Basic_Acoustics_from_Speech_to_Features_using_MFCC.ipynb

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    "# Basic Acoustics \n",
    "##### Udacity's VUI Concentration\n",
    "\n",
    "## Speech signals\n",
    "\n",
    "Speech propagates as a longitudinal wave in a medium, such as air or water. The speed of propagation depends on the density of the medium. The simplest form of sound that we can describe is called a sinusoid. This waveform corresponds to a pure tone and as we will see later forms the basis for all more complex sounds. Since a sinusoid has such a pure shape it is a useful starting point when describing the properties of sound waves.\n",
    "\n",
    "Three kinds of measurement can be taken from a sinusoid:\n",
    "\n",
    "* **Amplitude:** the size of the displacement of the sinusoid above and below the mid line. This corresponds to the energy in the sound wave and hence how loud it appears to be. There are many ways of measuring amplitude; since it relates to the size of the pressure variations in the air it can be measured in units of pressure. More often we talk about deciBels (dB) which measure amplitude on a logarithmic scale relative to a standard sound. The dB scale is useful since it maps directly to the way that humans percieve loudness.\n",
    "\n",
    "* **Frequency:** the number of cycles made by the sinusoid each second. A cycle consists of an oscilation from the mid line to the maximum, down to the minimum and back to the midline. Frequency is measured in cycles per second or Hertz (Hz). The period is the inverse of this -- the time taken for one cycle. Changes in frequency are percieved as changes in the pitch of a sound (although pitch has a more complicated perceptual definition so the two quanitities are not the same).\n",
    "\n",
    "* **Phase:** measures the position of the starting point of the sinusoid. Those starting at the maximum have a phase of zero while those starting at the minimum have a phase of π radians. Phase is best explained with reference to a rotating wheel. The phase of a sinusoid cannot be percieved but we can detect relative changes in phase between two signals, in fact this forms the basis of binaural hearing as the brain works out the location of a sound based on the different phases heard at the two ears. Ex. Try to listen Bohemian Rapsody using the right and then the left earplug.\n",
    "\n",
    "[http://web.science.mq.edu.au/~cassidy/comp449/html/ch03.html]\n",
    "\n",
    "### A sine function\n",
    "\n",
    "\\begin{equation*}\n",
    "\\ y(t) = A * \\sin(2 \\pi  f  t + \\varphi) = A \\sin(\\omega  t + \\varphi)\n",
    "\\end{equation*}\n",
    "\n",
    "where:\n",
    "\n",
    "* A = the amplitude, the peak deviation of the function from zero.\n",
    "* f = the ordinary frequency, the number of oscillations (cycles) that occur each second of time.\n",
    "* ω = 2πf, the angular frequency, the rate of change of the function argument in units of radians per second\n",
    "\n",
    "\\varphi  = the phase, specifies (in radians) where in its cycle the oscillation is at t = 0.\n",
    "When \\varphi  is non-zero, the entire waveform appears to be shifted in time by the amount \\varphi /ω seconds. A negative value represents a delay, and a positive value represents an advance.\n",
    "\n",
    "### Adding signals\n"
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EFYZhHrjI9Hqvvs+AlHJdSpnTtw8BQSFEspVzTe/xGSnlQSnlwfHxcQsuuzud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\nMo3msj2SWwyP7uhk0t7zeWE/q6RmbBBwt581V5UsGBgO942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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1061d9438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt \n",
    "import numpy as np \n",
    "\n",
    "fs = 100 # number of samples\n",
    "f = 6 # the frequency of the signal\n",
    "\n",
    "x = np.arange(fs) # points on x axis for plotting\n",
    "# compute the value (amplitude) of the sin wave at the for each sample\n",
    "y = [ np.sin(2*np.pi*f * (i/fs)) for i in x]\n",
    "\n",
    "% matplotlib inline \n",
    "plt.stem(x,y, 'r', ) # show points\n",
