Skip to content

Instantly share code, notes, and snippets.

@GCBallesteros
Created January 13, 2022 15:45
Show Gist options
  • Select an option

  • Save GCBallesteros/bfd5f773551c9debfdda1da96e161eb3 to your computer and use it in GitHub Desktop.

Select an option

Save GCBallesteros/bfd5f773551c9debfdda1da96e161eb3 to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "4e28de07",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy.signal\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "458db979",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fb523b94880>]"
]
},
"execution_count": 25,
"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": [
"x = np.random.randn(6000)\n",
"plt.plot(x)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "0d4e5086",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Power fourier transform')"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEICAYAAACktLTqAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAA3E0lEQVR4nO3dd5wU9f348df7jl6kgxTxQFAEQVRErNhQAY3GRGOJGjXBmqbfnwF7QSVdY+w9xqgodhClWAAVPJBeBOHo5ej94O4+vz9m9pjbnd2d7Ttz7+fjcY/bnZ2d+czu7Hs+86lijEEppVSwFOQ6AUoppdJPg7tSSgWQBnellAogDe5KKRVAGtyVUiqANLgrpVQAaXBXviAibUTkKxHZISJ/z8D2nxGRe9K93VzI9Gel/KFWrhOg8oOIlABtgApgF/AJcKsxZmcu0+UwBNgIHGQy0DnDGHNjOrcnIgboaoxZks7tepTRz0r5g+bcldMFxphGwLFAH+DuXCRCRApdFh8KzM9EsIqyP6/vTSqDlOz7PEr6s8pwulQWaXBXEYwxq7Fy7kcBiMhPRGSeiGwVkS9E5Eh7+bUi8lHofSKyWETedjxfKSK97cfdRGSciGwWkUUicqljvVdE5GkRGSMiu4AznOkRkVeAa4A7RGSniJwtInVF5DERWWP/PSYide31fyUik8O2YUSkS7T92cuGO9Y/X0Rm2sf8tYj0crxWIiJ/EpHZwK7wgCgiX9kPZ9np/YWInC4iq+z3rQNeFpFmIvKxiJSKyBb7cQfHdr4QkYdEZIpdxPKZiLS0X6snIv8VkU12Gr+zi2MS/azc0nW/iLxtb3+HiMwRkcNFZJiIbLC/13PinEYq14wx+qd/ACXA2fbjQ4B5wEPA4VjFNAOA2sAdwBKgDtAZ2IqVSWgHLAdW2dvoDGyxX2sIrASuxSoKPAar2KC7ve4rwDbgZHv9ei7pewUY7nj+IPAt0BpoBXwNPGS/9itgctj7DdAl2v6c27fTtwE4ASjECpYlQF3HZzXT/pzqR/k8q/ZnPz8dKAf+DNQF6gMtgJ8BDYDGwNvA+473fAH8aH8H9e3nI+zXbgA+st9bCByHVQyT6Gfllq77gb3Aufb39R9gGXAX1jnwG2BZrs9Z/Yv9pzl35fS+iGwFJgNfAo8AvwBGG2PGGWP2A3/DCgAnGWOWAjuA3sBpwKfAGhHpBvQHJhljKoHzgRJjzMvGmHJjzPfAKOASx74/MMZMMcZUGmP2ekjrlcCDxpgNxphS4AHgqgSONdb+hgDPGmOmGmMqjDGvAmVAP8c6/zLGrDTG7Elgn5XAfcaYMmPMHmPMJmPMKGPMbmPMDuBhrM/N6WVjzA/2fkZifdYA+7EuDl3sNE43xmyPst94n1W1dNnLJhljPjXGlGNddFphXVj2A28CRSLSNIFjV1mm5WvK6SJjzHjnAhEJ5cgBMMZUishKoL296Eus3F8X+/FWrAB1ov0crDLgE+wLR0gt4DXH85UJprVauuzH7RJ4f6z9HQpcIyK/dSyrE7b9RNMLUOq8kIhIA+CfwHlAM3txYxEpNMZU2M/XOd6/G2hkP34N687hTTvI/he4yw6+4eJ9VqUuF7j1jsd7gI2ONIUuAI2wvm+VhzTnruJZgxXsABARwQoqq+1FoeB+qv34S6zg3p8DwX0l8KUxpqnjr5Ex5ibHfhKt/KuWLqCjvQysYqQGjjQf7PL+WPtbCTwclt4Gxpg3Ukiv23tuB44ATjDGHIR19wMgcTdkzH5jzAPGmO7ASVh3R1dHWT3WZ+WWLhUAGtxVPCOBwSJylojUxgpIZVjltmAF8DOwyp5XAZOwcqItgO/tdT4GDheRq0Sktv13fKhiNklvAHeLSCu7kvFerNwrwCygh4j0FpF6WGXIiXgeuFFEThBLQxEZLCKNE9jGeqx6h1gaY+WCt4pIc+A+rxsXkTNEpKdYLX22YxXTVEZZPdZnpQJKg7uKyRizCPgl8ARWJegFWE0m99mv/wDsxArq2OW+S4Epodt4uzz5HOAyrBzjOg5U4CVrOFAMzAbmADPsZaE0PQiMBxZj1SF4Zowpxqo0/DdWpfASrEraRNwPvGq3ZLk0yjqPYdVfbMSq8BybwPYPBt7BCuwLsC6yr0VZN+pnpYJLjNE7MqWUChrNuSulVABpcFdKqQDS4K6UUgGkwV0ppQIoLzoxtWzZ0hQVFeU6GUop5SvTp0/faIxp5fZaXgT3oqIiiouLc50MpZTyFRFZHu01LZZRSqkA0uCulFIBpMFdKaUCSIO7UkoFkAZ3pZQKoLjBXUQOEZHPRWS+WFOt/d5efr+IrLanIpspIoMc7xkmIkvEmk7t3EwegFJKqUhemkKWA7cbY2bYQ55OF5Fx9mv/NMb8zbmyiHTHGv2vB9aEAONF5HDHQP9KKaUyLG7O3Riz1hgzw368A2t40fYx3nIh8KY9ZdcyrOFS+6YjsW6Wlu7k6x83ZmrzSimVET+W7uSbHzdlbPsJlbmLSBHW5MFT7UW3ishsEXlJRELThLWn+hRkq4h9MUjJmX//kiuenxp/RaWUyiNn/f1LLn/+24xt33NwF5FGWJMa/8GekOFp4DCsCXvXAn9PZMciMkREikWkuLS0NJG3KqWUisNTcLenVxsFvG6MeRfAGLPennW9EmtaslDRy2qsOTZDOnBgvs0qxpjnjDF9jDF9WrVyHRpBKaVUkry0lhHgRWCBMeYfjuVtHav9FJhrP/4QuExE6opIJ6ArMC19SVZKKRWPl9YyJwNXAXNEZKa97E7gchHpjTVzeglwA4AxZp6IjATmY7W0uUVbyiilVHbFDe7GmMmAuLw0JsZ7HgYeTiFdSimlUqA9VJVSKoA0uCulVAAFMriv376XbXv25zoZSikFQHlFJUtLd2Z1n4EM7ic8MoFT/zwx18lQSikAHv1kIWf+/UtWb92TtX0GMrgDbN9bnuskKKUUAFOXWcMMbN65L2v7DGxwV0qpmkyDu1JKBZAGd6WUCiAN7kopFUAa3JVSKoA0uCulVABpcFdKqQDS4K6UUgGkwT3PVVYa9ldU5joZSmVdRaWhXM/9pGlwz3NXvTSVrnd9kutk1Dj/9/YsPpu3DoDVW/dw6bPfsG23jleUTT9/5mu66LmfNA3ueW7KkszNjq6ie2f6Koa8Nh2Af09cwrRlm/l4zpocp6pm+X7F1lwnwdc0uCulVABpcFdZY4zJdRJqBGOMftZKg7vKjkmLS+k0bAxzV2/LdVICr9OwMdz53tz4K6pA0+CusmLCgg0ATFu2OccpqRnemLYi10lQOabBXSmlAkiDu1JKBZAGd6WUCiAN7kopFUAa3JVSKoA0uCvlkTYdV36iwV0ppQJIg7tSHonkOgVKeafBXSmlAkiDu1JKBZAGd6WUCqC4wV1EDhGRz0VkvojME5Hf28ubi8g4EVls/29mLxcR+ZeILBGR2SJybKYPIlOmLNnImDlrc50MpVSOzF29jdenLs91MpLiJedeDtxujOkO9ANuEZHuwFBggjGmKzDBfg4wEOhq/w0Bnk57qrPkyhemcvPrM3KdDBXFF4s2UDR0tK9nSBr0+CSGfzw/18lQUZz/xGTu8ukIm3GDuzFmrTFmhv14B7AAaA9cCLxqr/YqcJH9+ELgP8byLdBURNqmO+FKPfXFjwAsWLc9xylJ3vy123lh8rJcJ0MFUEJl7iJSBBwDTAXaGGNCZRbrgDb24/bASsfbVtnLwrc1RESKRaS4tLQ00XQrpZSKwXNwF5FGwCjgD8aYalklY037klD/PWPMc8aYPsaYPq1atUrkrUrlhPZQVX7iKbiLSG2swP66MeZde/H6UHGL/X+DvXw1cIjj7R3sZUr5knZeUn7kpbWMAC8CC4wx/3C89CFwjf34GuADx/Kr7VYz/YBtjuIbpZRSWVDLwzonA1cBc0Rkpr3sTmAEMFJErgeWA5far40BBgFLgN3AtelMsKrZ9u6vYPve/bRuXC9r+8xWccz2vfsxldCkQe3s7FAFWtzgboyZDES7MT3LZX0D3JJiupRydcNr0/nyh1JKRgzO+r4zXTzT6/7PAHJybCp4tIeq8pUvf3C0rNIKTqWi0uCeYeUVlfQZPo73v9c65UzR+k4VbtWW3Rx25xgW+rgPRKo0uGfYrrIKNu7cx70f+LOXm1J+9Nm89VRUGt6ctjL+ygGlwV35npbOKBVJg7vyrzSVx3z1QyknPTqBvfsrPL/nxtem8/fPFqUnAUplgAZ3VeMNHz2fNdv2UrJpV8z1nE0ix85bxxMTl2Q4ZUolT4N7hk1YuD7XSUjKkg07GTs39b5nXyzawHEPjUsoV5xtBXYbx0XrdrC/ojLi9fAmkH6ppLvule/489iFKW9n9qqtfPWDP8d/euXrklwnIWc0uGfYbSNn5ToJSTn7H19y439TH+740TEL2bRrH8s37U5DqjIjFNx//+ZMHh69IOa6c1dv47zHJmUjWSmbuHADT9sjZ6biJ/+ewtUvTUtDilQ2aXBXNV5hwYGsefHyzTHXXbN1T6aTo1RaaHBX/pWmZjIFBbFrZnU0SOVHGtzTZPe+8lwnocZKtdFMoWMDsQK5iDa7DIq9+yuoqAz2t6nBPQ0+m7eO7vd+yqyVW3OdlKzbX1HJ8jitTOLZWVae06nyCnw4pu/e/RVs2lmW0jY27Njr6ykKU9HtnrH84a2ZuU5GRgUuuJeVZ79VxqTFGwGYtWpr1veda/d9OI/+f/2CjSkEmn6PTODoBz+rev7fb5entL1EOYtl8rUIprLS8MKkpewqs+4Qr3xhKscNH5/SNvs+PIHjH05tG3720aw1Wd/n9r3Zu5gGLrjfohNaZ9XXS6wL2469yRdL7Sw78N5lG3dx9/tzE5qYPNV4XOiDnPvEhRsYPnoBw+3WPNOXb0nLdve5NP1UmXPlC1Oztq/ABffxCzbEXylPjSxeyZZd+3KdjJwKtTP39DmkKSYX+OBXsMfuJ5DNnF8+Msbw32+Xax2XBz44rWuGH0t3csc7s/ndm9/nOikJydNSDOau3kbR0NEsLd2Ztm0mW2Rz5D1jefbL1NubK/hq8Ubufn8uD30cuz+C0uCedRu273VdXrbfyrGW7sheWXM2mQQvA6leNEJDLE9Iw51cqqU2e/ZX8OgnqfcUBfL3apolu+0ivGh3dht3lgW+FYxXGtzTwGvg+n7FFvo+MoF3pq+qtnzN1j28PnV5JpKWcTktrdbfcI315Q+lTFtWvcPZtj376TN8PA99PD9HqcovGtyz6If1OwCYtmxTteVXvTiV16euyEWSUuY1vkqUy8Dc1duirO9drHXTfceQ89Y0YQf7wqSluUlHjoTuovbsr+DSZ7+p9toOuz5i3Hx/jueUbhrc0yBa4PJqi4e2xovW7UhpH5mW7CfwxrTMXNSSLUpZsHY7G3a4F50ZY7gn15OuhF1chscZC8evdJiH1Glw94lzH/uKrbtrTkuaUAzbX1FJ0dDRPD5+ccQ600pijwMD3nLa4RfnEVHKx1du2ZO1OpFQhfDUpdZdng9aa6bVSSMm5joJvqfBPc9IjF/x7n3VO2gt37SrqlNLUIQffVm5VdH83FeJtTaJ9TkmKhdFMVPs/gMTFvq3aa8XxhgWrPXHEMp+UyOD++Zd+ygaOjpvyuacYcgkEEn6//ULfvli9jpFZMP8NP3QE/kcvcqHzPOMFVsycmy58tZ3Kxn4+CS+WOTfi1i+xZOQwAf371dsoWjoaGY6xn0JTbbw4uTcVEal87f5/Yqt6dtYEmIdy559FSxa772uYNue/fz+zZmJpyHhd/jX2m17E56AYtnG1Mb+yaRQrr0kDWnM1TXPLZ4YYygaOpq/fZq7qRgDH9w/X2TNIJPOnMHlz33LL6N0Ix47d13UNrheKl7TWZzgxZQlG1mcQABORKKzAMWarWnXvsTGDErkcwxf9d0Zq13Xe2HysoTSkIrQ8AJuxW5LNiTWMeuMv32RjiRF2L53P6PCmvVmXvK/D2MM785Yxb7yyCEXXpi0lKKho9N+V/Tvz3M3FWPgg3u67Swr55ulm5hsl4k6bdy5jxv/O50bXpvu+t5Em+Ul4pUpy5geZ6IJN1e+MJUB//wq6f3GiqGbHRe5aMeeDxWFXn/P2ewc85l9iz9vTf6WRw8dNZvb354VtTlrNJt2lvHgR/Mpz/K4NmPnruO2kbN4YmJk5Xyo1dGcBI8ln9XM4J7Cb/Sd4pVRXwvlCFZuiT2lXCYC2v0fzednT38TsfyDmas56dEJGQtMqWZ0Yr3/+a+WsirOZwkH8nKL1u3gu7AWNOk46nR+Xys27U5oPtLyykr+8dkidpcduHPJhwsiwPrtVsuhaHdcv3/ze4a9Oydi+QMfzeelKcvSXkYd73PZusdqchyrxVOQphOslesE+I1bsIiWK7325dyfKENHzWHP/grKyitoUCe9X7cxhhWbreDr9sNKNAg5A33pjjIeHrOANpPruq7r1qP33MesO5CSEYPzovLTzWl//Ryw0ugUbTLyuau3M3f1dlo2OvA5pLtsedvu/TRpUDu9GwU+mGkNqfvoxT2rLS+vtDJB2boRKho6OuLzjiZAddU1NOeeoV9+KMiHNh8q749YL+wE8hoEDVYZeWUSv4pMnLTOETjdti/VHif2oYeOcVeZe67wrve8dSbyy4813mTkZTHqI1J10+vuxYi5MGPFlmpDQCfC63cda71Uytzz7VyrmcE9zaoCl/3lRqvMS7Un67h567jyham87KG1RFl5BXv3V1RdOOKdd5c88zXnPzEpofQ4K46/Wbop4vV0VA4n+0NPRL4Uc8TkSGM60uvs8Ry6+/Lqn+N+SKjysbyiMm5/DIM1fMDFT30dcyz/VI7dy1vzLUCnIvjB3e3bClv0yZy1SfU83FVWzp59FRmtKHUaWWy1TFgRY1q7UI73iLvH0u2esZ4vJ9+VbGHu6uQr74a9O6dqbI+QRH+HmfgcvQSDoHUE8yJUhJWMxydUr5CM9xl3uesTetz3aVUP6zFz1rmuF6qzSqROIlXlFZXVen57PQMrKw1vfbeiav4ByL9MQtzgLiIvicgGEZnrWHa/iKwWkZn23yDHa8NEZImILBKRczOV8ERFyzXvLCvnptdnxK1I2bBjLyPDKlN73Pdptenh0hmaKitNVfvZkFAHn1j7idauPBsdX8orwsubMr7LuFZ6yJUuWJu5cXtqwqQSXk+tWO3tY50qKzfvTuskJc5MxN3vz6X3g+MOvGYMkxdvrNYvxs2oGav406g5eT1Ov5ec+yvAeS7L/2mM6W3/jQEQke7AZUAP+z1PiUhhuhKbqCcdbUyr5QodZ1KFHZBWx2mV8etXi7njndlsCMvh7yuvrLpwhALoapdBj0TEU85UsG6Zb359Buc9llgxibWfyP1Cbjr6eGvXH/XNqe4cIC2jbaZyXbzbY91ALuVLUUS0ZJz6l885fvh4Ji32nqN3O6+mLotsKhyq9HX65YtTuejJKTG3v81uebN5l/tFx/mZjp27NqW74mTFDe7GmK8Arw2oLwTeNMaUGWOWAUuAvimkz7NT/zKRX4QNAfrXTxel7V4pVGzj1qSwqiLVsa/wYh5nzjlWkgzWLfPYee63rta2vKTY3leM9/z61WLvG3JLR5xLRr7cprp1WnHKVDorKg2LE+xw5Ec/fyayCa4XiXzuZeWVXPVi7Ltr5/bczvf3vo/snBZ+DmfiOhdeWR7qMJVpqZS53yois+1im2b2svaAs+xilb0sgogMEZFiESkuLU29jG3l5j2uV+aQFyctO/Ajt7/Bb5dupjiJjj9exGpXHnnipS+67NlX4blzyPgFmR0Lw3mc0S4E2cg1Hn73JzFfz9Q16FcvT0tbp5hUWh7F3XaWLsIiUq2CPN3fvdftxfr8KhNM1NY9+7jjndkR+39nRvSeu89kqSgn2eD+NHAY0BtYC/w90Q0YY54zxvQxxvRp1apVksnwbkdZOc+7TGxwvZ17TeU8C50sziaKbsEs+knlyNV72N+eGM3ifvrU19wUo7VBPqv2u0rzD/+lycsoGjq6WgVYplz81BSufXkakxZH9mKuyT6etYaj7vs06utevpt0XIdi3XEmesF5d8ZqVm2pXgy7d39FVcDPpaSCuzFmvTGmwhhTCTzPgaKX1cAhjlU72Mtyx/FtZapZXSqtPIwxbNyZ2Djt70xfFTHFmFO1nn9V5TLWv+1797NnXwX9HpmQYEq9CwXSUTFyL/HsSPN39aA99VqsC2M0ieZsZ6zYGrWPQ7K2703t8ygaOpo73pnlXqyY5OnrfNugxycxa+XWqrJoN1/GaAXz/sw1DP7X5ITTEGs8omSklMnzeJ4k+ntPVlLBXUTaOp7+FAjVGn0IXCYidUWkE9AVyH03zXApXP7dWp1s25P8D+/Zr5IbmTJ8irFoDsR2w9bd++h1/2ccee9Y1kWZqPvt4pVJlweGPpkHczyH5eZd+9JedBEEI4tXMWvV1qTff/QDn/Gb/7jX08xfu50Ln5zC0Q98xtsxhuiIZubKrdXGIoomvO/Ehf+OXfEZT2X4zUKeVC6nQ9z+6CLyBnA60FJEVgH3AaeLSG+sj6IEuAHAGDNPREYC84Fy4BZjTOa61iUrzV/gR7PWJLTZt6ev4u3pq1g0/LyMj2Pt/DFs8vDjefWbEs/bTqxiN0rHrgzEYD+PDZ5pqXzc2/bsr3ZXGG1bXy3eyCV9DolYno7vOjxzFWr622f4OPZ4HDnUuYl9SRbT5UsLo1jiBndjzOUui1+Msf7DwMOpJCofhb7MdA7Ju3dfZcZPklA9gDHJTTmXCL/mlbM9zHKq8iW5Wz3M/Zst6SrqiFbEWllpKCiI/cHnW8APfg9Vh1hfzY695TGHLo1WjBHNH9+aWe15tDLTdJwPsTrKhMquy7M4XG2y0pXC20bOyssJlr0Wd63dFjvt+RJElqY4wcbUZZFDVsTj9UIcXifV9+Hxnt4X7WfiHOJ7zdY9LFiXv0Mxh9So4F71vUU5P85/In6FzvoYQd75o/t2qbcmlrEqRr0KDb0ay79dxrD2av6a7RQNHc3ysGEP0hFj0hGoyitNRJv9D2dFdk7JJ1e/NC3q7EP5MHNSn+HjeTGFyUncLlA/rK/e5v+t7xIvm/cqvJ9IeOfDaJwVzqEJUwAqHCfqSSMmRp3QJZ8EP7i7XelTCChuPdq8umNU9eZRzqELMu3Vb5Z7Kot2+7jesWfbyfQckfEmfYjWMuKH9TtSarMfKy/4v6kr+F8aermG++qHUh4Zs8D1tYhhHMJ4GeM+Gq+n/sadZTyUZMX41t37OPHRiUm9Nxnhd0RuPcSTsW3PgaIeL/cL+VJcFuLr4O6lXey/JkTmWJeU5m+vwUyeII+Nj597d9t9tgbWijaDVUi3e8ZmZscxPvM734ucbCLT4o1zlO5mlunmtX2/IfH6jmzGz0TvKp05/UR4Gf8oGb4O7mPmuE9wEM+9H8xLc0os2RodMtvespu27auoxBjDiE8WsnDd9oiTP9bRZ3KavVSLdvIsw5UTe/ZVMHTUbLblUSVpriV6Xu2vMEndNaQ6DEg0vg7uiXYVTvZH7HXkt3yp6MqUigrDjrJynvnyRy5xGU8k1vcxY/nWjKUr1c5pufrastFbNly038D/pq3gze9WRgznm2nZGK00Yp8e13vkE/dis1iSucstK89Ma3FfB/dsdVR59JOFWdlPpnn6IcXISj/z5Y/0uv8ze1uRr8e6k0q2PbEX/xj3Q2obyFF0z6fildC58dKUZfz0qdQ6BgXF0tIDFdtei4+SuVZlqimur4N7opItxvEqVtfrTHJONpCq1Vui31buCuskEl7U4rUTST4ZN399SkMd5PN43m6ixR5ngPl+xdaspAWsiv5sS3TmqUSt3ZZYs+lM8XVwT/SCV7Ips1+q25Ci2ZDOOoSNOxOfkcrPonWn9yood3W5EG8oZjfpyOSmo/lxLIlmIjNV/hC3h2rQZPqLzQWvg2EFvEogYV6HRo5nf0UltQt9nU+KKpnJ2GuyUTNW8VyS40WlWzDPyBjiDbhVVl7Bn96ZndScqjWJW/m911xV6Y4ypmdoHH2vjDF0uSv2OO9edb3rE751mSA8m5Zt3FVt0utERfvqwqeWrKmMMdz/4Tx+jNOMOqnAnqGsu69z7pmoiPhkzjreKl7J3gzVYPvNjBXe2+56qUx68OP5VaNGlowYnGyyUpbuDOnXP26iX+cW6d1oAs742xcZ2e7HszNbT+UXJRt38crXJVmdvDtVNS7nrhJz8VNfR30t6E0/VfUxVZS/ijZ9HdwzcTfjx45IueiE479PyVK23ypnT/dnFtpeLtqup0O+dZ3PN5kcOTRTW/Z1cA+ieWsyN9pcOnPau/dVMDts4oeFKZT5ZsvxHkcHTFamikfSKby7+9pte5jskykBc9UiLRTbc9HpKlm+Du4FGbyapjJAWLZ5Pd2SmWIulpHF1afRe+/71XEH/8oHRUNHVxvlL136DB8XMZ9mPjr1L59Xe15pYMJCf0xwkqs6gHmrrUxXun9DoJ2YsuZfE5bkOgm+ti5POnDE4zaXaKqyNTemyr7Q+EpehtfOFxrcw+TDWNpKZYqPShVUijS4B4DWheWeXyok/VRmXFNohaqKavGG/B2fPl+lu2w83gQbSmWbBneVM29OW8E3P+amZ+cFHqZUTMRzk3LX5XyEjm/ja5m66/N1D1Xlb0Pfzf4sRyHpbvWQzCBY6fKMz0amVNmhOXellAogDe5K1SBaM1BzaHBXSqkcytSMchrclVIqhzJVoarBXakaxCfN8VUa+Dq4+6XjiFL5Qsvcaw5fB3ellFLuNLgrVYPo6AM1R9zgLiIvicgGEZnrWNZcRMaJyGL7fzN7uYjIv0RkiYjMFpFjM5l4PVGVUn6XyyF/XwHOC1s2FJhgjOkKTLCfAwwEutp/Q4Cn05NMpZQKpgVrMzNBT9zgboz5Cgifqv5C4FX78avARY7l/zGWb4GmItI2TWlVPvDr/xTnOgkqhkuf/SbXSVBZkmyZextjTGhKlHVAG/txe2ClY71V9rIIIjJERIpFpLi01D8ziiullB+kXKFqrAGiEy79NsY8Z4zpY4zp06pVq6T2rU0hlVLKXbLBfX2ouMX+H5qAcTVwiGO9DvYypZRSWZRscP8QuMZ+fA3wgWP51XarmX7ANkfxjVJKqSyJO567iLwBnA60FJFVwH3ACGCkiFwPLAcutVcfAwwClgC7gWszkGallFJxxA3uxpjLo7x0lsu6Brgl1UQppZRKjfZQVUqpANLgrpRSAaTBXSmlAkiDu1JKBZAGd6WUCiAN7kopFUAa3JVSKoA0uCulVABpcFdKqQDS4K6UUgGkwV0ppQJIg7tSSgWQr4O7ztWhlFLufB3clVJKudPgrpRSAaTBXSmlAkiDu1JKBZAGd6WUCiAN7kopFUAa3JVSKoA0uCulVABpcFdKqQDS4K6UUgGkwV0ppQJIg7tSSgWQBnellAogDe5KKRVAGtyVUiqANLgrpVQAaXBXSqkA0uCulFIBVCuVN4tICbADqADKjTF9RKQ58BZQBJQAlxpjtqSWzGj7z8RWlVLK/9KRcz/DGNPbGNPHfj4UmGCM6QpMsJ9nhDGZ2rJSSvlbJoplLgRetR+/ClyUgX0opZSKIdXgboDPRGS6iAyxl7Uxxqy1H68D2ri9UUSGiEixiBSXlpammAyllFJOKZW5A6cYY1aLSGtgnIgsdL5ojDEi4lp4Yox5DngOoE+fPlrAopRSaZRSzt0Ys9r+vwF4D+gLrBeRtgD2/w2pJjIarVBVSil3SQd3EWkoIo1Dj4FzgLnAh8A19mrXAB+kmkillFKJSaVYpg3wnljZ51rA/4wxY0XkO2CkiFwPLAcuTT2ZSimlEpF0cDfGLAWOdlm+CTgrlUQppZRKjfZQVUqpANLgrpRSAaTBXSmlAkiDu1JKBZAGd6WUCiAN7koplUPXnHhoRrarwV0ppXKo9UH1MrJdDe5KKRVAGtyVUiqANLgrpVQOZWoARA3uKpDybcTQozs0yXUSVA3j6+AetGn27jjviFwnQam89/dLIoa08jUhMzkRXwf3oGnRsE6uk+ALJSMG5zoJCWvm4bv9w9lds5AS/6tdK1hhS4tlXAQs464C7MTOLeKuc3ibxllISfIObdEg6ms/P65D1tKRZyVuKcvU8fg6uKvMaNckM+1us8kYaFwv1Vkk06e8Mn5W5LhDm2UhJdXd2P8wz+tef0qntOyzQZ3CtGwnKDTnnqKLj2mf6ySoGqy8Ij/vMxO5AEqaolDH5tHvALxoUr920u+9vO8hKe3bq/G3nZaV/cTi6+CeSIVqnSyV09WrXUCtguR+BOf2OJi3hvRLaf+PXtyz6nE+5Vyz7Xdn5Vf59RndWgFQFKNoIxdMAj+iWGe1181c1e9Qzjqyted9hnvyimM5tWvLpN9/SIoXFq8a1Mn9b8/XwT2WLq0b5ToJCWvaoA4neCibjeXyvh2rHr/xm+gXigcv7JHSfvJZyYjB3Dbg8Lwqm+3VoSklIwbTs0PTqOvkU3rdxMq4X9mvY9TX+h/equrxQxcdhYcSqqgG92qLiGRsPJZsCM94aGsZFwfHKBs++TArSLZuXBfIXLnWtScXVXueqS8qGdHuVpo3rMPVJxZFfZ/z9jvJmxAVRe3C/PpAE7n7jXVudzu4cdTy+0Zhd5CVOWzDnK3fZz70s/B1cPdSAdW0QfLlc14c1iryDiHeF/vkFcdmKDXefH776TFf93OF152DulU9TqWMOFal8i9j5FLjuWdw95iv9z6kadLbzrS6jsyCW9n1/51zuPsbw2J5ZSpZ9xiOSKK1UevGdTMaiA/O0KBgXvg6uMcS+mFnO5Nwfq+22d1hEpq4XPCcLSFevvb4jOy3YYIXjRv6d054H8d0PHDBD//RPnWl94vqOzedVO35FSccCOjxcn+/6BO90i5ee3e3nP1/rusb8z3Z8pPe7aoeP/LTntVeMwZqFRZwfFH8DFeGYrsnvVx6Ct9xbjeXNdPD5LDBdqCC+/0XROaKDny06b88t2xUJ+Kre/TinnlTNON2YYvW3tq5bodm3iudEg3YXpzQqTlg3eqn4q5BR1Z77tZJbOBRB3OhI2iFtGtav9rzYzu6B62Jt/ePWHZI8+rvddt+NG53Gycello9TCwt7WJLL2oXHggX0e6KbjmjS9ztuBXLHNOxqed0pOLkLtUrYw3QsG76z+FYMeCCsAzgBUd7Pz8SEajg/quTk2+H++I1fZJ4V/Uv8IwjWlGrsICrEqjs8Vps1LeoebWWNI3rRtbGv3Z9/BxetNxrsremB9WvnXIQDtcmhVtZ52Fc0ucQhg2MnSvr26k5j192DGcf2Zp/X3GMp+3+5tTOdDu4MdPvPpvOLsVyTi0a1uHxy6JvN9Z+Qgo9fjmhC/dBHlpJRSv7P+OIVq7LQ+L1onZWnoaE515vOj2ybP5Ox4V4zO9O5YKj26W1SLVx3VpV9W/hw3wkc+r/7sz4F7FouoYVH8WqO0xFoII7QKOwoBcq84rXtjbV1jVXnNCRl6+1guvdg49kycMDXddr2ejAj2NQz4OZee85cbf96MU9GXnjidVa0hSG/ThLRgzm1K6xf5gQu1hg9O9O4f1bTnZ97Wb7B3ndyZ1Y8vBA/vrzXlWvffzbU1gc5XidatcqoH3T+vzj0thjg6SzDPS6KB1v+tp3ByEvXHM85/dqF3H+hBisZq4AHVs0YOwfTqNFI/dcrzNjOvp3p0ZN2+CeYUV44n7sXj+PP/+sF/VqF/AzD71Fn7+6Dz8MP/Cd9WzfhOK7z+axX8S+EH3021N4+VfRi+1EJG5b8taN68UcQqJ7u4N44vJj+GboWTG3A9bd+tg/HPiMf3VSket6M+87h2+GWdu7+fQuTL0z/rZjivOlhM6V7m0PSm0/KQhccB9322m86cjhntmtNa9e15chp3Wma5QA/uaQfhzaomHEcrdbxQHd2/D4Zb3tZ8b1qi8i1CoscG1nPu3Osz0cRXWXHR/vx+IeZAoT/HZ7tGsSUaEXus1ubl8UKo2hVmFBtdvbWoUF1W7ZoykQYcrQM7n42OrB565BR/LsVcdFrJ9M8VbTBtUvXrULCxh104l0btmQ7u0O/NCi/ei++H+nuxa1AEz+05lRXwO45YwDOdLBPdty16AjY+bKWh8U+b25HbNbEciTVxzLezdXrxfo2KIBCx8aSOeWkedyuAKRaq2perQ7iJaN6lYVmTSpX5tOLRtGZHraNa3PGd0i26nHKlmuX9v9gjn8oqNiprF+ncJqmSEv7ruge1ULL2e9QGGBUOjS9Es4kPbBPdvS59BmnNfj4GrrRCs2+WbYmVHT0bRBHd6+8USecDSeGH9bfz681T3zlAmBC+5tm9SnX1i5cv/DW1FYIHx46ymuLWzcWrwAtGlc/YfZq0MTnr+6Dycd5q0TxZ9/ZuVuz3L8GAoKhFZ2MO7k4UcI7j/uAseyaJmIw1o1YtjAbgzqebD7Cg7O9vFOt59zBCUjBrv+MCB+hfWosIrJcD8MH8ivT+3EuY4f1BF2MU/bJvV47+aTErqrclv3uEObM/H/Tqeho2PJkW2tfYQXAbVsVDdqUUus19qHldE/eeWx/Oa02BXCXi5eTzuK0Zx3n4N7teWYjs1YNPy8iPc4v5IxMe4cIPL7Cz0tEPj8/05n/G3RL2Ze3DbgcO51qQsDb3ckXVvHL/IL3W0dcXBjK2NVYIW1rm2s78