MRSP_nonIdeal.ipynb

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    "<center>\n",
    "    <img src=\"./images/msp_header.png\">\n",
    "</center>\n",
    "\n",
    "#### Prof. Dr. -Ing. Gerald Schuller <br> Jupyter Notebook: Renato Profeta"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "# Non-Ideal Filters"
   ]
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    "%%html\n",
    "<center>\n",
    "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/wdFrdt3m0BU\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
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   "source": [
    "We saw that we can get perfect reconstruction in a filter bank, using ideal filters (ideally we remove all aliasing components). But in practice, we don't have ideal filters, they are not realizable, because their impulse response stretches from minus infinity to infinity.\n",
    "\n",
    "How can we obtain **perfect reconstruction** using realizable **non-ideal filters**, and still \"**critical sampling**\" (meaning the down sampling rate N is equal to the number of sub bands, as in the case of ideal filters)? Let's first take a look at the resulting spectrum when we use non-ideal filters. We start with the spectrum at the output of a non-ideal high-pass,\n",
    "\n",
    "<center>\n",
    "    <img src=\"./images/Lecture9-1.png\" width=600>\n",
    "</center>"
   ]
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       "<center>\n",
       "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/0E0vttSUhDU\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
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   "source": [
    "%%html\n",
    "<center>\n",
    "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/0E0vttSUhDU\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
    "</center>"
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    "Observe that the slope at $\\dfrac{\\pi}{2}$ and $\\dfrac{-\\pi}{2}$ is not infinite, but we get a more or less slow transition into higher attenuation towards lower frequencies. Hence we also get frequencies below $\\dfrac{\\pi}{2}$ (or above $\\dfrac{-\\pi}{2}$) in our signal. This will become a problem after downsampling by a factor of 2 (for now just the multiplication with the delta impulse train), as can be seen in the next pictures. Remember that for the multiplication with the delta train we get aliasing components at frequency shifts of $\\dfrac{2\\pi}{N}$, hence in this case $\\pi$,\n",
    "\n",
    "<center>\n",
    "    <img src=\"./images/Lecture9-2.png\" width=600>\n",
    "</center>\n",
    "\n",
    "Observe, even if we now used ideal filters for the synthesis for the high-pass part, we would still have the **overlapped aliasing component**, and hence no perfect reconstruction."
   ]
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   "cell_type": "markdown",
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     "slide_type": "slide"
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   },
   "source": [
    "## Filter Banks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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       "<center>\n",
       "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/OON4olsZxbk\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
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   "source": [
    "%%html\n",
    "<center>\n",
    "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/OON4olsZxbk\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
    "</center>"
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   "source": [
    "Filter banks consist of a bank of subbband filters which cover the entire frequency band of our signal, followed by downsampling in the analysis filter bank, and preceded by upsampling in the synthesis filter bank. This can be seen in the following pictures,\n",
    "\n",
    "<center>\n",
    "    <img src=\"./images/Lecture9-3.png\" width=600>\n",
    "</center>\n",
    "\n",
    "<center>\n",
    "    <img src=\"./images/Lecture9-4.png\" width=600>\n",
    "</center>\n",
    "\n",
    "In the picture, $x(n)$ is the input signal (for instance our audio signal), $y_k(m)$ are the downsampled subband signals (with k the subband index and m the index at the lower sampling rate), and $\\hat{x}(n)$ is the reconstructed signal.\n",
    "\n",
    "As described in lecture 2, $\\downarrow N$ Symbolizes downsampling by a factor of N (including removal of the zeros). If $x(n)$ is the signal we downsample, then we also write the downsampled signal as\n",
    "\n",
    "$$\\large\n",
    "x^{\\downarrow N}_{n_0}(m) :=x( mN+n_0 )\n",
    "$$\n",
    "\n",
    "where $n_0$ is the index of the first sample we keep in the downsampling, or the “**phase**”, with $0\\leq n_0\\leq N-1$.\n",
    "\n",
    "$\\uparrow N$symbolizes upsampling by a factor of N, including insertion of the zeros. If $y(m)$ is the signal we upsample, then we also write the upsampled signal as\n",
    "\n",
    "$$\\large\n",
    "y^{ \\uparrow N }_{ n_0 }(n) = \\begin{cases}\n",
    "        \\begin{split}\n",
    "            y(m),          & n=mN+n_0 \\\\\n",
    "              0, & else \\\\\n",
    "         \\end{split}\n",
    "    \\end{cases}\n",
    "$$\n",
    "\n",
    "where $n_0$ is the index of the first non-zero sample in the upsampled signal, or the phase, with\n",
    "$0\\leq n_0 \\leq N-1$."