    "graph2 = plt.plot(x,y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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29DtoqUospVgoWs2Xbt9NpIiIYRCRe0WkQ0TOiMj+JV7/JRE5KiLHROQtEdkZ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\nomwAcjOtcSlZciyvmqIc31PYhsXsqCu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/3RBj9OhUG4eLxdX8YLtv/iWvUgxMzuCam+eH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\ng5mZ1fwCPg+0lr77xigAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1061d92b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fs = 100 # number of samples\n",
    "f = 3 # the frequency of the signal\n",
    "\n",
    "x = np.arange(fs) # points on x axis for plotting\n",
    "# compute the value (amplitude) of the sin wave at the for each sample\n",
    "y = [ np.sin(2*np.pi*f * (i/fs)) for i in x]\n",
    "\n",
    "% matplotlib inline \n",
    "plt.stem(x,y, 'r', ) # show points\n",
    "graph2 = plt.plot(x,y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10ebb1978>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pmfXY55b5iRXbldwwf4amQzklgFfTGZ5SISAD0Sc3W5byEz10Jw2JygOUFmVhAK7QM8/m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\nsmBMhYDMp7fHR2+Pj7v//AW6Gz1XHfzDwsZb/lk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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ebb40f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fs = 100 # number of samples\n",
    "f = 6 # the frequency of the signal\n",
    "\n",
    "x = np.arange(fs) # points on x axis for plotting\n",
    "# compute the value (amplitude) of the sin wave at the for each sample\n",
    "y = [(np.sin(2*np.pi*f * (i/fs)) + (np.sin(2*np.pi*f/2 * (i/fs)))) for i in x]\n",
    "\n",
    "% matplotlib inline\n",
    "plt.stem(x,y, 'r', ) # show points\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Fourier Theory\n",
    "\n",
    "The Fourier Transform and the associated Fourier series is one of the most important mathematical tools in physics. Physicist Lord Kelvin remarked in 1867:\n",
    "\n",
    ">“Fourier’s theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.”\n",
    "\n",
    "The Fourier Transform deals with time based waves – and these are one of the fundamental building blocks of the natural world. Sound, light, gravity, radio signals, Earthquakes and digital compression are just some of the phenomena that can be understood through waves. It’s not an exaggeration therefore to see the study of waves as one of the most important applications of mathematics in our modern life.\n",
    "\n",
    "[https://ibmathsresources.com/2014/08/14/fourier-transforms-the-most-important-tool-in-mathematics/]\n",
    "\n",
    "\n",
    "Fourier theory says that any complex periodic waveform can be decomposed into a set of sinusoids with different amplitudes, frequencies and phases. The process of doing this is called Fourier Analysis and the result is a set of amplitudes, phasesand frequencies for each of the sinusoids that makes up the complex waveform. Adding these sinusoids together again will reproduce exactly the original waveform. A plot of the frequency or phase of a sinusoid against amplitude is called a spectrum. \n",
    "\n",
    "Any periodic signal shows a pattern of repetition in the time waveform which corresponds to the primary rate of vibration of the signal, known as the fundamental frequency. This corresponds to the lowest major frequency component in the signal and, in the case of voiced speech, equates to the frequency of vibration of the vocal folds. A vibration source like the vocal folds also produces what are called harmonics which are oscillations at multiples of the fundamental frequency. For example, a 100Hz source vibration will give rise to harmonics at 200Hz, 300Hz, 400Hz etc. In the spectrum of such a signal, the harmonics show up as spikes at these frequencies.\n",
    "\n",
    "The fundamental frequency can be measured from a speech waveform by looking for the period of oscillation of the signal around the zero axis. Estimates can also be made from the spectrum since it shows a large peak at this frequency and at each multiple due to the harmonics. Measurements can be made of the frequency of the major peak or of the distance between harmonic peaks.\n",
    "\n",
    "### Spectrograms and FFT\n",
    "\n",
    "A spectrum shows the freqency content of a short section of a waveform but it we want to see how the spectrum changes with time through a section of speech we need a different kind of display. A standard way of displaying this information is a spectrogram; this is a two dimensional plot of frequency against time where the amplitude at each frequency is represented by the darkness of the corresponding point in the display.\n",
