKNK79HE7BSHZrXml6vledN7/wV/dtND6z7mZqFfRDGj/z0E4O8B0NX4MIBjY17XroKhngZ00xwWbdIoNhBRfPHoWXzjf/90gf8t1ElILcRnrrMz3WOrqKeOpp50RLHCqKdRIgpyQicWOwOzvLijsKNQy6knbgjyEcW1h6ad83FDsdpNzDXhYvawTpAcxSldUZ3XKDwhnG625NTnV1znbgvu6B7jEYVXKmarliMCUtr3TOuebgYj9XoCdF0Eo576GW9yFNPNAFcfmML+qQZuOXY+dw513FKNQh/aHwP1ROftxa6j6Ec/9VI1KyJOM3N/t8qynrLhNI8ytKMEh2db6mtGQ936yDms9pJ1V49vJio1Cinlr+nq6d+SUv7fW7imXQd6YDYvokhx8VyDidnrP+7Cak+3fuiaNgqANYY0BS3LVMidLzwqiyjKxGwakmOop8AfKT2WIp21KMXiWoy9Ou02D5qyRmujFh5VWUl8LfS7jtYorj04jS8ePYtz7Qj7p5uuo+glTFewGsjwEYWmnpYpolB/Z6kntykjVczT/4SqiEJpFG7UQDv0ZuDD11pAKiU8CKh26QKtnHZRBXssz5xjLU5NC3OVslp9LcgZTzaU+H3jlXtxaz6i6Ec90SjUMVBPdN5emjntaKqMO9euVrqJcdr0jDjUE6O1hsXx82s4MN1Eu5fg6oPT8ITrKD59n8oE3Mpmm3n01SiklCmAF2/RWnYtbA+kzdIoEtMmARgtUiEDTxQRIU4zeAImWkkyiSTL2Dzsao3CSY/t5jUKZRhaoT/SzAZOGfXTKWjKGqCzT3QLD3Otcufm3xPVQ2u95tA0AEsPFRwF271XVWZ/9M4n8Kb3uvWn3Tg1wmSBetLrDDzPoZ6oTxj14iLk24/wLrSFrCc9SKgRePBzmk2iU2rzPaCqQK/ZO9lwKrMnQyZmp1ll9EdZcNT19gVX7sNj59acfmhkmE8udgstK3h6bOB7kHLzWsPwzCR+31V1kHW0q25ciCjKEj6GdRRZJvGd/38Cs5QAACAASURBVOPzePvnHsZqL8V0M8BUI3CE7c9oR7HZ87nXg2HE7DuEEB8RQvyoEOL76N/YV7aLMC6NworZ6w85aUe2nCt0otGent5xKmNrd/T04EyWtPDgN+qySY91s56aoYdMDjf7gYM/bMf76BT5/kVJrilgftfFv6c1UURyYFrxwWRs+XVu9xLHuAcVld//697T+PjdJx3jO8+iglMFR6GbAubEbJo6eGYA9cSdQTP0SsXshu/ZiIIchW5umBe5q9BLMviewHQrMO+tzbKeKCKtiio49QQoRwHAiSqoViNKM0PVEbJMQgi4m4BNer7KxGygmnri9/1KNzFObKKkMjta56ZxqRNjuZvg/lMrmnL2MdUMzPU7ttA2SQA7NqLQaEFlOb0cwHfrf68e56J2G2x67GZpFCmm9FxiwFZTE+54fBFv/tBdfbl8E1HkHEWcqJYUhqqROqJgGoXgEQcfcVpKPeUqs0soq2HAd/79IgpeLJdmEpmUTmV2Qczm1JMRs5VBmG0pJ0efG6ceVnqJ4cWd65WLWGitfM1n24p2unzfpHEUZJxMm3HhOmFyENXUE/Rx7JqagVtwZ7KeQvfzpeOEur5imBYevSRFU6fZmogiTs0GwmpC5ccyYrZ2LDdcPAtPAPefsgmUfO3Hc585OTZ+rs3aURvqKUmHop54dLDcjc09VjoueMCm8aN3PoGffM9t5ntykMcW2ujEqkBxumUjitsfVbrO4dnm2KrTh8FARyGlfH3Jv80ouHvSgPPIGw2P00yaG4baPeQfkJvun8f7bnm87wNPu+d8TQM1ueM7TkejoNGfJVk+id7l8eOWaRTqteu7qblB75f5lI8oUm1QhI4q8g7KoZ70l2tRilaoduQAf7jt37Y59RRUD0ai6IdHQQva2D/zkj1Y6SVY6cZWWyipzI7TzDiXvKOw6bF5jUL0LbgzjsJEihKBLwqFeFXoxqrymL9+LUpMeuygXb5Nj1WvD3Q1Nze6UZKZdul5QZtG3PJzrfVS/PFnjm5Y1HUiihJHW/V6oCqiKOp4VdTT7Y+exz/fe8Zs8ua1ozh6Rs2vmG4GmGoGJuuJNmQX7ZnYVEF/vRimMrslhHiTEOJPhBB/Sf+2YnG7Bfxm26jXpx3zdDNAw/cLxwdswVi/VhmVEYWuC/A8op5s7yb6fYPNiObnoEpbftzpZoDAEyw91qUkzq72hmpHQOc/MtvCicViSwfz3pmRIydHRjHwi46ijHqirLI8XUUPtxA664lRT2VtxuM0M5w7d260S6TiudPL3eKEO1aZvbDag5TA/qkGzuokBIIpuMvcNTZ8v7LgrskKBE1EkWUIPA+t0BuyMttGFJ1YtUzpxhmLKPpn5LV7CYSwWhf9DX99L0lx9cHpwvUDlIOzEYU615ceXsBvf+p+3HLMFcXXi6r02ErqKZcN1zfraYBGkWQqa4quw9lVt3J/qhlguumbZ4ZScvdOhptenb4eDEM9vQfAEQCvhJp6dyncArwLHmUFN6NizWSLBCbnPn9Mqqztd+OkJqLIaRS6/QM3JKnm+ulcVVk+SSaNoVjuxhBCGaVW6GPVTD9ztY0ffect+I2P3TPwfdMDdvn+yUJHV468o8gk7M7TK/Yf4t+T0exEimvPGzt6uOcmQqz2Eiel1WgU7HqcWuoaYZ07N3IUN1w8q1/XM0kEZU6N9IlnXLIHmVTOlWBaeDAKSa1JqF5PpQV3vtkIWDFbZT1NhP6QldmZLdyLUqNr0OffGKBRLKxG2DMROpXYoe82jOwlGQ5MNzDTCgoRRaKTFOhaAcC5trqXN9oHiXSeokZREVEw7WqlG5v30Ax8COHSnXQPVR2L/pae87w2M9X0MdWwGsVqN8Fkw0czGC1JZLMwjKO4Vkr5XwG0pZTvAvBdAF403mXtLrih58bCQ+Imp0oMGYEe2n46AP0u343ViNmeSz1Rkz3issvE2zi1O8rljiq+EkKgFXqmG6vNBFFrPn5+DXexMZ6V69Wv3z/V6NvnhvfDod2Zvkzw/WKjPX6NTEQRJZgMA3N9Le2mM330GnhKq638Zrw62wW7EUWEmVaAK/dPAVDDnei6EjxhBxdRDcUzdQTC6SeKRAoRBev1FKcZXvv2L+PzD86b3+XF7DjNEPheoVlgFbpximbgG/F7jc2ioGvC15PH3ScWjaMkhLk0V+WMfMy2QlOHQ8ikjSjoXOc1Pbe6wfYW5Fx7SS49toLK5RTvCosoqBgwKqOeKjaMdE9Ro8WCo2gEmG5ajWK1l2CmFQxMRx43hnEUZGkWhRDPALAHwKHxLWn3IT8u9GsnlgqzjIcFzxapehippUK/6MVEFJ2iRsGzYjIpmTGRiBKlUeTTK+n3k4x6ouihGVh6wYyH1M5nuZvgofnVgdoN8a9TzaDvjpdHFFmmuWzaeXrFhyktSY9dMxGFG7HRdd4/1ShkPdH14scnAfvIbMtxGvOrPRycbpoq21NLXTV5jjkKXpl9esWlqnjmU5yLKNwWHirD7NRSF196+Cw+cucTAFSUl68riTWVM7yYnaEVascSpTbSDV3qqewe7MYp7ju5gmdfOuf8vIx6UhGpV9iBJ5k0c8rpXDT8aOMRxQaynnqJ2dn7vu5sW8IoVDlQ+v2afg9n9aaCMKU1Cks9qZke4RjHwQ6DYRzF24UQewH8F6jurvcA+K2xrmqXIcqFnr/4wbvw1k+O1paKNIrJPpXZJC7222FUUU+xFqvJZnHaKcnUg8Opqdipo8hMZW6U2jbLJAqrr21uOfGrvSQb2JqDKK9B6ZuumK2bAhrRUxSynvg1omuyFqnJa3ljR8ZqbrKBdi9ldRRK0/FymUrHzyu66QVX7XOynhZWenoEqI/ZVoCz7cgkERA8No/izHIXngCuv0jtwHl6rW0zrr7nOgQ5aNqVUlTXKHEUSZY5rT0GVb/34iwXUdgxqHRN+Ho47jm5jCSTeFaJo0hyO/hmSD2r3M88Y5EiRXM0/Ihnvo0C+pxHE7Nj87wEXnFWxjAaBWA3PAurPVy6d9K067ditnYUvQTTrXCoQVHjxDBZT++QUp6XUn5OSnm1lPKQlPLPt2JxuwX5rIeVXlww0MOCisF4RJHXIqiyuF8n04Fidi7rid5HQaPIvTeiHgCb9UGZTqRZqPNnzlSzB8/0l7WSVImtE43+O961XHpssg4xm95nu5dgomGpvSRH6+ybbCBKM/OwkoEPfM85/onzHRyaaeKqA1NKsNafx8Jqz9RoTDYCrEUJ4kQa4wq4M7NPL3dxYLqJw3vU3/CiOzpmltMoqI4CsIIowXEUkmU96ToKYHCLiW6SohlaMbtAPZWkhhLufFyNqX3OZXlHUU49tUKv8Jmr9Fh1jsZmRxSVdRSDHcVyNzH3lGmBXlJrNJB60o5ifjXCgekGLt83CUA54plWgDiV6CUpVroxZluBurd3IvUkhBhYKzHMay