{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": "true" }, "source": [ "

Table of Contents

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "
\n", "FFT(Fast Fourier Transformation)\n", "
\n", "
\n", "
\n", "file:/Users/bob/Github/TeamNishitani/jupyter_num_calc/fft\n", "
\n", "https://github.com/daddygongon/jupyter_num_calc/tree/master/notebooks_python\n", "
\n", "cc by Shigeto R. Nishitani 2017-19 \n", "
\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# FFTの応用\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Fast Fourier Transformation(FFT)高速フーリエ変換(あるいはデジタル(離散)フーリエ変換(DFT))は,周波数分解やフィルターを初め,画像処理などの多くの分野で使われている.基本となる考え方は,直交基底による関数の内挿法である.最初にその応用例を見た後,どのような理屈でFFTが動いているかを解説する.\n", "\n", "いくつかFFTを解説する面白い動画があります.ただ,少し高度かも...\n", "1. [初音ミクを三角関数で描いてみた](https://www.youtube.com/watch?v=Gxaigb7yMbo)\n", "1. [A visual introduction.\n", "](https://www.youtube.com/watch?v=spUNpyF58BY)\n", "1. [From heat flow to circle drawings](https://www.youtube.com/watch?v=r6sGWTCMz2k)\n", "\n", "[Pythonで美しい動画を作ろう](https://qiita.com/Kohki_Mametani/items/3c7a44e2445958a5cc25#fn1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 周波数分解 \n" ] }, { "attachments": { "C10_FFTplot2d1.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "\n", "はじめの例は,周波数分解.先ずは,非整合な波を二つ用意しておく.\n", "\n", "\n", "![C10_FFTplot2d1.png](attachment:C10_FFTplot2d1.png)\n", "これを重ねあわせた波を作る.\n", "\n", "\n", "\n", "ゆっくり変化する波に,激しく変化する波が重なっていることが読み取れる.これにFFTを掛ける\n", "その強さを求めて,周波数で表示すると,\n", "\n" ] }, { "attachments": { "C10_FFTplot2d2.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "![C10_FFTplot2d2.png](attachment:C10_FFTplot2d2.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "![C10_FFTplot2d3.png](figs/C10_FFTplot2d3.png)\n", "\n", "もとの2つの周波数に対応するところにピークができているのが確認できる.広がりは,誤差のせい.\n", "logplotでも良い.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## python code\n", "\n", "scipyにあるfft, ifftを使う." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/bob/opt/anaconda3/lib/python3.8/site-packages/scipy/__init__.py:146: UserWarning: A NumPy version >=1.16.5 and <1.23.0 is required for this version of SciPy (detected version 1.23.4\n", " warnings.warn(f\"A NumPy version >={np_minversion} and <{np_maxversion}\"\n" ] }, { "data": { "image/png": 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", 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", 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from scipy.fftpack import fft # 古いライブラリではscipyのみで, fftpack -> fftかも\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "\n", "def func(x):\n", " return np.sin(x/(13))+np.sin(x/(2/2))\n", "\n", "\n", "x = np.linspace(0, 256, 256) #0から2πまでの範囲を100分割したnumpy配列\n", "plt.plot(x, func(x), color = 'b')\n", "plt.plot(x, np.sin(x/(13)), color = 'r', linewidth=0.8)\n", "plt.plot(x, np.sin(x/(2/2)), color = 'r', linewidth=0.8)\n", "\n", "plt.grid()\n", "plt.show()\n", "\n", "yy = func(x)\n", "out = fft(yy)\n", "\n", "def spectrum_power(x):\n", " re, im = x.real, x.imag\n", " return np.sqrt(re**2+im**2)\n", "\n", "plt.plot(x,spectrum_power(out))\n", "plt.xlim(0,128)\n", "plt.show()\n", "\n", "plt.plot(x,spectrum_power(out))\n", "plt.xlim(0,128)\n", "plt.yscale('log')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 高周波フィルター \n", "\n", "次の例は,高周波フィルター.たとえば次のようなローレンツ関数を考える.\n", "$$\n", "{\\it f1}\\, := \\,t\\mapsto 10+ \\frac{40000}{380+ \\left( t-128 \\right) ^{2} }\n", "$$\n", "\n", "これに(測定機器などからの)白色ノイズ(y_noise)が載ると,計測結果は次のようになる." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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D4/FEfWw6kk31jbSuW7ZMBTATAFBTowFQIpnDh/fD7f40/gUMQkFBFYBiFBf3wOu1Xh02bdoHt/uA4zFybTOXZNQ3lmiZ8wF8qrVuAgCl1AsAzgRQppQa4bPeJwOoczpYa/0IgEcAoKqqSldXV0dVCLfbjWiPTUeyqb6R1nX1auuz1laGsDlzpqG6elocSxaaGTOoc3XixHw0N1vbx42bierqmY7HyLXNXJJR31h87gcALFFKFSqlFIDzAGwDsAbA1b59rgOwIrYiCkJ4dHU5u2CG0y3DjB1LS04DzIhbRhguohZ3rfUHoI7TjwFs9p3rEQA/AnCrUmoPgDEA/hiHcgpCSLq6KKGXPWd7MsWdUx8w0qEqDBcxDWLSWt8J4E7b5n0ATovlvIIQDV1d1ghRc2q74YyWYZws99JSsdyF4UPSDwgZQ1cXjUI10/ECqeOWqawUcReGDxF3IWNgy724mNY5W2MyxJ1F3XTLjBsn4i4MHyLuQsbQ2ekv7kuW0DIZbhl+sEzyjfJwuWiSD/G5C8OFiLuQMZiWu1LAqafS9mRY7osXA6tWARdeSOtFRVQusdyF4ULEXcgYTHGvrKRYcyA54q4UcO65VgdvURH9ibgLw4Wk/BUyBhb3a64hYf3sZ4HLLgNOPjl5ZRoxAsjNFctdGH5E3IWMgcX90kutbX/7W/LKw7hclriLz10YLsQtI2QMZpx7KlFQYIl7Xx/Q0pLsEgnZgIi7kDGkqriz5X7xxeSm+da3AK2TXSoh0xFxFzKCvj6azi4VxX38eMrzvnAh8POfA889R3OuCkIiEXEXMgL2ZQ/HPKmR8re/Ab/5DX3+/vdp9OpDDyW3TELmI+IuZAQchZKK4l5ZSXllACAvD7jxRhL82trklkvIbETchYyALXcenZrK3HgjTZ794ovJLomQyYi4C2lHczP52E1S2S1j57jjyIIPNZl2KPr6gG9/Gzh8OD7lEjILEXchrRgYAObMAR5+2H97Krtl7CgFTJgA1NfHdp7t24Hf/95/BipBYETchbSivR1obQX27vXfnk5uGYCiZw4diu0cPPG2/S1GEAARdyHNaG31XzLpZLkDZLnHKu49PbQUcRecEHEX0oq2NlraR3mmo+Ueq1tGxF0IRkzirpQqU0o9r5TaoZTarpQ6XSk1Win1hlJqt29ZHq/CCkKmWO4TJ9KDypwOMFJE3IVgxGq5/xbA37XWcwHMB7AdwG0AVmmtZwNY5VsXhLgQynJPF3GfMIGWsVjv7HPv7Y29PELmEbW4K6VKAXwWwB8BQGvdq7VuA7AUwBO+3Z4AcGVsRRQEC7bYWdzfew+45BISfaUoj0s6MHEiLdnvrjVQWxtZ4cVyF4IRS8rfGQCaADyulJoPYAOA7wKo1FqzPdIAoNLpYKXUcgDLAaCyshJutzuqQng8nqiPTUeyqb5Odd2wYQqA49DSMog1a9biqaem4e9/n4HOziYUFJTjrbfeTkpZI6W2tgjAqXjjja3o72/Cxo2luOWWxRgc/ABTp4bnq/nkk/EA5mLXrk/hdu9PaHnjTTa1YyBJ9dVaR/UHoApAP4DFvvXfAvi/ANps+7WGOteiRYt0tKxZsybqY9ORbKqvU11vv11rsnO19ni0/s536POiRVpXVg5/GaOluZnKff/9tP7YY7QeyeV96CE65qc/TUgRE0o2tWOtE1dfAOt1AF2NxedeC6BWa/2Bb/15AAsBHFZKTQAA37Ixht8QBD/Y5w6Qa6apiT7v358+kTIAMHo0jVJlt0xzMy0jmamJ3TLicxeciFrctdYNAA4qpY73bToPwDYAKwFc59t2HYAVMZVQEAzMKJnWVkvcm5vTpzMVGDpKNRpxl0FMQjBinWbv2wCeVkrlAdgH4AbQA+PPSqkbAewH8OUYf0MQjhHIcgfSy3IH/AcymeK+fz9QXg6UlAQ/XjpUhWDEJO5a640g37ud82I5ryAEoq2N8qE3NQ0V93Sy3AGKmNm+nT6b4j59Ov19+mnw40XchWDICFUhrWhtpayKQGaIeyC3TE1N6Kn4xOcuBEPEXUh5HnkE+MIX6HNbGzBzJn2uqfG3WtPRLcOjVFnceQmEttzF5y4EQ8RdSHlWrwZWrSJLtrUVmDyZJpretct/v3S03AGy3lnUzdmZLr4YWLQo8PHilhGCEWuHqiAknMOHga4uslR7e6mzcfRoYOdO+n7kSBK4dBN3TkFw4IAVBVRXZ32/ezctBwaA3Nyhx4u4C8EQy11IeRobgf5+y79eVkbizuI3axYt080tw5b71q2Wf53FfeFCaz/Om2NHfO5CMETchZSHp5HjsMHycnJXcEbFuXNpma6W++bN1jbuYL3/fuDBB+lzIHEXn7sQDBF3ISUxXQ5HjtBnFr6SEuDLxugJFvd0s9zHjCGX0qZNtJ6To9HfT59LSqyHVVeX8/HilhGCIeIupBz79wOlpcCGDeV+oY78uagIuPBCEsDCQmDqVGt7OsGjVFncx43zHvuutNSqTyi3jIi74ISIu5ByrFtHwvXOO2OOuWQAS9yLi4GCAuCaa4DjjycLGEg/cQfI787iPX68v7gXFtJn8bkL0SDiLqQc69fT8pNPyhzFnUX8gQfoQTB2LK2HGq6fipxwAi1zcvzF3XTLiM9diAYRdyHl2LCBlvv2FWPbNmu7abkDlFWxqAg4+2wa6HTOOcNbznjw0EPAK68AL7wAlJaSShcXU+ij+NyFWBBxFxLKwACwcmXoofTm/h9/DFT5Mhb97/9a39ktdyY3F/iXf6HOyXQjP59mklq6FHC5BgCQSwYYfp/7Cy8Mnb5QSF9E3IWE8re/kXB98kl4++/YQZbqN74BFBb24/33re8CiXumUFAwCMAS93B97vEQ9yNHgC9+EXj66djPJaQGIu5CQuGBRu3t4e3/8ce0PP104KKLGvy+a2oiV0w6WujhEMhyD+SWiecE2ZxKOZJ88kJqI+IuJBROftUd3rSg2LSJXBVz5gBXXlnn911TU+Za7UBy3TJHj9Iy3OskpD4i7kJCYXEPZH3a2bwZmDePEoNNndqNZcuAm26i73p702+gUiTYxT0/n6JohlPcvd7g+wnpg4i7kFCisdw/8xlr/ZlngHvusdazyXJXivzuTuKuteWOEctdcELEXUgYg4ORWe5HjlCKAVPcAfKz5/haajaJO0D1dfrfmX72ePjcxXLPPGIWd6VUrlLqH0qpl3zrM5RSHyil9iilnvPNrypkIfX1lvCEYxFyAi27uLMFC2SHW8YcjFVU5Gy5swgXFIjlLjgTD8v9uwC2G+t3A7hPaz0LQCuAG+PwG0IaYs4kFIu4A4DLRctstNydxJ397cXFlA453HEEgRDLPfOISdyVUpMBfB7Af/nWFYBzATzv2+UJAFfG8htC+mKKezhumd27yWrlVLgm2WC5V1Z68bOfWVMKAoF97izuo0bRkrNJRouIe+YR60xM9wP4IQBfE8MYAG1aa25qtQAmOR2olFoOYDkAVFZWwu12R1UAj8cT9bGpQlvbSHzve6fgrru2YPLk4CZuOtX3rbemApiJ3NxB7NxZC7d737HvtCZ3i8nWrSegpGQU3nrrQwD2up4KoAhHj9bD7d45HMUfdjo7Pfjc59zYvdsaH9DbOx/19Tlwu//ht29dnQvAYijlAVCMN99cC5drMOrf3r59FoDJOHSoFW53mCPOYiDSdvzUU1PR0FCAH/xgV+idU5Ck3Lda66j+AFwG4EHf52oALwGoALDH2GcKgC2hzrVo0SIdLWvWrIn62FTh3Xe1BrR+4YXQ+6ZTfX/4Q63z87UuL9f65put7fffT/Xt6fHf//zztT79dGvdrOuiRXSMeZ5Mw+naXn651qecMnTfzZvp/3HGGbRsbY3tt6+91jpfuKxerXVvb3S/F2k7Pv98rWfNiu63UoFE3bcA1usAuhqLW+ZMAFcopWoAPAtyx/wWQJlSit8IJgOocz5cYPhVmF+1M4XOTvIZFxb6u2V+/3tavvGG//7NzUBFhfO5ssEt40Q4Pncg9k7VSDtUd+wAzj0XuPnm2H43XFpagI6O4fmtTCFqcdda3661nqy1ng5gGYDVWuuvAlgD4GrfbtcBWBFzKTOcdBb33/4WWL7c+TuPh8TJ5fIXjdNPp+Wzz/rvH464Z3KHqhP2ByNj97nHS9zD9bmzj//ll2P73XARcY+cRMS5/wjArUqpPSAf/B8T8BsZRTqL+6pVlLLWic5OsiwLC/3FncMjX3zR2q51cHHPhmgZJ0zLvaHB+n/ZLfdYY91ZOMO13Fnc64bpvbylhR5yAwOh9/3Rj4DXX098mVKduIi71tqttb7M93mf1vo0rfUsrfWXtNZpKFnDS6TiPjhIFlOs4W+RsnEj8LWv+d9gbW2Bk4KxW8bl8rc+OTmVx0MPB4C+93rFLWPHFPeqKuA//5M+c5tJluU+nLM/9fdb5QuUioHRGrjvPkozne3ICFUbPT3DL5p2aywUa9cCl10Gv3S4w8GqVcBTT5GFzbS2kkg7WVSmuJsWYUcHsGQJCfVLL9E2Pqe4ZfwpKiLhPnqUrOR9voCjRPncoxH3RL9xcsZKILRrxuul/0U6vgXHGxF3g74+YPJk4H/+Z3h/N1LLnRv7kSMJKY4fd91lDS5iq8kUAC4Li4MJ+9ztbhmPh+Y9vfBCEnetrVztPGWenWy13LneNTW0bG4mgXv7bVoPJO4HDkT2O5F2qJrivmdPZL8VKeYEIqFSEvNbJLfRgwcp8Vw8RvG2tQG33BL67SFVEHE36Oykm2f//uH93UjFnW/ARHcw9fQAP/0p8Oc/0zq7VpzE/b33aCi8eaMHc8sUF9PbR10dTeQhlrszXF8eENbcDPziF5RMraICmDaNtptiu3UrbQ/X7zwwQNcqJ2fom6vWwO9+Zz18GbOt7kzwsANT3EO1eW6PXL5/+ifgwQeBf/wj4CFhc8stwP33p4/LR8TdIFlzUrJYhvtKzEKZaHHn8vDDxC7u/f2WJfXuu/T/27HDOj5Qh6rHQ75invP0ww9F3APhJO41NcDMmZS7h990zDbLc9C+8054v8HtiP/3Xi/w6qvApZfS737nO/7THQL+DxPzmvf0kKVcXx/eb4dDJOLOljvfy1u30jLPIcNVTw/w/e+TazEc3nyTluny9ijibsANdjg7i4DUtdxDibvZkcq+YNNVFMpynziR1hsaQos7R8uky40VL8rLacki1dxMwjl5MuW851mpTHHnScXDtVbZJVNZSUuvF/j730ngWbjtbjfzHjEjZjZvJks5niGSpvhG6pYJ1pfw0UfAvfcCa9aELkN/P1BbS5/TJbmaiDso+sTjiW9+7EgIV9zvvRf4zW+OHzbLnRtxIHE3O7r27qWlaWU5dahqbYl7Xh753lncc3P9k2aZZKvlPmMGLbnzvLOTrGnOvxNM3HnKwlCwAI4bR8vubkvItmyhpb2tmeJu+qBZiAOFSLrd/h3y4RCtW8bMt+Mk7uxqCkesP/zQ+hzuxDPJRsQdwPPPA5MmWQ0jVcV93Tpgw4byiC13rS3xjaZc3JiDibvdcu/rIwGwd6h2d9PDlC3w8ePJEm1uJqHPCdAiL7oI+Nd/BaZMibwe6QyLO1vuAHUSsrizu+Haa8knDADbfTla6+qG+soBuo6DRhoau7h7vZa48+8GEvfCQn9rmoXYSdzb24HzziO/dSRE06Ha0+Pf/+N0b/H/JhyxNiPTRNzTiP37qYE3NtJ6qrpluruB7u7ciMX9j38EZs0iv3g05bJb7lxOU9zZGuMbka05ttz7+uiGP3yYtrO4T5hgWe6BXDIAcNxxwMMPkysim3C5yH1lD8+1W+719eRm6O6mB+3ZZ9N2u2vG6wWmTgX++7+tbSyI7JYxLfdA4s5tYPRof8s9mLh/8gk9VHZFmPurpYXe6rgcg4PAbbdZEUQmpluGo7x43U4klrtZfxH3NIIbKl/AVLHc9+4Fjj/eCmvr6iJxj9Qtw6/p69ZFVi67qAez3Bm23PmG5w5VAFiwAPjBD6ztAFnuDQ0kTmw5Cv4cdxwtzbea8eNpyeIOUHvYtYvE7ytfoW0ffOB/rkOH6BqZwsiCPMmXv9XjoWsCWG0nkOVeXu5vTbNbhh8OJhs30pLf8sKltdXqn+nooLLffTeNubBjumXYpQQEF/dwxLq723rAdHVRJJL5NpWKiLhjqLiHa7l7veQuiDXMKpC433UX3awrfNl5uruBvr6cYzdTuOI+eTItIw3xDNWh6iTugSx3gG4m/l/Z3TI7dtCDTBjKzJm0nDXL2ma33AFqD+ySOeMM+nvmGeDHP6YxBQCJO+BvrfIDmcW9psZy2wR6S+R7JBLLncU9HBdhfz/w9NMUptnSQlFB7ALi3zDFmzHdMqZvP5hbJhzLvauLIrzy8ujzv/wL8JvfhD4umWTZS64zfOHZ9xiu5V5TQ0/wpUvJKo2WQOLOIW1s0bK4cqOMtEM10oEt4Yp7QYG1jYWCH0BFRf4PS37AmG6Znh76mzcvsvJlC2y5n3SS5dKw+9wBag/s9po0Cbj+ekrqxoK/d6+/uD/5JD1U+Rz8NsC55E06OsiCHhgg95kp7nxOwBLeI0eoTRQUWN/xg72tDejoCC49Tz9N5W9spHOOHk3i2tFh/YbpdmFMt0x3N80ZoHV8LHc2Urq6qA7xcM/8/OeUSO+CC2I/lx2x3BG9W4YbR6xDnZ3EXeuhI0NZZNkiCVfc+bhILfdQbpnWVnIV8Csz4Gy5s1sGsCxCzonCggKIuAeCxX3uXGuCk0CWO4tbaSkN4HG5rP//yy9bQuz10hvhY4/RNSsttR643BFp9m90dNCD4stfpnXTLeNkuQP+1ntvL7kx5syh9UOHXEHrzPV87z06Z3k5lc8U9127ht57plumq8sKJXUSd+5jC8dyZ3HnmbE8ntjve62B//gP4K23YjtPIDJO3OvrraHZ4RKtW4ZFNpqL/NRTwAsv0GcncTenqLOLe6SWO4vy3r3+URIm7747NEQtHMu9rIz+mGBuGRPTcmdOPDFERbIUdstMnEhilZdHlizgL+49PdQ2iopImEtKgIceonQaJ5xAqR54cBF1ztP+TU0UqcTXiS33k06yzt3RQW2Shb+3l3571KihPnfuGzDFfccOMpq++EVaP3TIMOkdYHHfsIHa7axZ1m9xG+vvH9o5a7plurqs/1OsHard3STshYV0nwwOxj4lIXcO8wMo3mScuN9zD/nBA4kY43ZbjSRatwyLYTQX+b77gD/8wf94U9zNBxQLZbRuGTMM8RvfGDpJxttvA2edRcPaTcIVd45NnziRytTb69yhamL63AE6j2nFCxbz55MoXnABuUTGj7fEzxR3gATVHCtw3XXkNrzsMmrzLIbd3VZI5K5dJILsQtmzh4R+7lzrPB0d1O4aGsji7Omhh0xREQkuR/O0tFh9A6a4cwcuux9CWe78wNi3j0T8vPOGumWAoX53u1uGhdNugJn5jMJxr3R1WZY7u75itdy589k0juJJxol7eztdiGB5pr1eamQPPEDrkVjuDz9Mr1JA+Jb7ihXA178+tAwsmk7ibkYb2C13fghFarkDwKOP0gTM7If1eoEbbqDGbg7UMH+PRcBeXru48yt3a2v4ljsL+rx5Q+dUFQiXi8ZizJlD/S+mG8w+rL621nkgWHU1GS38YGdxB6gtjB5tXafGRvLZc2jkyJHU1pqb6RytrXSP5OXRdRwctNpuSwvwmc/QZ/Me5P6eefOoDvX1wS13820gP586h023jMtFbyd2vzu7ZTg1xqhRFOViN8COHrWMuEjdMtGKu8fjXy8uq1juYcINNlimuuZmuvjsg47E5/7cc/TH5wFCW+6vvQY8/rj/EG7z5nIS97Y2sqQ4n3d//9ByhTt5QXc3RRtccQW9LRQUAP/2b/TdunX0v5o7l6IZnEb18Su8fXsgcT9yxL9DlUXDFB0W97IyumHEJRMe99zjPwjIbrkHEvfTTqOlaShw++vuJreM2fk5d67VkT9tGrU93r+hwV/cAet6t7YC06fTuVgEARL3/Hxqh1OnAk1N+UHraYrgmWdSGzLdMmPH0gAve+SNmRKjrY3altnhz5iDu8LtUGW3TLTifv31wD//s7XOlruIe5jwhXLq8WdYlNmysLtlglnuDQ3Wb4RrufMNZSZY8npDi3tZmSXugayLUCP2APqdigp6g/jWt8gFww+2d94hH+m3v0372csI0APEvGlMcS8tHSruLS3OHaqLF9NSKUvwlQL++lfgjjtC10Mgkeb/IzBU3BsanMW9osLy3QNDH9im5Q4AJ59sWe7coWv+Bos7p4PgNtrd7R/Zwhw4QKOLc3Lo+44OW8FtcLvOzSU3K+Dvlhk9mh4SZgTY4CDdw9xZ39ISnriHGwrJlnuk8y8w+/b561LKumWUUlOUUmuUUtuUUluVUt/1bR+tlHpDKbXbt0zQc8kZ/seHstwBy/URic/dFHduIKEsd26o7ArhcgZzy7C4FxfTjWO3LrjTKhzXDFsdTEWF9T949116jeYMjRx+yccxTjHDzc1kQTlZ7izubO0A1typxcX+LpgLL6QbVYgcHljDaB1YLMyHgmlcACSW+YYxffLJVuoDdrMwLO75+f6WO4sVi7tpeBw4YF1jEvfgoZAeDz1c1q8Hvvtd2ma6ZZzE3eMhgeeHUmsrCXJ+/lAh5nu3sjKyUEjzPopU3Nvb/RPrpbJbph/A97XW8wAsAXCTUmoegNsArNJazwawyrc+bITjluELa7fcQ7llenrogrBwRWq5m+IeynJvbaWLHshy51SvgcT9a18D/vQn+sxWB8Pi3t9POTPOOIOEuaiIbiazjIzZKL1esuabmujVfeFCisbgDji23F0uEp8pU6ifYvlyukGzLbNjopk7lwbVMIGSr5nibrplAHLLmA+Kk0+mB/6WLTRrlklDg3+HKkDX2y7udsvdFPejR4Nb7pwu+pRTrIcOPzCamy1xr6+33rT57ZLdSX19gS13vnenTIk8WoaJNJDi6FH6Xe58Tlm3jNa6Xmv9se9zB4DtACYBWArgCd9uTwC4MsYyhsW3v00TNYfrcwfon23Gq4bqUGVfW1eXNaEzEL64b9tGx/GgikjcMnbrghuwk7j39VH42/PP07qT5d7fT1Z7Rwf5NHNz6UYyR9uajde03L1eEvDBQSrHlVdS3aZMofKuXWvNwgSQlf7v/04dgRMmiLjHm+3baRQqE0jczzuPOiHnzx8q7hwyyMyeTdftxBMtNwcTyOfOUSwck86We18fxdezuFPKghHHItr6+mgQII/E5vPZ28mUKXTv7NljibvWlpHGv292OAcSd75vQlnuV15JE9aYbhkmEstda3r4mC7O1lb6H9v/v/EiLiNUlVLTASwA8AGASq01p+pvAFAZ4JjlAJYDQGVlJdxud1S/7fF4sGaNGw8++DkcPHgIzc1lAIqwa9cA1qxZ5xiBsX79dADTAQAvvPABjhw5EUAx2toGAOTi6NEuuN0fDjlux45RABYBAF5/fS0OHz4DwAjU1R2B2+0wXM5HQ8MiAKPw2msDcLmAu+/eBGABvF5g1aq30Nf3OeTkaPT1Kaxe7UZODlBffxpKSjrQ25uHQ4dysG7dbgBVx86Zl9cCYDTWrduIrq42v9+rry/A4OASfPxxN9zuD9DYWIXcXC/cbooba2qqBHACHn10P4Bp0PoDuN3dGD16DtzusViz5h0oBezbdzwACkR/771dAMjvUld3BC+9tBfAaWhq2gq323JgnnPOHDzzTCUWLmxFbm4x3O73/crmcp2C7u5cuN0bEAqPxxN1u0hHYqlve/sIAGcBAFpa9sHtdh6O/NJLOfjDH2bh00/Hor/fsp5razfB7W4BUA0AePttqxy7d5cAWAgAcLn6sXFjM9ra8uD1jsCOHbsAVOH99zf7xPoz2LdvPfr6ZuDIkZFwuz9GQ0MBtF6C7u4dcLsb0NIyGYODs/DKK+tQXDyAgwdd2LhxMZ577gBKSynxzMGD8zEwkAO327I2tC4GUIWBAcDj2Y/W1jYA87FixT9wyint2LChDMAp0LoWAOXcaGysQV/fGBw61HOs/QPA5s1TAczEwEA9jh4dA7fbOavemjVnoqHhKDo7y9HUVOuzuukp1dXVD7c7vEE1LS1dxzwCL7/8ASZN6sbWrbNQXFyJtWvDnFUlUrTWMf0BKAawAcAXfOtttu9bQ51j0aJFOlrWrFmjjx4le/jaa7WePp1tY63r6pyP+eY3rX3efFPruXOtdUDrqVOdj1u50v/c/Pn884OXcfZs//P/+tfW56YmWpaV0fLRR7V+5RWtx4yhcl5xhdbz52u9dq3/Ob7yFVr+9a/0G598ovVdd9HnVavoO6W07uyk37/mGqs8L71E319yCe3T00PbH3iAth86ROv8GwCdG9A6N1frc8/VevVqWl+zxr+uH39M23NytD7xxKH/i1Wr6PfDYY395BlOLPXt6bGu1e9+F3zf732PrrvZnt59l74DtLbfjps3W+2pqkrrCy7Q+pxztD7rLK23b6fv/ud/qO0CWn/6qdZXX033ldZav/UWbX/jDVp//HFa37eP1l9+mdZvuMH6zcWLtb7oIv9yeL1ajxxp3UM7d9LnJ5+k7599duj99ctfan366UPv0R//WOsRI+h/MWqU/3fd3VrffrvWR47QOZYsoeXPfqb1v/+7de68vOD/Z5O//OWdY8e99x5t++pXtZ45M/xzOAFgvQ6gqzFZ7kqpkQD+AuBprbVvvCUOK6UmaK3rlVITADTG8hvhwL6rjg56feJMg4cO+b+ieb3UYdjcbHWy1NUNfb0K5HO3h3aZ5w2Gx0OdUzzq1Cn/dWkpuWLuuINehdva6PWVffx2v6DdLTN/Pi1vvdUaMKI1zW/p5HMHyAVTWWnFSvPw/61byX3i5JYpL6ftPHTbnslxwQKKm6+rowFTds49d+g2IXby8uivtzd09IXLZfl9c3LIvTZmDK13dg5Nq8xugzFjKP593z4a/WrvUD14kM43aZJ/hyqHK3IufvYxt7bSfcEu1MOHgV/+klIDezxWIjMmP59Gzf7jH+SW4fPxvchtlBPlAf5umbvvBs4/H1i0yH/ydrtb5r33gP/8T6tfizNkmv83gP7XWoc3PsPjsTo0uP+qtTVxkTJAbNEyCsAfAWzXWt9rfLUSwHW+z9cBWGE/Nt6wuHs8dKG4l98UY4D80GedRYN1OK7aSdwD+dz5IgP+eVrC8blfcYV/UiXGFHeARHP7dvLNBfO5c0RAe7t/WNfRo/7pXLdtc/a5c33MyS/4f8KpTJ0yB44eTTcK/2+d0vQ+9hjF9l911dDvhMTBIhzI586YD3q+/uxzLywcOjCKz8ujY81oGbND9cABMqY4LQEbHn/5C23nkav8Wy++SP09mzbRemMjzVO6apWzzx0gYeZzuFwkwHZxN1NauFwk7l1dlAP+iSes8vIYjIEBf4OOo1h4UB+nbLD73AF6EN1999By2unqsp6YXE424BJFLNEyZwL4GoBzlVIbfX+XAvgVgAuUUrsBnO9bTyim5d7dTYMogKHizkmT9u+ngRllZRQOGa7lboo7NygWu0BobfX8803iJO4lJdb+3Jic4txzcsh0mDqVbq4DB4Bnn7XOd/QovSGMH08W2LZtgS13Pg9TWUn1YXH3eq0bjBsk17ex0YpZFlKDaMT9hhtI9NhyD3beigp6mDc3Uxswo2U8Hv+IGA5bbGig+VivvdaKxmFBe+YZ6tT/859p/fBhuh+PHCHhcxL3heT6P9bupk61DK0jR6x7hikspPuE3zTZEOKHB4u1aTxxhyeLO+uDPVoGoIi0226j/8ddd/lnyDTp7Bwq7hwRlyiidstord8GEOiF5LxozxsNLO6ckjSQ5W5GfFRU0GtffX10bhmOkeeUtYHo6aEycTKnvDx/ceeyO92QTpZ7WVkvWlryUVREg0v27LEsH4AaZk0NhTaWlZFQe73+jbKkhKyrvj5/y52jI0xxHz2abgQu85gxdKM0NpLVFGhaPGH4CVfczZGoVVXA5z8ffP+RI63RpaWlZIC0tFAIJruD2HI/9VSrLIOD9BY3MEA5bhgWZnbHsIV/+LD1AGhvdxb3q66iBwKL/MKFlISvqcmazcusH1vufO+yyJuWO0DGE//fWNztk4q4XENdMGyc7d1LUTWlpRS5Z8d0y5jinpJumVSCX6P4wo0ZQw3DLu6mqFZU0IXo6IjMLcMxt/yEHj8+uLibIzV5aT5k7G4ZE45zHxiw6lhWRk+ewkJ6zd29m8Sd31bYLTNjBoWzsVCb1ppSlvVun5N0yRK6eZYto7KzZWG6ZXp66H8tMyelFtFY7k55f5wYN46MIX7DbG623DdFRXQfHTxoWe5clrVrqY2ZScicrFWXi+470xXoJO7jx9MUgXz+W28lI+T++y1xNwdjsc+dDTa23Plt2szRzjhNQsNltFvufP/yMeZIbhMnyz2V3TIpg2m5A3QBKitDi3txsX8CIWZgwDmrZEODJaIs7uPGBXfL2MW9sDC4z93EfMXkRllaSoV1uUjcd+ygt4+zzrL2q6ujclZWWu4je6MMJO7/8R/AN79J+XO2bbOsrOZmstJLSiy3DPv9hdSAhTcScXfK2OnEq6/SWAX+DR7EBNB9tHcvibPplgFouz3bp8sF5OVRUiQ+B+e+MTHdK4GYO5cS4T34IN3vgcSdYQPQ7FAF/B8qgQTayS0TqbhPmmRNZOL1iriHhEWdKSykBhVM3MeOpQZopg816euj715/nda9XvJln3wyrdfXk9hVVDhb7tu30wOCIwa4sRcVRSfu/LQ3xX32bCvR15ln0nLHDnptnjKFxJffQuwWWiBxd7mAL32JPvf3W+Le3u4feXD4sFjuqQZbsyzAgYhG3E88ke4Z89ymuPNcq3bLvabG2QgoKaGGe8MNdN4rrxy6T7iD3T7/eRLXbduc3TKm2HMudie3DBNIoE3LnXP68L3MxwQ6tquL3DIzZ1IZEp1XBshQcXe5AlvuixdToznpJFqaQmvS10cZFC+6iHxvW7eSRc8ieugQNXSn0W/btlFY4Z13OrtlzJlrwvG5A2SR5+UBhYVk8bBbhuFysZ9w3Dj/myqQ5e6U08UMQTMtC1PcxS2TeowaZaW4DUY04s6Y4s6iWVRkvSFOm0ZLFub+fmdxHzWKjJRLL6W2VF09dJ9wxZ0Nrv7+0Jb7wADdc8E6VE23jN2Fxfvz/cPGGYu6mfmV6e2lEbnFxVaHNGtTsI7sWMmIOVSdLPfKSpq+av9++oe6XCTkl1xCcaw87DeQf62318qQuGKF1ag5+VVPD3WmFhTQZzPe9aWXaPmrX1mNwBR3EyfLvazMP/0AQA2isBBwuUjc2XIHqIHw5NIcUzx2rH+DdbLcR4xwvvHMUDKONujpsdLC0ghBEfdUY9kyS1yDYYpdLOJun3sVGGq5A4HEnSx3zjhp5o7n/OvhivuJJ1rx+nbL3S7uAD1MQlnuubnUzufMoXBHPhePARgzht7eQ7ll6uvJCCsuHovSUipfU5M1GQ93QCeCjLTcWdyPHCEL/Ve/oqd6WxtdFBbh4mL/QQkmfX1Wb/6KFXSBi4r8M+SVlpLwae3vt3/lFWoU+fnAb39r/RaXzcQu7jk51lvFiBHWcU1N3PNvWe6TJ9MNdvLJtCwosMS9oiK45X7zzRTz62TlsQUIWMm/ALKuzBvFngpWSC4XXEB+8VBE06HKOIn7Aw/QfTV5stWOwxV3TkPMRpA5SUi44l5QYBk3Y8b4x+nb3TIA3UuhQiH5fGZHsJPlzn1zgcT9rbfo3I2NBSgtJf1obqZJf6ZOtfrwEkFGiztAF/Gjj6x9zNegYI2nr48iUXJzaUKL1atpFGhBgSV2ZWWW2G3dSu6Y9nZ6Kn/xi9RweUBRuJZ7eTk1LLae7ZZ7UVH/sTrm5pLP8qtfpX1KSqxYfLu422/iefOAr3wlcP3ZNcMDQAByUZnizjeAkF7Eyy3DIjpjBrkZtm3zN5wYJ3EfP96LOXOssowcSf07kydb+4fTocqwa6aiggwk9ok7We4c/hzIcm9ro7eBc8+lzlqGJwzhUbgmgdwy7xopa0pKaILx3FzSi3POSezsYxkh7m1tQ60Rs0Ft2mR1SIYr7g0N9EC4/nqyoLdupayJSlk3BFvuAPCv/0ppdt1uep275BIrix0QWNw5Xp5fbceMoTeNV17x359zU1944WE89ZRV9ocfBm68kT7zjTdiBJXNdJtEehNz2gbzxjjnHP910+cvpA98r+TkDB2NGgrTIjePzc31/8787OS+u/HGfVi3zn/bySfTCNRILXc+FrAsam6nprjzvWQaXPy/OHjQEub2dnrQrFoFXH21JcCFhWTQrV5N6atNAlnupriXlpK79OKLad2pnyGeZIS4t7b6R32YlvuoURQayC4Wc3SmU0PlC8nx4VdcQREz06YBl19unR+gi8UNZ/9+ipDhOR0XLPAvkxkKyYwcacXbch6LMWOojCyc9tF2Y8b0HrPU7bD1X1FB9Sgvt3yEkb5+O4k7dyDb6ySkF9wWCgsjtxxHjLCue7AHQyi3jMs1OET033wTuPfe6MT9wgvJ6ue3yfx8euCMHGm1Wb6nOMeT6Za57TYykjg1L0excPgvlZmWn/vc0I5Qp2iZzk6aupLTevD9+c1v0m/zZOGJIu3FXWsSdzPqo7CQnuRLl9KQYIAsaiCw5c4XkBsuh3bNnk0Xs6bGeuJygygrsyz3piZ6tXvzTRL14mJ/cTdDIQEr/wZAr3h8HvtwflNAQwk014EfYDk5ltUUqeXOr50uFzVQnh6MbxR77LKQPpjiHg3czuy+bJO8PMs1Eu54iNxcarPRiHtVFVnfbCTl51v143KOHUv3F4u7ffL299+njtzeXv8Ah9JSf1ePeU6GRb2jw5rX+KOP6PMtt1jnASh0s719qGsn3qS9uPf05KC3119IXS5qGC++SL5vIHxx521bt9IFNeedZJwsd3a/rFtndcJwmXJy/MPGADqOG5Yp7naLgFMFcL2CYRd3wBL3WCz3+fMtq4fLGU5UhpCacJuNtE0w3M5CuXRGjSJLP9KBOpdcQr7uWGLAzfuL61teTvcDhwubI1QBcpGy8Ju/zZO4m285dj++GXXHY1t27aLlBRcA1dWNfhlRhyNtR1qL++Ag8OGHZOra03wyEyfSRf34Y1o3xdN8dbRb7jt3kjg7WSe8j2m5m2Wyi3tRkdUw+Fiz5z2YuBcUWBEQZg4ZJ0y3DMNWUDx87oDVcGXO0/QlXpZ7KHHnuO5IhezMMymTZKh4/WCYlju34bIyClQwfe45OfRWyuHLb71FS3tosv1BaL/vTXFnK55TIE+cCNx55zYsWxZ9faIhrcX98ceBO+88CWPHUp5mYGgnkVLWd4C/tR7McuehzE44daia2MXd/B2zwdnFfdo0Ky+7ye2306jRn/zEuTz2OvCrKWCJe6RWGlvm9tGO/PDhGemF9IPvkUSL+6hRyRsL4eSWKS/3H9XNhtasWVa8uZO4l5aGFnfT186fa2vpYWLPjz9cpPUgpquvBmpqtuGOO+Yde8o7ZW577DF63erv9/8umLh3dATO0WH63O2WLWCJO79NmH5z03I33TI5Of552E1yc620qMFmYXNyy/C8pqa/MByqqii+397pc+GF9BZ0yimRnU9ILZySYIVLuOI+c2bi5gcNRUGB9cZgWu6m4WPe/+PGkRCzuJtumerqoW/UdnF3Shl88ODQ9B7DSVqLe2kpcN55jcjPpymEAjXY4mLKzcwdHeZ2xu6W4fM7EchyLymhcCoW94ICakxO4m633OOBk1vm1lud83aEQimKFHJiwYLIzyekFqZxESnhivtzzyU2jjsY48dbFrrpczdnZrNHe82fT7nnAf97/9Zbh54/WN05pPLgQStEMxmktbjbMUOb7CgVePowYKjlDoQn7uZF/tKXaCSrOXx/yhT/myiQzz0eOLllRo+WCTWEocTDcg8WLcO/kSwee8wKcuD2P3GilbIDGBqNs3y5s7g7oZQ1raGd9nb67dra0LnyE0nGiXuoBmdin8CCz8EEusBmh6r5NnDrrdY8pMxdd/lbL6bP3XTLxAMnt4wgOHHeecAJJ0R3LN8XkQ6AGk5Mt8qMGfTmvmgRjTznPDR2y/2qq4CVK2k6TtNAC0RBgb+4c1K99nYKz+7qErdM3ODQq3DJzbUmyHVyywRKnWpa7qavzclCvuQS/3W75W7G9cYKz4wzZ058zidkLo8+Gv2x4bplUgnuMOXAhU8/dX5zufxya7BiKOyGZGUlDWZsbyeXDJBccU9YtIxS6mKl1E6l1B6l1G2J+h2TUaMiHzXJlnokljvvY/e5hxPPa/rcTziBrIl49aYvXEgPG4lBFxJJOoq7yezZlmEVC3ZxHz2aDMajR620ImaI9nCTEMtdKZUL4A8ALgBQC+AjpdRKrfW2RPwe8/OfR96BM2oUpQBl/3s44n7DDRQ+VVBgXWCn7HNOsLXgcgE/+hH9xZNYYoMFIRz4vojEBZpKnH66NQl9LHD9OUV3QQF9vu8+4Mkn6btMtNxPA7BHa71Pa90L4FkASxP0W8c491xKbhUJxcWWewYIL1pm2jTgn/+ZPnNPfLidlqblLgjpyKWXUnK7k05Kdkmi46c/Bdavj/089pQhBQWU4vu666ycUclM05Eon/skAAeN9VoAi80dlFLLASwHgMrKSriDBXAHwePxRH0sAAwMLMDIkcXYtWsbgM+grm4nAMo+VFPzCdzu1hDHKwCfQ16eB2536BZD022djZaWOrjduyMub6z1TSeyqa5AetV38WKa/Dpa0qmugejrWwRgFEaOPAqgBF1dRzBp0mb80z8BF188Au3tI7FuHeUSTkp9tdZx/wNwNYD/Mta/BuD3gfZftGiRjpY1a9ZEfazWWl90kdbl5Vq/+qrWgNZPPUVLQOv33w/vHLm5Wn/2s+Ht299P5/7+96Mrb6z1TSeyqa5aZ1d9M6Gup5+utcul9dln0z191VWB901UfQGs1wF0NVFumToAprdpsm9byjFqFL1esZskHJ+7nfz88JMj5eZSbzzPeSoIQnqSn09uVtaOVHO1Jsot8xGA2UqpGSBRXwYgyLw/yWPmTJrct6oK+D//Bzj7bOu7cMW9oCCyzHcrV0ZWRkEQUo+sFHetdb9S6mYArwHIBfCY1nprIn4rVu66i4Ypu1xW7K9S5JgJV9zvuIPCEAVByB6Ki/3DobNC3AFAa/0KgFcSdf54MXLk0KRaeXmW4IcDJ+MXBCF7+PnPKab9D3+g9VQLDU3rlL+JYuRIeiInK+mRIAipz7x5wJIlqeuWEXF3gMVdEAQhFCLuaURenoi7IAjhkao+dxF3B8RyFwQhXMRyTyPEchcEIVxSVdwzKuVvvLjiCuD445NdCkEQ0oFUdcuIuDtw333JLoEgCOlCqlru4pYRBEGIARZ1iXMXBEHIIMRyFwRByEBS1ecu4i4IghADYrkLgiBkINXVwL/9G7BgQbJL4o9EywiCIMRASQnw618nuxRDEctdEAQhAxFxFwRByEBE3AVBEDIQEXdBEIQMRMRdEAQhAxFxFwRByEBE3AVBEDIQEXdBEIQMRGmtk10GKKWaAOyP8vAKAM1xLE6qk031zaa6AtlV32yqK5C4+k7TWo91+iIlxD0WlFLrtdZVyS7HcJFN9c2mugLZVd9sqiuQnPqKW0YQBCEDEXEXBEHIQDJB3B9JdgGGmWyqbzbVFciu+mZTXYEk1Dftfe6CIAjCUDLBchcEQRBsiLgLgiBkIGkt7kqpi5VSO5VSe5RStyW7PPFGKVWjlNqslNqolFrv2zZaKfWGUmq3b1me7HJGi1LqMaVUo1Jqi7HNsX6KeMB3rTcppRYmr+SRE6CuP1NK1fmu70al1KXGd7f76rpTKXVRckodPUqpKUqpNUqpbUqprUqp7/q2Z9z1DVLX5F5frXVa/gHIBbAXwEwAeQA+ATAv2eWKcx1rAFTYtv0awG2+z7cBuDvZ5Yyhfp8FsBDAllD1A3ApgFcBKABLAHyQ7PLHoa4/A/ADh33n+dpzPoAZvnaem+w6RFjfCQAW+j6PArDLV6+Mu75B6prU65vOlvtpAPZorfdprXsBPAtgaZLLNBwsBfCE7/MTAK5MXlFiQ2u9FkCLbXOg+i0F8KQm3gdQppSaMCwFjQMB6hqIpQCe1Vr3aK0/BbAH1N7TBq11vdb6Y9/nDgDbAUxCBl7fIHUNxLBc33QW90kADhrrtQj+D01HNIDXlVIblFLLfdsqtdb1vs8NACqTU7SEEah+mXq9b/a5IR4zXGwZVVel1HQACwB8gAy/vra6Akm8vuks7tnAWVrrhQAuAXCTUuqz5pea3vEyNpY10+sH4CEAxwE4BUA9gHuSWpoEoJQqBvAXAN/TWh81v8u06+tQ16Re33QW9zoAU4z1yb5tGYPWus63bATwV9Cr22F+XfUtG5NXwoQQqH4Zd7211oe11gNa60EAj8J6Nc+IuiqlRoLE7mmt9Qu+zRl5fZ3qmuzrm87i/hGA2UqpGUqpPADLAKxMcpnihlKqSCk1ij8DuBDAFlAdr/Ptdh2AFckpYcIIVL+VAK71RVUsAdBuvN6nJTaf8lWg6wtQXZcppfKVUjMAzAbw4XCXLxaUUgrAHwFs11rfa3yVcdc3UF2Tfn2T3dMcYy/1paCe6b0AfpLs8sS5bjNBPeqfANjK9QMwBsAqALsBvAlgdLLLGkMdnwG9rvaB/I43BqofKIriD75rvRlAVbLLH4e6/revLpt8N/wEY/+f+Oq6E8AlyS5/FPU9C+Ry2QRgo+/v0ky8vkHqmtTrK+kHBEEQMpB0dssIgiAIARBxFwRByEBE3AVBEDIQEXdBEIQMRMRdEAQhAxFxFwRByEBE3AVBEDKQ/w+WfrtHyfjZZgAAAABJRU5ErkJggg==", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from scipy.fftpack import fft, ifft\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "def func(x):\n", " a,b,c,d=10, 40000, 380, 128\n", " return a+b/(c+(x-d)**2)\n", "\n", "xdata = np.linspace(0, 256, 256)\n", "y = func(xdata)\n", "y_noise = 10 * np.random.normal(size=xdata.size)\n", "ydata = y + y_noise\n", "plt.plot(xdata, ydata, 'b-', label='data')\n", "plt.grid()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "これに高周波フィルターを掛けるとノイズが消えるが,その様子を示そう.\n", "\n", "先ずは,FFTを掛ける.\n", "これは次のようなスペクトル強度分布(spectral power distribution)(log scaleで)をもっている." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "out = fft(ydata)\n", "\n", "def spectral_power(x):\n", " re, im = x.real, x.imag\n", " return np.sqrt(re**2+im**2)\n", "\n", "plt.plot(x,spectral_power(out))\n", "plt.xlim(0,128)\n", "plt.yscale('log')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "低周波の部分に,ゆっくりとした変化を表す成分が固まっている.次のような三角フィルターを用意する.これは,低周波ほど影響を大きくするフィルター." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def filter(x):\n", " return (1-x/20)*np.piecewise(x, [x < 20, x >= 20], [1, 0]) # triangle\n", "# return (1)*np.piecewise(x, [x < 20, x >= 20], [1, 0]) # rectangle\n", "\n", "plt.plot(x,filter(x))\n", "plt.xlim(0,128)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "これとデータを各点で掛けあわせる事(complex(filter(i)*y.real,filter(i)*y.imag))によって,フィルターを通した値(filtered_out)になる.\n", "先ほどと同様に強度分布を表示すると,低周波部分を残して,高周波部分が切られているのがわかる." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "filtered_out = np.ndarray(256, dtype=np.complex128)\n", "for i in range(0, 256):\n", " y = out[i]\n", " re, im = y.real, y.imag\n", " yy = complex(filter(i)*y.real,filter(i)*y.imag)\n", " filtered_out[i] = yy #.append(yy)\n", "\n", "plt.plot(x,spectral_power(filtered_out))\n", "plt.yscale('log')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "これを逆フーリエ変換(ifft)して,表示する.\n" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/bob/opt/anaconda3/lib/python3.8/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return np.asarray(x, float)\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "invd_data = ifft(filtered_out)\n", "plt.plot(x,invd_data)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "となる.ノイズが取り除かれているのが確認できる.元の関数に加えたホワイトノイズにFFTを掛ければ分かるが,全周波数域にわたって均質に広がった関数となる.これを三角フィルターなどで高周波成分をカットすることで,ノイズが取り除かれていくのが理解されよう." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# FFTの動作原理\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "このように便利なFFTであるが,どのような理屈で導かれるのか? Fourier変換法は,この課題だけでも何回ものコマ数が必要なほどの内容を含んでいる.ここでは,\n", "その基本となる考え方(のひとつ)だけを提示する.\n", "1. 関数の内挿で導入した基底関数を直交関数系でとる.ところが,展開係数を逆行列で求める手法では計算が破綻.\n", "1. 直交関係からの積分による係数決定.\n", "1. 選点直交性による計算の簡素化.\n", "1. 高速フーリエ変換アルゴリズムによる高速化.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 関数内挿としてのFourier関数系\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "一連の関数系による関数の内挿は,基底関数を$\\varphi_n(x)$として\n", "\n", "$$\n", "F(x) = \\sum^N_{n=1}a_n \\varphi_n(x)\n", "$$\n", "で得られることを見た.\n", "Fourier変換では基底関数として$\\varphi _{n} \\left( x \\right) =\\sin \\left( 2\\,\\pi {\\it nx} \\right) ,\\,\\cos \\left( 2\\,\\pi {\\it nx} \\right)$をとる.関数の内挿法で示したように,この$x_i$での値$f_i, i=1 \\cdots M$と,近似の次数($N$)とでつくる係数行列,\n", "\n", "$$\n", "A=\\left[ \\begin{array}{cccc}\n", "\\varphi_0(x_0)&\\varphi_1(x_0)& \\cdots &\\varphi_N(x_0) \\\\\n", "\\vdots & \\vdots & \\vdots & \\vdots \\\\\n", "\\varphi_0(x_M)&\\varphi_1(x_M)& \\cdots &\\varphi_N(x_M) \n", "\\end{array}\\right]\n", "$$\n", "を求めて,係数$a_i$とデータ点$f_i$をそれぞれベクトルと考えると,\n", "\n", "$$\n", "\\boldsymbol{A}.\\boldsymbol{a} = \\boldsymbol{f}\n", "$$\n", "から,通常の逆行列を求める手法で係数を決定することもできる.しかし,この強引な方法はデータ数,関数の次数が多い,フーリエ変換が対象としようとする問題では破綻する.もっといい方法が必要で,それが直交関数系では存在する.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 直交関係からの積分による係数決定\n", "\n", "\n", "関数の直交関係は,\n", "$$\n", "\\int _{a}^{b}\\varphi _{n} \\left( x \\right) \\varphi _{m} \\left( x \\right) {dx}=\n", "\\delta_{\\it mn}C_{n}= \\left\\{\\begin{array}{lr}\n", "C_m & at\\, n=m \\\\\n", "0 & at\\, n\\neq m\n", "\\end{array}\\right.\n", "$$\n", "である.定数$C_m$は,$\\sin,\\cos$の三角関数系では次の通り.\n" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "xdata = np.linspace(0, 2*np.pi, 256)\n", "\n", "plt.plot(xdata, np.sin(xdata), 'b-', label='data')\n", "plt.plot(xdata, np.sin(2*xdata), 'r-', label='data')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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eWPMdREdL2batlO7uUu7dq71MluCwJX3fvlJ6eUn58KHmQ1t1DqNGKTPVpUuay2MpickfHh4uq1evLr28vF78fyTA48ePpa+vr/T09JQBAQEaSZkwyc00dA3IE+N9btO2uGhPLLOQlPKa6fkCEASU00Am+3PpEmzdquwVGtQVqlHjU8LCtjNixHxat66b6P5eXl78+eefvPHGG3To0IG7d+9C585w+3ayLB8shAqeyZFDneaTJ3pLZGciImDpUtVCMmNGvaVRmJMlrVyNO5Jhw4axbds2Zs+eTY04E3BeJl26dKxcuZIiRYrQtm1b/vvvPwdI6TxooQj2AYWFEG8IIVKhLvavRP8IIYoBmYFdMbZlFkJ4mV5nA6oBJzSQyf4sXKieO3e2eagvv/yds2enUbVqf7755t0kH5cxY0aWLVvG3bt36dOnDzRqpCpTJtPkn0yZlMn8zBlVoC5Zs2mTCgfu1ElvSV5QoIBqjL14sd6SJMju3bsZO3Ys3bt3p2PHjkk+LlOmTKxYsYKIiAjat29PVFSUHaV0LmxWBFLKSKAPsB44CfwmpTwuhBghhIgZ+NweWGpanpgpDuwXQhwBAlE+AtdQBMuWqeYzefPaNMypU/f56afepElTkY0bR1l8fLly5Rg8eDDLli1j7aZNqgH5ypUuX4guPmrVUlUWfv0V1q3TWxo7smiR0nwa+wZspmNHVVPr2DG9JYmTiIgI/P39yZUrFxOsqJFUuHBhpkyZwq5du5gyZYodJHRS4rIXOftDdx/ByZPKVjppkk3DREdLmTdvdwnu8o8/DifpmLjkf/bsmSxWrJgsVKiQDN+8Wcm2dKlNstkTW7+Dp0+lLFlSyhw59AkptbttNzRUyrRppfzwQ7tNYfU53LypHDWDBmkqj6XEJ/+kSZMkIFesWGH12NHR0bJ+/foyXbp08sqVK1aPkxjJzUeQ8vj9d2W0bt3apmEGDtzKf//NombNz2nVqozV43h5efHDDz9w7tw5ph09Cq+/rjKNkyne3soyd/euKoWT7Fi3TpWafTfpZkKH4eMDdeqoMFIbIw61Jjg4mOHDh1OrVi2a21AKXgjBlClTiIqKom+y/IG9iqEIrOH336FaNciZ0+ohLl+OZPz4Xnh752fVqmE2i9SoUSNq1qzJiFGjCG3aFNauVReTZErZsqqT4pIl8NdfekujMcuXq6Ywvr56SxI3bdvCxYtw+LDekrzETz/9xL179xg/fjzCxgCOAgUKMGzYMFauXMnff/+tkYTOi6EILOX0adUqrG1bq4eQElq0mE909El+/PFH0qe3vWKpEIKRI0dy584dpnt4qLCaZG1EV+0YSpdW1T2Cg/WWRiPCwlRJiRYtwMNDb2niplkz1XPjzz/1luQ5wcHBTJw4kVatWvHWW29pMubnn39O4cKFGThwINHJPJPRUASW8vvv6tkGs9CSJWEcPvwtefJU5KOPWmokGFSrVo2aNWvy/YoVPMuWLVmbh0Alc8+apfoWDBigtzQasXGjcvTbaHa0K9mzq5roTqQIJk+eTHBwMEOGDNFsTE9PT0aMGMHRo0exNoHVVTAUgaWYzUK5cll1+P370LPn/4ArzJgxxuYlbGwGDhzIzZs3+a1UKXVnmcwL+lesCJ9/rnrzBAXpLY0G/PGHyhtwUHar1bRurSqSnjqltySEh4czefJkGjRoQLly2qYhtWvXjjJlyjB06FAiIiI0HduZMBSBJZw/r0LnbLhb69cvhJCQ0VSqVIv69V8tIWErderUoWjRoky+cQNCQlR11GTO8OGqFE+PHi6eaBYRoWpXNW2qX6XRpNKihXp2glXBihUruHnzpl0cu25ubowePZrz588za9Yszcd3FgxFYAlmr6SVEQkBAbBw4f+AO/z8s+U5A0lBCEGfPn3Yd/o0e9OnVxeWZE6aNKpvyvnzMGaM3tLYQFCQalDtzGYhM7lzQ+XKTqEIfvnlFwoWLEiDBg3sMn6jRo2oUqUK3333XbJdFRiKwBJWrYJSpVSGpYWEhUGvXmG4u0/A17cmVapUsYOAiq5du5I+fXomZ82qzEMpIEOyZk2V5P3998qf75KsWgWpU0P9+npLkjRatVLVbi9d0k2EQ4cOsWPHDnr37o2bm30uZ0IIBg0axH///ZdsfQWGIkgq9+/Dtm1Wd4maMAHOnVtEVNR1Bg60r2czffr0dO3alWVXr3L77l3Ys8eu8zkLP/ygVgcff+x0Ie6JI6Vacdatq5SBK9DSFOiwZo1uIvz666+kSZOGbt262XWeRo0aUbJkSb7//ntzscxkhaEIkso//6g7aysUwZUrMGJENOnSjadMmTLUq1fPDgK+TO/evQmPjGS2m5vqBp8C8PFRpqHNm12ubL4KSf7vP+UfcBUKF4YiRXRTBMHBwSxatIhOnTqROXNmu87l5uZG//79OXbsGP/8849d59IDQxEkldWrVcZuxYoWH/r55xAV9RchIafo37+/5pFCcVGsWDGqVavGgtSpkSlEEYDq2lmhgvqbu1Rugdn/1LixvnJYStOmEBioS22r5cuX8+zZM3r06OGQ+Tp06ECePHkYN26cQ+ZzJIYiSAphYWpF0LSpSqSxgA0bVDh/zpwTyJcvH+3atbOTkK/SuXNnToSGcvjkSeVJTQG4u8PUqaoa9zff6C2NBfz1l7rJyJFDb0kso0kT1S970yaHT71w4UIKFy5MRStuzqzB09OTzz//nK1bt7J//36HzOkoDEWQFLZsUXc8FpqFwsJULZy8eU9x6dIWevXqhYcDs0XbtWuHp6cnCyAZ1mGInwoVoFcvmDLFaYtkvsytW7B3r7qouhrVqqm8Bwebh27dukVQUBBdunRxyArbzPvvv0/atGn59ddfHTanIzAUQVJYu1ZVOrMwyWfCBFU7v3z56Xh4ePD+++/bScC4yZIlC40bN2aJhweRK1c6dG69GTEC0qdXJaud3re3dq0S0pX8A2Y8PaFBA/j7b4c2lA4ICACgk4P7NWTMmJEuXbqwdOlS7t2759C57YmhCJLCunXg52dRNMeVKzByJDRr9owtW+bRsmVLfHx87CdjPHTp0oWbkZEEbNuWbHsUxEW2bCrRbNMmF1gM/fWXissvW1ZvSayjaVO1qnGQuURKyYYNG6hWrRoFrAjltpXevXvz7NkzZs+e7fC57YWhCBLj4kUVmG5hssrAgSrIyM9vOffv36dnz552EjBhGjVqRKZ06VgYHa3CaVIQH30ExYsrx3FYmN7SxENEhNJWjRpp0vJUFxo0UL4zB2ncw4cPc/nyZTpr0B3QGkqVKoWvry9Tp05NNl3MNFEEQogGQojTQohzQoiv4/i8mxDijhDisOnRI8ZnXYUQZ02PrlrIoynmEg0WdIrau1c1mPriC1ixYjoFCxakZs2adhIwYby9vWnTrh0rgWcpoJxuTDw9lXnu/HmYNElvaeJh1y61UrNTVqxDyJoV3n7bYdVuly1bhru7O21tqABsK7179+bixYvJJpTUZkUghHAHfgUaAiWADkKIEnHsukxKWdb0mGk6NgswDKgMVAKGCSHsGxBsKf/8A2+8oWKmk4CU6g7UxwdatDjBtm3b8Pf3t1vWY1Jo3bYtIcCmVatcwGCuLfXrKx/syJFw86be0sTBunUq1KlWLb0lsY369VWW8d27dp1GSskff/xBuXLlyJo1q13nSogWLVqQM2fOZOM01uLqVAk4J6W8IKUMB5YCSS3GUx/YKKW8L6V8AGwEnOfWKDxcFQhq0CDJy/bly2HHDhg1ChYtmo6np6fdsx4To1atWmTw9ubP27fh7FldZdGDH3+EZ89g8GC9JYmD9euhalUVeePK1K+vbjLsHEZ6/Phxzp07R/Xq1e06T2J4enri7+/PunXrOHfunK6yaIEWsYy5gCsx3l9F3eHHprUQogZwBvhMSnklnmPjrO8shPAH/AF8fHwIsrLmcEhISJKPzXToEGVDQzmaKxf3knBMeLgbn3xSkQIFosiZcweffTaLd955hxMnTnDixAmr5I2NJfLHpEr58qzasYOTEydyS8clNVh/DrbQsmVB5szJTaVKByhaNMSmsbSS3/PBA6odPMiF7t35z8F/D82/g6goqmXIwN158zj9+uvajRuLefPmIYSgbNmyDv8NxaZUqVK4u7szcOBAevfubfHxevwfxEtcjYwteQBtgJkx3ncBJsfaJyvgZXrdE9hsev0lMCTGft8AXyY2p8Oa13/1lZSenlI+fpyk3ceOVX3jN26Uct68eRKQmzdvtk7QeLC24fUff/whARlQqZKm8liDHk27Hz6UMnt2KX19pYyOtm0szeRfsED9YPbt02Y8C7DLd9CunZQ5c9r+B06AMmXKyGrVqunyG4qLdu3aycyZM8unT59afGxya15/DcgT431u07aYyuaelNIctzETKJ/UY3Vl3TqoXh3SpUt019u3YfRoZY+uUwemTZtGkSJF8PPzs7+cSaB+/fqk9vDgzwMHlJ0khZExIwwbpnID167VWxoT69erOFeNWivqTv36cP06HD9ul+HPnz/PkSNHaNWqlV3Gt4aePXvy4MEDlrt4N0AtFME+oLAQ4g0hRCqgPfBScRshRMy8+WbASdPr9UA9IURmk5O4nmmb/ly7pgqBJTGaY+hQ1Qzshx/g2LFj7Ny5E39/f4dmPSZE2rRpaVCxIiuioojeskVvcXTB3x8KFVJtLXWP+ouOVvVH6tWzuGyJ02IupminZkgrVqwAoGVL7dq72oqfnx+FChVi+vTpeotiEzb/AqWUkUAf1AX8JPCblPK4EGKEEMJck+ETIcRxIcQR4BOgm+nY+8BIlDLZB4wwbdMfC8JGT55UjVE++giKFoXp06eTKlUqunZ1rmjYVt27cx3YN2+e3qLogqcnfPedumHV/U9w+LBaRrpK74GkkDs3lChhV0VQtmxZ3njjDbuMbw1ubm74+/uzbds2zfyAeqDJrYiUcq2UsoiUsqCUcrRp21Ap5WrT64FSypJSyjJSyppSylMxjp0tpSxkeszRQh5N+Ocf1Ze4ZMlEdx00CNKmVauCJ0+eMH/+fFq3bk22bNkcIGjSadSyJW7A3xs36i2KbrRurRprffONzm0tzRdLB5Qkdyj168PWrZr/ce/evcuuXbtoZmU/EHvSrVs3PD09XXpVkEzWpBoTFaXC4OrXTzRsdNcuWLkSvvpKmXt/++03goODdcskTogsWbJQJX9+1t69q2pgpECEgPHjlSn75591FGT9elVSwo4RNrpQv75K4962TdNhN2zYgJSSxk5Ypjt79uy0atWK+fPn8/TpU73FsQpDEcTFgQPw8GGid2tSKnuzj48qbgbKSVysWDFq1KhhfzmtoFGzZhwAbixbprcoulG9uiokO3Ys3LmjgwCPH6tkk+RkFjJTo4Yq0Kixeejvv/8me/bsVKhQQdNxtcLVncaGIogLc1JMItmea9eqG5+hQ1Vg0b///svu3budykkcm8amCqjrfvtNZ0n0ZexYCA1ViX8OZ/NmiIxMnoogdWqlDDRUBFFRUaxbt46GDRvqmqGfEH5+fhQuXJhp06bpLYpVOOdfVW8CAqBMGciePd5doqJUYblCheDDD9W26dOn4+Xl5XRO4pi8WaYMudKk4e8jRxxaNtjZKF4cevRQPQsc3rMnIEBdMKtWdfDEDqJePThxAq5e1WS4PXv2cP/+fRo1aqTJePZACIG/vz87duzguJ3CZ+2JoQhi8/SpWrYn0ntg0SIVXTpqlIpGCQ0NZcGCBbRt25YsWbI4SFjLEULQqGJFNoSHE3HokN7i6Mq336rv7ttvHTxxQICyT3l5OXhiB2E2qZp6BtjK2rVrcXd3d0ivb1vo1q0bqVKlckmnsaEIYrNjh3J2JaAIwsKUOah8eTBXa1i2bBmPHj3C39/fQYJaT6POnXkMbJ81S29RdCVHDtVBbtEiB3Yyu3FD3S1b2OTIpShZUq2mNVIEf//9N1WrVrV7g3pbyZYtm8s6jQ1FEJuAAPDwUHbOeJg6FS5fVnZms8ly2rRpFC9enHfeecdBglpPnfbt8QTW2ine25Xo3191Mhs61EETBgaq5+SsCNzclH9t82abq91ev36dw4cPO2W0UFz07NmThw8f8vvvv+stikUYiiA2mzap2urxlJV4/FiVkqhTRz1ANcrYu3cvPXv2dFoncUzSpUtH9Vy52HDpkmqMkoLJmtXcNwL27XPAhAEBkCmT63YjSyq1aqns/DNnbBpmoynnpb6LONZ9fX0pUqSIyzmNDUUQkwcPVOhoAndrkyapkuujR7/YNn36dLy9vXnvvfccIKQ21PH15d/oaG4ZqwI+/VQphCFD7DyRlEoR1KypehAkZ8z/QzZ2xdu0aRPZs2fnzTff1EAo+2N2Gu/cuZNjDrM32o6hCGISFKT+Wc23+rF4+FDVEmraFCpVUttCQkJYuHAh7dq1c3obZkzqmsJIA3SvtaA/GTKoCLANG1RROrtx8aKyKSZns5CZAgUgb16b/ARSSjZt2kSdOnWcNmw0Lrp27epyTmPX+es6gk2bVK0I81U+Fj/9pJTBiBEvti1dupTHjx87ZSZxQpSrWZPM7u5s2r5db1Gcgo8/hpw5VfMauzVxM18UU4IiEEKdZ2Cg1WHKx48f5+bNm9SJ58bMWcmWLRtt2rRh/vz5PNG1jknSMRRBTAICwNcXUqV65aO7d1X/27ZtXzbvTps2jVKlSlGlShXHyakB7u7u1CpQgE03byJDQ/UWR3dSp1b1h3bsUGWm7EJAgApVKlrUThM4GbVqwf37cOSIVYdvMiV2upoiAPD39yc4ONhlnMaGIjBz9SqcPh3v3dr336s6WsOHv9h28OBB9u/f79SZxAlRt0EDrgBnli7VWxSn4IMPVHvqIUPskGsXHa3s5bVrJ7ntqctjzsy30k+wceNGihQpQt68eTUUyjHUqFGDokWLuozT2FAEZhJYtt+8CZMnQ8eOKiPVzP/+9z9Sp05Nly5dHCSkttQxpURvMhQBoBaCw4fDoUPwxx8aD378uCpslBLMQmZy5oRixazyE4SHh7NlyxaXXA3AC6fxrl27OHr0qN7iJIqhCMwEBqryoaVLv/LRd9+pPvbDhr3Y9vDhQxYtWkSnTp3IlCmT4+TUkIKlS/OGtzcbHRI36Rp07KhK6g8dqnHzGvPFMJH6VcmOWrVUWWoLw5R3795NaGgodevWtZNg9qdr1654eXm5hNNYE0UghGgghDgthDgnhPg6js8/F0KcEEL8K4QIEELki/FZlBDisOmxOvaxDiMoSPkHYkUnXLkC//sfvP++qitkZu7cuTx58sSqptXORJ0SJQgMDiZSlzKczoe7O4wcCadOqYxjzQgIUD8gFzRz2ETt2qq63969Fh22adMm3NzcnKbVqzVkzZqVNm3asGDBAqd3GtusCIQQ7sCvQEOgBNBBCFEi1m6HgApSyjeB5cD3MT57KqUsa3ro03Xi0iUV1hfHj27UKBVFEjPGPDo6milTplClShXKunhiUN1mzXgE7JvjPD2B9KZlSxUQMHKkKhJqM5GR6q44JZmFzPj5KZ+IhX6CjRs3UqlSJZddbZsxO41/c/Jqv1qsCCoB56SUF6SU4cBSoHnMHaSUgVJKs0rcjWpS7zwEBalnX9+XNl+4ALNnq163+fK92B4QEMDZs2ddfjUAULN7dwSwadUqvUVxGoRQZsBz52DxYg0GPHwYHj1SiWQpjSxZoFw5i/wEwcHB7N2712X9AzGpXr06xYsXd3qnsYcGY+QCYra7ugpUTmD/7kDMAD1vIcR+IBIYK6VcGddBQgh/wB/Ax8eHIPPF20JCQkJeObbosmVky5CBHXfuvFAKwNixxXBzy46f3x6CgsKfbx8xYgSZMmUie/bsVsthLXHJbytvpk7NuoMHqe6gc7HHOWhNxoxQqFB5Bg1yJ1eufbi7v0gusFT+PMuWURDY6elJuJOctyO/g4IFC5Jr5Uq2b9hAdByh2bHZvn070dHRZM2aNV4ZXeE3ZKZWrVr8+uuvzJo1i4IFCz7f7lTnIKW06QG0AWbGeN8FmBzPvp1RKwKvGNtymZ4LAJeAgonNWb58eWktgYGBr27Mn1/KVq1e2nT2rJTu7lJ+9tnLu16+fFm6ubnJgQMHWi2DLcQpv40MqFZNeoB8fOWK5mPHhT3OwR6sXCklSDl37svbLZa/SRMpixTRTC4tcOh3sHq1+kMGBSVp9969e8s0adLIsLCwePdxld+QlFLeu3dPenl5yd69e7+0XY9zAPbLOK6pWpiGrgF5YrzPbdr2EkKIOsBgoJmUMiyGIrpmer4ABAHlNJAp6Vy+rHwEscxCY8aoWvX9+7+8uzkCwNUyiROiTsuWRALbZs7UWxSnolkzDXwFUVHKP+DCTk+bqV5d2duSWL9j8+bN1KhRg1RJWD24AlmyZKFt27YsWLCAUCdN3tRCEewDCgsh3hBCpALaAy9F/wghygHTUErgdoztmYUQXqbX2YBqwAkNZEo65h9njH/UCxdg/nzo2fPl3uLPnj1jxowZNGnShHwxnQYuTpVu3fAEtqxdq7coToUQqmnN+fOwcKGVgxw5ovwDsW40UhTmaqtJMIPcunWLkydPUjOZ+VP8/f159OgRS5Ys0VuUOLFZEUgpI4E+wHrgJPCblPK4EGKEEMIcBTQeSAf8HitMtDiwXwhxBAhE+QgcqwiCgpRDq1Sp55vGjFEtCWKvBhYuXMjt27f55JNPHCqivUmbNSuVMmQg6IRj//SuQLNmytc5apSVq4J4AhFSHL6+sGuX6uqUAFtMN2a+yezv9c4771CmTBl++uknop2wRawmeQRSyrVSyiJSyoJSytGmbUOllKtNr+tIKX1krDBRKeVOKWVpKWUZ07PjW2Zt2aKa0JjyBy5dgnnzVB/inDlf7BYdHc0PP/xAuXLlqJUMk4L8ypRhf2goj69cSXznFITNq4ItW1T+QK5cWovmWvj5wbNnieYTbNmyhXTp0vHWW285Ri4HIYTgq6++4uTJk6x1wpV3ys4s/u8/ZQeKYRb67julEwYMeHnXv/76i9OnT/PVV1+5ZF2hxPBr1owoYMfs2XqL4nQ0bQpvvaV8BRYlyBr+gRck0U8QFBREtWrV8PT0dJBgjqNdu3bkyZOH8ePH6y3KK6RsRRDLP/DffzBnDvToAbljZTqMHz+efPny0dbcpDiZYfYTBDnh3YremFcFFy5YuCo4elTVLU9mZg6ryJIF3nwzQT/B7du3OXHihEtnEyeEp6cnn332GVu3bmWvhZnW9sZQBJkzP68v9N13anPs1cDOnTvZsWMHn332GR4eWqReOB9ps2VTfoLjx/UWxSlp0uTFqiAyMokrQsM/8DK+vrBzpyrcFQdbt24FSLaKAKBHjx5kzJiR77//PvGdHUjKVgRBQc/9A1euwKxZqhRx7HIw3377LdmyZaN79+66iOko/N58U/kJrl7VWxSnw7wquHgRNmzwSdpBW7aoTl158iS+b0rA1xeePo23OfSWLVtImzYt5cuXd7BgjiN9+vT07duXP/74g/Pnz+stznNSriK4elV5AE13H+PGqc0DB76827Zt29i4cSMDBgwgXTwN7ZMLhp8gYZo0gfLlYeHCfIn7CqKjlX/AWA28oEYN9RyPnyA5+wdi8vnnn5MxY0bmzp2rtyjPSbmKwPxj9PXl2jWYMQO6dXu5ppCUkiFDhvD666/z8ccf6yKmI3nuJ/j7b71FcUrMq4IbN1Izf34iOx87prpzJWMzh8Vky6bCtONQBHfv3uXYsWPJLmw0LjJnzswXX3zB9u3bOXDggN7iAClZEQQFqUSXN99k3Dh1Axd7NRAQEMDWrVsZPHgwadKk0UNKh5I2e3bDT5AIjRtD0aKPGD06kQiiGDcaBjHw81P9QGP98VKCfyAm/fr1I0OGDHzzzTd6iwKkdEVQowbXb7kzfTq8955qU2gmOjqagQMHkidPHj40dfJKCTz3E1x7pUqIAWpV8N57l7l4MZEIoqAgyJ//5SWmgVKMoaEQ6054y5YtpE6dmgoVKugkmGPJkCED7du3559//nmeRKcnKVMRXLumagz7+jJ+vMoYHTz45V1mzZrF/v37+e677/Dy8tJHTh3wa9qUKGCn4SeIlypV7vHWWzB6dDzZxoZ/IH7MfoJYYaRm/0ByqS+UFFq2bEm+fPno06cPERZ2cNOalKkITBr4bik//vc/6NJFBXeYuXfvHl9//TU1atSgY8eOOgmpD1Xef9/wEySCEKqV5fnz8XQxO3EC7t41/ANx8dprqhdojLvg+/fvc/To0RThH4iJt7c3EydO5NixY0yePFlXWVKmIggKgowZGftPGcLDYdCglz8eNGgQwcHB/Prrr8kyizghnvsJjh3TWxSnplkzKFMmnhpEhn8gYfz8YPv253+4rVu3IqVMMf6BmDRr1oxGjRoxbNgwrl+/rpscKVMRbNlCWKXqTJnmTqdOULjwi4+2bdvGjBkz+OSTTygVoxBdSsKvdGn2hYYSouMP09kxrwrOnYNXCkoGBancgfz5dZDMBfD1hZAQOHgQeOEfqFixos6COR4hBJMmTSI8PJw+ffqYe7Q4nBSnCFLdvQtnzrAxwo+wsJd7EQcHB9OlSxcKFCjA8OHD9RNSZ4x8gqTRooVKSh81SpUVAlSD6y1bXvTqNXgV80rJ5CcICgqiSpUqKcoXF5OCBQsycuRIVqxYoVtuQYpTBJmOHAFg7C5fOnSAIkXU9ujoaLp168bVq1dZsGAB6dOn11FKfTHyCZKGm5taFZw5A0uXmjaePAl37hhmoYTw8YFixWDLFh48eMCRI0dSpFkoJp9//jl+fn706dOHf//91+Hzp0hF8CxVBvaElX0pUmjo0KGsXLmSH3/8kSpVqugnoBOQ9rXXqJQ+veEnSAKtWqkcqZEjTauCOBodGcSBry9s28a2oCCklCnOURwbd3d3lixZQqZMmWjevDk3btxw6PwpThGkP3iEwKjqtGnvQfHiatv333/P6NGj6dGjR7JrOmMtvqVLsy8khBAH/yBdDTc3+OYbOH0afv8dpQhy5Xo5DM3gVfz84PFjgpYvx9vbm0qVKuktke68/vrrrFy5kjt37lCvXj1u376d+EEaoYkiEEI0EEKcFkKcE0J8HcfnXkKIZabP9wgh8sf4bKBp+2khRH0t5ImXGzdIf+0/AqN8GTIEwsPD+fTTTxkwYADvvvsu//vf/1JclFB8PM8nmDNHb1GcnjZtVETkyBESGRRk+AeSgmkFsGXLFt5++228vb11Fsg5qFixIqtWreL8+fNUqVKF4w7K8rdZEQgh3IFfgYZACaCDEKJErN26Aw+klIWACcA407ElUD2OSwINgCmm8exCyFqVxu5WqwZXr66ncuXKTJw4kU8++YRFixbh7m63qV2Oqh98gAcQtGaN3qI4PeZVQeTJM4hbtwz/QFLIkYOHBQty6Nq1FO8fiE3t2rXZvHkzISEhlC9fnmHDhnH//n27zqnFiqAScE5KeUFKGQ4sBZrH2qc5MM/0ejlQW6hb7+bAUillmJTyInDONJ5d6D/0J+rgzux/W9KgQQPu3bvHihUrmDhxoqEEYpH2tdeomC4dWww/QaJcv36dW7d+IY33B3QGBu4/QEBAgFP2pnUmthcsiAR833lHb1GcjrfffpujR4/SrFkzRowYgY+PD28VeZNaqXOzc8lWzefTostKLiBmo9urQOX49pFSRgohgoGspu27Yx0bZ3NXIYQ/4A/g4+NDUAKdjuLj8qOHXPVIT+k3i/P22+/j6+tLqlSprBpLL0JCQhwmb9m8eZlx4gTrV6zAK3NmzcZ15DnYA7P8wcHBzJgxg3/++Yfo6GiyuKfiPu5cnTmLsdOnkTdvXnr37u2U9m9n+A7+CA7GC/A8dYogC2/EnEF+W0nKOXz88cfUr1+fgIAADq7cwZNn1zh38wLhQRrfZEgpbXoAbYCZMd53ASbH2ucYkDvG+/NANmAy0DnG9llAm8TmLF++vLSWTZsCrT7WGQgMDHTYXP+MHCkBuXHsWE3HdeQ52IPAwEC5a9cumTNnTunh4SH79esnz5w+LaNz5JBr0reXJUs+kQsWLJKFCxeWgPziiy9kRESE3mK/hDN8BxXKlJE1QMoff7T4WGeQ31YsOYczZ6RcR315I2tJm+YE9ss4rqlamIauATFbMOU2bYtzHyGEB5ARuJfEYzXFsAAlnWoffIA7EPTXX3qL4lTs3buXmjVr4u3tzb59+/j5558pLATixg2ytfbl+PHUpEnTkaNHj9KnTx9+/PFHOnTooHthMWciODiYg0eP4pc5c6IN7Q1g3KgIqrGd9E3t43/SQhHsAwoLId4QQqRCOX9Xx9pnNdDV9LoNsNmknVYD7U1RRW8AhQHn6uqcgkmfMyfl06Zly9GjeoviNOzYsYMhQ4ZQtGhRdu/eTdmyZdUHpiV++S/8KFwYRowAT08vfvnlF3744QeWL19Ot27ddCsh4Gzs2LGD6Oho/KpUUZVan6dmG8Tm4kU4sfAg6QglbSM/u8xhsyKQUkYCfYD1wEngNynlcSHECCFEM9Nus4CsQohzwOfA16ZjjwO/ASeAdUBvKaXxi3Ai/EqWZO+jRzy5e1dvUXTn0qVLNG/eHB8fHwICAsiePfuLD7dsAR8fPEoWZcgQOHIEVptuh7744gtGjx7N4sWLGTFihD7COxlBQUGkSpWKt1u3hocPwbjZiJfvvgM/EaTemMt4a4wmeQRSyrVSyiJSyoJSytGmbUOllKtNr59JKdtKKQtJKStJKS/EOHa06biiUsp/tJDHQDt8GzYkHNg9b16i+yZnoqKi6Ny5MxEREYwdO5asWbO++FBKtSIw5Q907AiFCqlVgXkBMHDgQLp27crw4cPZuHGjHqfgVGzZsoXKlSuTum5dtcHFHb/24r//YO5c6JRrCxQvrspz2IEUl1lsYBnvdO+OG7BldWxrX8pi3Lhx7NixgylTppArV6zAtgsXVLMjU/6Ah4dqdHToEJjdK0IIpkyZQokSJejSpYvd48KdmUePHnHgwAFVViJPHpWFbfgJ4mTcOHCXkRS/v92u+SmGIjBIkAx58vBWmjQEmYr1pUT279/PsGHDaN++fdyNisx3szESozp3Vte34cNfrArSpEnDwoULuXv3LgMGDLC73M7Kjh07iIqKombNmmqDn59SBEbexUtcuwYzZ8KQxodwC3lsKAIDffEtXpw9wcE8e/hQb1EcTlRUFD169OD1119nypQpcZcgCQpSnbeKFXu+ybwqOHgQYhZxLVu2LJ9//jkzZ8583rA9pREYGKj8A2+/rTb4+sKDB4afIBZjxyrd2KuE/RsdGYrAIFH8GjUiDNitU610PZk1axZHjhzhp59+InNcSXXm/gO+vq/UF+rSBd544+VVAcCwYcPInz8//v7+hIWF2fkMnI+goCAqV65MmjRp1AbzBc4wDz3n+nWYMQO6doWsR7eoevk5cthtPkMRGCTKO927I4Atq1bpLYpDefjwIYMHD6Z69eq0adMm7p0uXoQrV+IsO+3pqdqg7t8P/8QIg0ibNi1Tp07l9OnTTJo0yT7COynBwcEcOHDghVkIIF8+1c3NcBg/Z9w41clz0IAoFV5r53pMhiIwSJRM+fJRLnVqthw+rLcoDmXkyJHcu3ePiRMnxl+VNpH+xO+9p65zsVcFDRo0oEGDBnz33Xc8TEEmt+3bt6v8gdgXNj8/dcEz/ARcvw7TpqnfToHHR+DRI7sXMjQUgUGS8C1WjF0PHxL26JHeojiES5cu8csvv/DBBx9Qrly5+HcMCoJs2VQd6jhIlUqtCvbuhfXrX/5szJgxPHjwgB9++EE7wZ2coKAgvLy8Xm3+5OcH9+6Bg8ouOzPff69WA4MH82KVZCgCA2fAt359ngF758/XWxSHMGbMGIQQfPvttwnvGI9/ICbdukHevK+uCsqVK0f79u2ZMGECN2/e1ERuZycwMDDu/gOGnwCAGzfUaqBLFyhYEPX3KFRINTuyI4YiMEgS1U1+gqAVK/QWxe5cvnyZOXPm0KNHD3Lnzh3/jpcuweXLidpvU6WCgQNh926InUs2cuRIwsPDGT16tM1yOzsPHz7k0KFDcfcfyJ9f2dBSuJ9g/HiIiDCtBqKjYds2h/S3MBSBQZLIUqgQb3p7pwg/wZgxY3Bzc+Prr19ptvcyFizb338fcud+dVVQqFAhunXrxsyZM7l165b1QrsAZv/AS47imPj6qjvgFFqP6eZNmDoVOnVSiwD+/VeF1TqgcY+hCAySjF/Rouy8f5/wkBC9RbEb5tVA9+7dyZMnT8I7b9kCWbNCyZKJjuvlpVYFO3dCQMDLn3311VeEhYUxceJEGyR3fgIDA/Hy8qJy5djtSkz4+cHdu3DihEPlchbGj4fwcBgyxLQhkUAELTEUgUGS8a1Xj6fAvoUL9RbFbvz4448Aia8GQK0IfH1Vr8ok0L27MvXGXhUUKVKE1q1b8+uvvxIcHGyF1K5BUFAQVapUib8/cQr2E9y69WI1ULiwaWNQkEpPT+yGRAMMRWCQZKp/8AEAQX/+qbMk9uHBgwfMnj2bDh06kDdv3oR3vnxZ+QgsuFvz8oKvv4bt2yEw8OXPBgwYwKNHj5g2bZrlgrsADx484NChQ/GbhUBl3+XJkyL9BD/8AGFhMVYD0dEqnNZB/a8NRWCQZLIVK0ZpLy+2HDyotyh2Yfr06YSGhvLZZ58lvrP5rtVC+22PHpAzp1oVxKRChQrUqVOHCRMm8OzZM4vGdAW2bduGlDLhRvVCpEg/we3b8Ouv0KGDSiAGVBjt/fuGIjBwTvyKFGHHvXuEh4bqLYqmhIeHM2nSJGrVqvWi2UxCbNkCWbJAqVIWzePtDQMGqJu92De+/fv35+bNm/z2228WjekKBAUF4e3tHb9/wIyfn7oynjrlELmcgVdWA+Cw/AEzhiIwsIha9evzBNi9YIHeomjK77//zvXr1/niiy+SdkBQkGoSkkT/QEw+/BBef/3VVUGdOnUoXrw4kyZNSnadzAIDA6latSpeXl4J72heMaQQ89CdO2o10L79SzUL1Y2GufSGA7BJEQghsgghNgohzpqeX6nKJYQoK4TYJYQ4LoT4VwjxbozP5gohLgohDpseZW2Rx8D++H34IW5AwPLleouiKRMmTKBYsWI0aNAg0X29bt9WPQisDOtLnVqtCoKC1MrAjBCCvn37cuDAAXbt2mXV2M7I/fv3OXLkSMJmITMFCiiPegpxGP/4Izx9Gms1YC5k6ICwUTO2rgi+BgKklIWBANP72DwB3pNSlgQaAD8LITLF+PwrKWVZ0+OwjfIY2JlMRYpQwdubTQcO6C2KZhw4cIADBw7Qu3dv3JJwh5/J3JvBhmV7z56q2VTszpVdunQhY8aMyaoYndk/kKCj2IwQ6gIYFJTs/QTBwZ5Mngzvvquajz3nxAkVRusgsxDYrgiaA+YehvOAFrF3kFKekVKeNb2+DtwGssfez8B1qF28OHsePuRRMumyNX36dFKnTk3nzp2TtH+mw4chc2Z4802r50ydGvr3VzkFO3a82J4uXTq6d+/O8uXLuXbtmtXjOxOBgYGkTp2aihUrJu0AX18VT3nmjH0F05klS/Lw5Al8802sDxzsHwDwsPF4HynlDdPrm0CCDTWFEJWAVMD5GJtHCyGGYlpRSCnjLNAuhPAH/AF8fHwIstKGGBISYvWxzoAzyF+oZEmiDh1i9pAhlG3XzuLjneEczDx58oQFCxbg6+vL4SRmTVc8dIi7xYtzzMbGMiVKuJE589t8+mkI48f/+3x7+fLliY6OZuDAgXxgCtnVGkd+B6tXr6ZEiRJJNnelTp2aysDpadO40axZnPs402/IGu7fT8WKFZWpU+cmt2+f4vbtF5+VXLaMdK+/zp7//lNNix2BlDLBB7AJOBbHoznwMNa+DxIYJwdwGng71jYBeKFWFEMTk0dKSfny5aW1BAYGWn2sM+AM8j+9dEl6g/y0WjWrjneGczAzbdo0Cchdu3Yl7YArV6QEKX/8UZP5x49Xw+3c+fL2hg0bypw5c8qIiAhN5omNo76D69evS0COGzcu6QdFR0uZI4eUHTrEu4sz/Yas4ZNPpHRzi5Znz8b6IDJSysyZpfzgA7vMC+yXcVxTEzUNSSnrSClLxfFYBdwSQuQAMD3fjmsMIUQG4G9gsJRyd4yxb5jkCwPmAJUsUWIG+uCdLx/vpE3LpmRQd2j69OmULl068bBGM5s3q+fatTWZ/6OPIHv2VyOIevbsyfXr11mzZo0m8+jFRlOVvXr16iX9ILOfIDAwWfoJrlyB//0PGjS4qWoKxeTIEVVfqFYth8pkq49gNdDV9Lor8EoLKyFEKmAFMF9KuTzWZ2YlIlD+hWM2ymPgIGqXKcOx0FBuXr6styhWY3YS+/v7x994JjYBAYRnzAilS2siQ9q08OWXqlfBnj0vtjdu3JhcuXK5fKbxxo0byZ49O29a6k+pWVNVYUuG+QSjRyv91qXLpVc/NN9oJMWxriG2KoKxQF0hxFmgjuk9QogKQoiZpn3aATWAbnGEiS4SQhwFjgLZgFE2ymPgIOq0agXA5pkzE9nTeZkxYwbe3t5JdhIjJQQE8LBsWavyB+Lj449Vb5uYrQ88PDzo3r0769ev59KlS5rN5UiklGzcuJE6deokKRrrJcwrrtgV+lycCxdg1izw94fXX4/DHbp5swohypnToXLZ9GuWUt6TUtaWUhY2mZDum7bvl1L2ML1eKKX0lC9CRJ+HiUopa0kpS5tMTZ2llMm3rGUyo1y3bmQCAlzUdBESEsKiRYt49913yZQpU9IOOnsWrl3jwVtvaSpLunTw1Vewbt3LEUTdu3dHCMFMF1W2R48e5datW5aZhcwUKKCSqZKZIhgxAjw8VNe6V4iIUIklDjYLgZFZbGAl7lmzUitzZjadPOmSWbBLly4lJCSEnj17Jv0g00XpocaKAKBPH5VtPHDgC7N43rx5adiwIbNmzSIiIkLzOe3Nhg0bAKhbt651A9SurUIpo6K0E0pHTp2CBQvUCjDOG/59+yA01FAEBq5F7YoV+S8sjPP//pv4zk7G9OnTKVWqFG+//XbSDwoIgDx5eGqHtoFp0qh48m3bXu5t3LNnT27evMlff/2l+Zz2ZuPGjRQvXpxc1v69ateGhw8hmRQ5HD78RVZ5nAQEvCi852AMRWBgNXU6dABg04wZOktiGYcOHWLfvn2WOYmjo1UUS+3aCfYntoUePVQl5kGD1HQADRs2JHfu3C7nNH727Blbt261zixkxnxnnAzMQ//+C0uXQr9+8Npr8ey0eTOULauaHTkYQxEYWE3htm3JC6yPeQvrAkyfPt0yJzGosL779zULG42LVKmUDfnQITCXcvLw8KBHjx5s2LCBCxcu2G1urdm+fTvPnj2z3iwEqgZHqVLJQhEMGwYZMkC8NQ2fPlXt63QwC4GhCAxsQKRNS4McOdh04QLh4eF6i5MkzE7idu3akTnzKzUS48d8MbLzP2qHDqrz5TffQGSk2vbBBx/g5ubGrFmz7Dq3lmzcuBFPT098bTVz1K6tOvm4cI+G/fth5UqlBLJkiWennTtVn0pDERi4Ig39/AiJjmbH2rV6i5Ikli1bxuPHjy1zEoNSBMWK2T2sz91dxZmfOQPzTFW88uTJQ6NGjZgzZ47LOI03bNhA1apVSZcunW0D1a6tlICLVmOVUvkEsmWDTz9NYMfNm1U4UfXqjhLtJQxFYGATtd9/H0/gn7lz9RYlSUyfPp2SJUtSpUqVpB8UHq68uHY0C8WkWTOoXFnlFZhvhD/88ENu3LjB33//7RAZbOH27dscPnzYNrOQGV9fpR1d1Dy0caO6xg8ZokxD8bJ5M1SqBOnTO0y2mBiKwMAm0vv5Ud3dnX+2bdNblEQ5fPgwe/futcxJDLB3r0PD+oSAMWPg6lVVigCgUaNG5MyZk+nTpztEBlswh43a5Cg2kyEDVKzokoogOlr1qM6fH3r1SmDHhw/Vb0wnsxAYisDAVjw9aVi4MMfu3+fKlSt6S5MgFmcSmzGH9TmwUUitWlCnjjITPX6snMYffPAB69at4z9HVaS0kjVr1uDj40P58uW1GbB2bRVj/+iRNuM5iGXLlON/5EhIsDFbQIDSGvXrO0y22BiKwMBmGrZoAcC6hQv1FSQBQkNDWbhwIW3btiVLvB67eNi0Cd56KwFPn30YPVr1J5kwQb3v3r07gFM7jSMiIli3bh2NGze2vKxEfNSurZLKXKhrWXi4Mge9+SZ07JjIzhs2KJNQUgsf2gFDERjYTImuXckD/OPETdeXLVvGo0ePLHcSBwcrR6UOd2uVKkHLlqq5+e3bkD9/furXr8/s2bOJNIcUORk7duwgODiYJk2aaDdolSoqE8tUydQVmDFD1RX67rtEylJJqTIIa9cGT0+HyRcbQxEY2IwoWpRG6dKx8dgxwsLi7CukO9OnT6dEiRJUrVrVsgMDAtTdqE7L9u++gydPXpSp/vDDD7l69Srr1q3TRZ7EWLNmDalSpaJOnTraDertrcxyLpKvEhKi8kF8faFhw0R2PnsWLl8GLfwpNmAoAgPbEYJm1aoREhlJoBPetR05coQ9e/ZY7iQGdfFJn17dlepA0aKqv/G0aapWTdOmTfHx8WGGk2Zzr1mzBj8/P9JrHf3SoIGKqXWBpLqfflIruLFjk5CEbnKsG4rAIFlQq2tX0gErnbBS5owZM/Dy8qJLly6WHSilKgmq87J92DBVi+jrr8HT05P333+fNWvWOF1P47Nnz3L69GltzUJmGjRQz06+Krh1C8aPh1atIEllrNavh4IF1UNHDEVgoAneDRvSEFgVEEC0uVCOE2DuSWyVk/j0adUzVsdoDlC1ab7+GlatUlWKe/ToQXR0NLNnz9ZVrtiYcxzsoggKF1ZxmE5qEjMzdKjK/RgzJvF9RUSEql+l82oAbFQEQogsQoiNQoizpuc4c/aFEFExmtKsjrH9DSHEHiHEOSHEMlM3MwNXJFMmmhcqxM2QEPbt26e3NM8xO4n9/f0tP9h896mzIgCVlZo7t+pm9sYbBalduzazZs0iyolKNK9atYqSJUvyxhtvaD+4EGpVsHmzCslxQo4ehZkzoXdvZdJLjAzHj6v8FFdXBMDXQICUsjAQYHofF09jNKVpFmP7OGCClLIQ8ADobqM8BjrSqHVrPICVS5boLcpzpkyZQsmSJXnnnXcsP3j9eihSRJUE1Zk0aWDUKBVOv2wZ+Pv7c/ny5ec9gfXm1q1bbN26ldatW9tvkgYNlCd25077zWElUsLnn0PGjGpVkBSy7NunsqZ1TCQzY6siaA6YKqIwD9V3OEmY+hTXAsx9jC063sD5yNyiBX7Ayt9/11sUAPbt28f+/fv56KOPLHcSP3ummqI4wWrATOfOqkrxwIHQoEELsmfP7jRO45UrVxIdHU2bNm3sN0mtWqoejxOah9auVekmw4YlPd0ky/79KgghwdoTjsHDxuN9pJQ3TK9vAj7x7OcthNgPRAJjpZQrgazAQymlOSD6KhBvBwshhD/gD+Dj40NQUJBVAoeEhFh9rDPg1PJHRdE0VSr6Xb/O/PnzyZs3b5y7Oeocxo0bh7e3N/nz57d4vsz791Pm6VP+zZmT+7GO1fM76Nw5M19+WYb+/a9Qq1Ytli9fzh9//EFWC2vYa30OM2bMIE+ePNy9e9euf5uyJUvisXw5Ie+84zT/B5GRgo8/rkDu3IISJfYRFJR4xz7Phw+pevYsF6tV47IznIeUMsEHsAk4FsejOepCHnPfB/GMkcv0XAC4BBRENas/F2OfPMCxxOSRUlK+fHlpLYGBgVYf6ww4u/xXGzeWAuTIESPi3ccR53Dv3j3p7e0te/XqZd0AX3whZapUUoaEvPKR3t9Bo0ZSpk8v5fbtpyUgx4wZY/EYWp7DnTt3pLu7uxw0aJBmY8bLd99JCXLH8uX2nyuJTJ4sJUi5apUFBy1erA7as8ducsUFsF/GcU1N1DQkVVP6UnE8VgG3hBA5AEzPt+MZ45rp+QIQBJQD7gGZhBDmVUluwLni4QwsJleLFlQHFs+dq2sv43nz5vHs2TM++ugj6wZYt06VBE6bVlvBNGDCBGW5mjWrCL6+vsycOVPXSK1Vq1YRFRVlX7OQGVMYaWYnCUh48ECZg2rWhKZNLThw7VoiMmQAreox2YitPoLVQFfT667Aqtg7CCEyCyG8TK+zAdWAEybtFAi0Seh4AxejQQM6ACcvXOBfnXoZR0dHM3XqVKpVq8abb75p+QBXr8Lx407lH4hJkSLw2WcwZw7Uru3PhQsXdHUa//777xQsWJCyZcvaf7IyZeD115Wj1QkYNUo1rvvpJws6mEZFwT//cK9yZeUsdgJsVQRjgbpCiLNAHdN7hBAVhBDmzKLiwH4hxBHUhX+slPKE6bMBwOdCiHMon4HzVtMySBq5c9OmZEk8hGDx4sW6iLB582bOnj1r/Wrgn3/UszmJyQkZMgRefx1Wr26Nj48PkyZN0kWOu3fvEhAQQOvWrS13yFuDEFC/vnK06hw6e+IETJoEH3ygnPhJZs8euHePe0nKOHMMNikCKeU9KWVtKWVhkwnpvmn7fillD9PrnVLK0lLKMqbnWTGOvyClrCSlLCSlbCuldM5CNQYWka1lS+pJydLFi3UxWUyZMoVs2bJZb6r46y/Il0/1y3VS0qeH77+H/fu9ePvtj1i7di1nzpxxuBxLliwhMjKSTp06OW7SBg3wfPRIXVB1Qkro2xfSpVP1oCzi77/B3Z0HlSrZRTZrMDKLDbSnSRM6AP9dvcpOB8d8X7p0iVWrVtGjRw+8EiwCHw9Pn6o4wKZNLVjr60OnTir6cMeOXqRKlYpffvnF4TLMnTuXt956yzoTnLU0aEC0u7tS2Drx228qt23MGMie3cKD16yBd94h0tY2nhpiKAID7alYkebZspHa3Z1FixY5dOqff/4ZNzc3+vTpY90AAQFKGVjk+dMHNzdlmrh3z4dChdozd+5cgoODHTb/v//+y8GDB+natWviO2tJpkwEv/kmrF6d+L524PFjlTz21ltgccL6lSvw779gjzIcNmAoAgPtcXMjfdOmtHRzY8mSJYSGhjpk2gcPHjBz5kw6duxIrlzxpqQkzF9/qfW+r6+2wtmJChWge3c4ffoTQkJCHNq0Zt68eXh6etIx0c4r2nO3alVlpD9/3uFzjxwJ16/Dr79a4es195xu3FhzuWzBUAQG9qFJE3pFRBAcHMyyZcscMuW0adMIDQ3liy++sG4AKdWyvX79RHoLOhejR0P69OXJmLEGEyZMINwBtXgiIiJYtGgRTZo0IVu2bHafLzb3zH0lHGweOnFChe92757E6qKxWbMGChSAYsU0l80WDEVgYB/q1uUdT09KZM3K/8wd2O1IeHg4kyZNom7dutbbqw8eVLd6LmAWislrr8G4cRAcPIirV6+y0AEtQ9etW8etW7fo1q2b3eeKi2c5c0LJkg5VBFJCnz7KUW+xgxhUnaRNm5RZyMn8T4YiMLAP6dMjatWipxDs27ePgwcP2nW6BQsWcOPGDetXA6AuKkJAo0baCeYgevSAKlXq4e7+FqNHj7V7VdJffvmFHDly0DDRFlx2pGlTVZf74UOHTLdsmaoaPXq0FQ5iUEmKYWGqWYGTYSgCA/vRqhVd7t4ltbc306ZNs9s04eHhjBw5kooVK1LPlpK+K1ZA1apW/pfri5sbTJsmkHIQFy6c5Y8//rDbXMeOHWPjxo306dMHTx0b9tCsGURGvsj7sCP370O/fsonY01Fc0D9vrJlA2sq4doZQxEY2I/mzcksBO2LFWPRokU8tNOd25w5c7h8+TIjRoywPqnp3DkVzWHPMsp2pnRp+PLLlkAxBg8eY7ccjp9//pnUqVPTs2dPu4yfZCpVAh8fdYG1M198AffuqX4DViUDh4cr/0CzZk6TTRwTQxEY2A8fH3jnHT4JDSU0NNQuce5hYWGMGjWKKlWqUN+WkhDmO2gnXLZbwrBhbmTLNphz546wYIH2Tvrbt2+zcOFC3nvvPYsrnmqOu7v6vv7+G548sds0mzbB3LnQv7+qcGEVmzfDo0dO+/syFIGBfWnVirJnz9K0Vi1+/vlnHj9+rOnwM2fO5OrVq7atBkApggoVVEaxC5MmDcyf3xEoQ79+gwgL0zZZf+rUqYSFhfHpp59qOq7VtGmjlICdehSEhipTUJEiSW84EycrVqiw5Nq1NZNNSwxFYGBfWrYE4JsSJbh//z5TpkzRbOgHDx4wfPhwqlevTm1b/sH++0+1/nJhs1BMGjZ0o1698QQHX+Lrr7X7ez9+/JjJkyfTqFEjijlL+GONGsruvnx54vtawbBhcPEizJgB3t5WDhIVpRpON2pkwyD2xVAEBvYlXz6oUIGK+/ZRv359fvzxR54+farJ0EOHDuXevXtMnDjRttXAn3+q52SiCACWLauLl1c9fvllJDdvPtBkzEmTJnH37l2GDRumyXia4OGhbjb++kvV5taQPXtUzkDPnkrfWM3OnXDr1vObImfEUAQG9qdVK9izh6H+/ty5c4eVK1faPOThw4eZMmUKvXr1oly5crYN9scfytNauLDNcjkLmTLB+PHfExUVTKNGA20e7+7du4wfP55mzZpRyYmKpQHKPBQSAhs2aDbkkyfQpQvkzq1yNGxi6VJIndrpykrExFAEBvanXTsAqp47R5MmTZ7H/FtLdHQ0ffr0IUuWLIwaNco22a5dgx07ktVqwEzfvmUoUeIzDh2axtSpATaNNWTIEEJCQvjOqkwqO1OzJmTOrKl5aMAAOHtWOYkzZrRhoIgI+P13lfPgREXmYmMoAgP7U7CgysdfvJgJEyYQGRnJl19+afVwkydPZseOHYwbN47MmTPbJtvSpSplVId6OY5g48aRuLsXoV+/7ty6ZZ2jfu/evUyfPp2+fftSokQJjSXUAE9PZXZZuVIVDLSRTZtg8mSVN1Czpo2DBQTAnTvQoYPNctkTQxEYOIaOHeHIEQqFhdGpUycWL17Mn2bbvAUcPXqUAQMG0LhxY95//33b5Vq4UMWjJyOzUExy5kzNDz/MJiLiP2rVslz5Pn36lK5du5IrVy6+/fZb7QXUik6dVFlQGyuSPnwI77+vSgFpsvhZskQtKfTMwE4CNikCIUQWIcRGIcRZ0/Mrt2dCiJpCiMMxHs+EEC1Mn80VQlyM8VlZW+QxcGLatVPpr0uW0KlTJ9566y0+/PBDLl68mOQh7t27R/PmzcmcOTOzZs2yvSPWiRNw+LC6iCRjPv20GhUrfsWJE9Pp2zfp1UmllHzyySecOnWK2bNnk9EmG4md8fWFXLmUYrcScy2hGzdg/nxl1reJp09V2GirVk5fxNDWFcHXQICUsjAQYHr/ElLKQCllWSllWaAW8ASI6dX5yvy5lPKwjfIYOCs+PlCnDixejIe7O8uWLSM6OpoWLVokKeP48ePHNGnShGvXrvHnn3/i4+Nju0yLFqmkpHfftX0sJycwcDTp09dl8uReLFjwd5KO+eWXX5g5cyaDBg2ibt26dpbQRtzdlUJft06ZYqxg7lz1kxg6FCpW1ECmtWvVKsXJzUJguyJoDswzvZ4HtEhk/zbAP1JK+6UBGjgvHTvCxYtkOHmSQoUKsWzZMk6ePEm9evW4k8A/761bt6hXrx779u1j6dKlvK1Fr9foaPVfX6eOUlLJnLRpPdi06XeEKEu3bq3ZtCl+57GUkl9++YV+/frRvHlzRowY4UBJbaBzZ1V7yIqy5ydOQO/eUKsWDB6skTwLF6rSsDY7GuyPkFJaf7AQD6WUmUyvBfDA/D6e/TcDP0kp15jezwWqAGGYVhTx9S0WQvgD/gA+Pj7lly5dapXMISEhpHNi731iuLL87qGhVG3dmqs1a3JxwAAAdu7cybfffkvGjBnp168f1apVe27yiYqKYsuWLUyZMoWQkBAGDx5M9erVNZEl49GjlPvkE04OGsQtC+92Xfk7+O23NEyd+iWwjUaNGtG9e3eyZMny/PM7d+4wbdo0AgICqFq1KsOGDSNVqlT6CRwP8X0HFbp3JzpVKg5OnZrksZ49c+Ojj8oTHOzJjBn7yZrV9n4OnvfvU6VdO662acOFXr3i3EeP31HNmjUPSCkrvPKBlDLBB7AJOBbHoznwMNa+DxIYJwdwB/CMtU0AXqgVxdDE5JFSUr58eWktgYGBVh/rDLi6/PK992REmjRShoQ833Tw4EFZtGhRCcgCBQrIjh07ynfffVfmyZNHArJs2bLy0KFD2srx/vtSpksn5ePHFh/qyt9BdLSU7dqFSfhSurm5S09PT1m7dm3ZrVs3Wbt2benp6Sk9PT3lt99+KyMjI/UWN17i/Q7Gj5cSpDx1Ksljde8upRBSbtigjWxSSim//17JcfJkvLvo8TsC9ss4rqmJmoaklHWklKXieKwCbgkhcgCYnm8nMFQ7YIWUMiLG2DdM8oUBcwAny1Qx0JwePfB48kR1/zZRrlw5jh49ypw5cyhWrBi7du1i7969lCtXjmXLlrFv3z7Kli2rnQwPH6qw0Y4dnTq22x4IAbNmpSJfvm/JmPEE3br15eHDh2zatIn79+/Tr18/Tp8+zbBhw3B3wiqZidKpk8o2njkzSbvPnQuzZsHAgaCZG0RKNWi1ak7XiSxe4tIOSX0A41HmHFCO4u8T2Hc3UDPWthymZwH8DIxNyrzGisCFiY6WIXnzSlmlin4yTJ6s7tb277fqcJf/DqSU8+btlunSSVm5spTPnuktjeUk+B20bi1l1qxSPn2a4Bi7d0uZKpWUtWpJGRGhoXDbtqnf1+zZCe7mUiuCRBgL1BVCnAXqmN4jhKgghHiukoUQ+YE8wJZYxy8SQhwFjgLZABvTRA2cHiG40bgx7NoFx487fn4pYdo0eOstKF/e8fM7CXnzPmXOHFVPp18/9WdJNnz0kWoekECm8fXrKgctVy61OPXw0HD+WbPUSrNtWw0HtS82KQIp5T0pZW0pZWGpTEj3Tdv3Syl7xNjvkpQyl5QyOtbxtaSUpaUyNXWWUobYIo+Ba3CrXj2VDTpjhuMn37MHjh5VlcRSOG3aqFIK06bBxIl6S6MhNWuqBMF4emU/e6ZC+x89UkVBNW2r8PCh0izt27uU2dHILDZwOBGZMqn/xHnzVLEwRzJtmvoHdYHYbkcwZoz6Kj7/XF0UkwVubkrR79ihlH4MpIRevdT9wIIFqtagpsyYoSrW9e6t8cD2xVAEBvrw6afq7mn2bMfNefMmLF6s4s3Tp3fcvE6Mm5u6IFaooHznBw7oLZFGdOumsnlj9b/45ht1/zF8uB2qQkdEwKRJakWiZXCDAzAUgYE+vP22iqqYMEElATmCSZPUP+sXXzhmPhchTRpVoidbNlUk8/JlvSXSgKxZlcKfO1f1AgB++QVGj4YPP1QKQXOWL4erV9XyysUwFIGBfnz5JVy69KIxjD15/BimTlXlpgsVsv98Lsbrr79o/Vunjqq34/L07w9hYTBpEr/9ppzizZurRYKtZapeQUr46SfV07JRI40Htz+GIjDQj6ZNlVPvhx/sH7Yyc6YyRfXvb995XJhSpVSpnps3lTKwsmSP81CkCLRuTcTEX/m48yOqVVPFQDWNEDKzfTvs3w+ffabsbS6G60lskHxwd1fL6H37YPNm+80TEaHu1vz8NKomlnx5+21YswYuXIB69eCBNl0udWNPza/xDA1mcNb/sXq1BhVF4+Pbb1Vdoffes9ME9sVQBAb60q0b5MmjUjvttSqYPl3Zbk31jQwSxtdX9Xg5cQLq14f79/WWyDo2bQK/L8qzM11d+kVPILOXnWpdBgSoG5nBg5XDxQUxFIGBvnh7qxCOfftU72CtefRIje/rq65qBkmifn31dfz7r2rcfv263hJZxh9/QOPGyvJYYukw3G7fVCZIrZESBg1SNzMunJtiKAID/XnvPShRQv1DRUQkvr8ljBunjN0//GAHD2HypkkT+OcfFUX0zjtw5ozeEiWNadNUUm/58hAUBJkaV1PZc+PGqR7VWrJ6Nezdq0xDTt58JiEMRWCgP+7uqi/g2bMqPV8rrl5VvoEOHVSgvIHF1KyprB6PHyv/gT1dObYSFaViAXr1UoE7mzbB8wrb48apMOUhQ7SbMDwcvv5aOaVd1DdgxlAEBs5B06bKBjF4sHbhKv37