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authorJoshua Baer <joshua.baer@ost.ch>2022-08-16 10:28:32 +0200
committerJoshua Baer <joshua.baer@ost.ch>2022-08-16 10:28:32 +0200
commite63dbdeedff258f834311a449d935e7945d6c9db (patch)
tree291b0b44832f76c2ad97496b890dd1a65784e714 /buch/papers/fm
parentMerge branch 'master' of github.com:JODBaer/SeminarSpezielleFunktionen (diff)
downloadSeminarSpezielleFunktionen-e63dbdeedff258f834311a449d935e7945d6c9db.tar.gz
SeminarSpezielleFunktionen-e63dbdeedff258f834311a449d935e7945d6c9db.zip
signal m draw
Diffstat (limited to 'buch/papers/fm')
-rw-r--r--buch/papers/fm/03_bessel.tex8
-rw-r--r--buch/papers/fm/Python animation/Bessel-FM.ipynb73
2 files changed, 71 insertions, 10 deletions
diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex
index 5f85dc6..45f2dfd 100644
--- a/buch/papers/fm/03_bessel.tex
+++ b/buch/papers/fm/03_bessel.tex
@@ -157,14 +157,14 @@ jedoch so \(-1 \cdot J_{-n}(\beta) = J_n(\beta)\) und daraus wird dann:
\sum_{n=- \infty}^{-1} J_{n}(\beta) \cos((\omega_c + n \omega_m) t)
\,+\, \sum_{n=1}^\infty J_{n}(\beta) \cos((\omega_c + n\omega_m) t)
\end{align*}
-Da \(n\) immer ungerade ist und \(0\) nicht zu den ungeraden zahlen zählt, kann man dies so vereinfacht
+Da \(n\) immer ungerade ist und \(0\) nicht zu den ungeraden Zahlen zählt, kann man dies so vereinfacht
\[
s(t)
=
- \sum_{n\, \text{ungerade}} -1 \cdot J_{n}(\beta) \cos((\omega_c + n\omega_m) t).
+ \sum_{n\, \text{ungerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t).
\label{fm:eq:ungerade}
\]
-schreiben.
+, mit allen positiven und negativen Ganzzahlen schreiben.
%------------------------------------------------------------------------------------------
\subsubsection{Summe Zusammenführen}
Beide Teile \eqref{fm:eq:gerade} Gerade
@@ -179,7 +179,7 @@ ergeben zusammen
\[
\cos(\omega_ct+\beta\sin(\omega_mt))
=
- \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t).
+ \sum_{k= -\infty}^\infty J_{n}(\beta) \cos((\omega_c+ n\omega_m)t).
\]
Somit ist \eqref{fm:eq:proof} bewiesen.
\newpage
diff --git a/buch/papers/fm/Python animation/Bessel-FM.ipynb b/buch/papers/fm/Python animation/Bessel-FM.ipynb
index 74f1011..ef6300b 100644
--- a/buch/papers/fm/Python animation/Bessel-FM.ipynb
+++ b/buch/papers/fm/Python animation/Bessel-FM.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
- "execution_count": 4,
+ "execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
@@ -11,10 +11,11 @@