   ]
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    "So the only hope we have to **obtain perfect reconstruction** with non-ideal filters (and still critical sampling) in filter banks, is that somehow the aliasing from different subbands cancels out during the synthesis process, when we add up all the subbands (if we add e.g. the low pass signal and the high pass signal for the reconstruction); or in other words, we would like the sum of all aliasing components at the output of the synthesis filters to become zero. The question now is: how do we obtain this goal?"
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   "cell_type": "code",
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   "metadata": {
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       "<center>\n",
       "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/q-H7xff6fcI\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
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    "%%html\n",
    "<center>\n",
    "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/q-H7xff6fcI\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
    "</center>"
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   "source": [
    "We could now analyse all the aliasing components, to find out when they cancel each other. This is how researchers actually approached this problem first, for instance in the first derivation of the so-called Time-Domain Aliasing Cancellation (TDAC) filter banks by Princen and Bradley <cite>( J. P. Princen, A. W. Johnson und A. B. Bradley: Subband/transform coding using filter bank designs based on time domain aliasing cancellation, IEEE Proc. Intl. Conference on Acoustics, Speech, and Signal Processing (ICASSP))</cite>,\n",
    "\n",
    "or using the aliasing component matrices by Vetterli et al.\n",
    "But it turned out that a simpler mathematical approach is possible by just using the goal of overall perfect reconstruction of our filter bank, regardless of all aliasing components. This is now the goal of the following derivation. Here we need to analyse in more detail what happens in the filtering and downsampling process in our filter bank.\n",
    "\n",
    "To come to a solution, we need to **apply the z-transform** to our filter bank with non-ideal filters. "
   ]
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   "source": [
    "### Analysis Filter Bank"
   ]
  },
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   "execution_count": 5,
   "metadata": {
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       "<center>\n",
       "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/j90eowFD2l4\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
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   "source": [
    "%%html\n",
    "<center>\n",
    "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/j90eowFD2l4\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
    "</center>"
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   "source": [
    "<center>\n",
    "    <img src=\"./images/Lecture9-5.png\" width=600>\n",
    "</center>\n",
    "\n",
    "Just the filtering can be written with the convolution equation,\n",
    "\n",
    "$$\\large\n",
    "y(n')= \\sum _{n=0} ^ {L-1} x(n'-n) h_k(n)\n",
    "$$\n",
    "\n",
    "The filtering and subsequent **downsampling** by N of the k'th analysis filter $h_k(n)$ of impulse response length L can be written as a downsampled convolution sum with phase offset $n_0$, simply with the substitution $mN+n_0 \\rightarrow n'$ (and have the new argument $m$ of y)\n",
    "          $y^{\\downarrow N}_{n_0}(m)= \\sum _ {n=0 }^ {L-1} x(mN+n_0-n) h_k(n)$ (2)\n",
    "          \n",
    "          \n",
    "(see also lecture 1) where m is again the downsampled index (at the lower sampling rate). $n_0$ Is our **phase index** for the downsampling. Often we assume $n_0=0$, which means we start downsampling at the first sample (keeping the first sample). \n",
    "\n",
    "In this way the sum only computes the values which the donwsampler keeps. The downsampling in this equation is now the hurdle to simply applying the z-transform to turn the convolution into a multiplication, for easy invertibility. "
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "### Block Transforms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "-"
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   "source": [