4E5HcU3TgbuU1wm2sUFYJhWURxru3OfzYFd7n0WJqvwHectMtJdBaIk+WTo56mGkWaif4PPOGIvnyq2YM6/a8KMaVv6pYR1RW/xfGe5PQCzys4Cjc9lkcUvp2znXu4902r2hBydGSoghzNcGKxg0v2TuDSuQlDAQFKo7COQtUh5DUKnsp7ZqWHw7MtNAM1Dc7RKKjgLufMiHoCgLNt+3pPqGMXqSelUdBnNag6myKKVsOHlOr+ovfDr0nZzvmu40s4NNPEkT0t5+d5arCXpCbKydM+aSbh5SKK8xRRbFSjYIJzlEpzHaum3NF79D3haBSh7ylKiF0D0+GgUsymiIKoJ7WpuMI4isA8Y6vdBKtEPQ1owjhu9JtH8dtCiBMARJ/X/L8APra5S9o9OL3cxXQzKBTc9NgObL3grQ+qCo3KNIrv/9Ob8cobjuCXX/U0AK6YzecARGmG6WZgxWwpDa2RZBJRKhH4HoTun5QfXDTJIwq9OyUKKvDcNFIupB8d4CiSTHH41IxQceR+4XWceqLrEhiNokg9OemxrHvsZJNTT8WIAgDO6R0sGap8ncaJxQ6eeckeXLJX9dI6fr6Di+cmsNSJsU/3qmqxlhlco/A8mx47v9LDIU09HJppuhoF1egU6igs9UQ1GEdmW1jsRKamBHArs1uh7YI7yOj0KKLQn0HeUVRtYgAVUTw7F03Q39D7kVKazKpm4JkW3oSURRS05sXNjij0xmi6GaCXRH2ynvR9MdXQ1JN1HJXU0xARhZRSR58NzLZCCKGYBOpzdn4ttmL2NkcU/RzFaQC/N+DvH9zEtew6/NDbv4xX3HAYB6ftVKEozdBNNiOicMXsmx9awEfvPInf/L5nGsPDp589erZtOHPA7kDTTKodtC58KojZmTTRR5wqzrbh21bYjkahjY0Qig9vFRwFL0zLzIN9eLY5OKJIVERBzqcbp6WOgovZtGuzaZRFMZscR8P3nIhiMqwWs/eZB1Wt3/RnYsfIMoknFjv4jmccwaXGUazhhkuUzkACJUUURFMQ+MzsiDnFPROhYzTpM+4bUWjq6T9/19ONvuHlW3ikGQK2+RhkdEx6bMN1RoMK7tq9BA8vtPGvn3tJ4Zi8uZ+aBW/Tq/MRDq+PKYjZG9QoeBS0Fql2OWfbfRwFS3LIZz0FnnCoJ/7+qA8ZR8wiinaUohtn2D/dxGtfcDmeeekeTDUDc/+da0dazN5+jaJf99iXbuE6diXOLHcxv9zD3ITtdNqL1QjIsojikYU2UilxjS4yKsMqyy5RIycFojTDZ++fx/tueQy//j03FKinc+0ImXRpJr7zXe7G1lHorKbAoZ4sj01iNgCEnihoFDSbIUoyFlGQIXUH/FBEceOV+3DT/fOFCWcctiBMHbMTpyjuSa0+A9hdm88iinyLDXqIm4GHVCqDq7KegsIMi4Kj0MaRDxsiw73UiRGnEodnWoZiOb3cNUaeHMVEw8dKN0Er9E1dDEARBfTc75zOUjLfIB9RNJlGQbv9l1x7wKw9P8iJusdW9azKo0vUU+gK5gXqKWe86P0fmCmOZAw8j6Ui0/vwNfXkHoe6AgNWOCcdY8PpsYzmWu0p+quRq3LnoPviwHQTD55ZMc9d2ZhWp/I8zdDy3M1OwjYrVC9zYLqJPZMhXvpUlUxKn+HCag+rvQTT+l5KdAp71TM0TgyT9VSjAt0kQ1fnsRMo02etJMXzLR/5On7pg3cBUKX8/3TP6cJr2j1VYEM7kYa+Eck5tHuJcUJ0XuKouXDNKSOeIkvZNy715GY9hY5hzDsKgab+Pe02iQIJ2ICfJJVY0pzy8y/fi9VeYlpul4EXhAGobDPRzg10AWAMSrmYrQ1S6CHLpMmommr4jNpzjReF/rRTp/ekUiFLROXAN/QJVahPN1Vrk0mdXprXKGx6stvXSOksjMrIzft2u8e6RpwykgAbUfBCysCz9SDDUE+t0DMRREGj0E4vb+DXcoWXHGFgeXbSA1TWk1eIKJKSiMKcY5OoJwBY7ca2E29FEgXNUd9XiCjU/V7Vir/sGtuIIjWf24Fpt6U+OYrH9RCr2VZgovztqqWoHcWIoAEmZAQItKPq5VoYA2qHShWof/DPD+CNf3M7vvKwO1V2qRM7edXEgZKBW+0lZmdFRovGbvJMq3xEQYhSd7QntfBQ70maXk+AS7XQ+ULfM/x0IaLweBfXDIudGFMN38zDIGNThiSzTesAVGY+rUWp6TcV5ainsspsXkVLNBxg5yRwXYOq1o/o4TGPayqPHIrPHBFPkQSA2YkQy93EjLCcNtSTGhRESQSEgFF0KasZyDs7Wr+hnlJFY/meMNTTuXZkmgSa4+vjkQ6SZIras5legxyFTY8FbCYWOQ7KfsrXvNB9WkYbhiwi42Nby6inTHJH4e6g+xVkDgN3kmGKhi/QDPxK50lObf+0arlOkYe6nm4mFzfkZUK/1SgSM7PkwLQbfZGjeFQ7iulmYHqvbVd1du0oRgQ9EN04y7UhtkZ5LXfzt3sJzqz0kGUSp5a6SDOJn3nfVw3FAQAPnl5xqCnKdqDzLa7ZBnM8HRNwIwdOGS2xNFXSKAyHLaUxQpZ6shoFGS2pJ+EFvmdoB1NHYSIKAT63YXEtxp6J0EQe3Bh049T5Pkqkk5VTVUvRiRPTaI52emRHylIIaUeuqCc79Ihz7byOoul7ODTTROgLPKLHk5r0WJZVZXaV+lrMtAIsd2OzUaA1tkKb9eSI2YI76swYw8DLUU85MTtOpTmOEbNXI+OYzPH1qXgExHt49aOeskwN6mkGHp56ZAZCALc/dt5Ju6XMnLxeQJ/pZKPEUfieiYh4u5FmZcFdeUSxmRrFai8ZGFHQ80YGnbLhTGV2Ra+3MkeRlEYUrqNoBj6mmwEe0/ffjK6jALBpUzTXi2GaAk4KIf6rEOIv9PfX1Wmx9oHoxKnz0HEhci3Hpa72VOfJ82sRTi13ccPFsziz0sMXH1oAoIzP/adX8PSLbOuDhu8hSqShYnjJP+1OjKNgTooPxXEiikJ6bGYjCj3AyA7Xsbtt285CGK69KGbznkgZljox9kw2jNHoRPbB+Zn3fRVv/tDd5nsyllzMLsNalJoB9Dxtkf6vqqNoBIp6IuqKaJrAF06mSkPTchfPTTjdWOl6cOGffgaoh3mlm5jd7iwTsztRYjQCgil4zGsUeeopV0ehPj/1Wq5RcNoJgFN5T9ch8AXLVqremZJhbIU+Ds408dzL5nRDSHsOcrR5ipU+44kyRxFwp6ypp8C2S+cp0WmW9aGeNic9FlBOJ/SL88c5uJgN2Owro1FU0E2ljoI0il5qqM19JdMc90018Og51d1humWTEPo1Ah0nhoko/gpAD8A36u9PAPhvY1vRDsW5dmQmTQFAVz8Q3dilnnhYnN/5UEbTI2fbWOkmpnKVaJZHzrbRjTM87ciM+ZuG5nXJUThVuxlFFLoDZZIZA5tm0hhUrl3EqXR6AfFZFyqi4NSTcPQL9TOrQ5RRT256bIS5idC8jgv8J853cHLJVjObgrCS6IOjE6WY0XMkCtST7xVCc/psmqGPVEojhvOeRSZTJbFC/iVsfCzXbMip0HWh9zvbCrDSja1GwbOeSqgnnpXENQrfz+tCeeopQyNwhweplOfQed/5iXxJpuoowpLmhnnwMagA8O3XH9HvxUYtjcBD6ItCqmpfjYJl0ZlzhDaK5AY8L/BzDKKeHji9gnd8/mF8+I4Tpb/Pd4MNNPXUL+sp8IQZA3veRBQe5iZD8z0AJ3Isc8Z07rU4xbm2at9B9xzH3qmG6WYw3Sx2EdhqDOMorpFSvhW655OUcg39ayuelPjArY/jx951qzFg1Ko57yiWKyKKLJOmWIya5FE1Ju1k7j25DACFiCJOLPW0wKpw8xEFYJ1CkknMTYWFNdmmgPZ7QpJm5veAS7VQyBt4wjwIEw2XguIpoJT1xKknZ75zkhZqNLhGUUU9taPEaDh03Y2Y7RWpJ1p/Mx9RNGxEkeQiCsA6inzHV16XAFj+fLYVYrlTpJ4mdMHaai9xDILViCTSlPU1yr0HMwpV/yhi6ctck5jORRR8gqG6VhKhZ6nBfgaH7m2KWL79+sPmvXBMNYNiRNFPo6iinvT74NRPmhWbAqr3GZTqf4Szqz288g8+h//28XsruxZzh5BkUus7RfqLQNrVrHYUpLX5nsDh2RZOLXVNNBQn0kR3ZcejjUwnStSs9orZ8PunGqYz8Wyr2BJ/qzGMo4iEEBMAJAAIIa6BijAuKHSiBJm0O90u1ygSW93JNQoeUXC9ghzFFfuVo6Bdxr0nl+F7AtcdZhpFoMQyOl9ZMZbjKPT50yxDK/Ax1fCN86DusA0mZjuzNDL7ewBOwR3tBCmVEGARBaXT5iq6F9dizE2GpZlM3ThzhL8kU5HMoKwnFVGUU0/5DBSAZT3lNAoyeqoFAxOztVG6dO+k+T2hTKMgAz/TCrDSTUwXVJrbQQVry53YMXgBu04kNNPx3PGzuYiCRT3NwDWgHEQBOnUUvjdUHYWNKNTarz00jasPTJkUawJvh03op1Eoob5IPZlqcUb9uBGFfZ+HdaPFdsX9ca4dmdkegwroCFajqG4K2Ag8E1FQlmHoCxyZbaETp2YzFqeZuU5l4jhd93ZPRRR7KxwFp6OmW9V937YK/QruCL8C4JMALhNCvBfAiwG8bpyL2okg4ZTy+8mQdXREMaWrO7lGwY0df6DuOq564diIghzFCq45OOXsFPNittswzjqKUHPtS1rQpgdtdiI09QyqlbjbDTUfUcSJq1GQM6IbPPBKxOzQ7s6tIVJZT3sY9eRGFFmBi59pBTbrqeIhX+PUU66Owi+rzOZ1FJm91nSekBXpcSNM1dZ54241m7xGEZj0WF75Tg5pRYumBDM4So+i5Rk+fLfPiyrpvHQc3owxb8SNmG0cvXJGXEOqAhnxFjv+b//gswsdgPmYVALd86XUExN+uTOiXmFuC5ryrKdDMy08NN9Gu5cYw81BDoRTN4X3F6fOtL0w8NAM/UJftI/e+QQu2tMyGwia5uhEFKyGZs9EiCjNcLCpnFmZRkH37Fqsmk5elGtzQuCOYqYVDl3/Mi4M0xTwnwB8H5RzeB+AG6WUnx3vsnYe6EMnPaFrvk/B5zRURRScV6Vh6ZfriIIemntPLju0E0BiduZ0mzRrYumx5HRsRKEeNDJggKWqQpa94mZsaI3CNMFzx3XSz4xGQU0BSzSKdi9BlGTYM1lBPeWSAFQbbLa7jFK87dMP4o3vud28huogqiIKLkwTklQa+oiyeei6Am7H2TLqKXAEaFESUVjqqROnWFyLnN09b6LIC+78Co2CX3NaP8AK7pyIwhrjmVZ5RMGbCYasjqJfPj6nhQjPv2IvXnjVPud1k82goMNRe5kyMbvBZiqYgjs2kjZPCZmCO68koqjQKejncxNhpTOM0szod4AeAlVCPf3Gx+7BO79wzFxzE1Fo+jfwbCo19flKUmkjitKsJxKzE5xfGxxRCIHSLgJbjX5NAZ9H/wBcAeAkgCcAXK5/dkEhYo4BsDunXpKhl9gRoVVZT/zGlhKYaQaYbYUIPIEoTbG0FuPkUhdPO5JzFFrM7paJ2anKFDnb7pmRklyjCDyhH05LrQAuRRQl7u6VaxQ+1yhSa2DJkdBOkP6nAiRAdcUEgLmJBpqBavvBI6xernNnous7uEZxx+OLuEN3IgUUNSElChEFn3BXELO1iEvzH0z9g0lHddNjLfU0Ya4VIWR1JfnjkKF+YqnjGO3J0I0OCRRRJLqVBc96KsuiccVsK66TAZlquI7CZxEFjyTzw5rKQPc4p7bKMNXwCwa7EyVOF2GOwCtSTw3fGxhReGwDQjv4KuqJ1rNnItRtQorvM0oyJ53YahSshX2aYWG1h+VujJ6+5tPNAL4nTCsR3xPGUdBIXL5pLM96sumx/TQKchTTDRWdbreY3Y96+l39fwvAjQDuhBKxnwXgNtgsqJEhhPgOAP8DgA/gHVLK/577fRPAuwE8H8BZAP9WSvnIRs87CuhDp12x0wagm5hmdlVZT/RzCnnphqf87QXNe+ZDUcrKKaWeMonljkq9vPqgmqZGXKl50KTdBfOGcl4J9USGvGGMKI8orGFsFCIKVkehH2hqT0DjMCf1SE1aW5Rmjp5AGkWoefROnGKpE7vXsGuNAFCSHls24U6LuDRRjg8jAuBMDouSzBj5I3ta8IRr3Dm1xak4wDqvJxa72M8qbTlXX6ZR0H3kpCQ7EUVZeqw9TjPwEadJoY6CtBP+nvnn0596crOeqjDZKI4w7cSpmXyYB9F8Uspc1lOxyJI7CvW36rM9NKMdhX6e3vmFYzhxvoO3fPf1AGy67h5NE6n7yl0L/5xpXWomhj3/wqpqi7PSTTARqr5rQgjMTYSm71XgCTOc6vRyF5mODqcrNAqlEarP8Wy7h16SVUYU5EBonfkGlluNyjtBSvkyKeXLoCKJ50kpb5RSPh/Ac6FSZDcEIYQP4I8BvArA9QBeK4S4PveyHwNwXkp5LYDfxzYOTKKHLS9mA4ruaepCNCeicDQK9fWVmm6inUhT97npxkVeGFA3yFqU2vkSPIMpyTCvDfI1B3IRhaZyeDWsjQrsDo0LeLTewLc7VtvkzBrYRq6OolnSZpzCc+J1+QhOMvB8VxslmdmdtwJVqbvUidHuJWZXSC1ASD8gg2YjijLqSUUUZIAN/cbacvCIi4xj6CtagWcqcSPOO4gCMBkxp5a6OeqpPKIw17/E2XF6i3wGva04zRwDTl/nxWyftfDgGVrDGBwjNJfoDBxTTb/Q04wcRRlCRnvlC+74eQFFtTmOQt9XRD3Rxuvmowv4zP02bX21524myiKnXpJhhqUT2zoKa9jpXlvpqtnpdC3ouJ5QkU4r9DE3GeLUctckRVAaMd1XZ5a7uPv4krMBIKdInYrzIAdCG4CAaX/bgWGynp4qpTSVUVLKrwF4+iac+4UAjkopH5ZSRgDeD+B7cq/5HgDv0l9/EMC3iu3oiAW7O6BdB6dRljsxwkDRAE5EUfL1VQfUzv+wdhQNX4W85sHJPWRh4BVENkKSZUazuGTvBBqBZzUKqfr5c97eGe1J1BN7kMhRGCNakQ5qIopcwZ3POPAFFlHQa+iakVPMi7ZkDFoN5SiWOyrTjK7NSc0Dk34Q54xs4HvFCXd6R+np6MheA6sJ8PRYbswv2Tvh7Ea5fpCy6wHYnV+UurvVKkeRj+hopx96XkEwB1zqyY0oKhyFb9NjE3MOb6j0WKqt4RFQGSYbQYEC6kTl7eEB+/6TLHOznoLyiCLgjiIgR6GeG3JQUeo24KSvqVFnWZZQnnoKA1Ggnk4bRxEjSlLT34wilYDpJkdmWzi11DPP2XQuPfYP/teD+Il332buM+5IB0cU6nzDtocfF4bJerpLCPEOAH+jv/9hAHdtwrkvAfA4+/44gBdVvUZKmQghlgDsB7DAXySEeAOANwDA5ZdfvglLKyJPvp1y2QAAIABJREFUPfGsnJVuonbvgQfQyMhcRgg5EKUlnMYRPc2sGXpOoVw+3G/4njPXgSNJpdm5H5hu6lx+Sz01ctlG3FEYQ8XeR0c/ZDY91kM7ivG6v7oFL77mAABXh8hPuOM9pMio04MwySIKeoDyPY1MRBF66ESped/tnuq+SoLhZTqisFlP6hhVTQEDT2V5ZVKy8aY2cljRRXhcKAaAH3rB5c5QIK4f0Hno/XLnwI32ZFghZuc0Ip65lUmXMgKsY+IpvIDdWOSznnhEYaMo3j222uDYhof992RTDb/QoK8TJ6VCtjq/jmYS6RT1lQ1TSlK3RTc55MOaeqIOsnGa5Z4z9fXsRFD5PvNidsP3ICCcZ4EcxXJHJWVQlDCnNz482jk821ITDvXf58Xsx8+tYbWXmIhjz0RonoWyqmz+c7qXhm0PPy4M4yheD+CnAPxf+vvPAfjTsa1oBEgp3w7g7QBw4403juVKknHLi9kAsKrbAHCeeXYidHY6+YjCUE8624IenPxurBEU6RRA7UqiNDOGbN9UA7MTgYkoqFeOEEDSJWrF0i42oihST/x93H9qGfeedIXwfFNAQz2xa3BisYO5yRAXa81lIrSOsyyi4GmfE6FqzU0P01qUYj+U82n4numNY41sOb8PWAdENSHUdtzs4Fk1d94If//zL3WOxetK8hrFbMtSGbxKeqJCo8g7arseRhmxz533egrLqKeKXk+ptBMMeR1FP+opr+NUYbIZYC1OnbkLnWgI6ilTCSC+JxD4tpkhp34y6UYUgefBEzD6DzmoiHVWpp9PNnzj8Msq0PMahTq2NG1EhBBmU0Ijcec0RUQRMl/bkdkW7jm5bK5b3lGcXu4687lnJwKcUrW1lY6CRiFPFzSKHRpRSCm7UPrA72/yuU8AuIx9fymK2ge95rgQIgCwB0rU3nIU02PtzSmlMui2WZuaNdwuqaO47pDSEqigi1oHGI0iyDkK9rBO6WOGvmp1kaS2B9RU0zfVwYAquAs8ASGK1FMjEKyFh73xqCiQt6yg5+y4zknvRz0FngB7fvDcy+aMqDlRFlHk0mPJkEyEvtOSnATtU0sdHJptwvOEzhbTjoKNQlUZPrZnf6xFcpooR63S6fehL0y1MM8oKgOPWKzxtemxBCfrqYJ6smK26+zo/zQXUWRVEUUF9WQK7tKMOTUxVBfSYR3FlK467yap2XF34nRwRJEq6onWXhpR5MRsyjpSQrl9nuJUaTAUDbYjtZZ+hrWXqHkkNIBLRXqWCmwGPk6zueVnVyNcrTVAchg+oyQP72lhYbVnNkJ5MfvkUhdRapuH8nulSqMQQuDqg1Mm7d062R0mZhOEEMeEEA/n/23CuW8FcJ0Q4iohRAPADwH4SO41HwHw7/XXPwDg07JqmPKYQTecMXa5TpMh2621Qh+TjcAJy1d7ak7zcy6bw7v+wwvxLU85CACGG+2WFDnRcQk0DGYi9E2qYZcVLlGra0DNL/C1QU0Zv03HpBvdpZ60ozCCrn0YqC+TErPdgi+qzCbHRH/33Mv3mr+fYK2k8xP66GsyYs3QfVApEeDUctdkhXmepQpo91y2W1bUkzAT5XjTQ0BPxeMRRT9HwdprpLnIhO/oHY2iIj02Tz3lI4o4yxyjwAcXNZyIQh2/SsxOpfu503nyEcXj59bwxvfcjk6UGt0q32Mpj0l9Tj4jpBNnlREFfb5xYsegApY+444iyzmKwBOmkHEy9B3qCbDaRLuXYLrpV0ZOmabiGr4tHOVf91gUQDi3FplrbiMKt7ZDSpgMMJ4e2+4lJsGFrtMeRl/l6184/u6nvgk/921PAcBpu50rZt8I4AX63zcD+ENYvWJkSCkTAD8N4FMA7gXwt1LKrwshfl0I8Rr9sncC2C+EOArg5wH88kbPOyroYSujngA3R105imJEMdUMIITAtzzloB1MFJBGUU49cZqBRq5ONHxd5SrRS1KjDcy2AqywiMLXvX3IENJNxkehxo6YXdQoCDw9ds9EiKmGz3aENj1W/R05CjujboJpNnmNgtIGQ89GFFwbWDMRRRdH9uhCOOYo7CS04i4yTqWto9BGgtMGvCngIEfB60rIYXBtgfpHcaOtMmOKjpc+f6L++JQ+QLWJ5/w6+Qze6wmwzrq/mG0px6o6in++9zQ++fVTeORs27lP+oHeL6dYO1EyHPWkJ+gBNirKF9xxYxz6nqF0VI8pK2arNRBNmWCyUZxeSOAp4maSo++ZXf5iWz0/p5e7Zl2KMcg7Cpd6Auz8komGinqiJHMj41xG1t7JRmFUKsdU07bu2O55FMNQT3mq5w+EELcDeMtGTy6l/ASAT+R+9hb2dRfAD270PJsB23rAbQpI4A9hM1Q3Ne/LtBolhYcZUA+JGkZU3kyNP6wHWUQBUPaIfeBUROFqFKFfHD+pJtypY/KHk6pquUYBuK0aQt/Dv/+mK/GK6w8b+oa3GQdU5k5PZHj2ZcxRhEEh60lKGKoIsA/DRKgoDQKlyJ5c6uIVN6iH0ufUE3O6gPqspnSLf2pf7glFo+V35BQlSKlqO5p9jKPKAnOdHDdmsxMh2lFa0AtUNOWel5wbRabGyZKzy7JS6ikuRBSD02N5HYWv6cG8wXloftVcu6E1ikZZRFFNPfGuqirl1FK1Qrip2lkmjY4DUJsN+15XmUYBWEfR7qWY6hNROKNkAx8rUPoidUl49Fwbl++fxKnlLq45OI17dKNOuuaU7p0XswGYliEUoURpZrQOtTbdgl47in1TxRYkVchPY9xqDEM9PY/9u1EI8UYMJ4I/qWA0CiZqTzlCpXAqlicbfqEyO5+ZAsAU+tiIIpf1xIzCIe0oWqGvU0Glw/VS1hPNYaaWGvmiOR5R8JRAynriGgUAfOvTD5vXhL7iiq87bFuhU4WwqXb2Ba49OO1wsRMNr6BRqDXZ5oA2InOvQbuXYnEtRi/JzO7Nd6gnYa4lkO9fRdcBpdQTFdyZa9M3ouDUk2vgAUs55Y02H5JEyHfvtU5WRxQsW4m+B8oL7oCSrCd9nEy6dRRqzV7BgD50RrWVUZ/HkBpFsyyiyCodRcCiGX7fCqHSU7v5iIJd22sOTOGp+p6bbPpMo3DT1duRes6qJvnxbCtbMyNw5X6VZPLIQhtrkaKLrj1km3OSkyNHwddGP6NuBKGOVqLEdRSrOUext0KfKEM4RLbaODGMwf9d9nUC4BiAfzOe5ewsrPYSnFzs4LrDMzY91jQDzDA32UA7Ytw9S++cagS5grukMFwGgBmYMoyYfYBRT4pLVg7GOIqJwPws0a2reZO50joKLmbnsp4OzzZx1YEp3HjFXnz0zicAuCE3xw0X7zEP1t7JBl50da4vUKMYUQDKIFDVsRGzc4ZmLUpMuu0RrVGUUU9k5Ll+RLOiPd3CI05dA0QFd5ySqIJbcOdqFIDNec/zzrxTrT2Wu1ZOYQF22iD9LNOTCJNMFiIKTqMQ+HGSEmeUNzg8oohS9/OogokonK7Ag7OeotSlntT78J2IIs1FFL/3b59jvlZda0mj0L2TmEZx2d5Jq4cMQT01AjXVsBV6eOTsmtHHrmOOgp6xPSXpsSRwU9cEagkSpVlpUsYeE1Gsw1EMMXBqnBjGUfyYlNIRr4UQV41pPduO+ZUeTix2lOh88yP4088+hLt/9RXm4eGC7N6pECe0gBUGOY2i6edaeKS4ZK7YKZKa/nWTVI0ozRli/rBy6ol2x73EFjjRDn65G+uZw7mZEqzYTAiVOlvawkPnz//Hb3sK3vgt1+CLR23ZStUu8+/f9GLz9fve8A2FXXUrVFlPUkqXi04zw7+T0c3Tb+0oxalldZ3JUfCq8QL1lLqOqKkHNWW6dUi+f1OSZoVmgWXgM8TzGgVgp9rNtFxKYdI4Cl5HAb3WvJhtDQIZQdX5VjqiNGG6FZjcfg5aVsraRgQsouBpoyvdGGe0kYtSmnIoSttwcJiIQu+UpZQDKrOtINvL6UGt0HML7nLpsRwTDd90cOWDgAC12Zls+CYyK1BPCXMUrJbG81RU8chC20QBvN2/dRTKuPNGhVMNRXXNa6o5JOqpEFG4YvZ6HEVVEsJWYRgx+4ND/uxJgXd8/mG8/q9uAQCcb0eqUCaViGhQEaOeeOjoaBSBjSiIf6+knkJbR9EMix+HI2YXsp6kaZlMPwfULlVpFJ7Tn4gMtKGWhNvSuliZ7WGmFeLQrHVwg3aZgOJs8+/VjjjNHLor5jte5mgBy12v9RKcWnJ7YQWebRPtG+rJM+cg0Jxv0xQwzZyHnGgYa0Cq21YEnk0MsHSOPRY5iLyTpPdeVkdh0mNziQA8Pbalp/Nxfp3wUy+9Bn/+o88vrFUIoh1tO3decc8/94fn2+Zr0igG0U6AbURIEUWUZkgzOTA9Nslc6oneI+l+RJ1WCb18vjVdE9rkrOrnjNNcHPQ589YhtK4r9k/ikbNtk7109cFpkK/sp1EIIbBnomEiitAXhno6WaZR6A3FuiKKnVpHIYR4GoAbAOwRQnwf+9UsVKPAJyWW2dxjeog7cVq4Ibtxiov3TBiD3WB9dFqhj4mG2vXTjr+vRqHrKMpaH1RRTys9dSN6QjjzIAD7wAZaO8hHFPSA8hRTwIbveSNxmDmKYAgDUgYzNztOc4bcRhT5+oy5yRDtXqoiiqUOPGEzvzzPzggpRhRuxEJNAaXUHD+rOG7orDC+06xC4HmQumqaNApuMIxGUUU9cTF7UHpsarOVaDpfXLLGi/ZM4KI9dmwrh3IUvDjQ1ptwg0O0E52Xj8Pth8lc1hONBx6Kekoyx6Fy45+PMPNoBKrYlAZxATbhYS3Ki9k5jYJ1reWt5gHgygNT+Mx98/jC0QXsmQhx9YEpTDcCrLDphCbrKbdh2jsZ4pGzbX08q1FQ9lRPp8rSMd70smvwnc+8qPT9lcEkIezAyuynAng1gDkA381+vgLgJ8a5qO1EL04Rp9KZXdDTM48Be6N1YyXatUIfq3ooDW+WZ1MHU/Oaqqwn0ijyIi5gjUIr9Iwhmgh9NHxPG127M+NZJUmq0mN9z2Y95dtX+MJ1FCQ2540EGWd+jvWCz8122zlLW5PACu4A9UBJCS0uxjgw3TSOikcUtDs3M6QdastWZgPK+efrKKS0731QwR3gtsXwGT0zNxnqNNm8mF3UKPKV2VajUK9RVeTWsVPGVv44/aBqR7LC3/H+VoDrKKI0LdBzVZjK1VHQNRwYUaSyoFHwiCLfcDEPmkZH7dPp3L1EbZD6Fdw51BNLjwWAK/dPIUozfOLuk3jlDUcQ+Gr86UovcWiqqYZfWNvcZIj4jJuGHKUqorhi/yQeOL1qNqBh4OE/vfJppe+tH0Lf23kRhZTywwA+LIT4Rinll7ZwTdsKiiKi1FIkq73E7HJMHYU27NxR8KwdW4yUYLYVODMrOGiYy1qUFoRswN1l0051ouGr+ohuhjQTJouCPxyZBIsoSMzWNzIrkMsPLlLHcR+CRuBh31QD59rRwCKsKpDx6OYiCrVWNz2WHCbNFGj3Uqx0Y9PSGXCNSJ56crKq2DwKOr9LPamfmzbwfQykHfOaabEVDj3yI99wBZ596VzBiEyEbr8efl66x0hoNk37MtvyoaVbmsRDNusz58hFFJxS5MV8D51pY0JrSHGiIpfGEJ9zM1BtNSiiMI5ikEZBldlsY9Ribb7zQ6HyoBktPHJci1KzY59uBo5T5xjkKAB1/3zr0w8BsFEipyTnJhvOPQRY7UIdT1FP7V6Cs+0ennPZHB44vWrWl//bYUFt2rcD/ainX5RSvhXAvxNCvDb/eynlz451ZdsEenB7sb0ReWvvDhOzW6Fvi6kCrlH4xil04tTsuEqznvQNuNyNKwfSA+rho9bISqOgm8bO6+aZETReM/A802TO7izVQ+SxWgRqZ8DPyXFopqkcRZ8CoX6ws7BdjYIG6wA2NZSL82QAFlYjJ7LhO3mT9eQXB8bQPArrKDLsnSr2XyJj128GQ3HOtfvaKhqIIgpu4PMtVMzYTxZR8DGuS1IakT7ss0YOL6dR2GFNbtbTg2dW8NQjM7jj8UX0dHrsMOcQQjgZSHQNq7rH8s61vDIbUFodOet81XseRFOR41TnTo3GNqkLUulcHERX5tNjAeDKA6qWwhMwnROso7BrnZ0IC05s76Tbtrzhe3jwzCqkBK45OIV/vtdGXqNutvLa0lai391wr/7/NgC3l/x7UqLHKCba4fA236bXk3YUVqh0NQoSqk4vd7Ea2Z1OHnSzLnWSUurJ1GY0lFN66uEZPPXIDBqB0FlPaeGGjzWdQ5XZgFvARcbI90TpkJoyR3F4tjVUJkwVJhifnU9fze946bWqAlyN25xf6RmNhtZOoA0a7VBdR6EjCr3ubpI6RXJkjGi3Nyg9FlBV09RLaxiUUk+MClO/c8VsXs/QDHynriIc8rwk4Nu/o6jF7kwX1yI8NN/GC65U7VbiJBtaowBUTYPRKGJrqMtgqVFq4eGmx3bjDHcdX8QjC6rC2au41xqBh14uouhEVlucbgbmveZ34HTvqYjC/VwOz7TQCj08/4q9JuWVMgn5ffFdzzyClz3toHPcOeYoKFo5147gewKvfMYRADZqHfba5qGy1TTjkWR43y2PFQZ1jQv9qKeP6v/ftSUr2SGgG6mX2BtxyXEUqXloW4Fvdk/5Ooqn6NS6+0+tGDG4KusJUM7owHQxC4JTT0IIfOrn/hUA4LP3z5sUSnrgHI1Ci9nGuGnNJfCEMVIe0yhaunqYH4fj0EzTMbDrBZ+b7QyoyYrpmy1WaT65FmFhtYeF1Z7J+uKvBZiY7RP1xLKq2DwKQH2++YI7wEaNVbthIF81LSupkTzMPVJSmV2IKPxiwV0z9FThXOpSdINAxZY2q8yegwzObY+cBwB807UH8BefP2YonWGN2RSbSdEhMXuIpoBcW6P32EtSvOHdt5t6nKqddzPwdb2HSz2Rw5rk1FNFHUWTpceSE/A8gV/6jqeZwj6ARRTsevz0y68rrGkulwFJ7+1fXXfAzE8x1NOIEYVKuVX3wD/dcxpv/tDdeMrhGTz/ir0D/nLj6Ec9fRRApbuSUr6m6ne7GSSo8dbf1BYj9IXm2Em080xEke/1tH+6iQPTTdx3agXP0x9kWURBN+ByJ3Z2WOb3WiDP79JoIFEvsSI4nb8XZ3oOs8cKj2Sh/YPv2QdHGWf9PkvmELz62Rc7u6b1wlJPeY3CGrKqiOLuRTUdjEcUXgn1VBZRqLbTAejZ7CWpM2eBdp5La+q9l31G9rXWiKfZOnbdpXUU5RpFWcEdRRR5CmkQqBGiaa3uUE/qZ7c+eg6hL/CCK1WBZKzTY4fRKAAdUfSG0yiMLhMrmohnh7UCH6eXurr7Kw3CqqaeAHcwmKIo7SwYG0lXp8fmNQoAeP2Lr3JeTynPg8bCzjnUkzDH/t7nXmL+liKKUTMHA+bgH9YJCEudaKRjrfvcfX73O1uygh0GG1HYnS8NA5pthejGdn51K+S52LaFB90YTzsyg/tPrZi87P0lEQOltq70yqkn4t3LekAlueZqdMOTs1MFd3ZnlacUfJ0yClRPYiN8y1MOGt52FExWRBRJmhWqnI1GMRFisuGbGcVORFEiZuc7gGaZRDtKMdUMHI3CaTanncb5NXWOMh0pf55Et7YeNqJ4zmVzeN7lc2bqGj9Wvl8VrzUgB9oMPUezGJbysumxLuUYsOyZW4+dw7MuncMUNbJLh6+jAGjKnesoBk24W+wUnXIr9ExkQvUIfgX1RM+XO3Y4MY5jSs9yAEoiCiZm5ynbMlBEMdBRTLgRxWQjwFTDxyuuPwKp99vtaGMRBc96OragUnHJNlVlVW4WKt+9lPIm+gfgSwDOAzgH4Ev6Z09K9HhEkbgRxexE6EQUrcCvjCgA4KlHZvDA6RXcdP88ZloBrr9otnC+fNFRHmTI8rs0G1HYQj3aKVOtBx9NSpW9ZTx5fh2jCtb9YCKKQh0Fb1pXzHridB13FGVZT7wpIGAfzBndnhqA7rbL32u18cqDZ9JQ+/Jh8KKr9+ND/+eLc9FceR2Fn3PsgPpspLTC7LAUoCm4y1F7VFvTjVPcfWIJN165F0II08guToaPlvgkR+oVVk09qfMv6uhtyqmjsH+zog1+v6wnoCSiMNMlA1S18OB1FPm08jJQRmE/7Qooitk/+/Lr8O4feyEmGr45PkU8o2Y9BZ6dLXNM12wsd2M8eHoFz/rVT+Fe3cBwHBi4YiHEdwF4CKq9+NsAHBVCvGpsK9pmmPTYxBZhkZg92wqQZNKEkK1GtUYBKEfRSzJ87K6TePE1B0pDTtdRlIjZOTqGQHUEatCKG0KTIws8YUW9rJj2yB/EphHlvZEF635oNSz11EtS02KCt6qgB+raQ9P4Nzdeipdce8Ch3Dj1xOmXqqaARtxsBU5bdb6jM7tcHVFMlqQwm3OajCRd0DjizhCorqPgA2ryldn5Od2DEHiiMI+C/k/SDHc8vog4lXihpp2o7UQ0ZNYToPSAVb2zpw3K5KCIwkRvbkSRxyDqic+n7zgahV/Z8qJfemwZyrKeyrCHVWz7nsDl+yfx/CvUdQ18NQeErtOo941Kpc9HFDGOLbSRSdXQcFwYtingy6SURwFACHENgI8D+IexrWobQUaWRxQkZtPugnZEraBCo9AG62lHlCjWiVP8qwraxik6GlBH4fw88MyO2c6D8Mz5AHvTArRDzUqrg+m9qPex+U6Cr580iulmgOVu4jat863Bf+sPPBsAKiOKMo0iZBw4AIeK4I0I3V5Pdpfb8IvN9Ti48cnPS1gveAEgwGd5WGfE02NTNldiWMrLy0UUtn28ynoiw/I0HemSIVqPRnHl/kl86munsNpLTJv6yu6xet02enML7vIYFFGQ4aUxu07WEyvu47AaBavM7vOZ79f96vP9u/Kgdj5Vz08zsNTayFlPWls6346MDVruJubr82txvz/fEIZZ8Qo5CY2Hoaqzn5Qw6bG60hOwGTHWUagd0UTD1lE0AlGgnq47NGN6xXzzdQdKz+d0Au1TmV2MKKy+kOdaidoJWOvvpIR64hxwWWbOZkI5UoE1rVEQxZOwSW5lD9kUq0GYdeYcFyMjIYRJnQQshz3TDJz3mm8KCKiHrJ8+wc9DYvawBrvfsfIRBXdGXHjNWLuKYQ0NTTeMTZW+m/VEG4pJttlZT68nAPiGq/cjySRufeScOV4Vn0/TD8mg8QJU+huasQ70iyisrgcoirITp1jrqUi1GXim5UWeejrbjjDZUG36X3jVPnz79YcrIyAA+LanH8J7f/xFZtZ9FUjMrrpu/Dkf1VGQRvEwixyWOzEWtaC9OEZhe5iI4jYhxCcA/C1UFtQPAriV+j9JKT80ttVtA3hlNjUCNBGF3lXQjd4KfUOphL5nxezQGvcr9k3CEwKX6dm3eTjU0zoiCk5j5dNj6YH1hHB2VlGOe3Yiilzm1DgwEfo2omgFwFKuKWDJDp0q3A/ONB1KjE/f49EF7xm0yiIKnuJcViG9tBaVpi9zcKE5XodGUYZCROG515+ynJSBt86Jr3kQPGEdhfueVUSRb7kRBmJdvZ4A4MYr9iH0Bb780FlkUpo07iqEvofz7TLqSa3hm649gA/eflytsyqiMJy/dRTn1yIzi4LOz8fcEu55YtlE+i+6ej9edPX+vu8v8D28+NryTR4HtdWp0juaOqtQiOEjwjxC38NalBjaqRl4WO7Gxh4tbnNE0QJwGsC3AHgpgHkAE1D9n149tpVtAxLdTA9Q2U/0EK8Y6knd2JQh0wp8Y9xdjcIa9f/yXdfjV15zQ+U5OTdbLmZXUE++axxpDYDligO2izSUQlBuYFuh62zGgYmGmpvdS1JjJBJOjZTsRGnXeYDRToBt062+dq8FcfK8pQMX7rkRbLCIYlDWCKfxNqpR2MFReeopn6Wm5n1n0qZ6DuugAl+YxpROFOUJXcvgFlsajSLJhn5vEw0fz71sL7708FkcP98ZGJUFnjAROZ/bQVrUS5hR9iuoPdqIrfKIQlfw8ygl1FTNF48u4Dc+dg+yTOKek8u44eI9Q7239UAIgbnJsLr2gzZiG6ArA52EcGxhFYEn8NQjM1hh1BNd13FgmFGorx/b2XcYeI8gXnBnsp50REE59xMNzxlKk9coAODbrrfT4crgNkYrM5Q+fuwlV+HluvcMgUcUXFBXa7cahVvA1UfMHrNGAVgumTQKQFMsJn2zeO5JbXgO5lKLAyeisD+nYiyAUU8tl3oKcrtrQEVhgyKKfAuPKkM2DMyEu8Q6dfzv9s48SJK6yuPfl0dVdff0THfPTDMw3XOAM4wjOMAMIKKrcogogssq4skaGi7rfeyu7HpgxO5GELuGu96xhLoQ4bUEHniwXoiroREueHJpyALqIMcMyMAc3V3H2z8yf5m/zMrMyqzMrKzqfp+Iia6qycr8ZWXm