{
 "metadata": {
  "name": "",
  "signature": "sha256:04d53f93727554c3fbbb0e9ed397de2b19cb3f2ed85ecf8d339ef03ffe407720"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "phs = linspace(0, 20* 2*pi, 1024, endpoint=False)\n",
      "g = cos(phs + 0.4)\n",
      "plot(g)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7ff3aae05dd0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VUZ+dHd7OPKoNdpSx5HCnwEJqDK4EcLjy+5He30a95qphb9alNFGqzUe7gNxG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\nCgoKAPx/kWhp/HDAmDwAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff3aaf9c310>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.signal import freqz"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(abs(fft.rfft(g[:512], n=512)))\n",
      "xlim(0, 400);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7ff39e1bc390>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(abs(fft.rfft(g[512:1024], n=512)))\n",
      "xlim(0, 400);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff39e1abc90>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Starting phase for first window:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "angle(fft.rfft(g[:512])[10])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "0.39999999999999808"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Starting phase for second window: (no phase change!)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "angle(fft.rfft(g[512:1024])[10])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "0.40000000000000219"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Phase at the end of the window:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "0.4 + (10 * 2 * pi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "63.23185307179586"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we wrap the phase:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(0.4 + (10 * 2 * pi)) %(2* pi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "0.3999999999999986"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "However for a frequency that has a fractional cycle the ending window phase is:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(10.1 * 2 * pi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "63.46017160251382"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And wrapped:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(10.1 * 2 * pi)%(2* pi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "0.6283185307179551"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's see a concrete example:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "phs = linspace(0, 23.4* 2*pi, 1024, endpoint=False)\n",
      "g = cos(phs)\n",
      "plot(g)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7ff39e0b91d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0pk0TxaoaY9v7A2JMsYP2Wm2L6BhAm3XZF2AwltA7lvfE6sye39AGD99HM0+i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\nd6EAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff39e1abf10>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(abs(fft.rfft(g[:512], n=512)))\n",
      "xlim(0, 50);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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S5tIXIyIkRaUNly9f/uZ8oVCgUCg02ZTe1KryDMBFF8Gf/mnqxc+b15r3NLPuGRoaYmho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\n/j9VuS+bUUZgvwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff39e05d9d0>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = abs(fft.rfft(g[:512], n=512))\n",
      "argmax(X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "12"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The precise center is at 23.4 / 2.\n",
      "\n",
      "Because the number of cycles is not an integer, the starting phase for the second window is different:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(g[:512])\n",
      "plot(g[512:1024])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7ff39e087b50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GB+woIJVXNUnFm972lkhZBBBRMfUAmOcZVADQ3BmhURJ/2K62ja46np/334jo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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff39e15f610>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Starting phase first window:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "angle(fft.rfft(g[:512]))[12]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "-0.9519681448511772"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Starting phase second window:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "angle(fft.rfft(g[512:1024]))[12]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "-2.8196061225509639"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Phase difference:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "angle(fft.rfft(g[512:1024]))[12] - angle(fft.rfft(g[:512]))[12]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "-1.8676379776997867"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The total elapsed phase for the bin should be:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "12 * 2 * pi"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "75.39822368615503"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "But what actually elapsed (adding the phase difference measured) was:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "12 * 2 * pi + __"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "73.530585708455249"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Which if we count cycles in that phase accumulation we get:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "_ / (2 * pi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 136,
       "text": [
        "11.702756183942927"
       ]
      }
     ],
     "prompt_number": 136
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Must multiply by two because we split the signal into two windows and get the frequency we put in (to the presicion allowed by the sampling rate):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "_ * 2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "147.0611714169105"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Phase Vocoder"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Two sine tones ( Second one 4 times the frequency and half the amplitude)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f0 = 203.3\n",
      "p0 = 0.3\n",
      "N = 4096\n",
      "\n",
      "test_phs = linspace(0, (f0 * 2*pi), N, endpoint=False)\n",
      "test_sig = sin(test_phs + p0) + 0.5 * cos(p0 + (test_phs * 4))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 145
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = rfft(test_sig[:512])\n",
      "plot(abs(X))\n",
      "# xlim(0,1000);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7ff39c940790>"
       ]
      }
     ],
     "prompt_number": 146
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = rfft(test_sig[:512])\n",
      "plot(abs(X))\n",
      "xlim(10, 40);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7ff39c8dcf50>"
       ]
      }
     ],
     "prompt_number": 147
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "argmax(abs(X))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 148,
       "text": [
        "25"
       ]
      }
     ],
     "prompt_number": 148
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(argmax(abs(X)) + 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 149,
       "text": [
        "26"
       ]
      }
     ],
     "prompt_number": 149
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The frequency we are looking for is in between. Let's do STFT with overlap:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hopsize = 128\n",
      "winsize = 512\n",
      "win_start = linspace(0, len(test_sig) - winsize, hopsize)\n",
      "\n",
      "stft = []\n",
      "\n",
      "for start in win_start:\n",