    "To look for a solution for invertibility, perfect reconstruction and alias cancellation, we now take a detour to fast implementations, using transforms, like the **DFT** and its fast implementation, the FFT. This is also the approached used by the Short Time Fourier Transform (**STFT**). If we **divide our signal** into **blocks** of length N, \n",
    "\n",
    "$$\\large\n",
    "\\boldsymbol x (m)=[x(mN),x(mN+1), ..., x(mN+N-1)]\n",
    "$$\n",
    "\n",
    "$$\\large\n",
    "=[ x^{\\downarrow N}_{0}(m),...,x^{\\downarrow N}_{N-1}(m) ]\n",
    "$$\n",
    "\n",
    "where m is the block index or index at the lower sampling rate. You can imagine the signal as a long horizontal sequence of samples, which we subdivide into small blocks of length N. We then stack those blocks on top of each other. Then going vertically down, we obtain downsampled versions of our signal at different phase lags,\n",
    "\n",
    "<center>\n",
    "    <img src=\"./images/Lecture9-6.png\" width=500>\n",
    "</center>\n",
    "\n",
    "The DFT computes a block with N frequency or subband values for each **signal block** $\\boldsymbol{x}(m)$.\n",
    "\n",
    "If $\\boldsymbol{T}$ is the DFT transform matrix, then the DFT of each signal block is\n",
    "\n",
    "$$\\large\n",
    "\\boldsymbol y(m)=\\boldsymbol x(m)\\cdot \\boldsymbol T$$\n",
    "\n",
    "where $\\boldsymbol y(m)$ contains the DFT coefficients,\n",
    "\n",
    "$$\\large\n",
    "\\boldsymbol y (m) :=[y_0(m), y_1(m),...,y_{N-1}(m)]\n",
    "$$\n",
    "\n",
    "Here, $y_k$(m) is the $k$'th DFT coefficient for block $m$. Hence index $k$ denotes the subband or frequency, and index $m$ is the block index or time at the lower sampling rate.\n",
    "\n",
    "Hence, if we keep $k$ fixed we obtain a time signal, for the $k'th$ subband. If we keep m fixed, we obtain a spectrum for block m.\n",
    "\n",
    "That is why this is also called a “time/frequency” representation, since we have both, time (m)  and frequency (k) indices in it.\n",
    "\n",
    "This shows that the DFT is simply a special case of an analsys filter bank with critical sampling (and perfect reconstruction through the inverse DFT)."
   ]
  },
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   "source": [
    "#### Python Example:"
   ]
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   "execution_count": 6,
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       "<center>\n",
       "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/A4Ik_Io2JrA\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
       "</center>\n"
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   "source": [
    "%%html\n",
    "<center>\n",
    "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/A4Ik_Io2JrA\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
    "</center>"
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  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
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   "source": [
    "# Imports and Configuration\n",
    "\n",
    "%matplotlib notebook\n",
    "import pyaudio\n",
    "import numpy as np\n",
    "import scipy.signal as signal\n",
    "import struct\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.mlab import window_hanning,specgram\n",
    "from matplotlib.colors import LogNorm\n",
    "from matplotlib.ticker import FuncFormatter, MultipleLocator\n",
    "from ipywidgets import ToggleButton, Checkbox, Button\n",
    "from ipywidgets import HBox, interact\n",
    "import threading"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
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   "outputs": [],
   "source": [
    "# Parameters\n",
    "CHUNK_SIZE = 2048 #Blocksize\n",
    "CHANNELS = 1 # Audio Channes\n",
    "RATE = 32000  #Sampling Rate in Hz\n",
    "N=8.0     #Downsampling/Upsampling Rate\n",
    "FORMAT = pyaudio.paInt16 #conversion format for PyAudio stream\n",
    "NFFT = 1024 #NFFT value for spectrogram\n",
    "OVERLAP = 512 #overlap value for spectrogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "# LP Filter\n",
    "[b,a]=signal.iirfilter(8, 1900.0/16000,rp=60,btype='lowpass')\n",
    "#Memory for the filter:\n",
    "zd=np.zeros(8)\n",
    "zu=np.zeros(8)\n",
    "LPFilterOn=False\n",
    "\n",
    "# LP Filter Frequency Response\n",
    "w, h = signal.freqz(b,a)\n",
    "f = w*16000/(np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
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   },
   "outputs": [],
   "source": [
    "# Function to Plot Spetrogram\n",
    "SamplingOn=False # Turn Donwsampling/Upsampling On/Off\n",
    "ctr=0 # Control for plotting\n",
    "def run_spectrogram(toggle_run):\n",
    "    global zd, zu, ctr, SamplingOn, LPFilterOn\n",
    "    while(True):\n",
    "        if toggle_run.value==True:\n",
    "            break\n",
    "            \n",
    "        #Reading from audio input stream into data with block length \"CHUNK\":\n",
    "        data_stream = stream.read(CHUNK_SIZE)\n",
    "        shorts = (struct.unpack( 'h' * CHUNK_SIZE, data_stream ));\n",
    "        samples=np.array(list(shorts),dtype=float);\n",
    "\n",
    "        #start block-wise signal processing:\n",
    "        #Low pass filter *before downsampling*:\n",
    "        if LPFilterOn==True:\n",
    "            [samples,zd]=signal.lfilter(b, a, samples, zi=zd)\n",
    "\n",
    "        #Compute a block/an array of a unit pulse train corresponding a downsampling rate of N:\n",
    "        #make unit pulse train with modulus function \"%\": \n",
    "        s=(np.arange(0,CHUNK_SIZE)%N)==0\n",
    "        #The sampling:\n",
    "        #multiply the signal with the unit pulse train:\n",
    "        if SamplingOn == True:\n",
    "            samples=samples*s;\n",
    "\n",
    "\n",
    "        #Lowpass filtering *after upsampling*:\n",
    "        #filter function:\n",
    "        if LPFilterOn==True:\n",
    "            [samples,zu]=signal.lfilter(b, a, samples, zi=zu)\n",
    "\n",
    "        #end signal processing\n",
    "\n",
    "        #play out samples:\n",
    "        samples=np.clip(samples, -32000,32000)\n",
    "        samples=samples.astype(int)\n",
    "        #converting from short integers to a stream of bytes in \"data\":\n",
    "        data=struct.pack('h' * len(samples), *samples);\n",
    "        #Writing data back to audio output stream: \n",
    "        stream.write(data, CHUNK_SIZE)\n",
    "\n",
    "        # Update Plot\n",
    "        if (ctr%4 ==0):\n",
    "            arr2D,freqs,bins = specgram(samples,window=window_hanning,\n",
    "                                        Fs = RATE,NFFT=NFFT,noverlap=OVERLAP)\n",
    "            im_data = im.get_array()\n",
    "            if ctr < 16:\n",
    "                im_data = np.hstack((im_data,arr2D))\n",
    "                im.set_array(im_data)\n",
    "            else:\n",
    "                keep_block = arr2D.shape[1]*(16 - 1)\n",
    "                im_data = np.delete(im_data,np.s_[:-keep_block],1)\n",
    "                im_data = np.hstack((im_data,arr2D))\n",
    "                im.set_array(im_data)\n",
    "            fig.canvas.draw()\n",
    "        ctr+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
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   "outputs": [],
   "source": [
    "# GUI\n",
    "toggle_run = ToggleButton(description='Stop')\n",
    "button_start= Button(description='Start')\n",
    "box_sampling = Checkbox(False, description='Downsampling/Upsampling')\n",
    "box_LPFilter = Checkbox(False, description='LP Filters')\n",
    "\n",
    "def start_button(button_start):\n",
    "    thread.start()\n",
    "    button_start.disabled=True\n",
    "button_start.on_click(start_button)\n",
    "\n",
    "\n",
    "def on_click_toggle_run(change):\n",
    "    if change['new']==False:\n",
    "        stream.stop_stream()\n",
    "        stream.close()\n",
    "        p.terminate()\n",
    "        plt.close()\n",
    "toggle_run.observe(on_click_toggle_run, 'value')\n",
    "\n",
    "def box_samping_changed(box_sampling):\n",
    "    global SamplingOn\n",
    "    if box_sampling['new']: \n",
    "        SamplingOn=True\n",
    "    else:\n",
    "        SamplingOn=False       \n",
    "box_sampling.observe(box_samping_changed, names='value')\n",
    "\n",
    "def box_LPFilter_changed(box_LPFilter):\n",
    "    global LPFilterOn\n",
    "    if box_LPFilter['new']: \n",
    "        LPFilterOn=True\n",
    "    else:\n",
    "        LPFilterOn=False       \n",
    "box_LPFilter.observe(box_LPFilter_changed, names='value')\n",
    "\n",
    "box_buttons = HBox([button_start,toggle_run])\n",
    "box_checkbox = HBox([box_sampling,box_LPFilter])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "# Create a Thread for run_spectrogram function\n",
    "thread = threading.Thread(target=run_spectrogram, args=(toggle_run,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "# Start Audio Stream\n",
    "# Create \n",
    "p = pyaudio.PyAudio()\n",
    "    \n",
    "stream = p.open(format=FORMAT,\n",
    "                channels=CHANNELS,\n",
    "                rate=RATE,\n",
    "                input=True,\n",
    "                output=True,\n",
    "                frames_per_buffer=CHUNK_SIZE)\n",
    "\n",
    "\n",
    "\n",
    "input_data = stream.read(CHUNK_SIZE)\n",
    "samples = np.frombuffer(input_data,np.int16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "658ef67e01de4cb1835b095b74b99c95",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(Button(description='Start', style=ButtonStyle()), ToggleButton(value=False, description='Stop')…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "99cc854ccc8b4c568a240ec63660c227",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(Checkbox(value=False, description='Downsampling/Upsampling'), Checkbox(value=False, description…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Initialize Plot and Display GUI\n",
    "\n",
    "display(box_buttons)\n",
    "display(box_checkbox)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "arr2D,freqs,bins = specgram(samples,window=window_hanning,\n",
    "                                Fs = RATE,NFFT=NFFT,noverlap=OVERLAP)\n",
    "\n",
    "\n",
    "extent = (bins[0],bins[-1]*32,freqs[-1],freqs[0])\n",
    "im = plt.imshow(arr2D,aspect='auto',extent = extent,interpolation=\"none\",\n",
    "                     norm = LogNorm(vmin=.01,vmax=1))\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Frequency (Hz)')\n",
    "plt.title('Live Spectogram')\n",
    "plt.gca().invert_yaxis()\n",
    "plt.xticks([])\n",
    "\n",
    "def handle_close(evt):\n",
    "    # When everything done, release the capture\n",
    "    stream.stop_stream()\n",
    "    stream.close()\n",
    "    p.terminate()\n",
    "    plt.close()\n",
    "plt.connect('close_event', handle_close);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Fast Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<center>\n",
       "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/eGXhSd0UorA\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
       "</center>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%html\n",
    "<center>\n",
    "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/eGXhSd0UorA\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "As the name says, the FFT has a fast implementation. Compare it to our filter bank: per subband we need to calculate the convolution sum. If we have filters of length L, that means we have L multiplications per output sample (we neglect the sum operations) for each sub band. Without down samplers, we get LN multiplications for each block of N input samples for each subband, leading to $LN^2$ multiplications for all subbands for the block of N input samples. \n",
    "\n",
    "Now we can reduce this amount by only computing the output samples which the downsampler keeps. This reduces the computational complexity by a factor of N, resulting in LN multiplications for each input block of length N, to obtain N output values (1 value in each subband). In other words: each sample in a subband is computed by a filter of length L which needs L multiplications in the convolution sum. We need L multiplications per sample.\n",
    "\n",
    "If we compare it with an FFT, it only needs on the order of $Nlog_2(N)$ multiplications (“order” meaning: up to a fixed factor) for each block. Hence for each subband sample we need log(N) multiplications. Compare this with the L multiplications per sample for the critically sampled filter bank.\n",
    "\n",
    "Since usually we have $L>log_2(N)$, this is **more efficient**.\n",
    "\n",
    "**Example:** If N=1024 subbands, then we need filters which are longer than L=1024, and $L>>log_2( 1024 )=10$\n",
    ". Hence in this case, we save more than an order of a factor of 100 in complexity using the FFT!\n",
    "\n",
    "Another interesting effect is, that we obtain **perfect reconstruction** using the **inverse FFT** for the synthesis process, even though the equivalent FFT filter bank has no perfect filters. So this might give us a hint on how to obtain perfect reconstruction without ideal filters.\n",
    "\n",
    "The question is, what is the **equivalent FFT filter bank**?"
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  }
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