"from scipy.fft import fft, ifft, fftfreq\n",
"import scipy.special as sc\n",
"import scipy.fftpack\n",
+ "import matplotlib.pyplot as plt\n",
"import matplotlib as mpl\n",
"# Use the pgf backend (must be set before pyplot imported)\n",
- "mpl.use('pgf')\n",
- "import matplotlib.pyplot as plt\n",
+ "# mpl.use('pgf')\n",
+ "\n",
"from matplotlib.widgets import Slider\n",
"def fm(beta):\n",
" # Number of samplepoints\n",
@@ -42,7 +43,7 @@
},
{
"cell_type": "code",
- "execution_count": 114,
+ "execution_count": 9,
"metadata": {},
"outputs": [
{
@@ -56,6 +57,18 @@
"needs_background": "light"
},
"output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
}
],
"source": [
@@ -120,7 +133,7 @@
},
{
"cell_type": "code",
- "execution_count": 85,
+ "execution_count": 6,
"metadata": {},
"outputs": [
{
@@ -164,7 +177,7 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 98,
"metadata": {},
"outputs": [
{
@@ -187,6 +200,54 @@
"plt.plot(x, y, '-')\n",
"plt.show()"
]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 130,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[<matplotlib.lines.Line2D at 0x7f2bc2c41880>]"
+ ]
+ },
+ "execution_count": 130,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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WmATsBJaIyNxaSk7OMsY8VOPaTODHQD5ggKXOtQdilas2Dh0/TUVVtRddn6WqAqk8iWnRxtbCVRrk3cI9/PD1NVzYvwtP35NPq/RG/rutf9Nuh1zjnXBgFcGiP9iVrH0u9HassHBgC5w85E/EUITUNDtbU0UQM26UqhwHFBtjNgOIyEzgehpXhP4qYJ4xZr9z7TxgMvCyC3Kdwz/NWs6HG9xfHJRCNdemLOCutPmMkmLSpYqjJoOF1UN5tupqPq8e4fqYicaXB2fx+7vGkNGiCcpz/ZvQ/Xzo0MM7wQB6X2jDU7d8rIogwp7VduunIgBrHir8q52heF0UJ4FxQxH0AKITt+8ExtfS7iYRuRjYCPyzMWZHHdfW+lctItOAaQC5uc1LMXz3xN5cNjSnWdfWRdvjO7lw1aNkH1zJoTZ9Kcq+mxPpnWl7YhcXlM7nilP/yZauk1k0/N853aJ9wx0mIW1bpvKVvG60TGuCEjhcYpOOXfZD7wSL0KqjfeBt/cz7scLCnjVWOWb75CiO0HUkLH3eRo516u2vLCHGleL1jeAN4GVjzCkReRCYAVzWlA6MMdOB6QD5+fnNqkhx2RB3lQAly+Glu22M+Y1P0SHvVjqkRLldKk/BZ7+h78eP07d6O9z1F2jf3V0ZkpX1b9nt0K/GZ7xeE+wDp+p0/FfRBpHSQug8EFrUscgvXkR8FLtXqiKIATecxbuAXlHfezrHzmCM2WeMiXjangHGNPbawFK+EV643tbGfeADOG+KXeQSTVpLuOT7cOccW+3qhRvg+H5fxE041r9pH0RZg+MzXq9xNlQxYhJJdkrX2Ighv8kZZsOHNXIoJtxQBEuAgSLSV0TSgSnAFyp/i0i3qK/XAeuc/XeBK0Wkk4h0Aq50jgWbY3vhz7fYGOp734QuA+pv3//LcMdMW1Fp1t26SjVWTh2xZhqv1g7URi/H2rljUfzGDConD8PBbcFQBC1aQZdBmnMoRmJWBMaYSuAh7AN8HTDbGFMoIj8RkeucZt8RkUIRWQl8B7jXuXY/8H+xymQJ8JOI4ziwGAOvfRMO74bbZzZ+OtrnIrjuf2Hbp/Dxz72VMdHZ8glUn7bpH+JFhx7QoZcqAoAyJw6ka56/ckTIGX5WJqVZuOIjMMa8Dbxd49iPovYfBR6t49pngWfdkCMuFDwLRe/B1b9oelWm826zD7FPfmlnCb0v8EbGRKdoHqS3tXb7eNJrPGz7XCNUIqmfgzAjAGseWjPHhrNmdGi4vXIOurK4KRzaBe/9EPpfBmMfaF4fX/mFLaz+xnd1gVJzMAaK59scQPFe0dprPBwpgUM74ztu0Nizxj5w23sctttYcpzw7LJ19bdT6kQVQVOY9yMwVXDtk+c6hhtLehu45n/sitjPfu2qeElB+QY4tAMGXBH/sXuNs9tkNw+VFkJOXnBmRdnD7FaL1DQbVQSNZetndvp54T/FHqY2cBIMux7+/is4sscV8ZKGSJGYePoHIuSMgBatbdWyZKW62trjg2IWAujQE1p2gFL1EzQXVQSNwRh491HrLLzwu+70ecVj1uH50ePu9JcsFM2z2S479Iz/2KlpdmFZyfL4jx0UDm6FiqPBUgQi1k9QWui3JKFFFUFjWP+WXbDy5R9Aei2lEptDZj8Y83VY9gLsLXanz0Tn1FHYvgAG+mAWitB9tA1VTNYQ4MjDtmvA0qZkD7M+AtOstaZJjyqChqiuho/+CzL7Q94t7vZ9yb/a7Ikf/ae7/SYqWz6Bqgp//AMRuo92cuBv8E8GPyktBMS/GgR1kTPcVktLdkd+M1FF0BDr37BOqEsfsaYBN2mbDePut0mz9m92t+9EpHi+XcmdO9E/GbqPtttkNQ/tWQ2d+7s3M3aLiKlKzUPNQhVBfRgDf/8f6DwARtzkzRgTvgUpafDZb7zpP1EwxjqK+11iU3f4RWZ/WzQ9WRVBaeHZcM0gEUl+V6aKoDmoIqiPbZ9b38DEb3tXW6BdVxh1B6z4k0YQ1cfeIpth0k+zENiw4W7nwa5l/srhBxXHbB2CIDmKI2R0gA65GjnUTFQR1MfC30GrTBg5xdtxLvgOVFfC4unejhNm/AwbrUn30dZcWFnhtyTxpXy93fqderouNHKo2agiqIt9m2y00Nj7vLeHdu4Pg662aY5Pn/R2rLBSNM+WJuzYvFoUrtJ9tHVaJ1t+mzJHEQTNURwhZzjsK0o+Be0CqgjqYtEfbN755qaSaCrjHoDj+2Dta/EZL0xUHINtnwVjNgDJ6zAuXwepLSGzr9+S1E72MDuz3rvRb0lChyqC2qg4BitehuE3QjuXi9nURb9LbX79xU/HZ7wwseXv/oeNRtOpD7TqBCVJ5icoW29TPge1FnfEia3moSajiqA21rwKFUfsgq94IWJnBbsKbAlG5SzF82zYaFCytYrYFMzJVqSmfD1kD/Fbirrp3B9SWtiZi9IkVBHUxrIZ1h6dG+c0x+fdbh94S8KTldtzjLH+gb4X+xs2WpOcPLuSNVlWGJ86YpP9ZQVYEaS2sKHeEV+G0mhcUQQiMllENohIsYg8Usv574nIWhFZJSLvi0jvqHNVIrLC+cyteW3c2bPGJhUbc2/8sytmtIcRX7MLzE4dje/YQWVfsa2G5WdaidromgeVJ2H/Jr8liQ/lzkrqoEYMRcgecja6SWk0MSsCEUkFfgtcDQwDbheRYTWaLQfyjTEjgTnAL6LOnTDGjHI+1+E3y2ZYh9h5HoeM1sXou+H0MXUaRyieb7dB8Q9EiOTaSRbzUCTXf5BnBGAjmg5shYrjfksSKtyYEYwDio0xm40xFcBM4ProBsaYD40xkV9mIbZIffCoOA4rZ8Gw66B1pj8y9BpnncbLX/Jn/KBRNM/+e3Tq47ckX6TLYGuPTpYc+OXrbV6soP0ONckaDBiNHGoibiiCHsCOqO87nWN1cR/wt6jvGSJSICILReSGui4SkWlOu4Ly8vKYBK6TDW/bxFXn3+NN/41BBEbfabNsJntW0orjsPXT4ISNRpOWbh86yTQjCHLEUISI6ao8SZMCNpO4OotF5C4gH/hl1OHexph84A7gSRHpX9u1xpjpxph8Y0x+VlaWNwKumgXte0Lvi7zpv7GMnAKSYtNOJDNbP4WqU8EzC0Xommd9SslA+frgm4XApnfXyKEm44Yi2AX0ivre0zn2BUTkCuAHwHXGmDPFeo0xu5ztZuAjYLQLMjWdo+VQ/D6MvKX5ZSjdon03GDAJVr4M1VX+yuInxfMgrRX0vtBvSWonZwQc3QPH9votibecPASHdwU7dDSCRg41CzeeeEuAgSLSV0TSgSnAF6J/RGQ08BRWCZRFHe8kIi2d/S7AhYA/6/YLX7X1iEfe5svw5zDqdjiyG7b+3W9J/MEYKHrPZhttkeG3NLWTLA7jiJklqKklaqKRQ00mZkVgjKkEHgLeBdYBs40xhSLyExGJRAH9EmgLvFIjTHQoUCAiK4EPgceNMf4ogpUzoevI4ITHDZoM6e1g9St+S+IP+zbZ6I+gmoXAriWAxHcYRyKGwjAjAI0cagauVFoxxrwNvF3j2I+i9mv9azbGfA7kuSFDTOwtsukCrvyZ35KcpUUrGHotrH0DrvlVsBZTxYOi9+w2iI7iCG06Q7tuSTAjWG9NdB37+C1J44iOHOo+ym9pQoGuLAZYNds6Z/Nu9luSL5J3s41iKprntyTxp9jJNhr0cMVkcBiXrYOsQf77zhrLmcghNQ81lpD8sh5ijI0W6nepLRITJPpeCq27JJ95qOJYcMNGa5IzwtYvrjzVcNuwUr4+PP4BiIocUkXQWFQR7FxiUxjk3eq3JOeSmmZTTmx8B04e9lua+BHJNhoKRTDcSX1c5Lck3nDioA1aCIt/AGzkUJeBGjnUBFQRFP7VppQYco3fktRO3i02p836t/yWJH4Uved/kfrGkuhmiMh9hWlGANZPoGsJGk1yK4Lqalj7uo1MyWjvtzS103Osrcq1Zo7fksSHM0XqLw2Hg7zzQEhJS9xqZWGLGIqQNRQObNPIoUaS3Ipg5xK7UGb4DX5LUjciMOJm2PRh4i9cAhvpcXB78LKN1kVaOmT2T1wzRPl6aNHaFoYPE9lD0JxDjSe5FcHa16xZaNBkvyWpnxFfs4vd1r3htyTeEwkbHRAC/0CE7CGJa4YoW2fNLGGJGIoQSYeRqCY7lwnZr+siZ8xClwfXLBQhZ4R961z7ut+SeE/RPDut79ir4bZBIXsY7N+SmGaIsEUMRdDIoSaRvIrgjFnoRr8laRgRGHY9bPkEju3zWxrvOHUEtn0ejmihaLIS1AxxfD8cLQ2ffwA0cqiJJK8iCItZKMLwG6x5aP2bfkviHZs+hOrTMPBKvyVpGtlOHaayBDMPhTViKIJGDjWa5FQEYTILReg6Ejr1TWzz0Ia3IaNjOMJGo8nsB6npiffQCWvEUASNHGo0yakIImahYTf4LUnjOWMe+thO2RONqkq7cG7QVXYhXZhITbNhpIlmhijfAOltoUOI/DXRaORQo0lORRAxCw2+2m9JmsbwG+wq1kRcXLZjIZw4AIO/4rckzSN7aAKahpyIIRG/JWkeGjnUaJJPEYTRLBSh2yi7uCwRzUPr37bmlQGX+y1J88geAoe2W4d3olC+IRxVyepCI4caTfIpgjCahSKIWLk3f2TfnhMFY2DDW9D3EmjZzm9pmkfEoZootXIjEUNZg/2WpPlo5FCjST5FsPY1++Y5OCTRQjUZfoONrNnwN78lcY/y9baQyJCQmoXgbM6hRDEPRezqYZ4RgBM5pIqgIVxRBCIyWUQ2iEixiDxSy/mWIjLLOb9IRPpEnXvUOb5BRK5yQ546iZiF+l8OGR08Hcozup9vl/sXvua3JO4R8XkMCpnPJppOfSAtI3EeOmdCR8OuCLRaWWOIWRGISCrwW+BqYBhwu4gMq9HsPuCAMWYA8ATwc+faYdgax8OBycDvnP68IUyLyOpCBIZdB5s+sCmCE4ENb0OPMdC+m9+SNJ+UVPv2mSjJ58o3ODmGQhoxFCFSrWxfgqYJdwk3ZgTjgGJjzGZjTAUwE7i+RpvrgRnO/hzgchER5/hMY8wpY8wWoNjpzxvCbhaKMOwGax7a+I7fksTOoZ2wa2lw04A3hayhiWOPLl8PXUJUlawuzpjsEuB32VkAs++xMxyXceNX7gHsiPq+0zlWaxun2P0hoHMjrwVARKaJSIGIFJSXlzdP0sqTNjwxrGahCD3zoX1PW0sh7Kyda7dhdN7XJGswHClJjJla2COGIiRS5NCupda0nZbhetehUffGmOnGmHxjTH5WVlbzOrn2CbjleVfl8oXI4rJNH8DJQ35LExtrX4ecPOjc329JYify9hn2BUwnD1kTapgjhiKktoDOAxJDEZSvty+xbXNc79oNRbALiDYk9nSO1dpGRNKADsC+Rl7rLmFdHFOT4Tfaco5hjh46XGIXkg2vaUkMKZE36LBHDpUnSMRQhOwh4f9NwJmlDfXkGeaGIlgCDBSRviKSjnX+zq3RZi4w1dm/GfjAGGOc41OcqKK+wEBgsQsyJT5nzEOv+S1J84nUV0gEsxBAx96Q1ir8b58R+cOaY6gmWUOsXf30Cb8liY3y9Z7N0mJWBI7N/yHgXWAdMNsYUygiPxGR65xmfwQ6i0gx8D3gEefaQmA2sBZ4B/i2MaYqVpmSAhG7pmDT++E1DxW+BtnD7aKfRCAlBbIGJYYiSMuwii0RSIQ04UfL4fg+z2ZprvgIjDFvG2MGGWP6G2N+5hz7kTFmrrN/0hhzizFmgDFmnDFmc9S1P3OuG2yMCbGdwweG3RBe89CRPbB9gfV1JBKJEDlUvsEq5xTvIrnjypmcQyFe9X1mXUdAZwSKj4Q5emjdG4AJdr3o5pAIkUOJEjEUoXN/SEkLt5/gjLnOm9oQqgjCzBnzUAijhwpfsw+bRIhMiSbskUOnjtrkeYn0u5yJHArzjGADtGwP7bxZdKmKIOyE0Tx0tAy2fZY4TuJowh45lCg5hmqSNSTchYMijmKPoh5VEYSdnvk2DUCYzEPr5gIm8fwDEP7IoUTJMVSTsEcOeRgxBKoIwk/04rKw2KXXvm7TF3hk7/SVsEcOla+3aVg69fVbEnfJHgKmGvaGMOfQsX1wrNzT2tGqCBKBMC0uO1oOWz+1yitRFvfVJMyRQ+UbbNnNsJULbYgwVyvb6/g2PJylqSJIBHqMseahta/5LUnDrH/Dvpklon8gQpgjhzw2QfhGphM5FEZFEPE3qWlIqZeIeaj4/eA/fNa8at84c4b7LYl3hDVyqOI4HNiWeP4BgLR0GzkUxpla+QZIbwsdeno2hCqCRGH4jcGvXHa4xJqF8m5OXLMQhDdyaF8RYBJzRgDhrVYWSQnu4d+MKoJEIQzmoTWvAgZG3Oy3JN4S1sihcu9t0b6SNRQObIHTJ/2WpGmUb/A8sEIVQaIQBvPQmjnQbRR0GeC3JN4S1sih8vXWjp4IKcFrI2uw9U+FqVrZiQNwdI/nszRVBInEiJuseWjt635Lci77NkHJcsi7xW9J4kMYI4fK1ls7emoLvyXxhjBWK4vTLE0VQSLRfbR1xK6a5bck57J6DiAw4mt+SxIfwhg5lKgRQxHCGDnkcbK5CKoIEgkROO82m77hwDa/pTmLMbD6Feh9IbTv7rc08SFskUOnT1r7eaL6B8BGDmX2D5ki2AAtWkOHXE+HUUWQaOTdarerZ/srRzR7Vlm7bF6CO4mjCVvk0L5iaz9P5BkB2PsLy28CVtYug6zfyUNUESQanXpD7gWwarZ9Ew8Cq2bbKXki5haqi7BFDiVqjqGaZIcscihOKcFjUgQikiki80SkyNl2qqXNKBFZICKFIrJKRG6LOve8iGwRkRXOZ1Qs8igO591mTRIly/2WBKpOW0UwaDK0zvRbmvgRtsih8g0gqdZZnMiEKXLo5CHrZ4rDLC3WGcEjwPvGmIHA+873mhwH7jHGDAcmA0+KSMeo8983xoxyPitilEcBm74hNT0YTuPi+XCsDEbd6bck8SdMkUPl6yGzH6S19FsSb4kkbgtDbYJyx78Uh+SMsSqC64EZzv4M4IaaDYwxG40xRc5+CVAGZMU4rlIfrTraN/DVc+wbuZ8sfwnaZMHASf7K4QdhihwqW5f4/gGwMx5JDYefoGyt3YZgRpBjjNnt7O8BcuprLCLjgHRgU9ThnzkmoydEpM7XERGZJiIFIlJQXl4eo9hJwHm3w/G9UPSefzIc2wsb34GRtyVubHp9hCVy6PRJ2L8psfM/RUhLtwvmwmCyK1tnI4Y69vF8qAYVgYjMF5E1tXy+4PkzxhigTu+kiHQDXgS+boypdg4/CgwBxgKZwMN1XW+MmW6MyTfG5Gdl6YSiQQZOgrZdYemMhtt6xarZUF2ZnGYhCE/k0N4N1m6eiPUhaiNrSEgUQaGV1eOIIWiEIjDGXGGMGVHL53Wg1HnARx70ZbX1ISLtgbeAHxhjFkb1vdtYTgHPAePcuCkF+wZ+/t1QPA8O7oj/+MbAij/ZRW45w+I/fhAIS+RQRFFlJ8GMAOzDdf9mqDzltyT1U7Yubn87saqaucBUZ38qcE5uAxFJB/4KvGCMmVPjXESJCNa/sCZGeZRoRt9tH8jLX4z/2DsLoHSNlSFZCUvkUGmhDS7I7Oe3JPEhDNXKjpbbqmTZ4VAEjwOTRKQIuML5jojki8gzTptbgYuBe2sJE/2TiKwGVgNdgJ/GKI8STafeMOByWPYiVFXGd+wlT0N6Oxh5a3zHDRphiBwqWwddBideVbK6CEO1soijOE6KIKZf3hizD7i8luMFwP3O/kvAS3Vcf1ks4yuNYMy9MOsu6zQe8pX4jHlsLxT+1Y7dsl18xgwqWYNh1UwbOdSqo9/S1E7ZWuhzkd9SxI9I5JAqgjPoyuJEZ9Bk6zRe8nT8xlz2gq2hPPb++I0ZVIIeOXTiIBzelTyOYrBrJTL7BduJX7YWWneGttlxGU4VQaKT2gLG3Q+bPoDStd6PV10FBc9Bny8lR1x6QwQ9cijyVpwsjuII2UOCvaisbJ2dDcSpkp8qgmQg/z4bvbLgt96PtW4uHNoO46Z5P1YYCHrkUGmh3SbTjACCHTlUXe0ogvj9JqoIkoHWmTD6TpuR9Eipd+MYA58+aVP9DrnGu3HCREqKffuMPHCDRtk6aNne08LogSR7GJiqYM4KDu2AiqNx8w+AKoLkYcK3bLqJxdO9G2PLx7B7BVz4HUhJ9W6csJEz3IbSBiUbbDRla+2bZ5xMEIEhZ4TdBlFBx9lRDKoIkofO/WHotbD4aVsH1Qs+fRLa5sDIKd70H1Zy8uD4Pjjq4WysORhzVhEkG537Q1qGVdBB44wiUNOQ4gWXPAKnDnnjK9i2ADZ/CBO/DS0y3O8/zERy+ATtoXNkj30pSDZHMdgZa/bQ4P0mYIM6OvSCjPZxG1IVQTLRdYRNUb3w93Bsn3v9GgPzH7NhqmMfcK/fROGMIgiYGcKHN89AkTM8eL8JnI0YiiOqCJKNSx+FimPw6a/c67PoPdixEC59GNJbu9dvotA6E9r3gD0Be/s8k2MoSXNB5eTZNA5eBlA0larTds1JnJWzKoJkI3uIjSBa9IezhS9ioeo0zPuxXaCTzHmFGiKIb59la61Pp01nvyXxhyCa7PYVQ/XpuKcEV0WQjFz+GKS3gb99P/ZIloW/g/J1cNV/JmfNgcaSM8Kme66s8FuSs5QWJq9ZCIJpsvNpXYcqgmSkbRZ8+d9h80ew5i/N7+fANvjocRh8DQy+2jXxEpKc4bY2w96AxK1XVTppjkf4LYl/REx2QZoRlK6BlBY2CWAcUUWQrOR/A3rkw1vfg0M7m359VSW8Os0m77r6cfflSzS65tltUN4+9xVB1SnoOtJvSfwlaCa7Pavtque09LgOq4ogWUlNg5uetrmBXp3WdJPFxz+3DuJrn4COud7ImEhk9ofUlvYPPQhE5IgoqGQlZ7hdXRwUk92e1b78JqoIkpnMfvZBvu0zeOO7jfcXrHoFPvmFLUE58hZvZUwUUtOClWpizyqrmLoM9FsSf8kZYZ2zQcgOe6TULjoMmyIQkUwRmSciRc62Ux3tqqKK0syNOt5XRBaJSLGIzHKqmSnxZOStNqR05Z/hbw/bhFf1seZVeO2b0Psiq0SUxpOTFyBFsNo6JJPdwR+kVBOl/s3SYp0RPAK8b4wZCLzvfK+NE8aYUc7nuqjjPweeMMYMAA4A98Uoj9IcLnkYJnwbFj8FM2+vPa66sgI++CnM+Qb0zIcpf7J53ZXGkzMcjpXB0VpLe8cPY3wzQQSOzgPszKg0ACa7M+a6+DvwY61Ndz1wqbM/A/gIeLgxFzp1ii8D7oi6/jHg9zHKpDQVEbjqZ7a05Xs/hP89H867HfpcaPOx7F5l6x4f2mHNQV/5b1041hwif+Cla6Ctj8X5juy2uY+S3VEMwTLZ7VkNHXKhVa2GFU+JVRHkGGN2O/t7gJw62mWISAFQCTxujHkN6AwcNMZEiunuBHrUNZCITAOmAeTmqnPSdURg/IPQ/zL45JewbEZUVTOB3Inw1SdhwBV+ShlusqPi1vv7qAjUUfxFckZA8Xy/pfB1ltagIhCR+UDXWk79IPqLMcaISF3ext7GmF0i0g/4wClYf6gpghpjpgPTAfLz8wOYzzdB6DIQvjYdvvobG/NeXQmd+tqYayU22nSGdt38jxyKjB/n1auBJWc4rPiTNdnFqTTkOVQct6uKh3/Nl+EbVATGmDpfAUWkVES6GWN2i0g3oFbjpzFml7PdLCIfAaOBvwAdRSTNmRX0BHY14x4UL2iRAd3O81uKxKPbebB7pb8y7FltlXscs1sGmsj/890rYeAkf2QoWwem2hf/AMTuLJ4LTHX2pwKv12wgIp1EpKWz3wW4EFhrjDHAh8DN9V2vKAlFt1E2VLHimH8yqKP4i0R8JSUr/JNhzyq79el3iVURPA5MEpEi4ArnOyKSLyLPOG2GAgUishL74H/cGBOpov4w8D0RKcb6DP4YozyKEmy6j7Jvfn6Zh04dsbV61VF8loz2Nnpo9wr/ZNiz2pYM7djbl+FjchYbY/YBl9dyvAC439n/HKhVzRljNgPjYpFBUUJFt1F2W7ICcifEf/zSQsD4ZoIILN1GwfYF/o2/Z5V1WvtUMlRXFitKPGnfzRbw8evts2S53XYf7c/4QaX7aDi8C46Wx3/sqtN2RuDjb6KKQFHiTfdRZx/I8WbXMmjXHdrVFgiYxHQfZbd+KOiydVB5EnqcH/+xHVQRKEq88dNhXLJcZwO14afDOACzNFUEihJv/HIYnzxk00/3UEVwDhGHsR8ztZJlkNHBJoH0CVUEihJvoh3G8SQyns4IaqfbKH9MQ5FZmk+OYlBFoCjxxy+Hcckyu+3uny060PjhMD590kZy+aycVREoih/44TAuWW7j1DVdSO344TAuXWPTuPisnFURKIofRBzGp47Gb8xdy32NTAk8ZxzGcVTQkbF8/l1UESiKH/QYYx3G8XroHNsLh7b7/uYZaDLa26LxO5fEb8xdy6BNFrSvM/FyXFBFoCh+0DPfbncujs94AQhRDAW9xllF0NiyrbFSstwqZx8dxaCKQFH8oXUmdBkEO+L09rljMUjKWTu4Uju9xsGJAzYltNecOAjl6+3s0GdUESiKX/QcZ2cE8Xj73LHI5t1v2c77scJMTyf12Y5F3o+1qwAwkDve+7EaQBWBovhFr3G2ZOT+zd6OU1UJOwugl/8PnMDTZZBd3LUjDia77YvsLE1nBIqSxPSK09tnWSGcPga9fMh2GjZSUqDn2Pg4jHcsshlHAzBLU0WgKH7RZTC0jMPb53ZH0fTSjO+Notd4mwjuZJOq6TaNgM3SVBEoil+kpNjoIa8VwY5FtlZyx1xvx0kUeo4FjH1Qe0VkluZHTYpaiEkRiEimiMwTkSJn26mWNl8WkRVRn5MicoNz7nkR2RJ1blQs8ihK6Og1HsrWwsnD3o2xY5GdDfgcohgaeoyxtnsvzUMBm6XFOiN4BHjfGDMQeN/5/gWMMR8aY0YZY0YBlwHHgfeimnw/ct4YsyJGeRQlXPQah3379GhWcLgEDu1Q/0BTyGgP2cO9rVi2Y5GtC9Ghl3djNIFYFcH1wAxnfwZwQwPtbwb+Zow5HuO4ipIY9BoPKS1gy9+96X/rZ3YbEBNEaOhzkX1rrzzlft/GwNZP7W8SkFlarIogxxiz29nfA+Q00H4K8HKNYz8TkVUi8oSItKzrQhGZJiIFIlJQXu5DOTlF8YL01tZPsOUTb/rf8pENh+x2njf9Jyp9L4bKE974CfYWwdE90O8S9/tuJg0qAhGZLyJravlcH93OGGOAOlfGiEg3bBH7d6MOPwoMAcYCmcDDdV1vjJlujMk3xuRnZWU1JLaihIe+F9uMl15EqWz5BPp8CVJS3e87kel9gfUTeKGgt3xst30vdr/vZtKgIjDGXGGMGVHL53Wg1HnARx70ZfV0dSvwV2PM6ai+dxvLKeA5IBieE0WJJ32+ZBPQbfvc3X4PbIWD26FvcN48Q0OrjnYWtdUDk92Wj6FDLnTq637fzSRW09BcYKqzPxV4vZ62t1PDLBSlRATrX1gTozyKEj56joW0DPffPiP9BejNM1T0+ZIN7a1w0aVZXW39QX0vDox/AGJXBI8Dk0SkCLjC+Y6I5IvIM5FGItIH6AV8XOP6P4nIamA10AX4aYzyKEr4aJFho4fcdhhv+QTa5kDWYHf7TRb6XgLVp91d+V26Gk4eDJxyTovlYmPMPuDyWo4XAPdHfd8KnJNw2xhzWSzjK0rC0Pdi+OCntkxiWxd8YMZYRRCwN89QkTsBUtJg80fQ/8vu9Lk5eP4B0JXFihIMBlxht8Xz3elvz2o4Wgr9LnWnv2SkZVvInQhF7zXctrEUz4esIbZudYBQRaAoQaDredaMs/Edd/rb6ATnDbzSnf6SlUFX2ZXfB3fE3tfJw7DtM9tnwFBFoChBICUFBk6CTR9A1emG2zfExr/ZVAlts2PvK5kZ6Dy0i96tv11j2PSBLVQ/aHLsfbmMKgJFCQqDJsOpw7B9YWz9HC2DXUth0NXuyJXMdBlowzw3uqAINr4LrTqdLX4TIFQRKEpQ6HepTTcRq3koYtMOoAkidIjYf8ctn0DFseb3U11lf5cBkyA1phgdT1BFoChBoWU76H8ZFL5m482by9rXoX1P6JrnmmhJzdCvQuXJ2BT0ts/h+F4YHMxZmioCRQkSeTfD4Z3Nz0Z6bJ+1RefdpGGjbpE70dZzWPNq8/tYMwdatAmkfwBUEShKsBh8tV1lvOYvzbt+7WvWITniZlfFSmpSUmH4jda005x8UJUVdpY35BqbZDCAqCJQlCDRsp21SRf+1ZYzbCpr/mJLYKpZyF1G3ARVFbDuzaZfu+l9u5o4L7jKWRWBogSNvFvhWDkUz2vadQe22jj1vJvVLOQ2PcZAZj9Y/lLTr135MrTKtP6fgKKKQFGCxqDJ1ia95I9Nu27JH0FSYfRd3siVzIjAmHth++dQurbx1x0usbOIUXdAagvPxIsVVQSKEjRS0+D8qTYdwf4tjbvm9AlY/qK1Q7fv7q18ycqouyC1JRQ0QUEvfd6mGB97n2diuYEqAkUJImOm2oRnn/+mce1X/AlOHIBx07yVK5lp09ma3Zb/yS7aa4iKY3aWNnCSNSsFGFUEihJE2neH8++GZS82nOfm9En45H9sgfo+F8VHvmTlS/8CVacap6AXT7drBy7+vvdyxYgqAkUJKhd9z24//Fn97ZY8DUdK4Mv/pk5ir+ncH/JugcXPwIFtdbc7vh8++7VdSdwreCklaqKKQFGCSsdecME/2qiTTR/W3ubgdvjwv+wDJ0DF0BOay35o1xa89T1b96E23vuhzTZ6xWNxFa25xKQIROQWESkUkWoRya+n3WQR2SAixSLySNTxviKyyDk+S0TSY5FHURKOS/4VMvvDa9+0ESjRnD4Bs6faWcC1v/JHvmSkYy+4/EfWmb/g/517fsXLsOIluPC70HVE/OVrBrHOCNYAXwPqLLYqIqnAb4GrgWHA7SIyzDn9c+AJY8wA4AAQbNe6osSbFq3g1hfg1BF4/hrYvdIeP7gDXroJSpbB16ZDx1x/5Uw2xj4Aw663b/4f/xIqT9nEcouegte/besdf/nf/Jay0cRaqnIdgNRvlxwHFBtjNjttZwLXi8g64DLgDqfdDOAx4PexyKQoCUfXEXDXqzDrTnjqYmjX3VYfS20BN/3Rhowq8SUlBW6cbrPFfvhT6zxOSbWRWwOugFueD/S6gZrEIx9qDyA67GEnMB7oDBw0xlRGHT+nrnEEEZkGTAPIzdW3HyXJyB0PDy2BZS/YBU0dc+H8e6yZQvGHFhlw0zN2sdj6t2yOp4GTYMi1oXPaN6gIRGQ+0LWWUz8wxrzuvki1Y4yZDkwHyM/Pr8NDoygJTKtO1u6sBAcRGHC5/YSYBhWBMeaKGMfYBUS/tvR0ju0DOopImjMriBxXFEVR4kg8wkeXAAOdCKF0YAow1xhjgA+BSEq+qUDcZhiKoiiKJdbw0RtFZCcwEXhLRN51jncXkbcBnLf9h4B3gXXAbGNModPFw8D3RKQY6zNoYpYtRVEUJVbE1LUgIsDk5+ebgoICv8VQFEUJFSKy1BhzzpovXVmsKIqS5KgiUBRFSXJUESiKoiQ5qggURVGSnFA6i0WkHKgnB2y9dAH2uihOGNB7Tg70nhOfWO+3tzEmq+bBUCqCWBCRgtq85omM3nNyoPec+Hh1v2oaUhRFSXJUESiKoiQ5yagIpvstgA/oPScHes+Jjyf3m3Q+AkVRFOWLJOOMQFEURYlCFYGiKEqSk1CKQEQmi8gGESkWkUdqOd9SRGY55xeJSJ+oc486xzeIyFVxFbyZNPd+RWSSiCwVkdXO9rK4C99MYvmNnfO5InJURP5P3ISOkRj/X48UkQUiUuj83hlxFb6ZxPB/u4WIzHDudZ2IPBp34ZtJI+75YhFZJiKVInJzjXNTRaTI+Uxt8uDGmIT4AKnAJqAfkA6sBIbVaPMt4A/O/hRglrM/zGnfEujr9JPq9z15eL+jge7O/ghgl9/34/U9R52fA7wC/B+/7ycOv3MasAo4z/neOej/r1245zuAmc5+a2Ar0Mfve3LpnvsAI4EXgJujjmcCm51tJ2e/U1PGT6QZwTig2Biz2RhTAcwErq/R5npghrM/B7hcRMQ5PtMYc8oYswUodvoLMs2+X2PMcmNMiXO8EGglIi3jInVsxPIbIyI3AFuw9xwWYrnnK4FVxpiVAMaYfcaYqjjJHQux3LMB2ohIGtAKqAAOx0fsmGjwno0xW40xq4DqGtdeBcwzxuw3xhwA5gGTmzJ4IimCHsCOqO87nWO1tjG2YM4h7FtSY64NGrHcbzQ3AcuMMac8ktNNmn3PItIWWwjpP+Igp5vE8jsPAoyIvOuYFP41DvK6QSz3PAc4BuwGtgP/bYzZ77XALhDLMyjm51eDNYuVxEVEhgM/x745JjqPAU8YY446E4RkIA24CBgLHAfedwqTvO+vWJ4yDqgCumPNJH8XkfnGmM3+ihVsEmlGsAvoFfW9p3Os1jbO1LEDsK+R1waNWO4XEekJ/BW4xxizyXNp3SGWex4P/EJEtgL/BPybiDzksbxuEMs97wQ+McbsNcYcB94Gzvdc4tiJ5Z7vAN4xxpw2xpQBnwFhyEUUyzMo9ueX304SF50taVgnSV/OOluG12jzbb7oYJrt7A/ni87izQTcqRbj/XZ02n/N7/uI1z3XaPMY4XEWx/I7dwKWYZ2macB84Bq/78nje34YeM7ZbwOsBUb6fU9u3HNU2+c511m8xfm9Ozn7mU0a3+9/AJf/Mb8CbMR633/gHPsJcJ2zn4GNGCkGFgP9oq79gXPdBuBqv+/Fy/sF/h1rR10R9cn2+368/o2j+giNIoj1noG7sM7xNcAv/L4Xr+8ZaOscL3SUwPf9vhcX73ksdpZ3DDv7KYy69hvOv0Ux8PWmjq0pJhRFUZKcRPIRKIqiKM1AFYGiKEqSo4pAURQlyVFFoCiKkuSoIlAURUlyVBEoiqIkOaoIFEVRkpz/D6Xje5gjPs+cAAAAAElFTkSuQmCC",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "ratio = 2\n",
+ "first = 1\n",
+ "(length,) = x.shape\n",
+ "slop = int(length/6)\n",
+ "second = ratio-first\n",
+ "odd = ratio % 2\n",
+ "\n",
+ "first = int(first * length/ratio) + odd\n",
+ "second = int( second * length/ratio)\n",
+ "slop = np.array(np.append(np.zeros(first-slop) , (np.arange(slop))/slop))\n",
+ "#steep = np.ones(int(first * length/ratio)+ odd) - np.exp(-np.arange(int(first * length/ratio) + odd)/200)\n",
+ "steep = (np.ones(first) + slop)*0.5\n",
+ "\n",
+ "step = np.append(steep, np.ones(second))\n",
+ "m = np.sin(30 * 2.0 * np.pi * x) * step \n",
+ "plt.plot(x, step, '-')\n",
+ "plt.plot(x, m, '-')"
+ ]
}
],
"metadata": {