    "\n",
    "<img src= http://web.science.mq.edu.au/~cassidy/comp449/html/wideband.gif />\n",
    "\n",
    "An FFT, or Fast Fourier Transform, is an efficient implementation of a Discrete Fourier Transform. The algorithm transforms a sum of sinusoidal signals into into its pure frequency components. In the following quiz, we will demonstrate adding sinusoidal waves together and then deconstructing them back into their component frequencies.\n",
    "\n",
    "* **choose_frequencies** choose three frequencies in a range from 1 to 50. These are the number of full cycles each sinusoidal wave will have in one \"time unit\". Running the definition will produce a visual of the three chosen frequencies as well as a new wave that is the sum of the three. This is similar to an acoustic signal, which is the sum of many sinusoidal waves. The waves may have different phases and amplitudes as well. Here's an example of a choice of (3, 8, 1) for the three frequencies.\n",
    "\n",
    "* **add_the_waves** second definition is where the waves are created. For this demonstration, we will only create three. This has been done for you with the utils.make_waves function - take a look at to understand how it works. You just need to add them together. This simulates an audio signal, which is really just sinusoidal waves added together. In audio signals, the sinusoidal waves are created by sound vibrations and may be at varying amplitudes and phase as well as frequency. To simulate this variety, the utils.make_waves function provides random amplitudes and phase shifts.\n",
    "\n",
    "* **demo_fft** An FFT can be created with a variety of library functions including scipy.fftpack.fft , which we'll use in this quiz. Read the linked reference to understand how to use it in code.\n",
    "\n",
    "This FFT algorithm will create both positive and negative values, but we'll just display the positive ones. When you're done, you should see something like the following, showing peaks at the three frequency values originally provided!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def sinusoid(freq):\n",
    "    \"\"\"\n",
    "    return a sinusoidal of random amplitude and phase for a given frequency\n",
    "    :param freq: \n",
    "    :return: \n",
    "    \"\"\"\n",
    "    phase = np.random.random()\n",
    "    amplitude = 2 * (np.random.random_integers(1, 10))\n",
    "    return amplitude * np.cos(2 * np.pi * freq - phase)\n",
    "\n",
    "\n",
    "def get_wave_timing(num_samples=500, range_of_time = 5.0):\n",
    "    \"\"\"\n",
    "    provide an array of time values of size num_samples spread evenly over range_of_time\n",
    "    :param num_samples: int \n",
    "    :param range_of_time: float\n",
    "    :return: int, float, np.array\n",
    "    \"\"\"\n",
    "    # sample spacing\n",
    "    spacing = range_of_time / num_samples\n",
    "    # array for time samples\n",
    "    t = np.linspace(0.0, range_of_time, num_samples)\n",
    "    return num_samples, spacing, t\n",
    "\n",
    "\n",
    "def make_waves(t, freqs):\n",
    "    \"\"\"\n",
    "    convert three frequencies into arrays of discrete values representing sinusoidal waves\n",
    "    :param freqs: [float, float, float]\n",
    "    :return: [np.array, np.array, np.array]\n",
    "    \"\"\"\n",
    "    w0 = sinusoid(t * freqs[0])\n",
    "    w1 = sinusoid(t * freqs[1])\n",
    "    w2 = sinusoid(t * freqs[2])\n",
    "    return w0, w1, w2\n",
    "\n",
    "\n",
    "def display_sinusoids(time_array, f1, f2, f3, sum):\n",
    "    # plot three frequencies with random phase shifts on y axis\n",
    "    plt.figure()\n",
    "    fig, ax = plt.subplots(4, 1)\n",
    "    # plt.subplot(411)  # 3 rows, 1 column, fignum 1\n",
    "    ax[0].plot(time_array, f1)\n",
    "    ax[0].set_title('1st frequency component')\n",
    "\n",
    "    # plt.subplot(412)  # 3 rows, 1 column, fignum 2\n",
    "    ax[1].plot(time_array, f2)\n",
    "    ax[1].set_title('2nd frequency component')\n",
    "\n",
    "    # plt.subplot(413)  # 3 rows, 1 column, fignum 3\n",
    "    ax[2].plot(time_array, f3)\n",
