Blatt02.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zunächst immer mathematische Bibliothek laden"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hier werden verschiedene Funktionen definiert (Sinus, Sinusquadrat, Rechteckpuls, Sägezahn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Verschiedene Signal Funktionen\n",
    "def sinus(t,A,f):\n",
    "    return A*np.sin(2*np.pi*f*t)\n",
    "\n",
    "def sinus_quadrat(t,A,f):\n",
    "    return A*np.sin(2*np.pi*f*t)**2\n",
    "\n",
    "def rechteck(x,w,offset):\n",
    "    s=-w/2+offset\n",
    "    y=[]\n",
    "    for p in x:\n",
    "        if p >s and p < s+w:\n",
    "            y.append(1)\n",
    "        else:\n",
    "            y.append(0)\n",
    "    return np.array(y)\n",
    "\n",
    "def saege(x,w):\n",
    "    y=[]\n",
    "    ymax=1\n",
    "    m=ymax/w\n",
    "    for p in x:\n",
    "        y.append(m*p%w)\n",
    "    return np.array(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hier wird eine Zeitreihe angelegt und das Signal (sig) wird für die aktivierte Funktion berechnet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Zeitachse und konstanten definieren\n",
    "\n",
    "dt = 0.001\n",
    "t=np.arange(-1,1,dt)\n",
    "\n",
    "#sig=sinus(t,2,5)\n",
    "#sig=sinus_quadrat(t,2,5)\n",
    "sig=rechteck(t,1,0)\n",
    "#sig=saege(t,0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nun wird in der ersten Zeile die diskrete Fouriertransformation der Funktionswerte durchgeführt. \n",
    "Danach werden die Ergebnisse in zwei Hälfen symmertisch um Null angeordnet. Diese Sortierung ist notwendig da der Algorithmus die Komponenten nach einem bestimmten Schema ausgiebt. \n",
    "Dokumentation: https://docs.scipy.org/doc/numpy/reference/routines.fft.html#module-numpy.fft"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Fouriertransformieren Doc: https://docs.scipy.org/doc/numpy/reference/routines.fft.html#module-numpy.fft\n",
    "ft=np.fft.fft(sig)\n",
    "\n",
    "#Umsortieren\n",
    "N=int(len(ft)/2)\n",
    "nft=np.concatenate((ft[N:],ft[:N]), axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Da in der diskreten Fouriertransformation ein konstanter Zeitschritt dt angenommen wird, werden nur die Koeffizienten ausgegeben. Im Folgenden wird die zugehörige Frequenzachse generiert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Frequenzachse erstellen\n",
    "wu=np.fft.fftfreq(len(sig),dt)\n",
    "#Umsortieren\n",
    "w=np.concatenate((wu[N:],wu[:N]), axis=0)\n",
    "\n",
    "#w-Werte mit koeffizienten Verknüpfen\n",
    "fs=list(zip(w,nft))\n",
    "#Array nach größten koeffizienten sortieren\n",
    "fs.sort(key=lambda a:abs(a[1]),reverse=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nun werden die Plots der einzelnen Funktionen erstellt.\n",
    "Dokumentation der Plot Befehle: https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplots.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2a93bd54d30>]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot1\n",
    "#SignalPlot Doc: https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplots.html\n",
    "fig, axes = plt.subplots()\n",
    "axes.set_title(\"Zeitraum\")\n",
    "axes.set_xlabel(\"Zeit t in s\")\n",
    "axes.set_ylabel(\"Amplitude\")\n",
    "axes.plot(t,sig,linewidth=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Erstellen des Fourierplots mit Zoom. Um vollständigen Plot zu betrachten letzte Zeile auskommentieren!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-25, 25, 0, 1000.0]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot2\n",
    "#FourierPlot vom Betrag\n",
    "halb=len(t)/2\n",
    "fenst=len(t)/20\n",
    "unten=int(halb-fenst)\n",
    "oben=int(halb+fenst)\n",
    "fig, axes = plt.subplots()\n",
    "axes.set_title(\"Frequenzraum\")\n",
    "axes.set_xlabel(\"Frequenz f in Hz\")\n",
    "axes.set_ylabel(\"Amplitude\")\n",
    "axes.plot(w,abs(nft),linewidth=2)\n",
    "#Zoom in\n",
    "axes.axis([-25,25,0,max(abs(nft))])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Erstellen des Rücktransformierten Plots. Um die Anzahl der Koeffizienten zu beeinflussen maxAnzFour ändern!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2a93bdedc88>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot3\n",
    "ys=[]\n",
    "#Die Größten Koeffizienten Plotten\n",
    "maxAnzFour=len(t)\n",
    "for f in fs[:maxAnzFour]:\n",
    "    #Rücktransformation von \"Hand\"\n",
    "    y=f[1]*np.exp(1j*f[0]*t*2*np.pi)/len(t)\n",
    "    #Umsortieren\n",
    "    yn=np.concatenate((y[N:],y[:N]), axis=0)\n",
    "    yr=np.real(yn)\n",
    "    #Realteil der Rücktransformierten speichern\n",
    "    ys.append(yr)\n",
    "    #Plotten der einzelnen Funktionen\n",
    "    #plt.plot(t,yr)\n",
    "#Synthetisierte funktion initialisieren\n",
    "synthsig=np.zeros(len(t))\n",
    "for y in ys:\n",
    "    #einzelne Rücktransformierte addieren\n",
    "    synthsig=np.add(synthsig,y)\n",
    "#Plotten der \"Groben\" Funktion\n",
    "fig, axes = plt.subplots()\n",
    "axes.set_title(\"Rücktransformierter Zeitraum\")\n",
    "axes.set_xlabel(\"Zeit in s\")\n",
    "axes.set_ylabel(\"Amplitude\")\n",
    "axes.plot(t,synthsig,linewidth=2)\n",
    "axes.plot(t,sig,linewidth=2)"
   ]
  },
  {
   "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}