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     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import numpy as np\n",
    "import wave\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io.wavfile\n",
    "import operator\n",
    "from IPython.display import Audio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mechanical Correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Parts (a) & (b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# You will need to both fill in code and add code\n",
    "from scipy.linalg import circulant as circ\n",
    "\n",
    "s1 = \n",
    "s2 = \n",
    "\n",
    "\n",
    "S1 = \n",
    "S2 = \n",
    "print('Circulant matrix of signal s1:')\n",
    "print(S1)\n",
    "print('Circulant matrix of signal s2:')\n",
    "print(S2)\n",
    "\n",
    "auto_s1 = \n",
    "auto_s2 = \n",
    "\n",
    "corr_s1s2 = \n",
    "corr_s2s1 = \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Audio File Matching\n",
    "\n",
    "This notebook continues the audio file matching problem. Be sure to have song.wav and clip.wav in the same directory as the notebook.\n",
    "\n",
    "In this notebook, we will look at the problem of searching for a small audio clip inside a song.\n",
    "\n",
    "The song \"Mandelbrot Set\" by Jonathan Coulton is licensed under <a href=\"http://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0</a>\n",
    "\n",
    "If you have trouble playing the audio file in IPython, try opening it in a different browser. I encountered problem with Safari but Chrome works for me."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import wave\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io.wavfile\n",
    "import operator\n",
    "from IPython.display import Audio\n",
    "%matplotlib inline\n",
    "\n",
    "given_file = 'song.wav'\n",
    "target_file = 'clip.wav'\n",
    "rate_given,  given_signal  = scipy.io.wavfile.read(given_file)\n",
    "rate_target, target_signal = scipy.io.wavfile.read(target_file)\n",
    "given_signal  = given_signal[:2000000].astype(float)\n",
    "target_signal = target_signal.astype(float)\n",
    "def play_clip(start, end, signal=given_signal):\n",
    "    scipy.io.wavfile.write('temp.wav', rate_given, signal[start:end].astype(np.int16))\n",
    "    return Audio(url='temp.wav', autoplay=True)\n",
    "\n",
    "def run_comparison(target_signal, given_signal, idxs=None):\n",
    "    # Run everything if not called with idxs set to something\n",
    "    if idxs is None:\n",
    "        idxs = [i for i in range(len(given_signal)-len(target_signal))]\n",
    "    return idxs, [vector_compare(target_signal, given_signal[i:i+len(target_signal)])\n",
    "                for i in idxs]\n",
    "\n",
    "play_clip(0, len(given_signal))\n",
    "\n",
    "#scipy.io.wavfile.write(target_file, rate_given, (-0.125*given_signal[1380000:1380000+70000]).astype(np.int16))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will load the song into the variable `given_signal` and load the short clip into the variable `target_signal`. Your job is to finish code that will identify the short clip's location in the song. The clip we are trying to find will play after executing the following block."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Audio(url=target_file, autoplay=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Your task is to define the function 'vector_compare' and run the following code. Because the song has a lot of data, you should use the provided examples from the previous parts of the problem before running the later code. Do you results here make sense given your answers to previous parts of the problem?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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   "outputs": [],
   "source": [
    "def vector_compare(desired_vec, test_vec):\n",
    "    \"\"\"This function compares two vectors, returning a number.\n",
    "    The test vector with the highest return value is regarded as being closest to the desired vector.\"\"\"\n",
    "    # The transpose is a gotcha! Stupid numpy\n",
    "    # your code here\n",
    "\n",
    "print(\"PART A:\")\n",
    "print(vector_compare(np.array([1,1,1]), np.array([1,1,1])))\n",
    "print(vector_compare(np.array([1,1,1]), np.array([-1,-1,-1])))\n",
    "print(\"PART C:\")\n",
    "print(vector_compare(np.array([1,2,3]), np.array([1,2,3])))\n",
    "print(vector_compare(np.array([1,2,3]), np.array([2,3,4])))\n",
    "print(vector_compare(np.array([1,2,3]), np.array([3,4,5])))\n",
    "print(vector_compare(np.array([1,2,3]), np.array([4,5,6])))\n",
    "print(vector_compare(np.array([1,2,3]), np.array([5,6,7])))\n",
    "print(vector_compare(np.array([1,2,3]), np.array([6,7,8])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 1\n",
    "Run the following code that runs `vector_compare` on every subsequence in the song- it will probably take at least 5 minutes. How do you interpret this plot to find where the clip is in the song?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import time\n",
    "\n",
    "t0 = time.time()\n",
    "idxs, song_compare = run_comparison(target_signal, given_signal)\n",
    "t1 = time.time()\n",
    "plt.plot(idxs, song_compare)\n",
    "print (\"That took %(time).2f minutes to run\" % {'time':(t1-t0)/60.0} )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 2\n",
    "In the space below, write code that uses `song_compare` to print the index of `given_signal` where `target_signal` begins. Then, verify that your answer is correct by playing the song at that index using the `play_clip` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# your code here"
   ]
  }
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