{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time-Frequency analysis with missing data\n",
    "\n",
    "## `Stft` objects\n",
    "\n",
    "Short-time Fourier transforms (STFT) of signals can be handled using `Stft` objects. This is a wrapper for the `ltfatpy` package. \n",
    "\n",
    "### Transform and inverse transform\n",
    "`Stft` takes as input the parameters of the STFT, namely the hop size `hop`, the number of bins `n_bins`, the window type `win_name` and length `win_len`, as well as two other parameters, `param_constraint` (see tutorial on the constraints on the transform length) and `zero_pad_full_sig` (see tutorial on boundary effects).\n",
    "   \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pyteuf import Stft\n",
    "from madarrays import Waveform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "stft = Stft(hop=16, n_bins=512, win_name='sine', win_len=256,\n",
    "            param_constraint='pad', zero_pad_full_sig=False)\n",
    "print(stft)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The inverse transform may obtained from the direct transform by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "istft = stft.get_istft()\n",
    "print(istft)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example on a synthetic real signal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a signal composed of two sines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nu1 = 1/33\n",
    "nu2 = 3/16\n",
    "duration = 0.5\n",
    "fs = 8000\n",
    "t = np.arange(0, int(duration*fs)) / fs\n",
    "x = np.cos(2*np.pi*t*nu1*fs) + 0.5*np.cos(2*np.pi*t*nu2*fs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute STFT and display the spectrogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = stft.apply(x, fs=fs)\n",
    "print(X)\n",
    "_ = X.plot_spectrogram(dynrange=100.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the negative frequencies are not displayed since the STFT of a real signal is symetric hermitian, and that boundary effects appear at the beginning and the end of the time axis.\n",
    "\n",
    "Reconstruction is obtained by:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = istft.apply(X)\n",
    "print('Reconstruction: {}'.format(y))\n",
    "print('Reconstruction error: {:.3f} dB'.format(10 * np.log10(np.mean(np.abs(x - y)**2))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Example on a synthetic complex signal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a waveform composed of two sines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "nu1 = 1/33\n",
    "nu2 = 3/16\n",
    "duration = 0.5\n",
    "fs = 8000\n",
    "t = np.arange(0, int(duration*fs)) / fs\n",
    "x = Waveform(np.exp(1j*2*np.pi*t*nu1*fs) + 0.5*np.exp(1j*2*np.pi*t*nu2*fs) , fs=fs)\n",
    "\n",
    "print(x)\n",
    "np.real(x).show_player()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = stft.apply(x)\n",
    "print(X)\n",
    "_ = X.plot_spectrogram(dynrange=100.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that all the frequencies are shown since the signal is complex.\n",
    "\n",
    "Reconstruction is obtained by:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = istft.apply(X)\n",
    "print('Reconstruction: {}'.format(y))\n",
    "print('Reconstruction error: {:.3f} dB'.format(10 * np.log10(np.mean(np.abs(x - y)**2))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example on a real sound"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load test sound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ltfatpy import gspi\n",
    "x, fs = gspi()\n",
    "x = Waveform(x, fs=fs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that one may also use static method `Waveform.from_wavfile(filename)` in order to load a `Waveform` object from an audio file."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Apply STFT and display properties of Stft data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "X = stft.apply(x)\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get a related Istft object, apply istft, display properties of reconstruction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = istft.apply(X)\n",
    "print('Reconstruction: {}'.format(y))\n",
    "print('Reconstruction error: {:.3f} dB'.format(10 * np.log10(np.mean(np.abs(x - y)**2))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that `x-y` computes the difference between two `Waveform` object and returns a new `Waveform`, that may be displayed or processed, as below. Many operators can be applied in the same way to `Waveform` objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(figsize=(12,2))\n",
    "x.plot(y_axis_label=None)\n",
    "\n",
    "plt.figure(figsize=(12,4))\n",
    "X.plot_spectrogram(dynrange=100.)\n",
    "\n",
    "plt.figure(figsize=(12,2))\n",
    "(x-y).plot(y_axis_label=None)\n",
    "plt.title('Error signal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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