7/3eDf/3V1qLbfg9SpZa8ZpX5DGIvP3oCwBVFFAVoiTPx+MI2Vank2nB8LTj1uIj3/stfrX3AP7qWccmbluzDOw/2K1RnHfCBhBRYPUeNwQ1NnV914zbONxs44+PLWDdpBamajlO++/c+RCu+fF9eNb29Ti42MJTjumOPiyCqXE70KxMp4jnS5kG791/CJtmxjE9XsNjh5dwoOGankrUKHoKCrdJ0ZsBbNG3X44Jd7rD0ylb7Lz28ijGlOnJuTB1y/ScwDXTwJZ1E5hsWF5znTQEfRTdqzEiwnsv2Nn1uZUwyXsahUl+k/lOt+1ZTUBOqY/yTU+rx2w8dqSJxabmo4joR6GjVojruzQKf+y6qaPmlnQGgs5sfdfB8Fj/uz0FRcgslMv0pKKeQnkUwc50DNsyurK4UyfcGeT5NsIVc1udDo4sBZsM1S3lo0hvegKAM45diw/f9Fvs2DCJd5y7PXHbQNMl7fde3bDx4t1zaHfYqzsWr1E4Y1YaxdSYjXaHcfsBZbGCAAAgAElEQVQfD+DsHf7CzDIMLLUZzM7v9tGbHVdrGRoF4GRnt9qLkf+nnvN+k+0AP6z5vv2HsXntOFY1bPz+0cMYP1S+6SmNj+IrAD4F4GsAqqlINSB0jUJpEYD/MK8Z6/ZRzM+MY8w2sWbcxqa147jt/edlOmavPIo4opzgylmoTAoGUZdzVA//VPONaZC3ms9zI/difnocdz7wOBa0XgR6dE/UBKhMEnpoLKDlHYTs4Y75xK/6CzhJdLqZTV8t67/jqpTObFWfqkwfhe4H8TWKYBZ3mmO0XJ9DwJnqxuOH25YqZ2mzld6ZDQB7tkzjNWduwStO3xxZXUBHN7FFOb1NgzA97lQqjku4i/JRAM5EqfwPzvk49dDU8/u/9z4KyyBs37AKZTA3NYZOTO0lPyk2n0bRbHfw2OEl7JqfgkGOM1vNG1U7sxeY+cOljWCI0AWFnvWpUDbVux54HGO2ielxG2ftmMUt7zmn76zIYHhs+odTnyz0fdim4TkpLa2Eh7JV6w+nHmmjtksbFtkPm9aO49t3Pohmm73Vu3KeAtH2W7VdWFB49apCX6nbfp8K1XCmbpkhc5P2WtcoEnIo9G2VYzkqSi0tRE5UjppXDE1oA8FM+rhQ2l6Y5EQ3LUU4s1ttJ+qpoUXTqfBYJ48i/X1gmwaufGG8Hy68LQA3Ezz6GKqkfWzUk/JRLAQFBQBs1wSFsunrloInza7qKcz65coLnxIoH6Ojnrs8IdWWYWCh2cYjh5YwO1nHUruDxxea3iKgzPDYNLPbh4joSgDfBuDpVcz8s9JGVRF6aQldo1AoH8XePx3BaVtmvMk1T+p8rU+NwopwZgNBQRGoHtt2nJRR2cH6dmWanjbPjHtCQQndll7VNmIC3Dwzjjc950k4363AqUjSKHTTk7o2Ro/wWCCN6SnooxjP8dADrmnI1Uy8SB3ND6KilcKO77QOUcskLLr9JYKmJ0LTnUAboUXGocVWl0+jSNTYk56ZtRM13I14gej5KJTpScuKDmoUhue0VwUSyzI7AUGBFcZvBdD/QqxmEfY9sQhmYHZ1HY8fcdo0q37nBw43wcylJMymmeFOBPAqAGfBNz2x+35ZoZe/jtIo9Bth13wxN5zTM8JZ+WQyPUU4swHn4dAzs/1aT9zV0F4XFHbI9FEGm9b6IcK6RtEK2el1DIPwN+cd3/W56WkUwe/UbS08dsEXFPq+azGCopfA9/w97fw+CkAJr2A+hup13XL7SFim4eXieDkXfYTHBk1PjkahujQqapaBhabT9Kqs+0BNlElCWdVEiysz7kc9BRNhp8ZtzGq+LNtQgqKNp86twWKzg3NCQSGDwssCz6lRKA10drIBwOnH3e4wJhsWnlho4UiznVhdoO9jp9jmJQCOZebBlCmsEF1F1XtQKPSEr5PmiyvtW7cMtJaiW6HGEa9RkHceqnERoBraB3sAGNoq1tMoSkq4A4DNa/2kpQnNma1KgWdZCYWdv4qaaQQKpanjxEU96VpML41C73CX10eh7y+8H5WBq/JeuivNpgyPNfx+FGGNosNOLSzd3FYzjdw9E3qh9hvuK66jsqFjGxe5hTJV7SS1gDv+qMnAPaRHd02N13DtG07LfwJ9op67PCHV+jWZnawH5qut6ybwq70H8KfDzVIERZq74XY4fbOXPVE+CjUJmwZ5yV9AcRoF4EdxZDI96T4KO7hC1k1Pfrilk0AY5aNwtivfR7FhdcNbzY/bTrVSZ9LtZLbdemMPm54s30dxcLGFSWV6ismjsAIaRfLvr4ca582jADRBEZqUlYbZ6rimp5CPIu0kbiiBE/JRqO8fXAhWLK5Zhlcvqaww6TSmJ9X0q5eP4omFoEZxvGZ2AlTCHWOh2cm0CCuDInwU+jWZXV0P5KGoNq5l5VKkET1TAH5NRLcg6KNYduGxAUHhqrVrxmw8/MQiaqbhOZvXrap5zUiKQN1EUZnZceg9FYLObMKBI90Jd2rCCJiePI3C0OL4y3ugTIMwNzOGe/YdQt02XNOAWvFmm5jUeLtMT5YZKAroqOjBSUc/Vi2Tj8LZVjWGypNHoY+pS6Nwnc0qrDVcQDCtImNp4bH6xKyO98RCK2S2JG+V3qsIXr94pqeEVa9q4BVb68m7Dk40l9L0d2xYHdqO0Gx1sNBqx/bIGBRewl2O31U9m0ROcMcDYwve/21ZpwRFOQ7tNILiyqIPSkQzAP4LTm7GfQAuYeY/RWzXBnCb+/b3ZQsnpdoTack8SlBYTgSRbRJOmp8q1GHkCYospidtkmqENIrFgEbhT27hqKdB51EAjnP6nn2H0HAjkfQJMQtqkg5PsjXL0IoCtjGxLtmZbWUwPanfbrHl+A/StiSNQwnq8ISo4uWPLDn2Zr0uVBYTnWHEJdz5K3J9Aq1pWe1l3Qfqvk36rY9bvwqWQZ5mEcZwNeVmm1EzDRy3fhWuuvhEXHjSMV3HUvkiWbT1MlB9ZfLcM+penRmvwTYNL7gGcIozAuUJip53g96Xwu1D0QZwSc7jXgHgJmbeBuAm930UR5j5JPdf6RqMyj9YVbcCggLwH5wX7joGf3HKXKHHVau3qIS7OKyYVXHN0sJjtaKACy2n652+rT5RqVV26YLCVZEbtumbWNrZzThqmGGHp17C44kYZ3Zcwl0vZ7YnKJodtDO0Qo3DiNEoVP7DEdfZrEc9ZTFdWAah0+Gu/hLKvHgoNIHGRYMVieejSDDzPf1J63DLu8/xWghHoeclEBEuPW1Tl21e9WxR/e2rRGkURfgoVPKpKikEaBpFSbkUqbweRHQygJfDcWzfC+CLOY97EZy6UQBwLYDvA3hXzn3mRmkUqxt2l6BQk8QHLzmp8OOqmz6LRqEmfD0HAnB7DbihEQb5pifVrlL3Z0T6KHKE76Vhk1scsW4bfoJXpx8fhe870qkFigI2PTtunDNbJSnquR1xqMlmodl2yozn9VEoQR3aj7MS9hPi/KZL2SKtTLeEB4XKy+v3SzjqSVGWj6KWIuoJAKZjtAl/PwawmCzQVBfIBa25V1WE67H1g7oms64A1TWKrWsrMj0R0XYAL3P/7YdjKiJmfk4Bxz2KmR9wXz8IIK4gUoOIbgXQAnAVM38lZqyvB/B6ANi0aVPfg1ITzOoxG/e77UvXpOxwlYe65YRAZoldVw97OLs1kFhlGJ7zUNXC14+hr2gH4aMAgBPn1sAg4KjJhheVEs4cTkO4I5xClRlX4Z/KFq7LofDv7AisdgpnthOBtNBq5+5HoY89vB/VG1mV2FCnuNhqZxJOpqtRLHEo4U77zfSVdkAzrdD0lAavkGFS/xCTsNh08ocq91GE2hX3g/quCgFu2G7fb3ZCg8dssxJn9q8B/BDABVrToren3TERfRfAhoj/erf+hpmZiKLz3oHNzHw/ER0L4HtEdBsz/194I2a+GsDVALBnz564ffVEObP1MFivFWKJE2jdNtCwksszhwn3l1aEy4iriUVpFDXN8W1FaBRlC4pTt8zg1veci5mJmrdyztJWVOHlUYS+pooC6t3t9O2B6CgjIN3kpcqYt9weD3mIC/FVJrkjzbZjetI1igzXx3T3A3BXUqYiEPU0QNPTZEJ4bBqUgEh6Li03gRDIFlFYBl6tp1w+iqCgABytgsjRjKfH7dKys5Ou1sUALgVwMxF9E8AXAKQ+S2Y+J+7/iOghIjqamR8goqMBPByzj/vdv/cQ0fcBnAynLWspKNOT3s1qEBpFzTQyh+95fo3QuMJVQq2QRhFwZkflUZQsKAA//FE10Gm2OXONqbhJVp2femCUlhBsXNSthQDpBEXDNrHQajvhsaXlUbglNlwfgh71lMUZarhRT+1Odx6FIlDrSRcmpTWw6h31lIY0phzbIC97O0t5nDIowvSkfEtBQWF513PNeG3wzmxm/gozXwpgB4CbAbwNwCwRfYKInpvzuF8FcJn7+jIAN4Q3IKJpIqq7r