qwY0Y8ZoM14KpWJFlYmbI4cyGU2Z4ny1iR4+VD+h8eNVqaEVK2KZ6wsUUPGj8+ap6B4tmDABTp1Sz3YJRXIchiIwcA6EUHH+jx+rrGNbWbNGxQoOHAj589s+XgqnQAHYuVNFEvXurRZZjx7pLZVi715lBtq4Uf2EpkxRpaxeYfBg1Y2uRw91N28LZ84o31OLFi6ZNxAbQxEYOA8lSqh/1sWLrWo3+Jzbt8HfH0qWVH4HA03ImBH++kstsH7/XRVw3b5dP3kiI2HsWJWgHhmp/AHxNANTZMyoCtEdOQK2tN+MjFSmIG9v+PVX68dxIgxFYOBcDB6sjNE9e1rnnYyKgq5dVczj4sXghG0WXRk3N7XICgpSf+oaNaBvX7WQcySnT6ejcmUlS4sWcPiwUgiJ0rw5vP++0mbr11s3+YABylY2dSrkzGndGE6GoQgMnAsPD2XS8fSEZs1UXXlL+OILlR47aRK8+aZ9ZDSgenVV2LNvX3VTXKiQitaxd9moa9fUPcLHH5fn+nW1MvntN8ic2YJBJk9WadTt21veE2POHBWA0LcvvPuuZcc6MYYiMHA+8udXgeCXLimjdFIymqRUESETJyofg7+/nYU0SJdO/bn37FGBM716KWvczJmq5r+WXLqkktALFVLX4hYtrnHypIoKtTgqOE0aZeNKnVr9vk6eTNpxS5cq/0K9evDjj5aeglNjkyIQQrQVQhwXQkQLIeKNzxNCNBBCnBZCnBNCfB1j+xtCiD2m7cuEEMY63kBRo4YK/Th2DCpXVs/x8eSJWu6PHq3+UZPZP6mzU7EibN2qagemTauqe+bPD199pRLSrOXZM5Xh3Lo1FCyoFnlt28Lp09C37zkyZbJB6Hz5lGkoKkolSaxbF/++UVHqt9Whg7I//flnPN5o18XWFcExoBWwNb4dhBDuwK9AQ6AE0EEIUcL08ThggpSyEPAA6G6jPAbJiYYNVeD6o0fKM/nll6oIjpmQEHV7WKIEzJ8Pw4Yp+4QLFv1ydYRQ9f0PHFDx+5Urw88/Q5ky6iLes6dy2fz7b9yrBSmVj3/HDmV5adlSle5p2VIpmf794eJF9TW/8YZGQpcurSbMmVP91jp1goMHX8TGhoWplUOVKmq12aEDbNigtF0yw6bgVynlSQCR8NqsEnBOSnnBtO9SoLkQ4iRQC+ho2m8e8C0w1RaZDJIZ1aopY3T//ipe+8cfVQigtzdcuaLyBMqUUfHhvr56S5viEQJq11aPu3eVDX/dOuX2mT79xT4ZM0KmTMol9OQJBAdDaOiLcQoWVCb8tm1VUpvdwvQLFlTxpyNHKs21eLESLEsWVYv76VPImxcWLlSde5JpdrqQGmSGCCGCgC+llK9kaggh2gANzD2MhRBdgMqoi/5u02oAIUQe4B8pZal45vAH/AF8fHzKL1261CpZQ0JCSOdCvURj4+ryg/Xn4HXrFtm2byfd+fO4RUTwNEcOHlSoQHDp0g79B03J34G1REUJLl1Kw+XLabhyJQ3BwZ6EhHgQFSXw9o4mTZpIXn/9GTlzPqVw4RCyZUs4zt8e8nsEB5Nt+3bSnz2LR0gI4Vmy8LBsWe5XqoS0gybS43dUs2bNA1LKV8z4iZ6dEGIT8HocHw2WUjqsy6mUcjowHaBChQrSz8/PqnGCgoKw9lhnwNXlBxvPIVakRn6bpbGcFP8dOAF2k79585fe5tF+huc403eQqCKQUtaxcY5rvPz3zG3adg/IJITwkFJGxthuYGBgYOBAHOFV2wcUNkUIpQLaA6ulskkFAm1M+3UFHLbCMDAwMDBQ2Bo+2lIIcRWoAvwthFhv2p5TCLEWwHS33wdYD5wEfpNSmrM4BgCfCyHOAVkBDUtPGhgYGBgkBVujhlYAK+LYfh1oFOP9WmBtHPtdQEUVGRgYGBjohBFwbWBgYJDCMRSBgYGBQQrHUAQGBgYGKRxDERgYGBikcDTJLHY0Qog7wGUrD88G3NVQHEfj6vKD65+Dq8sPrn8Ori4/6HMO+aSU2WNvdElFYAtCiP1xpVi7Cq4uP7j+Obi6/OD65+Dq8oNznYNhGjIwMDBI4RiKwMDAwCCFkxIVwXS9BbARV5cfXP8cXF1+cP1zcHX5wYnOIcX5CAwMDAwMXiYlrggMDAwMDGJgKAIDAwODFE6KUgRCiAZCiNNCiHNCiK/1lscShBCzhRC3hRAJdHF3XoQQeYQQgUKIE0KI40KIfnrLZClCCG8hxF4hxBHTOQzXWyZrEEK4CyEOCSHW6C2LNQghLgkhjgohDgshXumK6OwIITIJIZYLIU4JIU4KIaroLlNK8REIIdyBM0Bd4CqqT0IHKeUJXQVLIkKIGkAIMD++dp7OjBAiB5BDSnlQCJEeOAC0cJW/P4BQzbnTSilDhBCewHagn5Ryt86iWYQQ4nOgApBBStlEb3ksRQhxCaggpXTJhDIhxDxgm5RypqlHSxop5UM9ZUpJK4JKwDkp5QUpZTiwFGieyDFOg5RyK3BfbzmsRUp5Q0p50PT6Mao3RS59pbIMqQgxvfU0PVzqTkoIkRtoDMzUW5aUiBAiI1ADU+8VKWW43koAUpYiyAVcifH+Ki52IUouCCHyA+WAPTqLYjEms8ph4DawUUrpaufwM9AfiNZZDluQwAYhxAEhhL/ewljIG8AdYI7JPDdTCJFWb6FSkiIwcAKEEOmAP4BPpZSP9JbHUqSUUVLKsqge25WEEC5jphNCNAFuSykP6C2LjbwjpXwLaAj0NplNXQUP4C1gqpSyHBAK6O6vTEmK4BqQJ8b73KZtBg7CZFf/A1gkpfxTb3lswbScDwQa6CyKJVQDmpls7EuBWkKIhfqKZDlSymum59uoDomu1OXwKnA1xkpyOUox6EpKUgT7gMJCiDdMDpr2wGqdZUoxmByts4CTUsqf9JbHGoQQ2YUQmUyvU6MCD07pKpQFSCkHSilzSynzo37/m6WUnXUWyyKEEGlNwQaYTCr1AJeJpJNS3gSuCCGKmjbVBnQPmLCpZ7ErIaWMFEL0AdYD7sBsKeVxncVKMkKIJYAfkE0IcRUYJqWcpa9UFlEN6AIcNdnYAQaZ+lm7CjmAeaYINDfgNymlS4ZgujA+wAp1X4EHsFhKuU5fkSymL7DIdEN6AXhfZ3lSTviogYGBgUHcpCTTkIGBgYFBHBiKwMDAwCCFYygCAwMDgxSOoQgMDAwMUjiGIjAwMDBI4RiKwMDAwCCFYygCAwMDgxTO/wEafhBvyrxpggAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(xdata, np.sin(xdata), 'b-', label='data')\n", "plt.plot(xdata, np.sin(2*xdata), 'r-', label='data')\n", "plt.plot(xdata, np.sin(xdata)*np.sin(2*xdata), 'k-', label='data')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\pi$" ], "text/plain": [ "pi" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy as sym\n", "x,y = sym.symbols('x y')\n", "\n", "sym.integrate(sym.sin(x)*sym.sin(x),(x, 0, 2*pi))" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 0 0\n", "0 1 0\n", "0 2 0\n", "1 0 0\n", "1 1 pi\n", "1 2 0\n", "2 0 0\n", "2 1 0\n", "2 2 pi\n" ] } ], "source": [ "for i in range(3):\n", " for j in range(3):\n", " print(i,j, sym.integrate(sym.sin(i*x)*sym.sin(j*x),(x, 0, 2*pi)) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\n", "\\int _{a}^{b}F \\left( x \\right) \\varphi _{m} \\left( x \\right) {dx}\n", "$$\n", "を考える.先程の\\ref{Eq:Orthogonal}式をいれると\n", "$$\n", "\\int _{a }^{b }F \\left(x \\right)\\varphi _{m }\\left(x \\right) dx =\\int _{a }^{b }{\\sum^N_{n=1} }a _{n }\\varphi _{n }\\left(x \\right)\\varphi _{m }\\left(x \\right)d x = \n", "\\left\\{\\begin{array}{lr}\n", "a_m C_m & at\\, n=m \\\\\n", "0 & at\\, n\\neq m\n", "\\end{array}\\right.\n", "$$\n", "となる.こうして,係数$a_n$が\n", "\n", "$$\n", "a_{{n}}=\\frac {1}{C_n}\\int _{a}^{b} F \\left( x \\right) \\varphi _{{n}} \\left( x \\right) {dx}\n", "$$\n", "で決定できる.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 直接積分によるフーリエ係数\n", "\n", "\n", "対象とする関数をまず作る.\n", "\n", "piecewise関数は階段関数で,振る舞いはコメント(\\#)を適当に外して確認せよ.\n", "初期設定." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "ename": "TypeError", "evalue": "'<' not supported between instances of 'range' and 'float'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 16\u001b[0m \u001b[0mxdata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m256\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 17\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'r-'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'data'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 19\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 20\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m\u001b[0m in \u001b[0;36mfunc\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0msym\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mPiecewise\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m<\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0many\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# step func\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 8\u001b[0m \u001b[0;31m# return 1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;31m# #F:=x->piecewise(x=0,1/2,x>0,x);\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mTypeError\u001b[0m: '<' not supported between instances of 'range' and 'float'" ] } ], "source": [ "%matplotlib inline\n", "import sympy as sym\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "def func(x):\n", " return (1)*sym.Piecewise((-1, (x<1/2).any() ), (1, True)) # step func\n", "# return 1\n", " # #F:=x->piecewise(x=0,1/2,x>0,x); \n", " #F:=x->piecewise(x<1/2,x,x>=1/2,1-x);\n", " #F:=x->piecewise(x<1/2,-1,x>1/2,1); \n", " # Piecewise(x, [x < 1/2, x >= 1/2], [-1, 1])\n", " #F:=x->piecewise(x>0 and x<1/2,-1,x>1/2,1); \n", " #F:=x->x-1/2; \n", "\n", "xdata = range(0, 1, 256)\n", "\n", "plt.plot(xdata, func(xdata), 'r-', label='data')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "上の通り, 積分をPiecewise関数に施すのは難しそう.\n", "sympy.Piecewiseではarrayに対応してないし,\n", "一方でnumpyはintegrateが数値積分.\n", "\n", "ここでは,Mapleの結果を残しておく.\n", "\n", "``` maplerestart;\n", "F:=x->piecewise(x=0,1/2,x>0,x);\n", "#F:=x->piecewise(x<1/2,x,x>=1/2,1-x);\n", "#F:=x->piecewise(x<1/2,-1,x>1/2,1);\n", "F:=x->piecewise(x<1/2,-1,x>=1/2,1);\n", "#F:=x->piecewise(x>0 and x<1/2,-1,x>1/2,1);\n", "#F:=x->x-1/2;\n", "plot([F(x)],x=0..1);\n", "F := proc (x) options operator, arrow; piecewise(x = 0, 1/2, 0 \n", "\n", " < x, x) end proc\n", "\n", "\n", " F := proc (x) options operator, arrow; piecewise(x < 1/2, -1, \n", "\n", " 1/2 <= x, 1) end proc\n", "\n", "\n", "\n", "KK:=3;\n", "N:=2^KK;L:=1-0;\n", " KK := 3\n", "\n", " N := 8\n", "\n", " L := 1\n", "```\n", "直接積分によるフーリエ級数\n", "\n", "``` maple\n", "2*Pi*1/L*x;\n", " 2 Pi x\n", "```\n", "\n", "``` maple\n", "> int(F(x)*cos(2*Pi*1/L*x),x=0..L);\n", "```\n", "$$\n", "0\n", "$$\n", "\n", "```maple\n", "> for n from 0 to N do\n", " a[n]:=2/L*int(F(x)*cos(2*Pi*n/L*x),x=0..L); \n", " end do;\n", "```\n", "$$\n", "a_0:=0 \\notag \\\\\n", "a_1:=0 \\notag \\\\\n", "a_2:=0 \\notag \\\\\n", "a_3:=0 \\notag \\\\\n", "a_4:=0 \\notag \\\\\n", "a_5:=0 \\notag \\\\\n", "a_6:=0 \\notag \\\\\n", "a_7:=0 \\notag \\\\\n", "a_8:=0 \\notag \n", "$$\n", "\n", "```maple\n", "> for n from 0 to N do \n", " b[n]:=2/L*int(F(x)*sin(2*Pi*n/L*x),x=0..L); \n", " end do;\n", "```\n", "$$\n", "b_0:=0 \\notag \\\\\n", "b_1:=\\frac{4}{\\pi} \\notag \\\\\n", "b_2:=0 \\notag \\\\\n", "b_3:=\\frac{4}{3\\pi} \\notag \\\\\n", "b_4:=0 \\notag \\\\\n", "b_5:=\\frac{4}{5\\pi} \\notag \\\\\n", "b_6:=0 \\notag \\\\\n", "b_7:=\\frac{4}{7\\pi} \\notag \\\\\n", "b_8:=0 \\notag \n", "$$\n", "ここで,オイラーの関係\n", "$$\n", "a[n]=c[n]+c[-n],\\, b[n]=I (c[n]-c[-n]) \\notag \\\\\n", "c[-n]= \\frac{1}{2} (a[n] + b[n]),\\, c[n]=\\frac{1}{2} (a[n] - I b[n])\n", "$$\n", "を使って,三角関数系から$\\exp$へ変換する.\n", "\n", "```maple\n", "> for n from 0 to N do c[n]:=1/L*int(F(x)*exp(-I*2*Pi*n/L*x),x=0..L); end do;\n", "> for n from 1 to N do c[-n]:=1/L*int(F(x)*exp(I*2*Pi*n/L*x),x=0..L); end do;\n", "```\n", "$$\n", "c_0:=0 \\notag \\\\\n", "c_1:=\\frac{2I}{\\pi} \\notag \\\\\n", "c_2:=0 \\notag \\\\\n", "c_3:=\\frac{2I}{3\\pi} \\notag \\\\\n", "c_4:=0 \\notag \\\\\n", "c_5:=\\frac{2I}{5\\pi} \\notag \\\\\n", "c_6:=0 \\notag \\\\\n", "c_7:=\\frac{2I}{7\\pi} \\notag \\\\\n", "c_8:=0 \\notag \\\\\n", "c_{-1}:=-\\frac{2I}{\\pi} \\notag \\\\\n", "c_{-2}:=0 \\notag \\\\\n", "c_{-3}:=-\\frac{2I}{3\\pi} \\notag \\\\\n", "c_{-4}:=0 \\notag \\\\\n", "c_{-5}:=-\\frac{2I}{5\\pi} \\notag \\\\\n", "c_{-6}:=0 \\notag \\\\\n", "c_{-7}:=-\\frac{2I}{7\\pi} \\notag \\\\\n", "c_{-8}:=0 \\notag \n", "$$\n", "\n", "```maple\n", "> F1:=unapply(sum(evalf(c[i]*exp(I*2*Pi*i/L*x)),i=-(N-1)..(N-1)),x):\n", "> plot({Re(F1(x)),F(x)},x=0..1);\n", "```\n", "\n", "![C10_FFTplot2d12.png](figs/C10_FFTplot2d12.png)\n", "\n", "\n", "```maple\n", "> evalf(2/3/Pi);\n", "```\n", "$$\n", "0.2122065907\n", "$$\n", "```\n", "\n", "```\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 選点直交性による計算の簡素化\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "ところが,実際に積分していては,時間がかかりすぎる.直交関数系の選点直交性を使うとより簡単になる.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 直交関数系の選点直交性 \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "直交多項式は,\n", "\n", "$$\n", "\\varphi _{n} \\left( x \\right) =0 \\,at\\,x_1,\\,x_2,\\,\\cdots x_{n}\n", "$$\n", "である.$n-1$以下の次数$m,\\,l$では,\n", "\n", "$$\n", "\\sum _{i=1}^{n}\\phi_{l} \\left( x_{i} \\right) \\varphi _{m} \\left( x_{i} \\right) =\\delta_{\\it ml}C_{l}\n", "$$\n", "が成り立つ.これは,直交関係と違い積分でないことに注意.証明は略.\n", "\n", "これを使えば,この先程の直交関数展開\n", "\n", "$$\n", "F \\left( x \\right) =\\sum _{l=1}^{N}a_{l}\\varphi _{l} \\left( x \\right)\n", "$$\n", "の両辺に$\\varphi _{m} \\left( x_{i} \\right)$を掛けて$i$について和をとれば,\n", "$$\n", "\\sum _{i=1}^{n} F \\left(x _{i }\\right)\\phi _{m }\\left(x _{i }\\right) = \\\\\n", "\\sum _{i=1}^{n} \\sum _{l=1}^{N}a_{l}\\varphi _{l} \\left( x_{i} \\right) \\varphi _{m} \\left( x_{i} \\right) \\notag \\\\\n", "=\\sum _{l=1}^{N} a_{l}\\sum _{i=1}^{n}\\varphi _{l} \\left( x_{i} \\right) \\varphi _{m} \\left( x_{i} \\right) \\notag \\\\\n", "=\\sum _{l=1}^{N}a_{l}\\delta_{\\it ml}C_{m}=a_{m}C_{m} \\notag\n", "$$\n", "となる.つまり,\n", "\n", "$$\n", "a_{m}=\\frac{1}{C_{m}} {\\sum _{i=1}^{n}F \\left( x_{i} \\right) \\varphi _{m} \\left( x_{i} \\right) }\n", "$$\n", "となり,単純な関数の代入とかけ算で係数が決定される.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 選点直交性を用いた結果 \n", "\n", "Pythonで扱うのを失敗しています.以下はMapleの出力." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```maple\n", "> KK:=4; N:=2^KK;L:=1-0;\n", "> for k from 0 to N-1 do \n", " c[k]:=evalf(sum(F(i*L/N)*exp(-I*2*Pi*k*i/N),i=0..N-1));\n", " end do;\n", "```\n", "```maple\n", "c_0:=0. \n", "c_1:=-2.000000000 + 10.05467898 I \n", "c_2:=0. \n", "c_3:=-2.000000000 + 2.993211524 I \n", "c_4:=0. \n", "c_5:=-2.000000001 + 1.336357276 I \n", "c_6:=0. \n", "c_7:=-2.000000001 + 0.3978247331 I \n", "c_8:=0. \n", "c_9:=-2.000000001 - 0.3978247331 I \n", "c_10:=0. \n", "c_11:=-2.000000001 - 1.336357276 I \n", "c_12:=0. \n", "c_13:=-2.000000000 - 2.993211524 I \n", "c_14:=0. \n", "c_15:=-2.000000000 - 10.05467898 I\n", "```\n", "\n", "```maple\n", "> F1:=unapply(sum(evalf(c[i]*exp(I*2*Pi*i/L*x)/N),i=0..(N/2-1))+\n", "> sum(evalf(c[N-i]*exp(-I*2*Pi*i/L*x)/N),i=1..(N/2-1)),x):\n", "> plot({Re(F1(x)),F(x)},x=0..1);\n", "```\n", "\n", "![C10_FFTplot2d13.png](figs/C10_FFTplot2d13.png)\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 高速フーリエ変換アルゴリズムによる高速化\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$\\sin, \\cos$と$\\exp$関数を結びつけるオイラーの関係を使うと,\n", "\n", "$$\n", "$$\n", "と変換できる.これを使うと,\n", "\n", "$$\n", "c_{{k}}=\\frac{1}{C_{{m}}}\\sum _{i=0}^{N-1}F \\left( x_{{i}} \\right) {{\\exp}\\left({{\\frac {-2\\,\\pi I}{N}}}\\right)}\n", "$$\n", "となる.$N = 8$の場合を実際に計算すると,$ z = \\exp(-\\frac{2\\pi}{8}I)$として,$z^8=1,z^9=z, \\cdots$を使うと,\n", "\n", "$$\n", "\\left[\\begin{array}{c}\n", "c_0\\\\c_1\\\\c_2\\\\c_3\\\\c_4\\\\c_5\\\\c_6\\\\c_7\n", "\\end{array}\\right] =\n", "\\left[\\begin{array}{cccccccc}\n", "1&1&1&1&1&1&1&1\\\\\n", "1&z&z^2&z^3&z^4&z^5&z^6&z^7\\\\\n", "1&z^2&z^4&z^6&1&z^2&z^4&z^6\\\\\n", "1&z^3&z^6&z&z^4&z^7&z^2&z^5\\\\\n", "1&z^4&1&z^4&1&z^4&1&z^4\\\\\n", "1&z^5&z^2&z^7&z^4&z^1&z^6&z^3\\\\\n", "\\vdots & & & & & & & \\\\\n", "\\vdots & & & & & & & \n", "\\end{array}\\right]\n", "\\left[\\begin{array}{c}\n", "F_0\\\\F_1\\\\F_2\\\\F_3\\\\F_4\\\\F_5\\\\F_6\\\\F_7\n", "\\end{array}\\right]\n", "$$\n", "となる.この行列計算を素直に実行すると,8×8=64回の演算が必要となる.これを減らせないかと考えたのが,高速フーリエ変換の始まりである.\n", "この行列をよく見ると同じ計算を重複しておこなっていることが分かる.そこで,行列の左側と右側で同じ計算をしている部分をまとめると,\n", "\n", "$$\n", "\\left[\\begin{array}{c}\n", "c_0\\\\c_1\\\\c_2\\\\c_3\\\\c_4\\\\c_5\\\\c_6\\\\c_7\n", "\\end{array}\\right] =\n", "\\left[\\begin{array}{cccccccc}\n", "1&1&1&1&0&0&0&0\\\\\n", "0&0&0&0&1&z&z^2&z^3\\\\\n", "1&z^2&z^4&z^6&0&0&0&0\\\\\n", "0&0&0&0&1&z^3&z^6&z\\\\\n", "1&z^4&1&z^4&0&0&0&0\\\\\n", "0&0&0&0&1&z^5&z^2&z^7\\\\\n", "1&z^6&z^4&z^2&0&0&0&0\\\\\n", "0&0&0&0&1&z^7&z^6&z^5\\\\\n", "\\end{array}\\right]\n", "\\left[\\begin{array}{c}\n", "F_0+F_4\\\\F_1+F_5\\\\F_2+F_6\\\\F_3+F_7\\\\F_0-F_4\\\\F_1-F_5\\\\F_{[ \\,\\,]}-F_6\\\\F_{[\\,\\,]}-F_7\n", "\\end{array}\\right]\n", "$$\n", "とすることができる.ここで,$z^4 =-1$などを使っている.右側のベクトルの計算でロスするが,行列の中の計算の回数を半分に減らすことができる.再度できあがった行列を見れば,同じ計算をさらにまとめるこ\n", "とができそうである.こうして,次々と計算回数を減らしていくことが可能で,最終的に行列部分の計算が一切なくなる.残るのは,右側のベクトルの足し算引き算だけになる.\n", "\n", "このベクトルの組み合わせは,一見相当複雑そうで,その条件分岐で時間がかかりそうに思われる.しかし,よく調べてみれば,単純なビット演算で処理することが可能であるこ\n", "とが判明した.こうして,2の整数乗のデータの組に対しては,極めて高速にフーリエ変換を実行することが可能となった.\n", "FFTでの演算回数は,データ数をNとすると\n", "\n", "$$\n", "N\\log_2 N\n", "$$\n", "となる.単純な場合の$N^2$と比較すると,以下のようになり,どれだけ高速化されているかが理解されよう.\n", "```maple\n", "> dN2:=[]; dFft:=[]; for i from 2 to 16 do N:=2^i; n2:=N*N; Fft:=N/2*log[2](N);\n", "> Fft/n2; printf(\"%10d %12d %12d %10.5f\\n\",N,n2,Fft,evalf(Fft/n2));\n", "> dN2:=[op(dN2),[N,n2]]; dFft:=[op(dFft),[N,Fft]]; end do:\n", "```\n", "```maple\n", " 4 16 4 0.25000\n", " 8 64 12 0.18750\n", " 16 256 32 0.12500\n", " 32 1024 80 0.07812\n", " 64 4096 192 0.04688\n", " 128 16384 448 0.02734\n", " 256 65536 1024 0.01562\n", " 512 262144 2304 0.00879\n", " 1024 1048576 5120 0.00488\n", " 2048 4194304 11264 0.00269\n", " 4096 16777216 24576 0.00146\n", " 8192 67108864 53248 0.00079\n", " 16384 268435456 114688 0.00043\n", " 32768 1073741824 245760 0.00023\n", " 65536 4294967296 524288 0.00012\n", "```\n", "```maple\n", "> with(plots):\n", "> l1:=plot(dN2): l2:=plot(dFft):\n", "> display(l1,l2);\n", "```\n", "\n", "![C10_FFTplot2d14.png](figs/C10_FFTplot2d14.png)\n", "\n", "\n", "```maple\n", "> l1:=logplot(dN2): l2:=logplot(dFft):\n", "> display(l1,l2);\n", "```\n", "\n", "![C10_FFTplot2d15.png](figs/C10_FFTplot2d15.png)\n", "\n", "\n", "```maple\n", "> l1:=loglogplot(dN2): l2:=loglogplot(dFft):\n", "> display(l1,l2);\n", "```\n", "\n", "![C10_FFTplot2d16.png](figs/C10_FFTplot2d16.png)\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# FFT関数を用いた結果\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "```maple\n", "> KK:=4;\n", " N:=2^KK;i:='i';L:=1-0;\n", " x1:=array([evalf(seq(F(i/N),i=0..N-1))]);\n", " y1:=array([evalf(seq(0,i=0..N-1))]);\n", "```\n", "$$\n", "{\\it x1}\\, := \\, \\left[ \\begin {array}{cccccccccccccccc} - 1.0&- 1.0&- 1.0&- 1.0&- 1.0&- 1.0&- 1.0&- 1.0& 1.0& 1.0& 1.0& 1.0& 1.0& 1.0& 1.0& 1.0\\end {array} \\right] \\notag \\\\\n", "{\\it y1}\\, := \\, \\left[ \\begin {array}{cccccccccccccccc} 0.0& 0.0& 0.0& 0.0& 0.0& 0.0& 0.0& 0.0& 0.0& 0.0& 0.0& 0.0& 0.0& 0.0& 0.0& 0.0\\end {array} \\right] \\notag\n", "$$\n", "```maple\n", "> FFT(KK,x1,y1);\n", "```\n", "$$\n", "16\n", "$$\n", "\n", "```maple\n", "> interface(displayprecision=2):\n", " print(x1);print(y1);\n", "```\n", "$$\n", "\\left[ \\begin {array}{cccccccccccccccc} 0.0&- 2.0& 0.0&- 2.0& 0.0&- 2.0& 0.0&- 2.0& 0.0&- 2.0& 0.0&- 2.0& 0.0&- 2.0& 0.0&- 2.0\\end {array} \\right] \\notag \\\\\n", "\\left[ \\begin {array}{cccccccccccccccc} 0.0& 10.05& 0.0& 2.99& 0.0& 1.34& 0.0& 0.40& 0.0&- 0.40& 0.0&- 1.34& 0.0&- 2.99& 0.0&- 10.05\\end {array} \\right] \\notag\n", "$$\n", "\n", "```maple\n", "> F2:=unapply(sum(evalf((x1[i]+I*y1[i])*exp(I*2*Pi*(i-1)/L*x)/N),i=1..N/2)+\n", " sum(evalf((x1[N-i+2]+I*y1[N-i+2])*exp(-I*2*Pi*(i-1)/L*x)/N),i=2..N/2),x):\n", "> plot({Re(F2(x)),F(x)},x=0..1);\n", "```\n", "\n", "![C10_FFTplot2d17.png](figs/C10_FFTplot2d17.png)\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 課題と解答例\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## 合成波のFFT\n", "\n", "\n", "下の例に従って,sin(i/13)とsin(i/2)の合成波を作成し,FFTをかけた後,周波数での強度を表示せよ.合成波(2*sin(i*2)+sin(i/2))との違いをのべよ.\n", "\n", "\n", "![FFTExplot2d1.png](figs/FFTExplot2d1.png)\n", "\n", "\n", "\n", "![FFTExplot2d2.png](figs/FFTExplot2d2.png)\n", "\n", "\n", "\n", "![FFTExplot2d3.png](figs/FFTExplot2d3.png)\n", "\n" ] }, { "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" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, 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