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@LeszekSwirski
Last active August 29, 2015 14:09
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Create pink noise
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{
"metadata": {
"name": "",
"signature": "sha256:75ae7daca500ac2f2f997ee0e2c39bb2f3364a3338e523f568c11970123a8c40"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"%pylab inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def f_to_psd(f):\n",
" \"Get PSD of fourier transformed signal\"\n",
" return np.abs(f)**2"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"$1/\\sqrt{f}$ filtering"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"\n",
"SFREQ = 30 #Hz\n",
"T = 60 * 2\n",
"N = SFREQ * T\n",
"\n",
"wns = []\n",
"F_wns = []\n",
"pns = []\n",
"F_pns = []\n",
"\n",
"# Do the below a bunch of times to get representative sample distributions\n",
"for i in range(100):\n",
"\n",
" # Generate white noise\n",
" wn = np.random.normal(0., 1, N)\n",
"\n",
" # Get Fourier transform of white noise\n",
" F_wn = np.fft.rfft(wn)\n",
" f = np.fft.rfftfreq(N, d=1./SFREQ)\n",
"\n",
" # Scale by 1/sqrt(f) (so that power, which is |Fx(f)|^2, is proportional to 1/f)\n",
" F_pn = concatenate(([0], F_wn[1:] / sqrt(f[1:])))\n",
"\n",
" # Inverse\n",
" pn = np.fft.irfft(F_pn)\n",
" \n",
" wns.append(wn) \n",
" F_wns.append(F_wn) \n",
" F_pns.append(F_pn) \n",
" pns.append(pn)\n",
"\n",
"# Plot averages of above calculations\n",
"\n",
"figure()\n",
"title(\"White noise\")\n",
"plot(arange(N), mean(wns, axis=0))\n",
"\n",
"figure()\n",
"title(\"White noise (PSD)\")\n",
"plot(f, mean(f_to_psd(F_wns), axis=0))\n",
"axhline(N, color='r')\n",
"\n",
"figure()\n",
"title(\"Pink noise (PSD, log log)\")\n",
"gca().set_xscale(\"log\")\n",
"gca().set_yscale(\"log\")\n",
"plot(f[1:], mean(f_to_psd(F_pns), axis=0)[1:], label='pink noise')\n",
"plot(f[1:], N/f[1:], c='r')\n",
"\n",
"figure()\n",
"title(\"Pink noise\")\n",
"plot(arange(N), mean(pns, axis=0), label='pink noise')\n",
"\n",
"show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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Yk5q/KCqmm7Q0ZVR22qsWav09LzqiDKoA+UiEIE4w9vglCBaiDFImiZ5BLQ0F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\n",
"text": [
"<matplotlib.figure.Figure at 0x1da9a0f0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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ssp0JaR8Q06frgyfi7pE8DZDW1la0mvipY4hV/sw8GsBoACCivQH8gpmHEdHv\nABwH4NLwU6ScmgTgTiK6AoFbpx+AqczMRLSciAYCmApgGICY4MsxAIK4bkDfCw9ki2iJexXWETfO\nQLWNSRm69XEdYyY3uctBLSaY+M7zdjFk5de/1r/2J8n+8svBvMjbbFNZpmqfaUM9TZblYW26drfa\nWP71jvNXbRMXWFDU22dLSwtapKnQxo4da12GbWI3caiXAJhARMMBzAFwJAAw80wimoAgMmglgBGh\nWwgARgC4DUAXAA8ys+FUEfHKX+aRR5JzoNjw8cfBpM+6SeDTup1MrUBV2SpL0rZOUW/aUMEs2NZp\nYvlnHdCzbBlw+unAHnsEv2+9Nb4+HTvsELQXeXSvaDvyceTxQIszGJL2q3eHbx5KUZ4dDXDbjk3f\nPnXjdsqKsZpk5ieZeUj4/QNm3o+Zt2bmwcz8obTdRcy8FTNvy8