9cBOBPAnTmPm8hC04kO0e22vjO7PNt93TIzr3jU5BJ2gAeqw5KmUSwpjULXONRfX6CUmUcRxgkD9fMFMn3X0yiiBcWjh5xI7lV15/rpYbThVahnDkkxeTXc7OVmh1NnSMehhtSlUZjklbkfs4MaRZZj+h3uQoJCM3WNxZieSsujMNML5SS8TOcEn5qtJRDGtWcdFEWUGVfXbVZz8q8Zt702rFNjdnV5FMx8CMDnAHyOiKbhOLTfBaf2U79cBeA6InotgN/BjaIioj0ALmfm1wF4MoD/IKIOHIF2FTOXKigW3YQ0/YEZhEaxcXoM+w9GlyeOQz1wYY0iXPBOTahR8fFBZ7a7uh2ARqGPTzVU6tf0FOWjAIBH3J4HqyKd2d2/mT4hJ1G3neZL7Q7nKscA+A9+lCnM6wdd0/Mo2pmOqfpRhFvg6pNVI0ajKK3WUwH10YDuro5RWKbhtQqo2vSkFnS5yoxb3aan97xgp/fsvPTUeS/ir2gyXS0318HzB/QLMz8C4OyIz28F8Dr39Y/h1JkaGItudIQeIeH5KEqqOAkAV5y/w+uslxZPUHR1vgsKAlU7SGkUUaanQeZR6KjqnocW25lt1kklPADgUbfdpmd6ikm4U99Ju8KtuxpF3p7ZQHx4rGUaXtTdmJ5H0c7mlNV7ZuuaYlTTKyCoTZbno1D+oHzPUy3F/apf57IqxqbFH2//98zJ81M458mzePLRfmLh7s1+KaEXnbyx/wH2oFrD3ZCx2HRqIemtISdq5bcItU0ju+nJveG6o566bdGWQX7UU2SZccOzfZdpYgtjuUXb9CqvaYn1UbhC/hFPUNhd24UnF8uknhFPioZtekI3v49C/e12ZnsmE9v0tltsdjJlg5sGYcnNnwm3QlXEh8cOuUZhp4h6iklKrQIvMzvH7zo/M45PXnZqbrNdPwz+iEPMYquNum34ERWW4dXrj2qyUiVxpifdZmt6k7/h51H00CjKNLGFsd3wWL14X1riy4w710tpFBORGkW3cE37ADds3+6d10xnUpxGQV6Z+zHbj4ZbbGXz5fhRT4jNo2jECIeyFgyWp1Hk9FGo+zVJo9CeherDY1XU03DNI2kZzVGXxIKnUfjCQdVfGuQEmgbb0ygSwmM1QXDYi3rytw82Lhpc1JNClVg42IdGoYRcd60nZ/wPPe7UwVE+JiMh6snKZHoyvZDL3GXGY8NjdSdssBVqpoS7uGx0M0ajGGB4bO48ilCf+MhjBTSKqgVF/g53VSIahYZyZuvJPOpBGrYLrFYmYZU6EB7r9ZggHIqIetIL6w2iH0UYyyQcaXJfpievpWZE9VgAuHf/IaxuWF6oc5JGccmeudSmxYZteIEBeX0UlhGjURgUcMKq14utdqYVabAHh3b+MVFPgwiPveCpR6NuGYlNftLg2fx7JNwpqhcUKnBhuOaRtIig0FBF89RFrVt+fsNIahSej8LA424NmKiigEGNYnA3sm0aeGKhiQ5nX2EmlfAAgHv2HfLq3wDhPIrgtXzF6ZtTH7dh+xpF3t/KN/3FR66N2aZXg6zD2SaauHOOm0DrAzA9bV47gdc989jc+/Ft/snhsYrKfRQF5FFUyWiOuiQWWx00bDOoUdjKmV3tiiQMkRP6Gq5hE1XwzjTIC5uLKjNuGoSt6ybw/BM3BKIoysYyCAeOBBPj0mL2MD0dabYDpeDVXEyUTxOoWwYOutpZaWXG9RV/LRi2mykzOyaKqcrw2KJQ40vyHdohgVslRZTwqBLRKDQWm23UJ+uaj8JPhBs2jQJwne1hjUJz4KkVa1z/BV2jaNgmPv6K3WUOtwvbNLxM0qSOZ1H4jYuCn+vXaW56rGv7vA+qbgoqLDO7y2fivx+3LU+DyXpMXaMImhyDgsjbZgA+iqJIE0UUbO5VdR6FcmaL6WnkcfIozEB5jLplYLJuYW2PapZV8E8vOgEnbgx22qvFaBQK/YExY0wfg0LlUQDZSzrEFQXUTXG6oFBCM+9KWV+B586jiIl60vfb0BLuorZNIs4vo2sO8VFPQy4oMuZRVG16Gq85ZfX18kCjhAgKjcVmtzObiPCNtzzTqwE/TFwc0RdD74JlRKyigwl5wb+DRl/xZc6jMOMEhb9P3fQUt3rPij6x5t2XL+xC5sOQszmu6VIvAs5sTdPUc2Z0U9YgyowXRT2Fpq9+K4OqN6VNNmx86Q1Px/ajJntvPISIoNBwfBR+ZraadDa53aNGAT3JLvwZEJwAjJiJalDoY8nszI7pDqdPHBt10xN1C81+0DWyvDHx8ZnZQR+Cfo5ZtJj48FgVMRed1Z+li15VpMnM1s9zGM7nqXNTVQ+hb4ZbvxwwTtST6Tmuh9Ev0Qv14AQnF1/w6Q9MXMLXoNAnxKw+il5FAQFgbtoX8J52lfNc9f3nLjMe27jIX/HrPbOBjFFPPfIougTFCEXmeJnZiVFP0ecpZGf474gBsqBMT55GMXo3mFppBUIj3QkjLPjiymAMilympx5FAcdsE9Pjdtd38uYHBFuHFuTMjqj1pB8rMOFnyaOIMVmpfYQjgQbVDrcIUmkUKtdoBBd8w4b8gi6tdgetDgdrPY3gDRalUcTVhYqbqAaFftzseRQq6ikkKNzz3zg91mVuMInym54K1CjiM7Od92OeoPD/L0uZ8WDCXbdGERYUI6lRpAiPbVRcYnw5MPx3xIBQeQZ12wiU8Bg1osqFW0a0hlS5RqE53sczmge8DncRq3HToIAjW2EY+YVio0AfRWxmtnsNx90JzojQDtMQ0EQ0Z7bfHTE6B2eQPUn6RZmHk6OelEYhgiIvozcTloTql92wDC08dvRuMGVaidIowqsvI8YhPCj0bmfhCb8XapIOaxSAI3TmZ7oFhUmUW0ssIzw2HExgeuVZuk1PWVuhKvQJVSVrxjqzR2CBpFd4jsP3xQz/+Qw7EvXkYlsGLn/WcThxbs1Im56ifBR+97phMz054+mnN0GcRgEAH33FKXjS7KrI7+TXKIoLIVWXI7wfpTWMRWgU/Tqzu7r6mdTV9c1wf59RMD2l6XBnhQSu0D8iKFxW1S1ccf4OAMAjbre50TQ9RWgU7utwuY9hSLgD+qskmiTknrV9fex38vsoitMo4kx/ZsiHYERcyzRYMRoF4Di0o0wyNSt9yfUq8TWKeCGgckeqLt+xHBj+O6ICVKx8eGIdBXwfRYTpKTQBeHH8Fdmk1VgncwiKrHkF+U1P3b6ffokTduGopCjtMA26JhI+7yiNAnAEyij4KPwy46JRDALRKCJYVbfw3gt24rk7j6p6KJmJ0ij8tqlh0xO6th0kvukp+20Yl0eRhEFFmJ40Z3Ze01OP6rEqWkf/76yNi+K+t2HNGI6ZanR9Z1Q0ihOOWY13nrsdz9i2LnYbL9pvBBd8w4YIihhe+4ytVQ+hL9RDrk+IasLo0ijURFVR1qpdgOkpy5xWjOlJ1yiKCY+N6kcBRGsUWVuhKsLnff3lZ0T+FrUM3f6qxDINvPnsbYnbqPtdTE/5EUGxzFCTb1RHty7zQ0xPh0GhInj66Z+c5MyOw6BiE+4Ky8yOSbgbi0q4KyAzG4gXzk79p+E3PaUhrlSJkJ3hXzoImfA0Ct1HEZtHga5tB4laOfcjKOJ6ZicxM1HLXQVYdwDnXXnHFSpUn3t5FH06s3U/TlqhVrOMygvoFUVcvoiQHdEolhk1L4+iO4N42PIoioh6yjL2T//lqbknDd3eXVbUU7hGka4dmlnyKCL6kfTi1WdswcwQltTvB0m4Kw4RFMuMKB9FnOlpWPIosna3AzTTUwaNoohS8UX6KLxmSjEJdyoqKapuVxr89rbphcsrn5a+LeywI0UBi0N0smWGejgCIZUxbSONPibbIlFjzeOjGLSQIyLvdywuMzsm4c7ujnrKkpldVLOmUWVmooa/fvZxOHcEoxeHDdEolhlJCXddGoUqM16ZjyJPeKzz3aylP4qgYZtYbHUyTdpR9PJRROdRZEm4G50if2VARHjX83ZUPYxlwcq8g5Yxic7smBIeVWdm96NRNGwD7zh3O857yoaih9UTpVEUZXrq9lG4tvVad9RTFqGuLmtSmQtBSEMlMwQRvYSI7iCiDhHtSdjueUT0GyK6m4iuGOQYRxUV4RJZZjxkq43r2TwolEmkH42CiPCWs7dF1nQqm6hiff0QZz4LaxREBKVUZMnMXukahVAcVd1BtwO4GMAP4jYgIhPAxwCcD2AngJcR0c7BDG+0sU2KNFdEFYYDqot6OmXzNN74nONw2taZSo7fLypyKnd4bExmthJEuqbVTzdCNbyV6qMQiqMSHwUz3wWgVx/b0wDczcz3uNt+AcBFAO4sfYAjjm0YkaWpY8NjK3JmN2wTf3ve6NmQVT5KXvkal5m9e/M0PvCSXQEB6lwrzlg9dnSrIAvDxTDfQRsB/EF7v9f9rAsiej0R3UpEt+7bt28ggxtmbMsITCgquigc9TQ/PYaNU2M4dv3EQMc36jRsA5ZBvRY6PVGXqKt6rEF48e65wOeev6GvPIphfsyFUaA0jYKIvgsgytP4bma+ochjMfPVAK4GgD179nCR+x5FbJNSJdzNrm7gR1ecNdCxLQcatlmIuS5LiG9cuY8kfOEizmwhH6UJCmY+J+cu7gcwr72fcz8TejBRswIN5e2YEh5Cf9Qts5BVuhLmacJslZkqy6QvzmyhKIY5j+IWANuIaCscAXEpgJdXO6TR4N9eelKgDENcK1ShP+q2UZBGof6m0Cg87SNDwp04s4WCqCo89s+JaC+AMwB8g4i+5X5+DBHdCADM3ALwJgDfAnAXgOuY+Y4qxjtq7JqfwvzMuPc+zvQk9EfDMgsJKc4SntyP6Uk0CqEoqop6+jKAL0d8/kcAz9fe3wjgxgEObVlix5TwEPrj9K0z6HB+V1iWwoa+6akPZ7ZcdyEnw2x6EgoiroSH0B+XnDqPS06d771hD+JKeEShZEmm8Fgzu19DEKKQmWMFcNKmKZx/wgZsP2qy6qEIGlvXTWBmoobZye6WpGE87SBLh7sVXhRQKA7RKFYAs5MNfOKVu6sehhDiqXNT+Nl7z021rTI9mZkS7iSPQigGuYMEYQTwe1dkFxRichTyIneQIIwAfkn4LP0onL+iUQh5kTtIEEYAI0OElIKIsGt+Cjs2iG9KyIf4KARhBOin/zUA3PDGM8sYjrDCEI1CEEaAfvpRCEJRyF0nCCNAVT3CBQEQQSEII4FpEAyqpke4IIigEIQRwCDKFPEkCEUid54gjACmQWJ2EipDBIUgjAAmiaAQqkMEhSCMAIYhiXNCdcidJwgjgEFUSLMkQegHERSCMAKYBolGIVSG3HmCMAI4UU+iUQjVIIJCEEYA0xDTk1AdIigEYQQwDcrUtEgQikSKAgrCCPDqMzbj0UNLVQ9DWKGIoBCEEeCZ29ZXPQRhBSO6rCAIgpCICApBEAQhEREUgiAIQiIiKARBEIRERFAIgiAIiYigEARBEBIRQSEIgiAkIoJCEARBSISYueoxFAoR7QPwuxy7WAdgf0HDGRVW2jmvtPMF5JxXCnnOeTMzR2Z2LjtBkRciupWZ91Q9jkGy0s55pZ0vIOe8UijrnMX0JAiCICQigkIQBEFIRARFN1dXPYAKWGnnvNLOF5BzXimUcs7ioxAEQRASEY1CEARBSEQEhSAIgpCICAoXInoeEf2GiO4moiuqHk/ZENE8Ed1MRHcS0R1E9NaqxzQoiMgkop8T0derHssgIKIpIrqeiH5NRHcR0RlVj6lsiOjt7n19OxF9nogaVY+paIjo00T0MBHdrn02Q0TfIaLfun+niziWCAo4EweAjwE4H8BOAC8jop3Vjqp0WgDeycw7ATwNwBtXwDkr3grgrqoHMUA+BOCbzLwDwC4s83Mnoo0A3gJgDzOfAMAEcGm1oyqFawA8L/TZFQBuYuZtAG5y3+dGBIXDaQDuZuZ7mHkJwBcAXFTxmEqFmR9g5p+5r5+AM3lsrHZU5UNEcwBeAOCTVY9lEBDRGgB/BuBTAMDMS8z8WLWjGggWgDEisgCMA/hjxeMpHGb+AYBHQx9fBOBa9/W1AF5UxLFEUDhsBPAH7f1erIBJU0FEWwCcDOAn1Y5kIPw7gL8D0Kl6IANiK4B9AP7TNbd9kogmqh5UmTDz/QA+AOD3AB4AcICZv13tqAbGUcz8gPv6QQBHFbFTERQrHCJaBeCLAN7GzI9XPZ4yIaILADzMzD+teiwDxAJwCoBPMPPJAA6hIHPEsOLa5S+CIySPATBBRK+sdlSDh53ch0LyH0RQONwPYF57P+d+tqwhIhuOkPgsM3+p6vEMgDMBXEhE98ExL55FRJ+pdkilsxfAXmZW2uL1cATHcuYcAPcy8z5mbgL4EoCnVzymQfEQER0NAO7fh4vYqQgKh1sAbCOirURUg+P4+mrFYyoVIiI4duu7mPmDVY9nEDDz3zPzHDNvgXONv8fMy3qlycwPAvgDER3vfnQ2gDsrHNIg+D2ApxHRuHufn41l7sDX+CqAy9zXlwG4oYidWkXsZNRh5hYRvQnAt+BESHyame+oeFhlcyaAVwG4jYh+4X72D8x8Y4VjEsrhzQA+6y6C7gHwmorHUyrM/BMiuh7Az+BE9/0cy7CcBxF9HsCzAawjor0ArgRwFYDriOi1cNotXFLIsaSEhyAIgpCEmJ4EQRCERERQCIIgCImIoBAEQRASEUEhCIIgJCKCQhAEQUhEBIUgCIKQiAgKQYiBiNYS0S/cfw8S0f3u64NE9PESjncNEd1LRJcnbPNMtzT87XHbCELRSB6FIKSAiN4P4CAzf6DEY1wD4OvMfH2P7ba4251Q1lgEQUc0CkHICBE9WzU9IqL3E9G1RPRDIvodEV1MRP9CRLcR0Tfdelogot1E9D9E9FMi+paqx9PjOC9xG+/8koh+UPZ5CUIcIigEIT/HATgLwIUAPgPgZmY+EcARAC9whcVHALyYmXcD+DSAf06x3/cBOI+Zd7n7FiQBLYIAAAD/SURBVIRKkFpPgpCf/2bmJhHdBqdW2Dfdz28DsAXA8QBOAPAdp0YdTDh9EnrxIwDXENF1cCqgCkIliKAQhPwsAgAzd4ioyb7jrwPnGSMAdzBzpl7VzHw5EZ0OpyPfT4loNzM/UuTABSENYnoShPL5DYD1RHQG4PQBIaKn9PoSER3HzD9h5vfB6VI33+s7glAGolEIQskw8xIRvRjAh90e1haclqy9Stn/KxFtg6OR3ATgl+WOVBCikfBYQRgSJDxWGFbE9CQIw8MBAP/YK+EOwNcA7B/YqIQVj2gUgiAIQiKiUQiCIAiJiKAQBEEQEhFBIQiCICQigkIQBEFI5P8BQvJJpXeSYDgAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"t = np.linspace(0, 10, 201)\n",
"noisy_s_t = s(t) + np.random.randn(201)/2\n",
"plt.plot(t, noisy_s_t)\n",
"plt.title(\"Signal\")\n",
"plt.xlabel(\"Time [s]\")\n",
"_ = plt.ylabel(\"Amplitude [arb.]\")"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x112dc7eb0>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"S_f = np.fft.fft(noisy_s_t)\n",
"f = np.fft.fftfreq(t.size, t[1])\n",
"power_spectral_density = np.abs(S_f)**2\n",
"\n",
"plt.plot(np.fft.fftshift(f), np.fft.fftshift(power_spectral_density))\n",
"plt.axvline(-freq, color='pink')\n",
"plt.axvline(freq, color='pink', label=f\"Sine component: $\\pm${freq}\")\n",
"\n",
"plt.xlabel(\"Frequency [Hz]\")\n",
"plt.ylabel(\"Power [arb.]\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Beating Signals"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"t = np.linspace(0, 10, 201)\n",
"noisy_s_t = s(t) + s(t, 3)\n",
"plt.plot(t, noisy_s_t)\n",
"plt.title(\"Signal\")\n",
"plt.xlabel(\"Time [s]\")\n",
"_ = plt.ylabel(\"Amplitude [arb.]\")"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Power [arb.]')"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"S_f = np.fft.fft(noisy_s_t)\n",
"f = np.fft.fftfreq(t.size, t[1])\n",
"power_spectral_density = np.abs(S_f)**2\n",
"\n",
"plt.plot(np.fft.fftshift(f), np.fft.fftshift(power_spectral_density))\n",
"\n",
"plt.xlabel(\"Frequency [Hz]\")\n",
"plt.ylabel(\"Power [arb.]\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.8.5"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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