    "    ax[2].set_title('3rd frequency component')\n",
    "\n",
    "    # sum\n",
    "    # plt.subplot(414)  # 3 rows, 1 column, fignum 4\n",
    "    ax[3].plot(time_array, sum, 'r')\n",
    "    ax[3].set_title('Sum of components')\n",
    "    ax[3].set_ylabel('amplitude')\n",
    "    ax[3].set_xlabel('time')\n",
    "\n",
    "    # adjust format of display to make room for titles\n",
    "    plt.subplots_adjust(\n",
    "         top=0.94,\n",
    "         bottom=0.11,\n",
    "         left=0.11,\n",
    "         right=0.97,\n",
    "         hspace=0.65,\n",
    "         wspace=0.2\n",
    "    )\n",
    "    plt.show()\n",
    "    return fig\n",
    "\n",
    "\n",
    "def display_fft(xf, yf):\n",
    "    num_samples = np.shape(yf)[0]\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(xf, 2.0 / num_samples * np.abs(yf[:num_samples]))\n",
    "    plt.title('Fast Fourier Transform')\n",
    "    plt.xlabel('frequency')\n",
    "    plt.ylabel('amplitude')\n",
    "    return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.fftpack\n",
    "# import utils as utils\n",
    "import random\n",
    "\n",
    "def choose_frequencies():\n",
    "    \"\"\"\n",
    "    # provide three frequencies in a range between 1 and 50    \n",
    "    :return: [int, int, int]\n",
    "    \"\"\"\n",
    "    \n",
    "    freq1 = random.randint(1, 51)\n",
    "    freq2 = random.randint(1, 51)\n",
    "    freq3 = random.randint(1, 51)\n",
    "   \n",
    "    return [freq1, freq2, freq3]\n",
    "\n",
    "\n",
    "def add_the_waves(freqs):\n",
    "    \"\"\"\n",
    "    create three sinusoidal waves and one wave that is the sum of the three\n",
    "    :param freqs: [int, int, int]\n",
    "    :return: [np.array, np.array, np.array, np.array]\n",
    "        representing wave1, wave2, wave3, sum of waves\n",
    "        each array contains 500(by default) discrete values for plotting a sinusoidal\n",
    "    \"\"\"\n",
    "    _, _, t = get_wave_timing()\n",
    "    w1, w2, w3 = make_waves(t, freqs)\n",
    "\n",
    "    sum_waves = w1+w2+w3\n",
    "\n",
    "    return [w1, w2, w3, sum_waves], t\n",
    "\n",
    "\n",
    "def demo_fft(sum_waves):\n",
    "    num_samples, spacing, _ = get_wave_timing()\n",
    "\n",
    "    # Create a Fast Fourier Transform of the waveform using scipy.fftpack.fft named 'y_fft'\n",
    "    y_fft = scipy.fftpack.fft(sum_waves)\n",
    "    x_fft = np.linspace(0.0, 1.0/spacing, num_samples)\n",
    "    \n",
    "    return x_fft, y_fft"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[6, 51, 18]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda/envs/dog-gpu-project/lib/python3.5/site-packages/ipykernel/__main__.py:11: DeprecationWarning: This function is deprecated. Please call randint(1, 10 + 1) instead\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ea11a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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L+Fwm7QQB15AApuOz8dPOqT9jBiTawY5Yzkvfo1I1ceWOhhtQntVzZ8wzwCAHbBvZEaUT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aKudrP44vTgsCl4xH2iOUqDTaSZSqRjxi0pwUBidqCA3xe3Mzmh60pi7iBOUXYD0Jo3iyvk4ltD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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ee28550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e847d68>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wSidf9spn+ABzWhqGnVnTHM1q+CYwmx7Zv0KG7wn4Uyel2d/dd9RrszEcpZMP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\nCQv4xhgTExbwjTEmJizgG2NMTPx/ZoNK22RvYrwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e847d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(choose_frequencies())\n",
    "waves_list, t = add_the_waves(choose_frequencies())\n",
    "display_sinusoids(t, waves_list[0], waves_list[1], waves_list[2], waves_list[3])\n",
    "x_fft, y_fft = demo_fft(waves_list[3])\n",
    "display_fft(x_fft, y_fft)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Feature extraction with MFCC (Mel Frequency Cepstra Coeff)\n",
    "\n",
    "> **With Feature Extraction we address problems like reducing noise in data due to environmental facts as well as variability of the speakers. **\n",
    "\n",
    "On the previous section we have seen that we can decompose the audio signal into different sine waves, and get a vectorial representation afterwards using FFT. However, we still have unnecessary information within the audio signal like background noise and pitches that the human ear cannot sense. This section is about: \n",
    "\n",
    "> * To reduce dimensionality of data\n",
    "> * To reduce noise in data\n",
    "\n",
    "### Mel Scale (1937)\n",
    "\n",
    "Mel Scale was created in 1937 to illustrate that: we are more able to distinguish among low pitches rather than high pitches, thus, above a set threshold, it may not necessary to include that frequencies.  \n",
    "\n",
    "### Articulation of sound: Cepstral analysis\n",
    "\n",
    "\n",
    "#### Why? Motivation\n",
    "\n",
    "A signal comming out from a system is due to the input excitation and also the response of the system. From the signal processing point of view, the output of a system can be treated as the convolution of the input excitation with the system response. At times, we need each of the components separately for study and/or processing. The process of separating the two components is termed as deconvolution.\n",
    "\n",
    "#### How? Cepstrum Analysis, The Math\n",
    "\n",
    "The source/filter model holds that the \"source\" of voices speech is dependent upon the vibrations initiated in the vocal box, and is unique to the speaker, while the \"filter\" is the articulation of the words in the forward part of the voice tract. The two can be separated through Cepstrum Analysis. We are more interesting in preserving the shape of sound made by the vocal tract rather than source which is unique for every individual since is the result of the vibrations made by the vocal cords. \n",
    "\n",
    "According to the source filter theory of speech production, voiced sounds are produced by exciting the time varying system characteristics with **periodic impulse sequence** (n) and unvoiced sounds are produced by exciting the time varying system with a random noise sequence. The resulting speech can be considered as the convolution of respective excitation sequence and vocal tract filter characteristics. If e(n) is the excitation sequence and h(n) is the vocal tract filter sequence, then the speech sequence s(n) can be expressed as follows:\n",
    "\n",
    "\n",
    "\n",
    "\\begin{equation*}\n",
    "\\ s(n)=e(n)×h(n)            .....................................(1)\n",
    "\\end{equation*}\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "The speech sequence has to be deconvolved into the excitation and vocal tract components in the TIME domain. For this, multiplication of the two components in the frequency domain has to be converted to a linear combination of the two components. For this purpose cepstral analysis is used for transforming the multiplied source and system components in the frequency domain to linear combination of the two components in the cepstral domain.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\\begin{equation*}\n",
    "\\ S(\\omega) = E(\\omega) \\cdot  H(\\omega)             ....................................(2)\n",
    "\\end{equation*}\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "This signal can be converted to the frequency domain through a discrete Fourier transform, or DFT (can use the FFT algorithm):\n",
    "\n",
    "\n",
    "\n",
    "\\begin{equation*}\n",
    "\\ |S(\\omega)| = |E(\\omega)| \\cdot |H(\\omega)|            .................................(3)\n",
    "\\end{equation*}\n",
    "\n",
    "\n",
    "\n",
    "Take the log to get a linear combination of both: \n",
    "\n",
    "\n",
    "\n",
    "\\begin{equation*}\n",
    "\\ log∣S(ω)∣=log∣E(ω)∣+log∣H(ω)∣                   .................(4)\n",
    "\\end{equation*}\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "Here's where it gets a bit tricky. By taking the inverse discrete Fourier transform, or IDFT, the signal can be split into the linearly combined log spectra of excitation and vocal tract system components giving cepstrum c(n) as a result. \n",
    "\n",
    "It should be noted that IDFT of linear spectra transforms back to the time domain, but **the IDFT of log spectra transforms to quefrency domain or the cepstral domain which is similar to time domain**. This is mathematically explained in the equation above. In the quefrency domain the vocal tract components are represented by the slowly varying components concentrated near the lower quefrency region and excitation components are represented by the fast varying components at the higher quefrency region. [http://iitg.vlab.co.in/?sub=59&brch=164&sim=615&cnt=1]\n",
    "\n",
    "Here's the final equation:\n",
    "\n",
    "\\begin{equation*}\n",
    "c(n) = IDFT(\\log |S(\\omega)|) = IDFT(\\log |E(\\omega)| +  \\log|H(\\omega)|) ....(5)\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Computation of Cepstrum\n",
    "\n",
    "<img src=\"cepstrum_computation.png\" />\n",
    "\n",
    "\n",
    "* s(n) is the voiced frame considered and \n",
    "* x(n) is the windowed frame. Here s(n) multiplied by a hamming window to get x(n) \n",
    "* |x(ω)| represent the spectrum of the windowed sequence x(n) \n",
    "\n",
    "* As the spectrum of the given frame is symmetric, only one half of the spectral components is plotted (second and third graph of the image below). \n",
    "\n",
    "* The log|x(ω)| represents the log magnitude spectrum obtained by taking logarithm of the |x(ω)|\n",
    "\n",
    "* c(n) shows the computed spectrum for the voiced frame s(n). The obtained cepstrum contains vocal tract components which are linearly combined according Eqn.(5). As the cepstrum is derived from the log magnitude of the linear spectrum, it is also symmetrical in the quefrency domain. Here also only one symmetric part of the cepstrum is used for plotting. \n",
    "\n",
    "<img src=\"speech_and_cepstrum.png\" />\n",
    "\n",
    "[http://iitg.vlab.co.in/?sub=59&brch=164&sim=615&cnt=1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "###  Putting it altogether: Mel Frequency Cepstral Coefficients (MFCC)\n",
    "\n",
    "Mel Frequency Cepstrum Coefficient Analysis is the reduction of an audio signal to essential speech component features using both mel frequency analysis and cepstral analysis. The range of frequencies are reduced and binned into groups of frequencies that humans can distinguish. The signal is further separated into source and filter so that variations between speakers unrelated to articulation can be filtered away. **This way we get 12-13 MFCC features to process in our sound**, which means a significant reduction of dimensionality of data. \n",
    "\n",
    "---\n",
    "\n",
    "In this short quiz, you'll write a function that converts a .wav file to MFCC features. You'll need a way to extract the signal from the wave file and then a method to convert the signal to MFCC. Here are the resources you need to write your function:\n",
    "\n",
    "scipy.io.wavfile.read (to extract the signal)\n",
    "python_speech_features.mfcc (to convert to MFCC)\n",
    "When you succeed in returning the correct file, you will \"see\" the MFCC spectrum in the output similar to the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Need to install speech_recognition libraries in order to use the modules\n",
    "\n",
    "# !conda list\n",
    "# !brew install portaudio\n",
    "# !pip install pyaudio\n",
    "# !pip install SpeechRecognition\n",
    "# !python -m speech_recognition \n",
    "# !pip install python_speech_features\n",
    "# !conda list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2111, 12)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.io.wavfile.read.html\n",
    "# http://python-speech-features.readthedocs.io/en/latest/\n",
    "\n",
    "from python_speech_features import mfcc\n",
    "import scipy.io.wavfile as wav\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.mlab as mlab\n",
    "import numpy as np\n",
    "\n",
    "def wav_to_mfcc(wav_filename, num_cepstrum):\n",
    "    \"\"\" extract MFCC features from a wav file\n",
    "    \n",
    "    :param wav_filename: filename with .wav format\n",
    "    :param num_cepstrum: number of cepstrum to return\n",
    "    :return: MFCC features for wav file\n",
    "    \"\"\"\n",
    "    \n",
    "    (rate, sig) = wav.read(wav_filename)\n",
    "    mfcc_features = mfcc(sig, rate, numcep=num_cepstrum)\n",
    "    return mfcc_features # MFCC sequence\n",
    "\n",
    "feats = wav_to_mfcc(\"a-team_intro.wav\", 12)\n",
    "feats.shape  # (2111, 12)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "editable": true
   },
   "source": [
    "Next AIND-VUI-Lab-Voice-Data-master/Lab Voice Data.ipynb"
   ]
  }
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