prj9jmDevwzk0nRYyTc4PL91irQGjbpH7EcoCZ9w4A4Pii5tXuBLu0bkSvGP0c0i333ahS1KxBbbbs3h+x3O2LrV+nkKYJdF2OFtCcYsW2OlFys307Nef1X59QVXGYDGfK6tV2rxASEW7ofxi7ysoZM2dd1G15GWXxqPZWK4PQxdFrUUHbJvWYfvfZHDd8fLXlH//2FBas3V4t9/j7s7ry+ITF3HjaYZzYuUVVy5dRN57E0Q9+FnM/F/Zux+TFG70lCvjZsR04pFmDtFRWjv7dKbRtUp8XJy/1tP4lx3Vg7Fz378P5uT50YQ8G2kU342/rT6tGdbnyxW+prDywTt1ahbw1pB+bd+2L2NZV/Q6tdrfiFH7ehvZb3z6XBoUXGbkoGTGY7veOZfe+ivCtAVYRSayewvVqxa/I9NLapEOzBrw1pF/UwBmr7N5LWxa3ONAwSvGdtb/Iu42j2me/eMb3wX3qnWdz+N2fRCy/om9Hjmx7UNRWDk5unX0a1ink/p/0YPSctVXLmtlfWl27PM1ZhOEW64rsnHn/I1qxcN0O6jtaloTX2ifKWQxSP0pwD2lYtxbHHdqMS1IYue/4ouZMu+ssWofdzXj58YU6sdzsqEg7qn2TqgtGyB8HHM4fB1htpZ1NGt2abobzUmnpDJy1Cgs4KcXvIKRHu8Qm4vjrJUfz10uO5oGP5kW85gwkzmAVuiP5+LeROfHwXs0n2ReswR6a5YZ/f/XrFDLjngGeKmXB/by/7uQixs1fz81nxB6UzNmfIlo+qlPLhny7dHPcdDg/gxv6d+aJiUuq7qbOPrJNzHSH1gvdSYdnlo5o05jBvdoyevaBWJBIxmzcH0+jTVjx3NEdmjBr1baYvchT5fvgHq0Xpoi4Bna3HGdoIKIfHxnE6X/7nJWb9zDm96fSqnFdzu/Vlo9nr+Whi46qqgA7qF5tPrr1FA5r3ZBRM1ZHTVuX1o2Ycc8AmjWoHbNHaDQf3HJyRFO1M7u1ZuLCDfzjF0dzxfNTAfjX5fEDW7ziES+cgT10cYl2a+pUt1ahL8dgB2ssmJJNuz11mAsVs+R6iLAurRt7/rwPqmed+80dFe3NU5xXoGubxhTfHb9uyVl2H36hD7nvgh4M6N6G614p9rz/2885gtvPsVrEfH/PgLgDjZ11ZBtG3nAifezv+OQuLbjvgu488NF8wCpKffKKYxk9ezQASx4eSC37/O/cqiFLS3fF3H546xinUMVrJvg+uId4b2ERfcXCAuGi3u15YuKSqlurx37RmxE/6xXRiqKnx2nTvP5Q3JpWHe3SW/Gfv+jNxIXrOemwlvTq0IQ6hQVJjwN+Q//O1cqhE9GyUV2euPyYasUa7ZvW55webRjQvQ1vfbeSD2auiXn7mozrUmjumqhMX5DCy9wF4fpTOjHJLl5K50WiTq0Cnv3lcVQaw/WvFtPDLq4Z3LMtu8rK+emx0UdNbdmoDht3Rhb7ADz1y+N49ssfaRDn7tFNvdqF/Om8bvx57EJqFxTwv9+cQMuwFkj1ahdyZrfInPdPerfn1W+Wc6pL00snL5OkQPXWUyLCtSd3cq2HOrRFg6rADla91tLSXfTq0ITZq7Z52hdYF7NZq7a5FuGkS8aCu4icBzwOFAIvGGNGZGpfE2/vHzF+RTQPXNiDBnUK+eslvTji7rERr//x7MO5sf9hVUGpVmEBjRJtdpKgRIJIk/q1+ekxVvHKh7eektJ+hw08MuprH916CuXOwl0X4a0Ipgw90Hrg+KLm3HFet5SGZ3W674LuHNqigesP3at0DVmbKYUFwulHtOar/3cGL0xeSs8oudlEzbhnALUKpSqX7jzfCgqEy6JUpod8eOspzF+z3fW1/oe3cm3b7tVNpx9W1e7da0MFsOp+Mn3xDS+eWfjQedUaMsCBrOLNp3dh/trtHONx+Ih7L+jOz4/r4LlRRTIyEtxFpBB4EhgArAK+E5EPjTHzM7G/eB1JnNo3rR+zGKOgQBLKbbaxi03SOZToDf07R61wyxavdybR1C4siGhBkoprw3Ls/73+BOrXKeRnT3+dtn2kKtlrx5DTOtOlVaOqu7yOLRrw4IWxmwkmItVilnZN60f02M22X/bryIzlW9O2vbp2Ze6RCbRDj9ZwIeS2AVHG1omy/2M81AemIlM5977AEmPMUgAReRO4EMhIcE/WZccfknJriQHd2/DytcdzmocORF4NG3hkzFy1glMcY3qHd/ePJ16v1WQNPKotT0xcwjk9vN1dtGtq1WH0aHcQF/bWyWRiGX5Rz/grJaBJg9q8NaRf1NZEXv1pYDe27t6f0hjzmSKJDNbveaMiPwfOM8b82n5+FXCCMeZWxzpDgCEAHTt2PG758uVpT0dNNWXJRjbuLKsRAeO7ks10atkwoqzWDyoqDRMWrGdA9zZ5X2SUqpkrtzJvzTauPMG/47DnIxGZboxxHTslZxWqxpjngOcA+vTpk+sGBoGSajNLPzm+KPm+ArlWWCCc0yN+B7Mg6H1I07wezjiIMlVTuBpw9pnvYC9TSimVBZkK7t8BXUWkk4jUAS4DPszQvpRSSoXJSLGMMaZcRG4FPsVqCvmSMSayO55SSqmMyFiZuzFmDDAmU9tXSikVXeBGhVRKKaXBXSmlAkmDu1JKBZAGd6WUCqCM9FBNOBEipUCyXVRbAt5nachveiz5KSjHEpTjAD2WkEONMa5jn+RFcE+FiBRH637rN3os+SkoxxKU4wA9Fi+0WEYppQJIg7tSSgVQEIL7c7lOQBrpseSnoBxLUI4D9Fji8n2Zu1JKqUhByLkrpZQKo8FdKaUCyNfBXUTOE5FFIrJERIbmOj1uROQlEdkgInMdy5qLyDgRWWz/b2YvFxH5l308s0XkWMd7rrHXXywi1+TgOA4Rkc9FZL6IzBOR3/v4WOqJyDQRmWUfywP28k4iMtVO81v2cNWISF37+RL79SLHtobZyxeJyLnZPhY7DYUi8r2IfOzz4ygRkTkiMlNEiu1lvju/7DQ0FZF3RGShiCwQkROzfizGGF/+YQ0l/CPQGagDzAK65zpdLuk8DTgWmOtY9hdgqP14KPBn+/Eg4BOsSdX7AVPt5c2Bpfb/ZvbjZlk+jrbAsfbjxsAPQHefHosAjezHtYGpdhpHApfZy58BbrIf3ww8Yz++DHjLftzdPu/qAp3s87EwB+fYbcD/gI/t5349jhKgZdgy351fdjpeBX5tP64DNM32sWT1gNP84Z0IfOp4PgwYlut0RUlrEdWD+yKgrf24LbDIfvwscHn4esDlwLOO5dXWy9ExfQAM8PuxAA2AGcAJWL0Ea4WfX1jzEpxoP65lryfh55xzvSymvwMwATgT+NhOl++Ow95vCZHB3XfnF9AEWIbdYCVXx+LnYpn2wErH81X2Mj9oY4xZaz9eB7SxH0c7prw6Vvt2/hisHK8vj8UuypgJbADGYeVWtxpjyl3SVZVm+/VtQAvy41geA+4AKu3nLfDncQAY4DMRmS4iQ+xlfjy/OgGlwMt2cdkLItKQLB+Ln4N7IBjrkuyb9qgi0ggYBfzBGLPd+ZqfjsUYU2GM6Y2V8+0LdMttihInIucDG4wx03OdljQ5xRhzLDAQuEVETnO+6KPzqxZWUezTxphjgF1YxTBVsnEsfg7ufp6Ee72ItAWw/2+wl0c7prw4VhGpjRXYXzfGvGsv9uWxhBhjtgKfYxVfNBWR0OxkznRVpdl+vQmwidwfy8nAT0SkBHgTq2jmcfx3HAAYY1bb/zcA72FddP14fq0CVhljptrP38EK9lk9Fj8Hdz9Pwv0hEKr5vgar/Dq0/Gq79rwfsM2+jfsUOEdEmtk17OfYy7JGRAR4EVhgjPmH4yU/HksrEWlqP66PVXewACvI/9xeLfxYQsf4c2CinfP6ELjMboXSCegKTMvKQQDGmGHGmA7GmCKs83+iMeZKfHYcACLSUEQahx5jnRdz8eH5ZYxZB6wUkSPsRWcB88n2sWS70iTNFReDsFpt/Ajclev0REnjG8BaYD/WFf16rHLOCcBiYDzQ3F5XgCft45kD9HFs5zpgif13bQ6O4xSs28jZwEz7b5BPj6UX8L19LHOBe+3lnbGC2hLgbaCuvbye/XyJ/Xpnx7buso9xETAwh+fZ6RxoLeO747DTPMv+mxf6Pfvx/LLT0Bsots+x97Fau2T1WHT4AaWUCiA/F8sopZSKQoO7UkoFkAZ3pZQKIA3uSikVQBrclVIqgDS4K6VUAGlwV0qpAPr/rvb1GfOLhykAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(np.fft.fftshift(np.abs(np.fft.fft(x))))\n",
"plt.title(\"Power fourier transform\")"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "e753a81e",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'The bandwidth of the FPI (sort of)')"
]
},
"execution_count": 37,
"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": [
"filter_ = scipy.signal.gaussian(100,3)\n",
"\n",
"plt.plot(filter_)\n",
"plt.title(\"The bandwidth of the FPI (sort of)\")"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "e7074fde",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'How the spectrum looks seen through the FPI (i.e after filtering)')"
]
},
"execution_count": 35,
"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": [
"x_filtered = np.convolve(x, filter_)\n",
"plt.plot(x_filtered)\n",