      "    X = rfft(test_sig[start: start + winsize]* hanning(winsize))\n",
      "    stft.append(X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 150
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "argmax(abs(stft[1]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 151,
       "text": [
        "25"
       ]
      }
     ],
     "prompt_number": 151
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(abs(stft[1]))\n",
      "plot(abs(stft[5]))\n",
      "plot(abs(stft[9]))\n",
      "xlim(10, 40)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 152,
       "text": [
        "(10, 40)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Yt174O7y4Ksxpn/84Iy0n0/fA06zfusHv0Dw3Xyv+rNv+kVv/6AM8/8izfock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\ngVKCFxEpUErwIiIFSgleRKRA/X/EYa73d56c1gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff39c83c190>"
       ]
      }
     ],
     "prompt_number": 152
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "imshow(angle(stft).T, aspect='auto', cmap=cm.gray, interpolation='nearest')\n",
      "gcf().set_figwidth(10)\n",
      "colorbar();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6jplFuLaQyJHkWH173nTTTZ26uHKkEOuNN97YqYtUt36ExN1F7usiRb9cOe6g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\n0mTTRRchWbFiBVasWLH4/eGHH/bT/YYkl4heh9F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       "text": [
        "<matplotlib.figure.Figure at 0x7ff39c79a610>"
       ]
      }
     ],
     "prompt_number": 153
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(angle(stft).T[24])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 154,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7ff39c6c9ad0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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f3/1usTf39PQUxsamxBqsXZkqJVIuUVcNBLOzwMMelm4/Jd3kLncEZBp7mf3o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\nYsigxK5QKBRDhv8Ph3zhcatfYgYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff39c79ab90>"
       ]
      }
     ],
     "prompt_number": 154
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(angle(stft).T[25])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 155,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7ff39c6062d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Yc7Y72vxDXTQcjb1JMRlNXQy1USi0e02/GLt3T0o3vuVfaAMIt2vCBeyum882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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff39c661c90>"
       ]
      }
     ],
     "prompt_number": 155
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's look at the unwrapped phase:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "unwrapped = [angle(stft).T[25][0]]\n",
      "\n",
      "for p in angle(stft).T[25][1:]:\n",
      "    while (p < unwrapped[-1]):\n",
      "        p += 2 * pi\n",
      "    unwrapped.append(p)\n",
      "\n",
      "plot(unwrapped, 'x')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 156,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7ff39c52bf90>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7ff39c634ad0>"
       ]
      }
     ],
     "prompt_number": 156
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A line! The frequency is constant across all the bins!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "delta_phs = diff(unwrapped)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 157
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(delta_phs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 158,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7ff39c463650>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6gqQtRU+X8/dTQN5OrkXSx4HnzezPK2ydyi5pA70rKj9ZPFzxJZX5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\nuVyuKZMPfpfL5Zoy/X8xFIKP8FRPmAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff39c940490>"
       ]
      }
     ],
     "prompt_number": 158
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now accumulate phase for the hop period:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "k = 25 # bin number\n",
      "num_cycles = k * (hopsize/ float(winsize)) # how many cycles of bin between STFT hops\n",
      "\n",
      "total_phs_k = num_cycles * 2* pi # Total accumulated phase for bin\n",
      "num_cycles, total_phs_k"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 159,
       "text": [
        "(6.25, 39.269908169872416)"
       ]
      }
     ],
     "prompt_number": 159
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Adjusted phase:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "phs_change = delta_phs[0]\n",
      "phs_change"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 160,
       "text": [
        "2.4488454978294771"
       ]
      }
     ],
     "prompt_number": 160
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Expected change:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "total_phs_k % (2 * pi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 161,
       "text": [
        "1.5707963267948983"
       ]
      }
     ],
     "prompt_number": 161
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Phase divergence:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "div = phs_change - total_phs_k % (2 * pi)\n",
      "div"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 162,
       "text": [
        "0.8780491710345788"
       ]
      }
     ],
     "prompt_number": 162
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "final_phs = total_phs_k + div\n",
      "final_phs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 163,
       "text": [
        "40.147957340906991"
       ]
      }
     ],
     "prompt_number": 163
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Estimate number of cycles in hop period from total accumulated phase:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "final_phs/(2*pi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 164,
       "text": [
        "6.3897458658478943"
       ]
      }
     ],
     "prompt_number": 164
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Multiply by overlap:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(winsize/float(hopsize)) *final_phs/(2*pi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 165,
       "text": [
        "25.558983463391577"
       ]
      }
     ],
     "prompt_number": 165
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now times the number of windows to match the original full length:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(N/float(winsize))*(winsize/hopsize) *final_phs/(2*pi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 166,
       "text": [
        "204.47186770713262"
       ]
      }
     ],
     "prompt_number": 166
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Yay! (or not...!) \n",
      "\n",
      "Original frequency was 203.3, but this still got us much closer to the original frequency than what the FFT bins provide:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(N/float(winsize))*25"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 167,
       "text": [
        "200.0"
       ]
      }
     ],
     "prompt_number": 167
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(N/float(winsize))*26"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 168,
       "text": [
        "208.0"
       ]
      }
     ],
     "prompt_number": 168
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "By: Andr\u00e9s Cabrera mantaraya36@gmail.com\n",
      "For MAT course MAT 201A at UCSB\n",
      "\n",
      "This ipython notebook is licensed under the CC-BY-NC-SA license: http://creativecommons.org/licenses/by-nc-sa/4.0/\n",
      "\n",
      "![http://i.creativecommons.org/l/by-nc-sa/3.0/88x31.png](http://i.creativecommons.org/l/by-nc-sa/3.0/88x31.png)"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}