llliiu/HW5.ipynb

## HW5.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MAT 201A Winter 2016 \n",
    "# HW 5 \n",
    "# Lu Liu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "from __future__ import print_function\n",
    "from __future__ import division\n",
    "from scipy.io import wavfile\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Glockenspiel.wav\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sr, src = wavfile.read('glockenspiel.wav')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.int16"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(src[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.float64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "src = src[:].astype(double) #change the data type from int to float\n",
    "type(src[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e449d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lags, a, lines, line = acorr(src, maxlags  = size(src) / 2); # autocorrelation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10ea70e10>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3NvMGPg2axcVyF2gC03eTUbGx4FRlpd2OobnQsaPE822UzQaYFr12KwYuw0Su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\n/wFu9OSnLHqFnAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef1cdd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(a[0:200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "75"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "argmax(a[50:100])+50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "108"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "argmax(a[100:125])+100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "interval1= 108-75"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1336.36363636\n"
     ]
    }
   ],
   "source": [
    "freq1=44100/interval1\n",
    "\n",
    "print(freq1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## piano.wav"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sr2, src2 = wavfile.read('piano.wav')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "src2 = src2[:].astype(double)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e61d9d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lags, b, lines, line = acorr(src2, maxlags  = size(src2) / 2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x111203090>]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Yq5RaQURfJ6Kvxc6ZD6CBiNYAuA/AtzJdc84c4Lvf5RtiypSOBycZnVlrWIPT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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f156350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plot(b[0:2000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "497"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "argmax(b[0:600])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1064"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "argmax(b[600:1200])+600"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "interval2= 1064-497"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "77.7777777778\n"
     ]
    }
   ],
   "source": [
    "freq2=44100/interval2\n",
    "\n",
    "print(freq2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## tom.wav"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sr3, src3 = wavfile.read('tom.wav')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "src3 = src3[:].astype(double)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38590"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size(src3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ea2fc90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lags, c, lines, line = acorr(src3, maxlags  = size(src3) / 2);\n",
    "#xlim(0,2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10e7c0210>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JSQklJSXZvNz3TJ/uZSd++tOcXVIicvPNvhHNxIlwzDFxR1M75eVw7bXQty/U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\nkpb/B1bWaktDHrQEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e648690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(c[0:1000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "252"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "argmax(c[0:400])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "704"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "argmax(c[400:800])+400"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "interval3=704-252"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "97.5663716814\n"
     ]
    }
   ],
   "source": [
    "freq3=44100/interval3\n",
    "print(freq3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis:\n",
    "## The results are actually similar to the results HW4, but the computational error is due to the different method.(one is DFT, one is autocorrelation)\n",
    "## In this home work, we have some truncation error. Because the value of lags has to be integer, which means the numbers after the decimal point are lost."
   ]
  }
 ],
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