"plt.title(\"How the spectrum looks seen through the FPI (i.e after filtering)\")"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "d60d2989",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'After going through the FPI the FFT of the signal is low passed')"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAEICAYAAACeSMncAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAp70lEQVR4nO3deZgcVb3/8fcnCUkghOyGkIWEHwFuRJYQNsErCsqqQS8iESUqykXhissVQVRA8RqvXhdcQBQURNniQkT2XQQSEiGBBAID2UnIELISQmY5vz/qTKjMdM/Se/d8Xs8zz1SdOlXnnOrq/ladOtWtEAJmZma56FHuCpiZWfVyEDEzs5w5iJiZWc4cRMzMLGcOImZmljMHETMzy1lZgoikIyS9IGmTpJPLUYdsJI2J9epZovIWSzqmFGV1RFKQtGce6z8o6TOFrFOxVdL+z5ekz0l6JR6/QzqR/5OSHilynUr2fmrv+JV0h6SpXdze2LjNXoWpYXWRdJSk5R3lK2oQiR8qayX1abXo28DPQwg7hxD+mu+HVyGFEJbGejUVetuSfifpskJvtxwkXSLp+iJuf7GkN+IHUMvfbqk3dkvaYkkXpNZr74OkqPs/lv16qm7rYvpRkppbteVvkuan5pskbUnNf72LZe8A/Ah4fzx+17RaXpYPxGK+n7pYj+NDCNeWsw61qmgHlKSxwLuA9cAHgVtSi3cH5heonF4hhMZCbKvSdae2Rh8IIdybTojHFcDAEEKjpMOB+yQ9FUK4s+Q1bGv/EEJdhvSXQwijsq0k6UHg+hDCb3IsdzjQlwK9r8w6q5hXImcAjwO/A7ZdRkp6EdgD+Fs843osLpob5z8a850k6SlJ6yQ9Kmm/1DYWS/qapHnA65nOriS9X9JCSesl/VLSQy1dLZJ6SPqGpCWSVku6TtKAuGy7M7Z4NfUdSf+UtFHS3ZKGpso5I25njaRvZusekXQWcDpwfsuZaGrxAZLmxbreJKlvXOcoSctjW1cBv5XUR9JPJL0c/37ScqWnDN0T6TNzSUPiGfAGSU9Iuqx1fuAYJV2N6yT9QpIytOU44OvAR2Nb5qYW797OvjosvpbrJM2VdFTrbXdVCOExkg/OfdvLl8v+j+tlPQ5LLdtrL2kvYGHMtk7S/RlWfzi1fFMMvi3b/aGSHoNFko5PpQ+QdLWklZJWxOMlY7eUpEMkzY7H1iuSfhTTW7+fxkl6OB4f98Zj7PpWeadKWirpVUkXtSrjsfharJT0c0m9O7nvtnW1StpTyefB+ljGTZ3cxm6SZkh6TVKdpM/G9L5KrpqHxvmLJDVK2iXOf0fST9qp1/ckzYr77lZJg1PLb5G0Ktb1YUlvTy07QdKCuC9XSPrvmD5U0m1xP70m6R+SeqTa8CdJ9fH1/kJqezsquVpfK2kBcHBn9gshhKL8AXXA54GDgAZgeGrZYuCY1HwA9kzNHwisBg4FepIEocVAn9T6TwGjgR0zlD0U2AB8mORq67xYh8/E5Z+O9dsD2Bn4M/D7uGxsrE+vOP8g8CKwF7BjnJ8Wl00ANgFHAr2BH8ZyjsmyT34HXNYqbTEwC9gNGAw8C5wdlx0FNALfB/rE8r9NEpzfBgwDHgW+E/N/Enik1fa37Vvgxvi3U6z7snT+mPc2YCAwBqgHjsvSlktIzpzTae3tq5HAGuAEkpOX98X5YVm2v90xkkrf9voAAo4ANgNHZzqW8tz/7R6HGbafsez4Oi7v4P3yIPH4bCdPe6/9tv2SZd02y+Px0gB8Nrbvc8DLgOLyvwC/AvrFMmcB/5ll+48Bn4jTOwOHZXk/PUbyPulN8r7Z0HIcpfL+Oh4/+wNvAv8Wlx8EHBZf+7HxtfpiR/u/9f4FbgAuIjkO+wJHdmafkQTiX8Z1DiB5f7w3tew/4vTdJO+D41PLPtROvVaQnAT1A/5E6n1F8lnVn+T9/xPgqdSylcC74vQgYGKc/h5wJbBD/HsXyXulBzAH+Fbc/3sALwHHxvWmAf8geR+MBp6hg+M2hFCcIBIPjgZgaJx/DvhStg+I1i8+cAXxzZFKWwi8O7X+p9sp/wzgsdS8SD4wWw6i+4DPp5bvHevbcnC2DiLfSOX9PHBnnP4WcENq2U7AVroeRD6emv9f4Mo4fVTcXt/U8heBE1LzxwKLUx8KGYMIyYdEA7B3atlltA0iR6bmbwYuyNKWS8gcRLLtq68RA3Vq+V3A1CzbX0wSoNfFv7+2emOvA9aSfJB8IduxlOf+b/c4zLD9QPKh2FLny1OvY3MqfR1waoZ911EQae+1b9kvXQ0ida2O3wDsStI99iapkzRgCvBAlu0/DFxKfM9nKpfkxKQR2Cm1/HraBpFRqeWzgNOylPlF4C+dfO237V/gOuCqdDkd7TOSD9UmoH9q+feA38Xp7wCXx7yrSE5cp5EEnDeAIe3Ua1pqfgLJe75nhrwDY30GxPmlwH8Cu7TK923g1tb7guRkaGmrtAuB38bpl0idNAJn0YkgUqzurKnA3SGEV+P8H0l1aXXC7sBX4uXYOiU3KEeTnC22WNbO+rull4dkjyxvtXxJan4JyYs/PMv2VqWmN5OcaWUqZzPJ2XVXZds+QH0IYUtqPlPd0/slm2EkbUzvt0z7sL26dEa29XcHPtLqNT0SGNHOtk4OIQyMfye3WjY0hDAohPBvIYTLu1jHrtS5o+OwtYmpOn8hlf5yKn1gCOHmHOqZ62vfnm1tj8cvJO3fneQsdmWq7b8iuSLJ5EySK9DnlHSVnpQhz27Aa6lyoAvHoKS9YjfNKkkbgP8h6XXoqvNJTixnKRnc8OlOrNNS942ptCUkV9gAD5GcLEwEngbuAd5NcuVUF1oNdGglvQ+WkOz3oZJ6Spom6cXY3sUxT0ub/4Pkyn5J7J5r6aL8AUlPy92SXtJbA092B3ZrdTx/nbc+97b7PGP7Yy2rgt9Yl7QjcCrQU0k/PiSXYgMl7R9CmJt97W2WAd8NIXy3nTyhnWUrgW03MSUpPU9yyb57ar7lDOmVVvk6spLkKqalnB2B9oZWtlfnzq7TUveWG6hjYhrA6yRnky312TW1Xj1JG0cBz8e00TnUJ1u9OrKM5Erks3mUma9c6tzRcVhK7b32Hcml7W+SBOsOB3OEEF4ApsS+9w8D09V2mPFKYLCknVKBpCvH4BXAk8CUEMJGSV8ETunC+i11XUXShYekI4F7JT0cMg+IaPFyrHv/VCAZQ9IVBUnX4t7Ah4CHQggLJI0h+ZB/qIMqpffBGJIeg1eBjwGTgWNIAsgAkqtvxXY8AUxWMjLvXJKeg9Gxfl8hOQHaF7hf0hMkr+miEML4LPVYGeuSPr46VIwrkZNJLvsmkPQbHgD8G0lf2xlZ1nmFpH+uxa+BsyUdqkQ/SSdK6t/JOvwdeIekk5Xc0DuH5BK9xQ3Al5Tc5NuZ5Izmps68WVqZDnxA0jvjDb5LiC9wFq3bmYsbgG9IGhZv5H2LpEsAYC7wdkkHKLk5fEnLSiEZYvln4BJJO0nah+yvR2e8AoxtuWHXCdeT7Ktj4xlWXyUDB7oStPPV1f2f73FYaO299h2pJ+lS61T7QwgrSfr2/0/SLkoGo/w/Se/OlF/SxyUNCyG0dNsRy0tvcwkwm+QY7B3PnD/QyfpDcm9gA7ApHr+f68K66bp+JHXcrSUJsM3trEIIYRlJoPhePHb3I7n6uj4u30xyv+Ec3goajwJn03EQ+bikCZJ2IumKmh7fr/1JAvkakpPD/0m1obek0yUNCCE0kOyX5rjsJCWDB0QyOrYpLpsFbFQyUGfH+D7cV1LLDfSbgQslDYr75786qDdQnCAylaSPbWkIYVXLH/Bz4HRlHqd+CXBtvMQ6NYQwm+RM4eckL3IdSf9tp8RutI+Q9G+vIQlos0leEIBrgN+T9OMuArbQyR3Wqpz5cb0bSaL4JpIbsW9mWeVqYEJs51+7Wl50GUlb5pFcNv8rphFCeJ7kILwXeAFoPfLqXJKzmVUk7b+hnbp2pGXI9hpJ/+ooc3wTTia5fK4nOSv6KqV94LVL+z/f47AIsr72HYkfct8F/hnbf1gnVjuD5AbsApL2Tyd79+NxwHxJm4CfktzHeCNDvtOBw0nel5cBN9H5Y/C/Sc7ON5IE+E6NqsrgYGBmrOsM4LwQwkudWG8KyX2Sl0kGHVwcth+C/hBJV9Ss1Hx/3hoZl83vSe7XrSK5h9LSDXodSZfSCpLX4PFW630CWBy7us4m2bcA40k+AzaRDGT4ZQjhgRiYTiI5sV9EcrXzG5LPBEjuaS2Jy+6O9epQyyiMmhbPlpcDp4cQHihiOTuTnIWNDyEsKlY5hSLp+8CuIYSu3K8yKxglw2ufCyFcXO66lIPyfz6o7Gr2u7Nit8lAJc9QfJ2km6l1JC9EOR+I3UP9SIYuPs1bN8AqiqR9JO0Xu2YOIbkc/0u562Xdh6SDY7dYDyXPG00G/lrmalkeavk7YQ4nGRXWcjl+cpbL63xNJrnsE0lXw2mhci/v+pN0Ye1Gcn/g/0iGApqVyq4k9+aGkPQOfC6E8GR5q2T56BbdWWZmVhw1251lZmbFV9HdWUOHDg1jx44tdzXMzKrKnDlzXg0hDCtFWRUdRMaOHcvs2bPLXQ0zs6oiqVNPmxeCu7PMzCxnDiJmZpYzBxEzM8uZg4iZmeXMQcTMzHLmIGJmZjlzEDEzs5w5iJh14J91r7Lo1dc7zPePF+pZsqbjfGa1pKIfNjSrBKf/ZiYAi6ed2G6+T1w9q1P5zGqJr0TMzCxnDiJmZpYzBxEzM8uZg4hZFuvfaGDyz1v/TH3HvjZ9XhFqY1aZHETMsrh7/irmLl/f5fVumr2sCLUxq0wOImZZ9JDKXQWziucgYpZFD787zDrkt4lZFr4SMeuYg4hZFg4iZh1zEDHLomcPBxGzjjiImGXROoZMuerxjPm2NDQx9oK/l6BGZpXHQcQsC7XqznrspTUZ87266c1SVMesIjmImGXR0/dEzDrkIGKWhYf4mnXMXwVvlkXr7iyAI6bdTwiBRy88ms1bG5nwrbv42KFjylA7s8rQ4bmWpGskrZb0TCrtB5KekzRP0l8kDUwtu1BSnaSFko5NpR8X0+okXVDwlpgVWKbOrBXr3uDl9VsAWLe5AYA/zlxawlqZVZbOXLD/DjiuVdo9wL4hhP2A54ELASRNAE4D3h7X+aWknpJ6Ar8AjgcmAFNiXjMzq2IdBpEQwsPAa63S7g4hNMbZx4FRcXoycGMI4c0QwiKgDjgk/tWFEF4KIWwFbox5zSpWKHcFzKpAIW4dfhq4I06PBNJfYbo8pmVLb0PSWZJmS5pdX19fgOqZmVmx5BVEJF0ENAJ/KEx1IIRwVQhhUghh0rBhwwq1WTMzK4KcR2dJ+iRwEnB0CKHlyn8FMDqVbVRMo510MzOrUjldiUg6Djgf+GAIYXNq0QzgNEl9JI0DxgOzgCeA8ZLGSepNcvN9Rn5VNysuP2po1rEOr0Qk3QAcBQyVtBy4mGQ0Vh/gnjiW/vEQwtkhhPmSbgYWkHRznRNCaIrbORe4C+gJXBNCmF+E9piZWQl1GERCCFMyJF/dTv7vAt/NkH47cHuXamdmZhXNX+xgliMPATZzEDEzszw4iJjlyDfezRxEzLLK9AWMZrY9BxEzM8uZg4iZmeXMQcTMzHLmH6Uyy+Ktb/Np65kV65m56LWsy826CwcRsxyc9LNHyl0Fs4rg7iyzLDw6y6xjDiJmZpYzBxEzM8uZg4hZBiEEGhqbc17/zcamAtbGrHI5iJhlcOnfFvCZ62bnvP7e37iT51ZtKGCNzCqTg4hZBtc/viTvbTyzwkHEap+DiJmZ5cxBxMzMcuYgYmZmOXMQMTOznDmIWLfW1ByoW72pJGVtbWxm0auvl6Qss1JxELFu7Uf3LOSYHz3ES/XFDySX/G0+7/nhg9RvfLPoZZmVSodBRNI1klZLeiaVNljSPZJeiP8HxXRJulxSnaR5kiam1pka878gaWpxmmPWNU8sXgvA6hJ8sD/+4hoANmxpKHpZZqXSmSuR3wHHtUq7ALgvhDAeuC/OAxwPjI9/ZwFXQBJ0gIuBQ4FDgItbAo9ZJfJ3L5p1TodBJITwMND6hxMmA9fG6WuBk1Pp14XE48BASSOAY4F7QgivhRDWAvfQNjCZVYx2fkrEzFJyvScyPISwMk6vAobH6ZHAslS+5TEtW3obks6SNFvS7Pr6+hyrZ2ZmpZD3jfWQ/Pxbwc7bQghXhRAmhRAmDRs2rFCbNTOzIsg1iLwSu6mI/1fH9BXA6FS+UTEtW7qZmVWxXIPIDKBlhNVU4NZU+hlxlNZhwPrY7XUX8H5Jg+IN9ffHNDMzq2Id/sa6pBuAo4ChkpaTjLKaBtws6UxgCXBqzH47cAJQB2wGPgUQQnhN0neAJ2K+b4cQWt+sNzOzKtNhEAkhTMmy6OgMeQNwTpbtXANc06XamRVbGUZheeSX1RI/sW6WQSGeE/GjJtYdOIhY91bET/psFxx+kNFqiYOImZnlzEHELAPftzDrHAcRMzPLmYOImZnlzEHEzMxy5iBi3ZvvfZjlxUHEjLYjfRub848uHslr3YGDiJmZ5cxBxMzMcuYgYkZxbo34dot1Bw4i1r35xoVZXhxEzMwsZw4iZmaWMwcRMzPLmYOIdW+++22WFwcRM4pzf9337K07cBAxa2X9Gw0F2U79pjfZ2tjcJt1fM2+1xEHErJX9L727INuZdsdzfHX63IJsy6xSOYiYFdGdz6xqk+afx7VaklcQkfQlSfMlPSPpBkl9JY2TNFNSnaSbJPWOefvE+bq4fGxBWmBmZmWTcxCRNBL4AjAphLAv0BM4Dfg+8OMQwp7AWuDMuMqZwNqY/uOYz6xsFq7ayKzFrwGlHaR18a3zM94rMatG+XZn9QJ2lNQL2AlYCbwXmB6XXwucHKcnx3ni8qMlX9hb+Zz6q8eKXkamI/yRule5c37bbi6zapRzEAkhrAB+CCwlCR7rgTnAuhBCY8y2HBgZp0cCy+K6jTH/kNbblXSWpNmSZtfX1+daPbOs1m9uoLGpmcam7a8Grn5kETfMWlrQskKAr02fx5wla1ulBzZvbeSNrU0FLc+s1HrluqKkQSRXF+OAdcAtwHH5ViiEcBVwFcCkSZM8GNIKqqGpmf2/fTcfnTR6u3QB37ltQcHLe7OxmZtmL2PG3JcZMaDvdssmfOsudurdkwXfzvttY1Y2+XRnHQMsCiHUhxAagD8DRwADY/cWwChgRZxeAYwGiMsHAGvyKN+syxri1ceMuS+XuSaJzb4SsSqXTxBZChwmaad4b+NoYAHwAHBKzDMVuDVOz4jzxOX3h+DHrqx78pFvtSKfeyIzSW6Q/wt4Om7rKuBrwJcl1ZHc87g6rnI1MCSmfxm4II96m1UfDyOxGpTzPRGAEMLFwMWtkl8CDsmQdwvwkXzKM8tXua4AAoGmZl9+WO3xE+vWLbUeenv/wtVFL3PJms1FL8Os1BxErFsKYfsHDB9/6bWilqdWfVnB30FvNcJBxAx8p9ssRw4i1i1Jre5zl/jLExyzrFY4iJhR/IFT7r6yWuUgYlYGvhKxWuEgYlYCrW+sm9UKBxEzM8uZg4gZ8NSydUXd/hsN/o4sq00OItatVMqtiEqph1m+8vraE7Nq1dgcyvrrgi/Vbypb2WaF5CsR65bK/fO0v3zwxbKWb1YoDiLWrXiMlFlhOYhYt+J7EWaF5SBiZmY5cxAxM7OcOYhYt+JfZDYrLAcRMzPLmYOIdSsq8Ve+m9U6BxEzM8uZg4h1K74nYlZYeQURSQMlTZf0nKRnJR0uabCkeyS9EP8Pinkl6XJJdZLmSZpYmCaYmVm55Hsl8lPgzhDCPsD+wLPABcB9IYTxwH1xHuB4YHz8Owu4Is+yzcyszHIOIpIGAP8OXA0QQtgaQlgHTAaujdmuBU6O05OB60LicWCgpBG5lm9mZuWXz5XIOKAe+K2kJyX9RlI/YHgIYWXMswoYHqdHAstS6y+PaduRdJak2ZJm19fX51E9MzMrtnyCSC9gInBFCOFA4HXe6roCICR3Mbt0JzOEcFUIYVIIYdKwYcPyqJ7Z9m5+YhkbtzSWuxptPLNiPY+9uKbc1TDLST6/J7IcWB5CmBnnp5MEkVckjQghrIzdVavj8hXA6NT6o2KaWdE9vXw95/9pHu8aP7TcVWnjpJ89AsDiaSeWuSZmXZfzlUgIYRWwTNLeMeloYAEwA5ga06YCt8bpGcAZcZTWYcD6VLeXWVG1/Dxt/cY3y1wTs9qS7y8b/hfwB0m9gZeAT5EEppslnQksAU6NeW8HTgDqgM0xr1lJ+PkQs+LIK4iEEJ4CJmVYdHSGvAE4J5/yzMyssviJdTMzy5mDiHULTc1Jd9bL694oc03MaouDiHUL37vjOQA2VOAQ3xbLXttc7iqYdZmDiHULT69YX+4qdOiVDVvKXQWzLnMQMTOznDmImJlZzhxEzCqEn2SxauQgYmZmOXMQMTOznDmImFUIlbsCZjlwELGa88qGLYy94O88/Hx1/R5N+p7IV2+Zy7t/8EDZ6mLWWQ4iVnOeXLoOgOsfX1LeiuThljnLWbLGDx9a5XMQMTOznDmImFUIf1u9VSMHEatB238a3/zEsjLVo2tO/dVjrPZXn1iVcRCxmnfZ3xeUuwqdNnvJ2nJXwaxLHESsBnmwrFmpOIiYVRDfF7Fq4yBiNcifxGal4iBiVkGCA6BVmbyDiKSekp6UdFucHydppqQ6STdJ6h3T+8T5urh8bL5lm2XmeyJmpVKIK5HzgGdT898HfhxC2BNYC5wZ088E1sb0H8d8ZkV14Z/nVfRP4rZ27h+f5NanVpS7GmadllcQkTQKOBH4TZwX8F5gesxyLXBynJ4c54nLj475zQrsrS6hG2ZVxzMiaefd+FS5q2DWafleifwEOB9ojvNDgHUhhJZTv+XAyDg9ElgGEJevj/m3I+ksSbMlza6vr64v0LPK0HLl4VMUs+LLOYhIOglYHUKYU8D6EEK4KoQwKYQwadiwYYXctHUT50+fB8CGN6qnGyub2YtfK3cVzNqVz5XIEcAHJS0GbiTpxvopMFBSr5hnFNDSwbsCGA0Qlw8A1uRRvlkbzc1vdWU1NDW3k7M6XPPPReWuglm7cg4iIYQLQwijQghjgdOA+0MIpwMPAKfEbFOBW+P0jDhPXH5/CH60ygrr6RXrt03XQnfW7U+vKncVzNpVjOdEvgZ8WVIdyT2Pq2P61cCQmP5l4IIilG3dXLPPS8xKqlfHWToWQngQeDBOvwQckiHPFuAjhSjPLBsP+DMrLT+xbjVh/eYGLr71mZq4D9Lagpc38LP7Xih3NcwyKsiViFm5/e9dz/GHmUtpaK697qzJv3iEhqbAfx09vtxVMWvDVyJWE5pi8EjfElGNfP1JQ1PtBUarHQ4iVhNagkct3xLxYEarRA4iVrNm+UE9s6JzELGaUsMXIv7BKqtIDiJWU2q5O8usEjmImFUJX4hYJXIQsZpSKyOyzKqFg4jVhJaflZ0+Z3mZa1I8Hp1llchBxGrKGw1N5a6CWbfiIGJWJXwdYpXIQcTMzHLmIGJWJXxLxCqRg4iZmeXMQcRqQnc4Sw++K2IVyEHEzMxy5iBiNeGWGn4+pMW85es7zmRWYg4iZlXip/f61w2t8jiImFUJ3xOxSuQgYmZmOcs5iEgaLekBSQskzZd0XkwfLOkeSS/E/4NiuiRdLqlO0jxJEwvVCLPuoDuMQLPqk8+VSCPwlRDCBOAw4BxJE4ALgPtCCOOB++I8wPHA+Ph3FnBFHmWbmVkFyDmIhBBWhhD+Fac3As8CI4HJwLUx27XAyXF6MnBdSDwODJQ0Itfyza548EV++89F5a5Gycxa9BohBM7+/Rz+tXRtuatjBkCvQmxE0ljgQGAmMDyEsDIuWgUMj9MjgWWp1ZbHtJWpNCSdRXKlwpgxYwpRPatR37/zOQAO22NImWtSGo3NgXnL13Pn/FXcOX8Vi6edWO4qmeV/Y13SzsCfgC+GEDakl4XkBxC61JMbQrgqhDAphDBp2LBh+VbPatCWhia2NjZvm//vW+aWsTaldef8VdumN29tpLGpuZ3cZsWX15WIpB1IAsgfQgh/jsmvSBoRQlgZu6tWx/QVwOjU6qNimlmX7PPNO9nzbTtvm5//8oZ2cteW6x5dvG16wrfu4vh9d+WKjx9UvgpZt5fP6CwBVwPPhhB+lFo0A5gap6cCt6bSz4ijtA4D1qe6vcy6pG71pnJXoSxe37r9j27d8cyqLDnNSiOfK5EjgE8AT0t6KqZ9HZgG3CzpTGAJcGpcdjtwAlAHbAY+lUfZZmZWAXIOIiGERwBlWXx0hvwBOCfX8szMrPL4iXUzM8uZg4hZDn7xsYl86MCR5a6GWdk5iJh10ZRDxnDifiP48UcPKHdVzMrOQcTMzHLmIGLWZf4mRLMWDiJmnbD/qAEd5jnloFElqIlZZXEQsaoRQtju605K6W279E3VI3Oe0w8tz3e9vdnY1HEmsyJxELGqcenfFrDXN+4oS9mV/Fsee3/jTp5b1X2++sUqi4OIVYXGpmaufWxxGWvwVhT50vv22jZ9ZYV8b9VTS9fR3FzBkc5qloOIVYU9L7qjrFcDjfED+refPJjhqa6t4/bdlbf17wNAcxkreMGfn+b8P80rW/nWfTmImKWc857/lzG9IX7l+g49275lWtKS7yRtq1QPJU6fs7wk5ZilOYiYpZx28PY3x/927pHces4RNDQmVxk79GwbKHr3St5GA3fcgV98bCLnvmfP7ZZfOvntGcs6dNzgQlTZrKwK8suGZsX08ro3SlZWQ6sfeXpHHNq7Nab3ynAl0quH4rqBE/cbwaoNW7Zbnu1bSkcO3DHP2ra1ZtObDNm5T8G3a5aNr0SsYjU2NXP1I4t457T7C77te7/87ozpYwbvlDH9/GP35m39+7DPrv3bLPvmSRMYMaBv1nV7ZOnm+upxe3eytp130GX3smbTmwXfrlk2DiJWsfa86A6+c9uC4mw79cuILXYb0JdePXvwj/Pf02bZO/ccyqyLjqFfn7YX7/++1zAeu/Boduzds82y5y87flt3V9oBowfSt1fb/IVw0GX3cuVDLxZl22atOYhYRVr86uslLW/+pcfyj6+9F4DRWa4octG7Vw926NmDF757PD897YBt6UP69SbLBUpBTLvjueJt3CzFQcQqUlMJh8veeNZh9OvTi549CvOpnmkrO/TsweQD3hqlVcwAYlZKDiJWcTZsaeCUKx4tWXkH7T6ooNtrCX/HvX3XNsv+Y2Ly/Vq7D+mHst5yL4xrH11MqORH7a0meHSWVYyX6jfxkSsfY83rW0tabqZnPwph1wF926TtNTy5F9ND0CvDcOFCunjGfC6eMZ/37D2MX58xKePIMrN8OYhY2c1ZspYJI3YpagDZbUBfLp28L+OG9itYt1U2ndm6JPr16cXN/3k4IwftyAuvbOSTv32iKPV5YGE9DyysZ59d+9McArsP6VeUcqx7chCxsvrRPc9z+X0v5L2d/UcN4JsnTWBwv9689/8earN8wm678L4Jw7cv+9T9uf+51XmX3RUfnjiKvz71MlPfORaAQ+IDh9meGTnt4NGctN9u7DGsX15DnT973ext038798htz7+Y5avkQUTSccBPgZ7Ab0II00pdByuv5Ws3c+T3HyjoNn82ZSJjhiSjqt4xcgBPr1gPwIFjBvLk0nUM2ql3m3U+PHEUH55Y2t8AGda/D3ec965O5z90j8EcOX4oAD//2IGc+8cn867DB37+CADDd+nD/V85KuOwZbPOUilvvEnqCTwPvA9YDjwBTAkhZHwYYNKkSWH27NmZFlkFajmWmgM8uXQtC1Zu4La5K5m1+DX69+3Fxi2NBSnnoN0HMWfJWgB+cMp+vG/CcAamgsSWhia++/dn+f3jS/jK+/aiV88efPywMfTvu0Ony7jpiaU89Hw9vzy969/SW7/xTab8+nGumXrwtsDWGXOXrWPl+jc4+/p/AfDERccwrP/2T58/vXz9tiDQEiALbcohozlg9EAOHjuY0YN3Kto9IyseSXNCCJNKUlaJg8jhwCUhhGPj/IUAIYTvZcqfaxBZt3krp1z5WJv0TG3N2voMC7Ll7ex2s+3qkCF31rxdeLm60t5M2+1KvVZvLO5T0ie+YwR/f3olE0bswu3nvYsP/fKfPLl0HYu+d0LGLz589MVX+divZ3LL2Ydz8Njq+o6qL930FH95cgWLp52Ycflnrp3Nvc++wq8+cRCHjRvC/t++G4DPvmscv/7HoqLVq3fPHrxtlz40NQd69lDy13rfa7t/yXQO45k9Ahr2GbELP5tyYE7r1nIQOQU4LoTwmTj/CeDQEMK5qTxnAWcBjBkz5qAlS5Z0uZyNWxq44E9PZ6lEp5Ja6tKFvJ3bbrY3VMbULIVlGhqa7X2auQ75bbd1WghQt3oTQ3fuw53zV2XeeDRq0I4sX/sGn3znWHr2EOOG9uPAMQP54V0L+dxRe7LHsH7s0LMHWxubGdKvNys3bGF4/z707CGaA9tuim/Y0sCi+tfZf/TArGU1NDVX5Vl0c3OgOYSso6mamgMzX1rDO/dMurlCCNv2zfo3GgghMHCn3ix69XXGDN6JZa9tZuErG1m/uYHevXrQq6d49MU1PLtyQ6euZA4dN5iNWxrZ2tTMO0YOoFcP0dQcaAqBpuaw7Zhu+SzZ7hMlh4+XTCcv3dHYIf04/7h9clq3WweRNHdnmZl1XSmDSKlP01YAo1Pzo2KamZlVoVIHkSeA8ZLGSeoNnAbMKHEdzMysQEo6ti+E0CjpXOAukiG+14QQ5peyDmZmVjglHyAeQrgduL3U5ZqZWeFV39AVMzOrGA4iZmaWMwcRMzPLmYOImZnlrKQPG3aVpHqg64+sv2Uo8GqBqlNOtdCOWmgDuB2Vxu3IbPcQwrACbi+rig4i+ZI0u1RPbRZTLbSjFtoAbkelcTvKz91ZZmaWMwcRMzPLWa0HkavKXYECqYV21EIbwO2oNG5HmdX0PREzMyuuWr8SMTOzInIQMTOznNVkEJF0nKSFkuokXVDu+rQm6RpJqyU9k0obLOkeSS/E/4NiuiRdHtsyT9LE1DpTY/4XJE0tQztGS3pA0gJJ8yWdV41tkdRX0ixJc2M7Lo3p4yTNjPW9Kf58AZL6xPm6uHxsalsXxvSFko4tZTti+T0lPSnptipuw2JJT0t6StLsmFZVx1Qsf6Ck6ZKek/SspMOrsR0dCiHU1B/JV8y/COwB9AbmAhPKXa9Wdfx3YCLwTCrtf4EL4vQFwPfj9AnAHSS/dHsYMDOmDwZeiv8HxelBJW7HCGBinO4PPA9MqLa2xPrsHKd3AGbG+t0MnBbTrwQ+F6c/D1wZp08DborTE+Lx1gcYF4/DniV+Tb4M/BG4Lc5XYxsWA0NbpVXVMRXrcC3wmTjdGxhYje3osJ3lrkARXrjDgbtS8xcCF5a7XhnqOZbtg8hCYEScHgEsjNO/Aqa0zgdMAX6VSt8uX5nadCvwvmpuC7AT8C/gUJIniHu1Pq5Ifg/n8DjdK+ZT62Mtna9EdR8F3Ae8F7gt1qmq2hDLXEzbIFJVxxQwAFhEHLxUre3ozF8tdmeNBJal5pfHtEo3PISwMk6vAobH6Wztqah2xu6QA0nO4quuLbEb6ClgNXAPyRn4uhBCY4Y6batvXL4eGEL52/ET4HygOc4PofraABCAuyXNkXRWTKu2Y2ocUA/8NnYv/kZSP6qvHR2qxSBS9UJyylE1Y68l7Qz8CfhiCGFDelm1tCWE0BRCOIDkbP4QYJ/y1qhrJJ0ErA4hzCl3XQrgyBDCROB44BxJ/55eWCXHVC+SLusrQggHAq+TdF9tUyXt6FAtBpEVwOjU/KiYVulekTQCIP5fHdOztaci2ilpB5IA8ocQwp9jclW2BSCEsA54gKTrZ6Ckll//TNdpW33j8gHAGsrbjiOAD0paDNxI0qX1U6qrDQCEEFbE/6uBv5AE9Wo7ppYDy0MIM+P8dJKgUm3t6FAtBpEngPFxVEpvkpuGM8pcp86YAbSMvJhKcn+hJf2MOHrjMGB9vBy+C3i/pEFxhMf7Y1rJSBJwNfBsCOFHqUVV1RZJwyQNjNM7ktzXeZYkmJySpR0t7TsFuD+eVc4ATosjn8YB44FZpWhDCOHCEMKoEMJYkmP+/hDC6dXUBgBJ/ST1b5kmORaeocqOqRDCKmCZpL1j0tHAgmprR6eU+6ZMMf5IRjo8T9KvfVG565OhfjcAK4EGkjOWM0n6o+8DXgDuBQbHvAJ+EdvyNDAptZ1PA3Xx71NlaMeRJJfj84Cn4t8J1dYWYD/gydiOZ4BvxfQ9SD5A64BbgD4xvW+cr4vL90ht66LYvoXA8WU6vo7irdFZVdWGWN+58W9+y/u32o6pWP4BwOx4XP2VZHRV1bWjoz9/7YmZmeWsFruzzMysRBxEzMwsZw4iZmaWMwcRMzPLmYOImZnlzEHEzMxy5iBiZmY5+/++WwYG0UQniQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(np.fft.fftshift(np.abs(np.fft.fft(x_filtered))))\n",
"plt.title(\"After going through the FPI the FFT of the signal is low passed\")"
]
},
{
"cell_type": "markdown",
"id": "b3837a55",
"metadata": {},
"source": [
"Strictly speaking the Nyquist theorem only applies to band limited signals (only contain a limited number of freqs) which is not the case. If it were, then sampling at twice the Nyquist frequency would allow you to perfectly reconstruct the signal (as seen through the FPI) if you took bands at twice the Nyquist rate. But since it is actually not the case then more oversampling is better.\n",
"\n",
"Lets show it.\n",
"\n",
"# Demonstration\n",
"\n",
"We will work in freq space because it's easier.\n",
"\n",
"1) Make a band limited signal by removing high freqs. Our `x` is white noise so it has a white spectrum."
]
},
{
"cell_type": "code",
"execution_count": 228,
"id": "645fd66f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Band limited signal in freq space')"
]
},
"execution_count": 228,
"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": [
"x = np.random.randn(6000)\n",
"fft_signal = np.fft.fftshift(np.fft.fft(x))\n",
"indices = np.arange(len(fft_signal))\n",
"middle_index = len(fft_signal) // 2\n",
"\n",
"fft_signal[indices < (middle_index - 50)]=0\n",
"fft_signal[indices > (middle_index + 50)]=0\n",
"\n",
"\n",
"plt.plot(np.abs(fft_signal))\n",
"plt.title(\"Band limited signal in freq space\")"
]
},
{
"cell_type": "markdown",
"id": "62ac5142",
"metadata": {},
"source": [
"2) Make a real space signal out of our band limited spectrum"
]
},
{
"cell_type": "code",
"execution_count": 229,
"id": "e97c0beb",
"metadata": {},
"outputs": [],
"source": [
"real_signal = np.fft.ifft(np.fft.ifftshift(fft_signal))"
]
},
{
"cell_type": "code",
"execution_count": 230,
"id": "851c0147",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/guillem/.pyenv/versions/3.9.7/envs/CataloniaCropClassification/lib/python3.9/site-packages/numpy/core/_asarray.py:102: ComplexWarning: Casting complex values to real discards the imaginary part\n",
" return array(a, dtype, copy=False, order=order)\n"
]
},
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fb51b42fdc0>]"
]
},
"execution_count": 230,
"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(real_signal)"
]
},
{
"cell_type": "markdown",
"id": "80c3026d",
"metadata": {},
"source": [
"3) Decimate and reconstruct signal to show that no loss of info happened"
]
},
{
"cell_type": "code",
"execution_count": 247,
"id": "798e6d64",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fb51ad209d0>]"
]
},
"execution_count": 247,
"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": [
"# Take one of every 20 samples this should surely destroy information\n",
"decimation_factor = 10\n",
"sampled_real_signal = real_signal[::decimation_factor]\n",
"\n",
"# Upsample so that it has the original number of samples again\n",
"zero_padding = np.zeros((len(real_signal)-len(sampled_real_signal)))\n",
"\n",
"tfd = np.fft.fft(sampled_real_signal)\n",
"tfd_A = tfd[0:len(tfd)//decimation_factor]\n",
"tfd_B = tfd[len(tfd)//decimation_factor:]\n",
"\n",
"\n",
"reconstructed_signal = decimation_factor* np.fft.ifft(np.concatenate((tfd_A,zero_padding,tfd_B)))\n",
"plt.plot(np.real(reconstructed_signal))"
]
},
{
"cell_type": "code",
"execution_count": 248,
"id": "789c8209",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reconstruction Error is zero!! Even after decimating and reconstructing\n"
]
},
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Reconstruction Error')"
]
},
"execution_count": 248,
"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": [
"print(\"Reconstruction Error is zero!! Even after decimating and reconstructing\")\n",
"plt.plot(np.abs(reconstructed_signal - real_signal));\n",
"plt.title(\"Reconstruction Error\")\n"
]
},
{
"cell_type": "markdown",
"id": "41d76079",
"metadata": {},
"source": [
"# Repeat the above but with a gaussian filtered signal"
]
},
{
"cell_type": "code",
"execution_count": 253,
"id": "e6beddcd",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'The actual spectra if we could take thousands of bands')"
]
},
"execution_count": 253,
"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"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"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": [
"x = np.random.randn(1000)\n",
"\n",
"filter_ = scipy.signal.gaussian(40, 10)\n",
"\n",
"# This is our filtered signal\n",
"real_signal = np.convolve(x, filter_, mode=\"valid\")\n",
"\n",
"plt.figure()\n",
"plt.plot(filter_)\n",
"plt.title(\"The 'FPI' filter\")\n",
"\n",
"plt.figure()\n",
"plt.plot(np.fft.fftshift(np.abs(np.fft.fft(real_signal))))\n",
"plt.title(\"The spectrum of our signal is not really band limited\")\n",
"\n",
"plt.figure()\n",
"plt.plot(real_signal)\n",
"plt.title(\"The actual spectra if we could take thousands of bands\")"
]
},
{
"cell_type": "markdown",
"id": "4096d078",
"metadata": {},
"source": [
"Let's see the impact of decimation. Before decimation"
]
},
{
"cell_type": "code",
"execution_count": 254,
"id": "3f216721",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Fouerier reconstructed signal')"
]
},
"execution_count": 254,
"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"
},
{
"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": [
"# Now decimate and reconstruct sampling every. Take one of every x samples\n",
"decimation_factor = 10\n",
"sampled_real_signal = real_signal[::decimation_factor]\n",
"\n",
"# Upsample so that it has the original number of samples again\n",
"zero_padding = np.zeros((len(real_signal)-len(sampled_real_signal)))\n",
"\n",
"tfd = np.fft.fft(sampled_real_signal)\n",
"tfd_A = tfd[0:len(tfd)//decimation_factor]\n",
"tfd_B = tfd[len(tfd)//decimation_factor:]\n",
"\n",
"\n",
"reconstructed_signal = np.real(decimation_factor * np.fft.ifft(np.concatenate((tfd_A,zero_padding,tfd_B))))\n",
"\n",
"plt.figure()\n",
"plt.plot(sampled_real_signal)\n",
"plt.title(\"What we receive on the GS\")\n",
"\n",
"plt.figure()\n",
"plt.plot(np.real(reconstructed_signal))\n",
"plt.title(\"Fourier reconstructed signal\")"
]
},
{
"cell_type": "code",
"execution_count": 255,
"id": "c9f1c14a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Reconstruction Error')"
]
},
"execution_count": 255,
"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(np.abs(reconstructed_signal - real_signal));\n",
"plt.title(\"Reconstruction Error\")"
]
},
{
"cell_type": "markdown",
"id": "d2ef7b24",
"metadata": {},
"source": [
"Ughh, reconstruction doesn't work now, but of course, we don't have perfect reconstruction because we don't have a band limited signal.\n",
"\n",
"# Encore\n",
"This is not the correct way to reconstruct a signal from samples. One would actually use sinc interpolation. With some copy pasted code."
]
},
{
"cell_type": "code",
"execution_count": 266,
"id": "4865bee0",
"metadata": {},
"outputs": [],
"source": [
"def sinc_interp(x, s, u):\n",
" \"\"\"\n",
" Interpolates x, sampled at \"s\" instants\n",
" Output y is sampled at \"u\" instants (\"u\" for \"upsampled\")\n",
" \n",
" from Matlab:\n",
" http://phaseportrait.blogspot.com/2008/06/sinc-interpolation-in-matlab.html \n",
" \"\"\"\n",
" \n",
" if len(x) != len(s):\n",
" raise Exception('x and s must be the same length')\n",
" \n",
" # Find the period \n",
" T = s[1] - s[0]\n",
" \n",
" sincM = np.tile(u, (len(s), 1)) - np.tile(s[:, np.newaxis], (1, len(u)))\n",
" y = np.dot(x, np.sinc(sincM/T))\n",
" return y"
]
},
{
"cell_type": "code",
"execution_count": 267,
"id": "cc44f172",
"metadata": {},
"outputs": [],
"source": [
"wavelengths = np.arange(0, len(real_signal))\n",
"reconstructed_signal_with_sinc = sinc_interp(sampled_real_signal, wavelengths[::decimation_factor], wavelengths)"
]
},
{
"cell_type": "code",
"execution_count": 270,
"id": "ac4cdb82",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fb51bf768e0>"
]
},
"execution_count": 270,
"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(reconstructed_signal_with_sinc, label=\"sinc interpolated\")\n",
"plt.plot(real_signal, label=\"Real signal\")\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 269,
"id": "f2d5b4e6",
"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": [
"plt.plot(np.abs(reconstructed_signal_with_sinc - real_signal));"
]
},
{
"cell_type": "code",
"execution_count": 271,
"id": "bd928ad5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Much better\n"
]
}
],
"source": [
"print(\"Much better\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "010e9177",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment