{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Kako narediti zglajen pravokoten signal?\n", "\n", "Pogosto nas zanima odziv vezja na pravokoten periodični signal. Nastopi pa težava, ko potrebujemo odvod pravokotnega signala. Odvod pravokotne funkcije bi bil povsod 0 razen ob prehodu, kjer pa bi bil odvod neskončen. S takim signalom pa ni mogoče izvajati numeričnih operacij. Niti v praksi odvod pravokotnega signala ne more biti neskončen. Če bi imeli tak tokovni vir priključen na idealno tuljavo, bi se na njej ob prehodu pojavila neskončna napetost, saj velja $u_L(t)=L \\frac {di(t)}{dt}$. Zato tedaj, ko potrebujemo odvod pravokotnega signala, moramo le tega preoblikovati tako, da ta odvod ne bo neskončen. Izdelavi in analizi takih signalov je tema tega Jupyter zvezka.\n", "\n", "\n", "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Pravokoten periodičen signal\n", "\n", "Pravokoten periodičen signal preprosto naredimo z uporabo SciPy knjižnice. Se pa pojavi problem odvoda. Če odkomentiramo zadnjo vrstico spodnje celice, bo Jupyter vrnil napako. Odvoda te funkcije torej ne moremo narediti." ] }, { "cell_type": "code", "execution_count": 423, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The slowest run took 5.84 times longer than the fastest. This could mean that an intermediate result is being cached.\n", "10000 loops, best of 3: 143 µs per loop\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAG8AAAAVBAMAAAC6Uq30AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n", "text/latex": [ "$$\\left ( -1.2, \\quad 1.2\\right )$$" ], "text/plain": [ "(-1.2, 1.2)" ] }, "execution_count": 423, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy import signal\n", "\n", "def Signal(t): # vzbujalni signal kot funkcija. Nato rabim še Ugt - vzbujalni signal kot niz (glej spodaj)\n", " return signal.square(omega* t) #+ Ug\n", "\n", "ts=np.linspace(0,1e-3,1000)\n", "omega=20/max(ts)\n", "y=Signal(ts)\n", "plt.plot(ts,y )\n", "plt.ylim(-1.2, 1.2)\n", "#dy=diff(y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "## 2. H funkcija\n", "Ideja je iz http://hplgit.github.io/primer.html/doc/pub/funcif/._funcif-bootstrap004.htmlm, kjer je opisan primer naslednje funkcije, ki omogoči zvezen prehod iz 0 v 1.\n", "\n", "\\begin{equation}\n", "H_{\\epsilon}(x) = \\left\\lbrace\n", "\\begin{array}{ll}\n", "0, & x < -\\epsilon,\\\\ \n", "\\frac{1}{2} + {x\\over 2\\epsilon} + {1\\over 2\\pi}\\sin\\left(\\pi x\\over\\epsilon\\right), & -\\epsilon \\leq x \\leq \\epsilon\\\\ \n", "1, & x > \\epsilon\n", "\\end{array}\\right.\n", "\\end{equation}\n", "\n", "Funkcija H je napisana tako, da omogoča realizacijo pravokotnega signala doložine $width$, s periodo $w_{single}$ in številom period $n_{repeat}$. s parametrom $eps$ se določa strmino prehoda iz 0 v 1.\n", "\n", "Funkcija H sprejme tri parametre, a = začetek stopnice, w = širina stopnice, x je niz vrednosti, v katerih naj se izračuna H. Funkcija vrne niz y, ki vsebuje eno periodo pravokotnega signala. y2 je niz, ki vrne vrednosti signala za $n_{repeat}$ period. \n", "\n", "dH je numeričen odvod funkcije H. dy2 je numeričen odvod za $n_{repeat}$ period. " ] }, { "cell_type": "code", "execution_count": 417, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "from sympy import *\n", "from IPython.display import *\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline \n", "init_printing(use_latex=True)" ] }, { "cell_type": "code", "execution_count": 425, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3000\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 425, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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EVAJvVCC0OvJZs4QXVt45VhHP077NXrMCA/66XZcBgjrESUXf6/DId+VRlK9Z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\n+A/mNTPzHz6N5TLRclTHang0ElidLi0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "eps=0.001\n", "astart=0.01 # zaćetek stopnice , najmanj eps\n", "width=0.04 # širina stopnice\n", "w_single=0.1 # dolžina ene periode\n", "n_repeat=3 # število period (ponovitev)\n", "\n", "def H(a,w,x):\n", " n=len(x)\n", " if w < a:\n", " raise ValueError(\"w must be larger than a\")\n", " elif a(-eps+a) and x[i]<(eps+a): y[i]=(1/2+(x[i]-a)/(2*eps)+np.sin(np.pi*(x[i]-a)/eps)/(2*np.pi))\n", " elif x[i]>(eps+a) and x[i]<(-eps+a+w): y[i]=1 \n", " elif x[i]>(-eps+a+w) and x[i]<(eps+a+w): y[i]=1-(1/2+(x[i]-a-w)/(2*eps)+np.sin(np.pi*(x[i]-a-w)/eps)/(2*np.pi))\n", " else: y[i]=0\n", " \n", "cas=np.linspace(0,w_single,1000)\n", "dt=cas[1]\n", "y=np.zeros(1000)\n", "\n", "H(astart,width,cas)\n", "dy_temp=np.diff(y)/dt\n", "dy=np.append(dy_temp,0)\n", "\n", "cas2=np.linspace(0,w_single*n_repeat,1000*n_repeat)\n", "y2=[]\n", "dy2=[]\n", "for i in range(n_repeat):\n", " y2=np.append(y2,y)\n", " dy2=np.append(dy2,dy)\n", "print(len(cas2))\n", "\n", "fig, (ax1, ax2) = plt.subplots(1, 2,figsize=(10,5))\n", "fig.suptitle('Levo signal, desno njegov odvod')\n", "ax1.plot(cas2, y2)\n", "ax2.plot(cas2, dy2)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Analiza fft H funkcije\n", "Npr. po https://gist.github.com/jedludlow/3919130 \n" ] }, { "cell_type": "code", "execution_count": 419, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 419, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f_s=100/(w_single) # sampling freq = 50 x osnovna\n", "fft_x = np.fft.fft(y)\n", "n = len(fft_x)\n", "freq = np.fft.fftfreq(n, 1/f_s)\n", "#print(freq)\n", "plt.plot(np.abs(fft_x))" ] }, { "cell_type": "code", "execution_count": 420, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "20\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 420, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n1 = 20 #int(np.ceil(n/20.0))\n", "print(n1)\n", "fft_x_n1 = (2.0 / n) * fft_x[:n1]\n", "freq_n1 = freq[:n1]\n", "\n", "plt.plot(freq_n1, np.abs(fft_x_n1),'.-')\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.ylabel(\"Amplitude\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Naredim še integracijo odvoda, da vidim, če dobro rekonstruira signal\n", "Integral odvoda funkcije mora namreč dati nazaj prvotno funkcijo.To tudi dejansko dobimo." ] }, { "cell_type": "code", "execution_count": 421, "metadata": {}, "outputs": [ { "data": { "image/png": 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XpWqdSr3hxIg0STPNC45MKATPfRQMoJSNCbWlGWPuBe5ddeyONc796TDL0gku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\nyO4Qy8THv/EMxXKNn7hxX5i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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "yint2=np.cumsum(dy2)\n", "\n", "plt.plot(cas2, yint)\n", "plt.xlabel('Čas')\n", "plt.ylabel('Signal')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Naredimo še zapis signala in odvoda v obliki funcije, ki vrača le vrednost v točki\n", "\n", "Odvod je analitično izračunan in vstavljen v funkcijo dH1.\n", "Odvod je izračunan kot \n", "$dH(x)=\\frac{1}{2 \\epsilon}(1+\\cos(\\frac{\\pi x}{\\epsilon})) $ torej\n", "\n", "\\begin{equation}\n", "dH_{\\epsilon}(x) = \\left\\lbrace\n", "\\begin{array}{ll}\n", "0, & x < -\\epsilon,\\\\ \n", "\\frac{1}{2 \\epsilon}\\left(1 + \\cos\\left(\\pi x\\over\\epsilon\\right) \\right), & -\\epsilon \\leq x \\leq \\epsilon\\\\ \n", "1, & x > \\epsilon\n", "\\end{array}\\right.\n", "\\end{equation}\n", "\n", "Velikost odvoda bo očitno odvisna od parametra $eps$. Pri manjšem parametru $eps$ bo odvod večji. " ] }, { "cell_type": "code", "execution_count": 429, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10 loops, best of 3: 91 ms per loop\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 429, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Lw38qIveKyD3Ai4D/r9fjajdEEwqJ3gpv0u6cWcdYeWxBxsixat/l03lp2yfS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\nVtgz0GlMBXGXSCjIWE+7FQlVkBeDcHamuWOWyynOx1fZO2DemO31UYx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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "eps=0.01 # funkcija se zvezno spreminja od 0 do 1 znotraj območja 2*eps\n", "astart=0.01 # zaćetek stopnice , najmanj eps\n", "width=0.02 # širina stopnice\n", "w_single=0.05 # dolžina ene periode\n", "n_repeat=3\n", "\n", "\n", "def H1(a,w,x):\n", " if x>w_single:\n", " x=x-np.fix(x/w_single)*w_single\n", " if x<(-eps+a): return 0\n", " elif x>(-eps+a) and x<(eps+a): return (1/2+(x-a)/(2*eps)+np.sin(np.pi*(x-a)/eps)/(2*np.pi))\n", " elif x>(eps+a) and x<(-eps+a+w): return 1 \n", " elif x>(-eps+a+w) and x<(eps+a+w): return 1-(1/2+(x-a-w)/(2*eps)+np.sin(np.pi*(x-a-w)/eps)/(2*np.pi))\n", " else: return 0\n", "\n", "def dH1(a,w,x): \n", " if x>w_single:\n", " x=x-np.fix(x/w_single)*w_single\n", " if x<(-eps+a): return 0\n", " elif x>(-eps+a) and x<(eps+a): return (1/(2*eps)+np.cos(np.pi*(x-a)/eps)/(2*eps))\n", " elif x>(eps+a) and x<(-eps+a+w): return 0 \n", " elif x>(-eps+a+w) and x<(eps+a+w): return -(1/(2*eps)+np.cos(np.pi*(x-a-w)/eps)/(2*eps))\n", " else: return 0\n", "\n", "\n", "\n", " \n", "cas=np.linspace(0,w_single*n_repeat,2000)\n", "\n", "y=np.zeros(2000)\n", "dy=np.zeros(2000)\n", "\n", "def test():\n", " for i in range(len(cas)):\n", " y[i]=H1(astart,width,cas[i])\n", " dy[i]=dH1(astart,width,cas[i]) \n", " \n", "test()\n", "fig, (ax1, ax2) = plt.subplots(1, 2,figsize=(10,5))\n", "fig.suptitle('Levo signal, desno odvod signala')\n", "ax1.plot(cas, y)\n", "ax2.plot(cas, dy)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\\begin{equation}\n", "H_{\\epsilon}(x) = \\left\\lbrace\n", "\\begin{array}{ll}\n", "0, & x < -\\epsilon,\\\\ \n", "\\frac{1}{2} + {x\\over 2\\epsilon} + {1\\over 2\\pi}\\sin\\left(\\pi x\\over\\epsilon\\right), & -\\epsilon \\leq x \\leq \\epsilon\\\\ \n", "1, & x > \\epsilon\n", "\\end{array}\\right.\n", "\\tag{}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "## 3. Pravokoten periodični signal tvorjen s Fourierovo vrsto\n", "\n", "Pravokotni signal naredimo s pomočjo Fourierove vrste,glej npr.\n", "\n", "http://mathworld.wolfram.com/FourierSeriesSquareWave.html\n", "\n", "\\begin{equation}\n", "f(x)= \\frac{4}{\\pi} \\sum_{n=1,3,5}^{\\infty} \\frac{1}{n} \\sin (\\frac{n\\pi x}{L} )\n", "\\end{equation} \n", "\n", "V konkretnem primeru smo vzeli n =1,3, .. 199. Spreminjaj n v drugi vrstici in glej rezultat." ] }, { "cell_type": "code", "execution_count": 431, "metadata": {}, "outputs": [], "source": [ "t = np.linspace(-np.pi, np.pi, 201) # t=pi*x\n", "n = np.arange(1, 100)\n", "n = 2 * n - 1 # liha števila\n", "f = np.zeros_like(t)" ] }, { "cell_type": "code", "execution_count": 434, "metadata": {}, "outputs": [], "source": [ "def test():\n", " for i, ti in enumerate(t):\n", " f[i] = np.sum(np.sin(n * ti)/n)\n", "\n", "f = (4 / np.pi) * f\n", "test()\n", "\n", "dt=t[1]-t[0]\n", "df_temp=np.diff(f)/dt\n", "\n", "\n", "df=np.append(df_temp,0)" ] }, { "cell_type": "code", "execution_count": 409, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 409, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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aPNZsMiKGSmI0BInXvrQupiMpuxlYK+lESXOAc0jXg2uTtAb4EvCOiPhhx/aF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\nZWZmZmYl4KTMzMzMrAT+HwdedJd2JuoDAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax1, ax2) = plt.subplots(1, 2,figsize=(10,5))\n", "fig.suptitle('Levo signal, desno odvod signala')\n", "ax1.plot(t, f)\n", "ax2.plot(t, df)\n", "\n" ] }, { "cell_type": "code", "execution_count": 410, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 410, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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O7UE8VlG+9mU1lHDy2CURsTEtPwgsSct72vZZTbUTseFmA+dkNp2h2XwySa8l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\nPFsNtXztS7NCafT5mtqVT8o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GxLfT+pcDXwTmA1cA74sejo/IwpPHmhVNPy9I3m1P2Uws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\nrACclJmZmZkVgJMyMzMzswL4/wEqgfnJ3tQMcwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df2 = np.zeros_like(t)\n", "for i, ti in enumerate(t):\n", " df2[i] = np.sum(np.cos(k * ti))\n", "\n", "df2 = (4 ) * df2\n", "\n", "fig, (ax1, ax2) = plt.subplots(1, 2,figsize=(10,5))\n", "fig.suptitle('Levo signal, desno odvod signala')\n", "ax1.plot(t, f)\n", "ax2.plot(t, df2)" ] }, { "cell_type": "code", "execution_count": 350, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 350, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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EnbGAnR1rjCk48Wwiqnm9OPg56YydTePmunGUuDP2jWmMMYUkm4jmOaOfA4F+/Fw3Scdq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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f_s=100/(np.pi) # sampling freq = 50 x osnovna\n", "fft_x = np.fft.fft(f)\n", "n = len(fft_x)\n", "freq = np.fft.fftfreq(n, 1/f_s)\n", "#print(freq)\n", "plt.plot(np.abs(fft_x))\n", "\n" ] }, { "cell_type": "code", "execution_count": 349, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "101\n" ] }, { "data": { "image/png": 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lku1UKWj2kYhIXE+SwlnAh4G309F95OH9IaWjUojtfeRKCiIikZ4khfcDs3q431FFy1cK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\nzyt2HCCdzTF7bJK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n1 = int(np.ceil(n/2.0))\n", "print(n1)\n", "fft_x_n1 = (2.0 / n) * fft_x[:n1]\n", "freq_n1 = freq[:n1]\n", "\n", "\n", "plt.plot(freq_n1, np.abs(fft_x_n1),'.-')\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.ylabel(\"Amplitude\")\n", "plt.grid()" ] }, { "cell_type": "code", "execution_count": 348, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 0.15836313 0.31672625 0.47508938 0.63345251 0.79181564\n", " 0.95017876 1.10854189 1.26690502 1.42526815 1.58363127] [ 5.44616867e-16 1.27291850e+00 6.76967709e-04 4.17045194e-01\n", " 1.19790455e-03 2.46699323e-01 1.70096583e-03 1.73384465e-01\n", " 2.18143173e-03 1.32425388e-01 2.64247785e-03]\n" ] } ], "source": [ "print(freq_n1,abs(fft_x_n1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "## 4. Tretja varianta / sigmunoidna funkcija\n", "\n", "Poglejmo še eno varianto (po https://kitchingroup.cheme.cmu.edu/pycse/pycse.html), signunoidno funkcijo:\n", "\n", "\\begin{equation}\n", "\\sigma(x) = \\frac{1}{1 + e^{-(x-x0)/\\alpha}}$\n", "\\end{equation}\n", "\n" ] }, { "cell_type": "code", "execution_count": 412, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 412, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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EbI6IjojoaG9vn6bSzGa2IwPDRMDSeR4+svpJ2e/cD6yqOV5ZOVerA7hXEsBy4CpJpYj4\nu4R1mRVCd98QAG3z3VOw+kkZCtuAdZLWUg6Da4FP1DaIiLUnPpd0D/CAA8FsfA73V0LBw0dWR8lC\nISJKkm4DHgSagbsjYoekWyrXN6X62WaNoNpTcChYHSW9bSEitgJbTzp3yjCIiE+mrMWsaA5X9lJY\n4jkFq6OsJ5rNbJK6K8NHSz2nYHXkUDDLqZ7+IVqbm5jX2px1KVYgDgWznDrcN0zb/FlU7t4zqwuH\ngllOdfcPeZLZ6s6hYJZThx0KloBDwSynuvuGaJvvO4+svhwKZjl1uH/YPQWrO4eCWQ6NjgY9Hj6y\nBBwKZjl0dLDEaHjdI6s/h4JZDnVX1z3ynILVl0PBLId6+r1CqqXhUDDLoR4vhmeJOBTMcqinshie\nh4+s3hwKZjl02MNHlohDwSyHuvuGaGkSC2cnXf3eGpBDwSyHevqHWTKv1YvhWd05FMxyqKdvyPMJ\nloRDwSyHevqHPJ9gSTgUzHKovMSFewpWfw4Fsxzq6R/2NpyWhEPBLGcigp6+IZb4wTVLwKFgljPH\njpcojQZLHQqWgEPBLGd6+spPMy/xnIIl4FAwy5nqYnjuKVgCDgWznOn2EheWkEPBLGcOey8FS8ih\nYJYzJ+YUfEuqpeBQMMuZnv4hmgSL5rinYPXnUDDLmZ7+8jMKTU1eDM/qz6FgljM9fcO+HdWSSRoK\nkjZI2iWpU9Ltp7j+a5KelPSUpB9LujhlPWZF0NM/5AfXLJlkoSCpGbgTuBJYD1wnaf1JzV4APhgR\nFwGfBzanqsesKLq9xIUllLKncBnQGRG7I2IIuBfYWNsgIn4cET2Vw0eAlQnrMSuEw/3DLJ3v4SNL\nI2UorAD21hzvq5w7nd8Avn+qC5JulrRd0vaurq46lmiWLxFBd/+Qn2a2ZGbERLOkD1EOhc+e6npE\nbI6IjojoaG9vn97izGaQ3sESQ6VRli1wKFgaKXf93g+sqjleWTn3cyS9A7gLuDIiDiWsxyz3XjrU\nD8DqpfMzrsSKKmVPYRuwTtJaSa3AtcCW2gaSVgP3A78eEc8mrMWsEPZ09wGweum8jCuxokrWU4iI\nkqTbgAeBZuDuiNgh6ZbK9U3AfwWWAX8pCaAUER2pajLLuz0negrLHAqWRsrhIyJiK7D1pHObaj6/\nCbgpZQ1mRfLSoX6WL2hlweykv7rWwGbERLOZjc9L3f0eOrKkHApmOfJSdz/nLfMks6XjUDDLieOl\nEV4+MuCegiXlUDDLiX09A0T4ziNLy6FglhMnnlE4z3ceWUIOBbOc2HOo8oyCQ8ESciiY5cSe7n7m\ntTbTvmB21qVYgTkUzHJib+V21MqDnmZJOBTMcmLPoX5WeZLZEnMomOXA6GiUn1FwKFhiDgWzHDhw\n9DjHS6O+88iScyiY5cDrdx75aWZLy6FglgN7uivPKHj4yBJzKJjlwN7ufpoEK9rmZl2KFZxDwSwH\n9hzq501L5jKr2b+ylpb/h5nlwJ7ufk8y27RwKJjlwEuH+rwvs00Lh4LZDHekf5ie/mH3FGxaOBTM\nZrh/6uwC4JLVbRlXYo3AoWA2wz204zWWzm/l0vMcCpaeQ8FsBhseGeUfdh3gireeRXOTF8Kz9BwK\nZjPYo7u7OTpY4iMXnpN1KdYgHApmM9hDO19lzqwm3v/m5VmXYg3CoWA2Q0UED+98jQ+sa2dua3PW\n5ViDcCiYzVBP7+/llSODfHj92VmXYg3EoWA2Qz2881WaBFe8zaFg08ehYDZDPbTzNTrWLGXp/Nas\nS7EG4lAwm4Eef6mHn716lI946MimmUPBbIbpOnqc3/rm46xsm8t/uHRV1uVYg2nJugAze93wyCi3\nfvtxDg8Mcd9v/iKL583KuiRrMA4FsxnkS1uf4ScvdPOVX30nF75pcdblWANKOnwkaYOkXZI6Jd1+\niuuS9BeV609KuiRlPWYzUUTwz50H+bW7HuGv//lFbnjfGv7tu1ZkXZY1qGQ9BUnNwJ3Ah4F9wDZJ\nWyJiZ02zK4F1lY/3AF+r/GtWSMdLI/QOlOg6epxnXzvKrteO8qPnDvLU/iO0L5zN5656Kze+b23W\nZVoDSzl8dBnQGRG7ASTdC2wEakNhI/CNiAjgEUlLJJ0bEa/Uu5gfPNvFFx7YeeaGZjXidOcj3tgu\nXv98ZDQYjWBkNBgeCYZHRhkcHuF4afTnvq6lSVxw9kK+eM3b+fglK5kzy08uW7ZShsIKYG/N8T7e\n2As4VZsVwM+FgqSbgZsBVq9ePaliFsxuYd3ZCyb1tdbYxGlWJ9UbD6XyyWZBU5NokmhtaaK1uYnW\nliYWz53FojkttM1vZd1ZC1m7fD6tLb4J0GaOXEw0R8RmYDNAR0fH6d68jenS89q49LxL61qXmVnR\npHyLsh+ovcl6ZeXcRNuYmdk0SRkK24B1ktZKagWuBbac1GYLcH3lLqT3AkdSzCeYmdn4JBs+ioiS\npNuAB4Fm4O6I2CHplsr1TcBW4CqgE+gHbkhVj5mZnVnSOYWI2Er5D3/tuU01nwdwa8oazMxs/Hzb\ng5mZVTkUzMysyqFgZmZVDgUzM6vSyY/rz3SSuoA9k/zy5cDBOpaTB37NjcGvuTFM5TWfFxHtZ2qU\nu1CYCknbI6Ij6zqmk19zY/BrbgzT8Zo9fGRmZlUOBTMzq2q0UNicdQEZ8GtuDH7NjSH5a26oOQUz\nMxtbo/UUzMxsDA4FMzOrathQkPTbkkLS8qxrSU3SHZJ+JulJSf9b0pKsa0pF0gZJuyR1Sro963pS\nk7RK0j9I2ilph6RPZ13TdJDULOlfJD2QdS3TobJV8Xcqv8fPSPqFVD+rIUNB0irgI8BLWdcyTR4G\n3h4R7wCeBX4/43qSkNQM3AlcCawHrpO0PtuqkisBvx0R64H3Arc2wGsG+DTwTNZFTKM/B/4+It4K\nXEzC196QoQD8GfB7nH5f9kKJiIciolQ5fITyDndFdBnQGRG7I2IIuBfYmHFNSUXEKxHxeOXzo5T/\nWKzItqq0JK0Efgm4K+tapoOkxcAHgL8CiIihiDic6uc1XChI2gjsj4gnsq4lIzcC38+6iERWAHtr\njvdR8D+QtSStAd4FPJptJcl9hfKbutGsC5kma4Eu4K8rQ2Z3SZqf6ocl3WQnK5L+D3DOKS79AfA5\nykNHhTLWa46I71ba/AHl4YZvTWdtlp6kBcB9wGciojfrelKRdDVwICIek3R51vVMkxbgEuBTEfGo\npD8Hbgf+MNUPK5yI+DenOi/pIsqp+4QkKA+jPC7psoh4dRpLrLvTveYTJH0SuBq4Ior7cMp+YFXN\n8crKuUKTNItyIHwrIu7Pup7E3gd8TNJVwBxgkaRvRsR/zLiulPYB+yLiRA/wO5RDIYmGfnhN0otA\nR0QUeqVFSRuAPwU+GBFdWdeTiqQWyhPpV1AOg23AJyJiR6aFJaTyu5uvA90R8Zms65lOlZ7C70TE\n1VnXkpqkfwJuiohdkv4bMD8ifjfFzypkT8He4KvAbODhSg/pkYi4JduS6i8iSpJuAx4EmoG7ixwI\nFe8Dfh14StJPK+c+V9kf3YrjU8C3JLUCu4EbUv2ghu4pmJnZz2u4u4/MzOz0HApmZlblUDAzsyqH\ngpmZVTkUzMysyqFgZmZVDgUzM6tyKJhNkaR3V/aqmCNpfmVfg7dnXZfZZPjhNbM6kPQFymvxzKW8\nTs2XMy7JbFIcCmZ1UFl+YBswCPxiRIxkXJLZpHj4yKw+lgELgIWUewxmueSeglkdSNpCeae3tcC5\nEXFbxiWZTYpXSTWbIknXA8MR8e3KPtE/lvSvI+L/ZV2b2US5p2BmZlWeUzAzsyqHgpmZVTkUzMys\nyqFgZmZVDgUzM6tyKJiZWZVDwczMqv4/f857H9gx+QEAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alfa=0.1\n", "x0=2\n", "x = np.linspace(-4, 6,100);\n", "y = 1.0 / (1 + np.exp(-(x-x0) / alfa))\n", "y2=1-1.0 / (1 + np.exp(-(x-x0) / alfa))\n", "plt.figure(2)\n", "plt.clf()\n", "plt.plot(x, y)\n", "plt.xlabel('x'); plt.ylabel('y2'); plt.title('$\\sigma(x)$')\n", "# plt.savefig('images/smooth-transitions-sigma.png')" ] }, { "cell_type": "code", "execution_count": 413, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 413, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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UjWTo8RjlssDd28PH+4AF4+1oZjeYWZuZtXV1dR3j4caWSSbJDWmUi4hES3n0XeQy9Im4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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f_s=100/(np.pi) # sampling freq = 50 x osnovna\n", "fft_x = np.fft.fft(y)\n", "n = len(fft_x)\n", "freq = np.fft.fftfreq(n, 1/f_s)\n", "#print(freq)\n", "plt.plot(np.abs(fft_x))\n" ] }, { "cell_type": "code", "execution_count": 414, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n1 = 20\n", "fft_x_n1 = (2.0 / n) * fft_x[:n1]\n", "freq_n1 = freq[:n1]\n", "plt.plot(freq_n1, np.abs(fft_x_n1),'.-')\n", "plt.xlabel(\"Frequency (Hz)\")\n", "plt.ylabel(\"Amplitude\")\n", "plt.grid()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "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": "3.7.0" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "Kazalo", "title_sidebar": "Kazalo", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }