{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt\n",
      "import matplotlib.image as mpimg\n",
      "import numpy as np\n",
      "import scipy.io.wavfile as wavfile\n",
      "from scipy import integrate\n",
      "\n",
      "plt.rcParams['figure.figsize'] = (15, 10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# sampling_rate, signal = wavfile.read(\"flute.wav\")\n",
      "# x = np.arange(len(signal))\n",
      "\n",
      "# testing with Andreas' toy signal\n",
      "y = lambda x: (0.5 if x < 0.25 or x > 0.75 else -0.5 )+ 0.5\n",
      "x = np.arange(0,1.0,0.001)\n",
      "signal = np.array([y(i) for i in x])\n",
      "x.shape, signal.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 88,
       "text": [
        "((1000,), (1000,))"
       ]
      }
     ],
     "prompt_number": 88
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(signal)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 89,
       "text": [
        "[<matplotlib.lines.Line2D at 0x123f75510>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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f+MYrlrgtW7ZM//fatWv9EhQ4CyagALQkh+DsjY+Px/j4+Jw/b0/Xvfo/yZMnT8Zll10W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\nShwAAEAh/wOt0GPnILctSgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x124042110>"
       ]
      }
     ],
     "prompt_number": 89
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Our lowest frequency should be the length of our signal.\n",
      "# We assume that the signal is periodic with the first period being the length of our signal.\n",
      "T = len(signal)\n",
      "f0 = 1.0/T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 90
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def a_coeff(x,y,i,f0,c):\n",
      "    return f0*2.0*integrate.trapz((y-c)*np.sin(2*np.pi*x*f0*i),x)\n",
      "    \n",
      "def b_coeff(x,y,i,f0,c):\n",
      "    return f0*2.0*integrate.trapz((y-c)*np.cos(2*np.pi*x*f0*i),x)\n",
      "\n",
      "def c_coeff(x,y):\n",
      "    return integrate.trapz(y,x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 91
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c = c_coeff(x,signal)\n",
      "a_s = []\n",
      "b_s = []\n",
      "\n",
      "for i in xrange(1,100):\n",
      "    a_s.append(a_coeff(x,signal,i,f0,c))\n",
      "    b_s.append(b_coeff(x,signal,i,f0,c))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 92
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fourier_value(x,a_s,b_s,c,f0,i_max=None ):\n",
      "    s = c\n",
      "    \n",
      "    i_max = i_max or len(a_s)\n",
      "    \n",
      "    for i in xrange(0,i_max):\n",
      "        s += a_s[i]*np.sin(2*np.pi*x*f0*(i+1))+b_s[i]*np.cos(2*np.pi*x*f0*(i+1))\n",
      "    \n",
      "    return s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 71
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "approximation = [fourier_value(i,a_s,b_s,c,f0,50) for i in x]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 93
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(approximation)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 94,
       "text": [
        "[<matplotlib.lines.Line2D at 0x12409c6d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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waxY0bQqHHQavvBI7kSRJktJJvorbpk2bWL58Ob///e9Zvnw55cqV46qrrkp2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\ni8MiE0mStOssbpKkQleyJJx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       "text": [
        "<matplotlib.figure.Figure at 0x10bd760d0>"
       ]
      }
     ],
     "prompt_number": 94
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}