{
 "cells": [
  {
   "cell_type": "code",
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   "source": [
    "from numpy import loadtxt\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy import zeros,exp,pi\n",
    "from numpy.fft import rfft\n",
    "\n",
    "def dft(y):\n",
    "    N = len(y)\n",
    "    c = zeros(N//2+1,complex) # only sums over the first half of the series assuming the data is real\n",
    "    for k in range(N//2+1):\n",
    "        for n in range(N):\n",
    "            c[k] += y[n]*exp(-2j*pi*k*n/N)\n",
    "    return c\n",
    "\n",
    "x = loadtxt(\"pitch.txt\",float) # load the waveform we are looking at\n",
    "%timeit c1 = dft(x)\n",
    "%timeit c2 = rfft(x)\n",
    "\n",
    "plt.figure(figsize=(16,8)) # set the figsize\n",
    "plt.subplot(1,2,1) # now plot the two histograms as separate figures on 2 rows with 1 column, and this is row one.\n",
    "plt.xlabel(\"$t$\")\n",
    "plt.ylabel(\"$f(t)$\")\n",
    "plt.plot(x)\n",
    "\n",
    "plt.subplot(1,2,2) # now plot the two histograms as separate figures on 2 rows with 1 column, and this is row one.\n",
    "plt.xlim(0,500)\n",
    "plt.xlabel(\"$k$\")\n",
    "plt.ylabel(\"$c_k$\")\n",
    "plt.plot(abs(c1),'r') # plot the absolute values, since the coefficients are generally complex\n",
    "plt.plot(abs(c2),'y--') # plot the absolute values, since the coefficients are generally complex\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
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