yPSMtfYOYdwnUZcm9WEz3B772X\nvE9bm376PMHChUGmzAsvBDp3dqsok1Lixt3Igwfr17lubLZuH8HixcnzIkR57rlKHWJfU7ePixv9\nmmuAI4+MryuN6ytJ+bsOL05j+NieP1cZU+NIcllGMQnXTfu2bGucLF0a315Mjdm8KXmXRDKq8M8k\nLr00OfZcWBLC9aRCp5iSbmjxGqmzukxuZF0dX31VmXYxzirJ04d/0EH6eRGmTq1dxhzMkyBG78r7\n1sPyN8WV8ndllbry+dvUAwD33GNe/sKFgKlHIq2xYYrJsaoGM9o+iNZbrzJCWYVJqpl60PDKPw3R\npGgqota3jUWQ1MjEIJulS4Mp8JLqtqnjr38Ftt02vn7AzO2T9gYUI2aFMpfZfXf9frZhfS4t/yTS\ndvi6cvuY1l0Py9+GGTNql2WNCsvTcFHNlJamngUL6tMus9DulL/JCTfJDCka6D/+UV1u1qgNoHqE\nZVzdYoi7it/9Tr1cl+/G1BKWBwllfRDsvbfZdqpzK2gvlr8ctSJvc9JJbuUp6rh1XHWVm3Jk0vaZ\npD03aSLO4vYpS19AUyr/u+5K3kZcoIUL7etKurimaYl/+Ut9DnwV118fDFk3QSf72Wfbba/C1YjI\nJJ//Sy8FeV5slCCRfhRskmxZlP9HH1WWyW84qukVVSSFPGZ5C6q3hVoPyz/abj7/PH27TBOQEPem\nWJb4/5KIkZ40kQcmeehNGkqcZZ6l7LSpAKIjQGX+/vfq37Zx/nmis/znzo0//vfeCzr6TM4RcyX3\nke3EN2Kd5dTEAAAgAElEQVR/k/MRTRAmlL8cLqhrsx99pA9YSJqlLkvs+8knpys7bcdl1mAF0+st\n06UL8MQT5nXElWUiS1EhoDY0vPKPhmG6UlgmT+fdd083ViCJv/yl8j3L8cj7xnVcm+yfVo7Zs2tH\nUcbVI3PCCWbpK0wt/0GD4utLU49qmx13rPxWWf7yNI5RRoxIJ0+WdnLHHen269w5fZ1Rog/XtOG/\ncfvPjxlWGsXUANPJGWcseOXviGgDdKX8TS+QfKPb7qtDHoqfl/Vt68KIxlHHIR9/XAev4L77avez\nwfYc5an8geoHrbDy5X2F8s96bVXKMuv4j3qQtU4T5S9vI88dnQbT60RUCeMue2cv0A6Uf/TCuso4\nmOdNYVN2GheFKfVw++gGyMnIcf1pqIfy11lySe1NKCFVtI/LDltRlmpSnqy4VmQmkXMmdca9Qcn7\n2/SbqZA7rZN45ZXgs2NH7/PPnagV4Gr0ZLSBiqifNPvarpeJ63DOQp6WiXx8JscqrplL5V+vqBd5\nHgYVKkUvlh1wQO32aeUeOTJI/NYIFqeKNHJvtJFdeWnPrU3fhjBG48YRebePI6JREK4s/6ibw3Qu\nXKA8FzcpYiJpGsS0PmV5PmATd9ENNwSfLpV/1miRLHXLxFn5qiydulnrkup+/vkg2isP5V/vjv+k\nOtNE+wD1uS/jrnc95TCh4ZX/OedU/3Zl+UdHqNrcAEmhnPW6+En1HH10/Pq0yl9+W0lKoyETJ2/c\ndVVZZnmkurB9yABqn3/cPqqQThvyUNSTJ7spJ65fwrXcRb0Bydfbd/jWmbxmGbKJo04axFUGttxS\npMzW4yqaxAVxyv+MM2qX1cvtM2pU/D4mlqCMjfJX+cltr5PJ/TJ0qF2ZOp59FthsM/21UbU3VbRX\nmvEW9UL1sI/ilX9O5JUC2KYxlUX5x8ksu2ZM9q/HzRR3U8QpKduZl1xG+0THT0QRcpvm9jHpII/D\ntv3XO2X23Lnq5dFzEudnT6v866F05evtLf86k7fyNyk/SflfeWV2eeqBLtUDoE97nIW4myLOIrZV\n5scdZ7c9EAwMPOYY+/1UlmBcG8qq/G3PRb2VP2Dm9rnxRv3+ZfX5E1WutypBXL3kMKXdKf+83T4m\nN4s8K5eKl1/OLo8JWa11OelcNA328OHZylYRd1P84Q/6dbZWnumE7TJxE3rEoXL7uPL5R8u5//7q\nwWQmiAyw7Y2bbqp/ncwV/TNxYvkt/5I4KNyRlyUjys3r4ZIHLhvZzJlB+JoL90+a+Oc337Qvr178\n9a/Au++q19l2+NpY/qpy4lJ8lAWd5W96HdNe73q6fYqWw4R2afmPHGmWvycNRSuaornlluxl6HKd\np/X518N1EXfdR4/Wd/yqBnnFYaP8oxOjA26uT97UI9qnCGS3D1B+y7/dKf+2NuDaayvTHbqiPTRO\nF/zkJ9nLsO2gBezzq4gbbNo0+7pM64jWpSJPt0+zUuZ70Vv+BWISapWGIjrGspLXTZK18aaxiNIk\n1wKCeZ1VrFiR32hwGVvlX2bF5gpV2nCb4y7rOWprA7797crvww5Tb1cW5d9uff6ulXUjKn9bir6p\n4upPq/x1lti66wInnmgmVxJxN7OImDJV/s3QzmySBKooq88/KteyZertfG6fnMjL8m8Gij5neSh/\nnRvls8+A6dPN5EqqI06piPluTeP8i74GRZFmgFrZMJW/LJZ/u1P+eVn+jd4wTdANwHGN7lymseB1\n+4llcfu5uglN5oQ2jfNnNhuA196wub/S3ttpw3VNMT2Ggw/OVw5T2p3yV42odEEzKP8hQ+pTjy4y\nxqXlL9wtccq/tVW/zjWm7aetLZ+0zJ78UU1WX2banfK3zaViSjMo/6Ibb1rlr5pNTeSEcTUuw+T6\n77KL2f5xx5ImEqo98OKLwA9+ULQU2ZgwoWgJ7Gi3yt9VMipBIyr/RpM5rdsnDpv9NtxQvy7ruTRV\n/s1KvUa9eyq0O+W/eHE+5TaaIm1E8ugItYmbz5qQzzRU1Sv/WsrSCdpMtDvln0fOGaAxb9hFi4qW\nwI48HrA2ln9ch2DWNMLyukZKEVIvvPKvP+1O+eeFt/zzJw/LPy4hXJTPPnNfv2p/mwlumoWyxL43\nE/6UG+KVf/6U+RybyBZnvcr7xz1kmpVmsvyTZvqrF6VX/ptuWrQEnnpRZuVvQtzMaJMm1U+ORqSZ\nlH9ZjrX0yn/QoKIlCGh0xdQIlHnka9H1t3eaye3jlb8hnToVLUFAI3b4NhpXXaVf55Vv+6YsCrEe\nlOVYiUt2VxFRySTyeDyeckMAmNnqsVJKy5/Aq/5OPYWrfvu/9v0HVi8/8IBi5TptZPHnpj3/jR1T\n/zp7bFTMsXbpzJVMdq7+UlBK5S9TFrePp1iKfh0sun6Pe4pyv5TF7eOVv6ch8Mq3QteuRUvgniI6\nfIvqZG4I5U9EnYnoOSJ6kYhmEtHF4fIxRDSPiKaFfwdI+4wiojeJ6DUiGiwt35mIZoTrrjYV0JXy\n32gjN+XY8L3v1b9OTz74h0++FKGIveUfAzN/DmAfZh4A4OsA9iGiPQAwgCuYecfw7yEAIKL+AIYC\n6A9gfwDXEa061OsBDGfmfgD6EdH+JgJ+/nmawyoHZbnIjURZUx+USflH29XVxqaUR6aZwktVJB4+\nM4tJ1zoB6AhATDWhUm2HAhjPzCuYeQ6AWQAGElEvAF2ZeWq43e0ANDNcVrN8uclWZmy/vbuyPPmw\ncKF6eZmUb9ko6wPThmay/Mvy0EkUg4g6ENGLABYB+CczvxKuGklE04noFiLqFi7bGMA8afd5ADZR\nLJ8fLk8W0OGJqvdJ95a/Pb17Fy2BmjKN84i2qx49ipHDJQ8/XP86vc8/AWZuC90+vQHsRUQtCFw4\nfQEMAPAegMvzEtBVHgwi4Gc/c1OWTZ2e9kGZrOtou1p33WLkcMlTT9W/zma/P40zmDPzMiJ6AMAu\nzNwqlhPRzQAmhz/nA+gj7dYbgcU/P/wuL5+vr23Mqm/vvdcCoMVUTADA5psDc+bULj/xRODdd4H/\n+R+r4jwJLFgA7L8/8NJL6fbv3j153tqiLW+beQHyJqq0ml2JpaWRLf/W1la0ZpyHNFb5E9EGAFYy\n84dE1AXAdwCMJaKezCy8s4cDEBMATgJwJxFdgcCt0w/AVGZmIlpORAMBTAUwDMA1+prHrPqWxg2g\nuqjihNfzRmmWm7Jjx2w3ksl5Wnvt9OW7YMWK9Pt27gxsu616ukmPWx58EDjwQLNtG1n5t7S0oKWl\nZdXvsWPHWpeRZPn3AjCOiDogcBHdwcxPENHtRDQAQdTPbAAnAwAzzySiCQBmAlgJYARX8keMAHAb\ngC4AHmRmIy9fGrdP3EX1yj8fshyryb4TJ6Yv3wVZ3D5rrw0MHuxO+XvLX4/Nuchb+e+1l9qdVZbr\nFav8mXkGgJ0Uy4+N2eciABcplr8AYAdbAdNcoLL0pjcLRPkr/6LJovzb2twe4+qruyurvWFznovK\nq1+W9l56NZlGkasuqnf7lJdGOE9Z3D4ffJDcp2HKE0/UznHh6vx17uymnCKR9UWSq9BEtxxwQPI2\nUcSAUt11KUt7L73yNzlRAwZU/467qP6twD3twfLfc8/49Vk7fNMMVvza12qXfeMbtctcnb+vfz17\nGePGZS8jC/K5+O9/zbfVkUZfTJ4cv74M7R1oAOW/xhrJ20yZEnz2CeOMVBdM9Dx4y9+MI46w2z7L\nsba1ATvvnH7/vBg2rPI9i+UPAF98Yb+PLnAhr3Y1alT2MtZfP3sZWZDPTZLuWGstu/JMEW8c3vLP\nwBdfmPnlVlstUO5CgcTt45W/GV26mG+bVSF9+SVw773p93eBSv6BAyvfs1r+rpS/Clft7DCjMffx\nFN3mk+qXjYyJE4GZM7OVpyIpLLnocyQotfInAo480mw7+bMslr9LdtutvvWtZjwCJCDLef3ii+Ln\nak6SvyzKPy/Lf3+jTFvJ5HV/mXgAgOQH5lprASNGBN979gS22y5++zTHs8UWwVujt/wzsuWWydtE\nlb6qAYincaNa/rvu6q6sX/4yeRsb5e/C8s+TQw5J3iZJflO3jy7VQppoobjAhaRltrhqq3n1qT3x\nhNl2JsfxzW+a15vmvKy5JnD77W7LzINSK39TpRK1/FU3TaNb/i457bTkbWzDCU85JZ0sQGMkbTO1\n/PfeW708TbvTKdI84vxd3Rd53V8bbOCm/qS2dlEkSN1lIMO772Yv0yWlV/4ys2aZbS/fNOusE3yK\ni666obp1q13mApcX2aWCNOlHsVH+RMDxxwODBqUWKTNxFqfJucvb7eNK+eelOMqu/F3Vn9QWvvtd\nu/JsKFvSwlIrf6D65Ce5gFRuH5EiOM7yL/sNJbPVVtnLSHo132qrdAOJ8jjegQP1Lq9LL618jzum\nHQyGFia1C5XbR5VQzeVD2sTy79ixfVn+upDbpHKPOy74zPqgj57zPEKYyxJuXhIx1NieeDHrl2zZ\niqgVU7dPXi6IrDfFOee4kQNIbny2CsV02403Ni9T0LVrddSNjNwJGHdMv/oVcPPN8fWksfxVndQu\nH4C6B5K8PK+UEUWXY4u455MibZjjZcz7+rmuIwulV/7iRN10U/L2QhmYRvvo/LPR7dIil0FknnBK\nRgzq2cRo9gM9porSFJWrLOmcubZ45Ck+kwb2ZZ0OVBUSWE+3jFx+tF21J8tfZ3wllSsCFLJmf62H\nYraNpMuLhlH+G24YfMaNxBQ3uGm0zw9+oC/LRd6P6E265prZy0zLhAnVsiQhb7P11vHrTW8Y1zeW\n/EBLsubyeNVW1alTXjZvlGLwkYnMro6r7Mo/iX79gs+kUb1lsPxtxtDkSamVv4w4kXFDp00sf9Wy\nejzt09YRlduFWypJluh61RiDNH0nqvUmyktXrqnl7zo2XvSH5NVuRFijidunbJZ/VuJCauXJmKIu\nxDPPDAxDkxQVNso/j/NSpBEoU3rlHw3jjJu1SOXzF6iifeIU6RZbmMuoQ244W22lb0hi0ImKPJS/\nrcJVyS2/ukavkWtZdMj1yeWoEpSleTDpyNtoUEWt6ejQoVzKP2s5n31mVm703HToEKRP3nbbbPVH\ny5XvN9UbcBze8neESaPaa6/gU5VES3XD6m5iZmCffexljEN2u0SJG3RiovwHD7aTxdbto1JCafyW\naS1/HfK+cQ8rE7dPWSxfIF75Ry19F26fUaOAq67KXg6Q/TymSYBnQ5LxlHc76NoV2H33fOswpfTK\n3+ZiiCHqy5fXrlMp+rgUti5uKrku1dP+8ceDTzmBWBpsO7lsLX/V9vLblanlnzbM1iRqIi6Vr4lr\nJM1NbzoCNy0m58uF22fw4OLTawhcK39VbH2RPv8PPwQuvthdHVloGOVvoyRUUTUq5f/jH+vLFsrk\n2GOr9xXjBkwwbUhZByjZKn8h18iR8esFSco/CZGaOI3lb3qjinIWLqx0/snb5RVbHX1wu5zr1/ah\nVwayKk9dDqS05UYfavXs8FXhyk3ngpI1HT02J+yII4D7769eplL+0YFM8uuY2E52b6yxhj53SxJp\nLbSo8hdRTzImyl+lMLI8nFQuF115wh2XRvnHPfzkfcX3Hj3SWcdx66PzRcShU15p+mrqZfmnYdo0\n9fKsspgaMqbn0/a8q1zAaSmLktdReuWfxvJXbW/SSXf33ZXvKgWZtSGlIVrnsGG1uXnibhjRd7H+\n+sDcudVymc51rDoOU5fH6NHAeeeZ1WO7jc4CdqX8xbJttkmWUeDCbWHToVyUJWmad8iWrHH6Sbj0\n+ZclaictpVf+AttoDJ3yjxuY07NnZZlK+f/ud+YyRPdNe1NEG2uHDrUDvkxumG99q1aWuBs4ybUg\nN/wsr9Gu3T66ffLo8FW1M6H8ZXfDmWfalw2YKdgi3D6/+IVbxSdnwNS15bT3T9p+JhXRezGPfqR6\n0jDK3xYbyz9OWcjrDjoomwxpUHVKR91VptZSz56Bnz/J7RNVaioFc+KJtcvkfeTpBsW5/853avdx\nFeo5fHjwF10ufme5UU1cAdtvH3yK+VtlLr88vm6ZG26ouBZFvVdeaS5bPfj9791a/sOGAXvsEXxP\nk/o6yvjx+nW2Pn/5WqsMsSi//a2+rLLRLpW/6ma3jc12bVGlbQg9ewKLFlUvi4ZZxil/ucGuvjpw\nzTXJln/0BlTJLj+AVK65rl1rl6ny6mcZ5CXvu9delfw9Nsr/k0/09Sa5COT1RxwR/BadzWmv9wkn\nJD+cow9mG1fJpZemnzLzT39K3iarha47FpvxLllcOzauXeH6lKc8laOLvPIvANXT3XYyl6hCe+op\ns4Ffxx5rVr4NUWsyavnbWktxk96I8pLOk+omkfeRz7dpp60tqg7fqBym9aj2EeG5cW9I0f1djsA2\nsa6Tzm+UX/6ytg/D9J4YOtR+Hx0tLerlurbsKuGiy347cX10eaO88i8I126fPfc0u5gHH6wu12VU\nho3lH3e8Onmi4YpnnFH9e6+9KhE8uvJMrdEs50RWjqpxByb1yLKfdFJl+Zln2o2/SLJcbcuJyqbb\npkOHaoV22WXVfVf1xvR67ruvernpW6ypEj/ggNoy0lr+Jm6fsit8mYZR/rYn1cRPG4dtOKRAThaX\nR7QPYOfzT2MxrVxZLfvmm1evf/LJ5LlPhUxtbWoZTj89+Mzi9pGXJyl/E8tfjEcAgqyl4iGbxvJP\n2/5kI8HkIUZUff3POgt47bX4OpLSFJjOmqXCtM1H26yrh2eU884zn/9XRZa31rI/CBpG+dtiojDi\nlqVV/rpyXTaEoUOB3/ym8lt3w3zve+nKl5W/7M/UoTo2IZMuUZfoME4zu5HoHNQpfxW2HZS2WV3z\ncPuoZOvcWW/5P/po8BmX/woAfv3r+PVZOnPTKv+k5UkWexxp3hgExxxT+R6tX5wnlRHQCDSd8jd9\nVUtyjRRJ587V7iVVg+7YEbjnnnTly8pfTINpgnyudtqpUpaQTyXnww/bjZoGgKefri0vreWvu86q\nxHWCuP4OG+USTUMhyrFpe3KHr+mcBUmzVblU8jpEKpYoecT5694yTPj+9yvfo9c2aayLKvKrTDSM\n8s/i9kljgZdt2LwgzsqWufbadGUBgcKWHy6m5cjTbF5/faUsFaIztVu3+FHT0b6SZ55RbyffiEkj\nknX1yJgkrpOt0agVmPTA6NsX+Nvf1HIkdfgOHQr071/ZPu7h6pIuXdRTqYo0KUIegU7BA0GacJv7\n0iba54ADqqf4tI3PNyWpTV1zTWVgZRkpqYrLjnyBL7gAGDu2dnkcZXb7RMuLKv/evYFTTklf9ldf\nVcIBbeRWzakrW/6irO22A/r0MSs/euPKKTjkdapoH3mmNlvLXzxM/vIXYMwY4J134uWM+qxdWM86\n2U48Meh3AardPiqFaDPGQKA7V6utBsyaVbv81lsr34kq0URJ7icbbB5s3boFUU26faPnMy7BY5wM\nIhOqzu2z5pqVdl5GGkb5Ry9Y9+7xk5nL248eXfGRmyqzXXax2z5JBtXv/v3TT8guN7g0A2O+8Y1q\nt4M8YYuYSQqwU2KqSd9Vlr/8OuzqoSg/AEWZV19dWZbW5/+jHwXXSJX1Mmuop859lGT5A5VOTLnD\nV1Ve9+7AnXdWX1NVnTJZOuGB8im8JJ9/2j4BMbCvUWkY5Z8UV266TuXDVm0rRvO6VP5RevUC3nwz\n+P7KK3Zly+cjjZ/0xRerlfW4ccHn0UcDL7xQWZ5VOa9YobZMTcuNun1kks5BtGMUAG68UV+Prg9B\nV6/qeHSWv8nxvv569bZx+8hTlsZZ/scdBxx1VHx/QNz4FV2Hfdw1EQ/8qDzi+OLKO/xwfblpydLh\na0sZ+wh1NIzyt0V3EQ47rHbZ2LHApEl25WRB5ZLJYi1FFV+vXpXvpn0X4tW3T5/q3EE2lr9q2ziL\n07R8HTrlH9fhu9tuwYC96LZpfP5x+8fJqttehGDaKH8g3vI3uf7RXFFJA+aAoJ2oRmzHKX+TmbDu\nvTd5G1XZNqRtc9/+dvI2H3yQruwiaBjlbxJxIa+zec3v1UvdkHXb64hai/K+srwqS8u2QcrlnXEG\ncNttld8i5A8A7rgDeO655PJ0sdBZlPObbwKXXFLr8zd9A+jbF7jlFrO6ZNeXSnnKo5pV9UffMExC\nPePcPi6yR8Y9BMSyjh3dd/ia9FUR6YMC0rghbR+eaUkKGY17Q9p6a+CRRyq/VeXMnKned9ddzeSr\nJw2j/G2xUVpx20YnBtGx447ARx+ZlRt3M9uy667AT38avN6L9M3dulXWb7xx/DSRgizKX7fNVlsF\nln90fdIAMcHuuwed17Zun7hon7hcOKZuH9U+UbePCUntw2Sug86d1cpfJLlLg9y/kaZdCuXv0sWS\ntSyiYF6GuClPX389MDhs5cjblZQXKWZiLQZXytyGzz4zHx3YsWO2iZltfOCAusHdf3/6fPJZRkEK\ndMew2WaBxST8x9de6/6GkftyVBazUOZRy19HkhKIktThaxNuaOpKEqjcPlnO71ZbBZkx+/QJZPjZ\nz4D99jPfX+f2iRLtZ8kTosoENIsXA0ceWbuN7QTtunpUlPEB0S4t/yyjAWWioymzkqaD2qbMrl3V\nM32ZkCY5lYi5NwlZlC2u1VZzM45C3FCvvqqebUvl9okqHJ1/W85dFFe/CCkU5bgYpGSr/MXx2NZ9\n4YWVgIMocll/+ANw6KG126jkYza3/P/zn+BPV1a03LjfScjlb7QR8Pe/py/LlrvuClJ1l43YW5CI\nOhPRc0T0IhHNJKKLw+XrEdFjRPQGET1KRN2kfUYR0ZtE9BoRDZaW70xEM8J1V6vqsyXuotX7TSGr\nK8fWYnCZRsC2j0QwcKD5tlE6dgQ+/tisvrjOV2Zg223VZeh8/qrOYebKOR01Kl52GXmwlSgnK7Zl\nqCx/k2ux4YbpQ43jMFX+O+1UCamWUbkp5bLWXNM+LYhLYyNuueq8H3FE+jTaeRJ7Spj5cwD7MPMA\nAF8HsA8R7QHgXACPMfPWAJ4If4OI+gMYCqA/gP0BXEe06nRcD2A4M/cD0I+IYsb/1WLT4QskR5nE\nle0KXYdv3LaDBuUjiylpQhTTnj/VNVLdpKrxA4D+nMZF+5i4fS66SL28tbW6XvG5ySaVcRJyzqU4\nsnb4yqTt8I07f7ZlydFqpm6faJ0qVA/id94B/vEP87KPOqo6R48nIPF5yMyfhl87AegIYCmAIQDG\nhcvHARABlIcCGM/MK5h5DoBZAAYSUS8AXZl5arjd7dI+uTBgAPDGG3nWkEwapSgmQcmzDh033ACM\nGGFefh4PTRvlr0P4902ifQQmrkJ5xLDMvHmVaI6kkF0x01Oac6cbVJRlHEUW5Dreeqsig7D8f/GL\nIG7fJMGgTl7xIJaPbYMNqkcPJ40kvvPO6lHIWXARxVUWEpU/EXUgohcBLALwT2Z+BUAPZhbzSy0C\nILKzbAxgnrT7PACbKJbPD5enxsSqMI3UyYLN65zLTr48/JQnn1yrvFxaqNtvn5zsyoXlf/31wLPP\nmvn8TcrTkcbtuOOOydvozucll6i3N+nwzRJKbIJ8jcS+u+8exO3r3qRcyHPttbUz3bkqW5A0X7Ec\n6NFIyj8x2oeZ2wAMIKJ1ATxCRPtE1jMROVZFY4L/Y4CWlhYALW6Ld8j221ePiE1LWRuNS7k22yz5\nRlV1wNpa/j16BH/yiFLZ8pdDYQVpHqZJY02y7J9GjnqHVuraxiOPAMuWVX5vtlmQJsMWk/EpHTu6\niVRTIebm+PhjfZ/BjBmBwSRGyNeL1tZWtAo/ZEqMQz2ZeRkRPQBgZwCLiKgnMy8MXTqLw83mA5Bt\nx94ILP754Xd5+Xx9bWOC/2OSZDKVvppOnYAvv6z8zqLg4jqS8ux0FseuinLJE1XqZJcPCBeWf1y5\nHToEHdWTJ1cG9h12WJDWYsECO1ltsLHEddvq3E5pO3zjyPIgiQ5i7Nw5SJAXh0peueOXOYg40g2i\ncs23vw1MmKCXTSyPuuLqZcS1tLSEhnHAWJG50oKkaJ8NRCQPEXUB8B0A0wBMAnBcuNlxACaG3ycB\n+CERdSKivgD6AZjKzAsBLCeigWEH8DBpHyPKZBk/9FDlu04BrrdeZcISE9Iq0j/+0W57VZ0m28yb\nB7z/fjD2QZDVtaBCpfzFa3W0PyLpdVwX5w9Uh8Ted1/1DGwuyCOCTJX/HzCz/G07X9Mq/7zCJpmD\nsQZPPFG9PC+9oDPqyhivn5Yky78XgHFE1AHBg+IOZn6CiKYBmEBEwwHMAXAkADDzTCKaAGAmgJUA\nRjCvOl0jANwGoAuAB5n5YdcHkxbbBiTnKRdWTrRRnH9+9UhWVx1F0ZBC2xmnbBH1RfO/5IXqpjv2\n2GB+XTnz6Kuv1k5EHkX2xbpI0R0li6vI5VuhyFfVyIrJZcSYC1yMuyk7scqfmWcA2Emx/AMAyjF/\nzHwRgJouHmZ+AcAO6cS0D/XMUrYp++8PnHtuME9oFNv8Jnm4UFwQJ0+HDtWuubzGSwifrvxgiMb2\nq+jTp5KHX3b76Oqx4eqr47NhJg1KIqqWQfaRy9uYIN4IXI17SSqrCFTyvPqqm1G5KrKO22kEGia9\ng4o8B0CZsO666rBCIDnFsG5dUgMT0Tj1OsY4JUsUvOG4JO7407zliDw1UeWfldNOy16GfG5NU43H\nYTvCN6ubSDfCNw9UE66YGAAmqGROe2yN9IBoWOWfpZHtvbd6dKktQpGcc07tSMUs8u27r3oQy2ef\nmc865IIVK/J3K8lccUVw85xxhnp9FsUt3AP1ujl1g+Xk5X37AmefDfz+99XbdusGnHWWfXpgVx2+\nRSiwuDpnzVJPH+mK1VarnXQoKs+FFwZBAdOn67dpNBpW+Wfh4UhvQ1b/nir+Os4KiwtNi5NFVvz1\nsPxNc9oLst4MZ5wRH96X5UHUvXvwKXIYxbmXXBD3VnrPPfF9KB07ApddBpxwgps6gcDgSZqK0rSs\nei7bklcAAAq/SURBVJOn4geAl16qvV+jhsbo0cGnrPxVNNIDoSmVf/TCpr1gOkv0kktq45rlm+mk\nk+LTLJtkZ3SZ26dMuHb7yOUmWcYnnKDONeMCuW6TEa+AWz/9Pfe4K6u9oRoMqjv37em8NExWT/li\n3Hwz8Kc/uStbWIW26BrIOefEW3ZrrFGbFA0IRtiefLJZ3WVshHmFegLBOdXFuadBJWunTu6U/7rr\n5m+xylx8MfDd7+rXRzuYf/5z/WQsQH4+/7POUi8fNkw9y15RbLZZuv3KaFDpaEjLX0xUoYqysWXp\nUvWITxNcdR4KRNrXK690W24jEfc25RJVB6tLOnYELr00yOgYh6uUH+eeay4bkNzG6m1c/OhH6UYB\n58H77+vHVCTRSMq/lJb/n/+cfNMAbhpoWsUP2F9ol3l7ymj5u8D1A1VHv37BTZ4H3/9+MDZBRne9\n8kipDATZYeOmJIyDCOjZM3m7pHEWKhqh3a63nv25u+OOfGTJk1Iq/+OPDyZAkCnjE9VGUdk0+ka4\nQVS4dvvkfc3XWy+fcu++Gxg50mzbn/wkefa1NOfhhBOAL76w32/s2GBa0O7dk9vht76VPJ6hvaE7\nPpFpoZGOvyHdPmXB9qY877xKI4ljm22Ap55KJVLDI87p/fdXZ8AsCzvskG2C8ugxEWWbP9k1pvMR\npKWRlKMN0ZH3jUC7U/4jR5pPEJ4VWxfFNtuYvSr/8Y9BzHtcbv9GamQ2iHM6ZEixcuiYMiXdfuJ6\n2c5A1Wi013ZpSiMdf7tT/tdcU7+6bCwzm8ndV1/dPo1xGXBhqa6/fvYy8iQpmZxLyujqTCJJ+TWS\nckxDIx1fu1P+9cTU8r/+emDjjd3W3V7j/Hv2bKwbKA650/CQQ4BPP9VvG0cZr5Onvukt8qBhlH8Z\nT7SJ8n/rLWDzzXMXJRU9eiRv40nPgQdW3ERnnhn8paER3wJ1FH3PZqU9vdmUMtqnUTCxyLbYIp/w\nRReN7KijgMWLk7ezpZ6ukTLTsaN6MJ8pon0dcwzwzDNuZMqbvGbVKjt5zKaWNw1t+Y8fDyxZUn9Z\nBPWKSc8LoupJTVzx9tvuy2xGRJvv1CmYD7fsvPSSfpJ5QSMpxzQ00vE1jPJXMWhQsfUX6YstayMr\nq1ye/NnBYLaO9tp/scEGwWcjHV9DK/+iKdLy33bbIH+Mp/3SSIrElPPPBw4/vGgp0qNLDti5c+Ca\n69+//jKlxSv/DNTj5tRZ0n36AB9+mH/9nuIYPRrYa6+ipXBL9+5uE/SViUZwzcl45Z+BRvf5e8pN\nnz5Bp3yz8ZvfANOmFS1FMjZjd8pIwyj/Mr4Cl1Emj6fROeig4K/MLFuWf2bYvPG2awa85e/xNBfC\nDdvoih/wyj8T3vL3eDyNSsMo/402KlqCWrzl7/E0F+0plLkhfP5ffVVORVtGmTwej8eEhlD+ZVSy\nTzyR32TfHo+nnLQnV29DKP8ysu++RUvg8XjqTXty+5TQpvZ4PB5P3njlX3L69ClaAo/HI2hPlr93\n+5SYJUuAtdcuWgqPx9Me8cq/xIhMgR6Px+Ma7/bxeDweQ8o6K18aiEvmxCIiLptMHo/HU2aICMxs\nFYjqLX+Px+NpQrzy93g8nibEK3+Px+NpQhKVPxH1IaJ/EtErRPQyEZ0WLh9DRPOIaFr4d4C0zygi\nepOIXiOiwdLynYloRrju6nwOyePxeDxJmFj+KwCcwcxfAzAIwE+JaDsADOAKZt4x/HsIAIioP4Ch\nAPoD2B/AdUSrMmJcD2A4M/cD0I+I9nd8PHWhtbW1aBGM8HK6xcvplkaQsxFkTEui8mfmhcz8Yvj9\nYwCvAtgkXK3qXT4UwHhmXsHMcwDMAjCQiHoB6MrMU8PtbgdwWEb5C6FRGoSX0y1eTrc0gpyNIGNa\nrHz+RLQ5gB0BTAkXjSSi6UR0CxF1C5dtDGCetNs8BA+L6PL5qDxEPB6Px1NHjJU/Ea0N4G4Ap4dv\nANcD6AtgAID3AFyei4Qej8fjcY7RIC8iWh3A/wJ4iJmvUqzfHMBkZt6BiM4FAGa+JFz3MIDzAbwD\n4J/MvF24/CgAezPzKZGy/Agvj8fjscR2kFdibp+ws/YWADNlxU9EvZj5vfDn4QBmhN8nAbiTiK5A\n4NbpB2AqMzMRLSeigQCmAhgG4JqsB+DxeDwee0wSu+0O4BgALxHRtHDZaABHEdEABFE/swGcDADM\nPJOIJgCYCWAlgBFSvoYRAG4D0AXAg8z8sKsD8Xg8Ho85pcvt4/F4PJ78Kc0IXyLaPxwU9iYRnVO0\nPCp0A97KChF1DAfgTS5aFh1E1I2I7iaiV4loJhENKlqmKOGgxVfCAYp3EtEaRcsEAER0KxEtIqIZ\n0rL1iOgxInqDiB6VovAKQyPn78NrPp2I7iWidYuUMZSpRk5p3VlE1EZE6xUhW0QWpZxENDI8py8T\n0aVJ5ZRC+RNRRwDXIhgU1h+BS2m7YqVSohvwVlZOR+B+K/Pr3dUIXIDbAfg6gnEkpSEMZjgRwE7M\nvAOAjgB+WKRMEn9GcM/InAvgMWbeGsAT4e+iUcn5KICvMfM3ALwBYFTdpapFJSeIqA+A7yAIWikD\nNXIS0T4AhgD4OjNvD+CypEJKofwBfBPALGaew8wrAPwNwWCxUqEZ8LZxsVKpIaLeAA4EcDPUg/EK\nJ7T29mTmWwGAmVcy87KCxYqyHMFDf00iWg3AmgjGqBQOMz8NYGlk8RAA48Lv41CCgZQqOZn5MWZu\nC38+B6B33QWLoDmfAHAFgF/WWRwtGjlPBXBxqD/BzEuSyimL8t8EwLvSbzEwrLRIA96eK1YSLVcC\nOBtAW9KGBdIXwBIi+jMR/R8R3UREaxYtlAwzf4BgDMtcAAsAfMjMjxcrVSw9mHlR+H0RgB5FCmPI\nCQAeLFoIFUR0KIB5zPxS0bIk0A/AXkQ0hYhaiWiXpB3KovzL7JaoQTHgrVQQ0cEAFjPzNJTU6g9Z\nDcBOAK5j5p0AfIJyuClWQURbAvg5gM0RvOWtTUQ/KlQoQ8Iou1LfW0T0KwBfMvOdRcsSJTRERiMY\np7RqcUHiJLEagO7MPAiB0TchaYeyKP/5APpIv/ugOhVEaQgHvN0D4C/MPLFoeTR8C8AQIpoNYDyA\nfYno9oJlUjEPgVX1n/D33QgeBmViFwD/Yub3mXklgHsRnN+ysoiIegLBWBwAiwuWRwsRHY/ANVnW\nh+mWCB7608N7qTeAF4hoo0KlUjMPQdtEeD+1EdH6cTuURfk/jyDL5+ZE1AlBVtBJBctUg27AW9lg\n5tHM3IeZ+yLonPwHMx9btFxRmHkhgHeJaOtw0X4AXilQJBWvARhERF3C678fgk70sjIJwHHh9+MA\nlNJACTP6ng3gUGb+vGh5VDDzDGbuwcx9w3tpHoKO/zI+UCcC2BcAwvupEzO/H7dDKZR/aFH9DMAj\nCG6svzNzqaI+QsSAt32oMo9BI6SlLvOr/0gAfyWi6QiifS4qWJ4qmHk6ggy0zwMQft8/FSdRBSIa\nD+BfALYhoneJ6McALgHwHSJ6A4EyuKRIGQGlnCcA+AOAtQE8Ft5H1xUqJKrk3Fo6nzKluI80ct4K\nYIsw/HM8gERjzw/y8ng8niakFJa/x+PxeOqLV/4ej8fThHjl7/F4PE2IV/4ej8fThHjl7/F4PE2I\nV/4ej8fThHjl7/F4PE2IV/4ej8fThPw/8L/Hmfudym0AAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x1d128358>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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n0u2qZvCWcM6v5X/wwdCoUYXDkmCSunlHRKKvUye/aNvMmX67qhm8JZ5/3r/n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\nAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x1d668198>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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y2GMPexqhXls1J55Yrth6r+K8JpBt6g2zHEwrG5cK7MEHKxsfXS7mt2supSgj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\nF8T5PRFxUfJSNIiANdcEFi6sPm8ixSc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"text": [
"<matplotlib.figure.Figure at 0x1d5299e8>"
]
}
],
"prompt_number": 120
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Voss"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"import scipy.signal\n",
" \n",
"white_noise_sigma = 3 #mK * sqrt(s)\n",
" \n",
"SFREQ = 30 #Hz\n",
"N = SFREQ * 60 * 2\n",
"OCTAVES = int(ceil(log2(N)))\n",
"\n",
"print (\"{} octaves\".format(OCTAVES))\n",
"\n",
"wnss = []\n",
"pns = []\n",
"F_pns = []\n",
"F_wnss = []\n",
"\n",
"# Do the below a bunch of times to get representative sample distributions\n",
"for i in range(100):\n",
" wns = []\n",
" for octave in range(0,OCTAVES):\n",
" # Subsampled white noise\n",
" wn_sub = np.random.normal(0., 1, ceil(N / 2**octave))\n",
"\n",
" # Resample with zero-order hold (e.g. 2* resample of 1,2,3 is 1,1,2,2,3,3)\n",
" wn = np.zeros(N)\n",
" for j in range(0,2**octave):\n",
" idx = arange(j,N,2**octave)\n",
" wn[idx] = wn_sub[:len(idx)]\n",
"\n",
" wns.append(wn)\n",
"\n",
" # Average together white noises\n",
" pn = np.mean(wns, axis=0)\n",
"\n",
" # Calculate FFT for confirmation\n",
" f = np.fft.rfftfreq(N, d=1./SFREQ)\n",
" F_pn = np.fft.rfft(pn)\n",
" F_wns = [np.fft.rfft(wn) for wn in wns]\n",
" \n",
" wnss.append(wns)\n",
" pns.append(pn)\n",
" F_wnss.append(F_wns)\n",
" F_pns.append(F_pn)\n",
"\n",
"# Plot averages of above calculations\n",
"\n",
" \n",
"figure()\n",
"title(\"White noises\")\n",
"for octave in range(0,OCTAVES):\n",
" plot(arange(0, N), mean([wns[octave] for wns in wnss], axis=0))\n",
" \n",
"figure()\n",
"title(\"White noises (PSD)\")\n",
"for octave in range(0,OCTAVES):\n",
" if (octave == 3):\n",
" ylim(ylim())\n",
" plot(f, mean([f_to_psd(F_wns[octave]) for F_wns in F_wnss], axis=0))\n",
" \n",
"figure()\n",
"title(\"Pink noise\")\n",
"plot(arange(N), mean(pns, axis=0))\n",
"\n",
"figure()\n",
"title(\"Pink noise (PSD, log log)\")\n",
"gca().set_xscale(\"log\")\n",
"gca().set_yscale(\"log\")\n",
"plot(f[1:], mean(f_to_psd(F_pns), axis=0)[1:], label='pink noise')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"12 octaves\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 39,
"text": [
"[<matplotlib.lines.Line2D at 0x26f43908>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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G6Q11+7phpzKiPrYcLyeypRg9N4TvQA6Dq8DdPtHmfQZKqQ+UUrsqpXZWSt1p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\njprInvR86RVcLVBPIdk5Yq8kAXZz8cDcABduD1zMQHbfndNNsT1LFZG40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xTXU45fEcDc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\nRK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x2565f9e8>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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glKoD1opIyPZoAUwoqkoiokgk/Km060uyOgeBYjKoghtOGsLovfaqdz98WKFg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\noy0ip18/y00puIKi4qrXX0Ctdidq5A1ydmoAwcifoEk8nG0P89+EsP7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Hkp9jyMMBzP+o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\nBw6KcDgFBw4cOHBQhMMpOHDgwIGDIv4fzS8GeSe8kokAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x283e5278>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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okvLBB+7jqq2PPGIe9piXUMSJ9Vln2a/NyoY0XHFFdXi+fRRZTOrTCzBZL7Lk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\nY/G0DZlccAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x2702de80>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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pvCNSBGbMgD59EnfvVq+xW5/nnoMDD0xdm1fSo6mVRaQgrFkDF13kE/rKlfDy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\nRK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x288f6908>"
]
}
],
"prompt_number": 39
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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