Comb Filtering Example.ipynb

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    "# COMB FILTERING EXAMPLE\n",
    "## a.k.a. What happens when you have 2 loudspeakers or microphones near each other\n",
    "In order to use this notebook, Choose \"Cell -> Run all\".  Then scroll to the bottom and play around with the sliders"
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    "### First, import everything we need"
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   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "from ipywidgets import interact\n",
    "from bokeh.io import curdoc, push_notebook, show, output_notebook\n",
    "from bokeh.layouts import row, column\n",
    "from bokeh.plotting import figure\n",
    "from bokeh.models import ColumnDataSource, Range1d\n",
    "from bokeh.models.widgets import Slider, TextInput\n",
    "output_notebook()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the functions we'll be using"
   ]
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  {
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   "execution_count": 5,
   "metadata": {
    "collapsed": true
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   "source": [
    "# Set up a couple globals\n",
    "num_freqs = 5000\n",
    "freqs  = np.logspace(np.log10(20), np.log10(20000), num_freqs, endpoint=True, base=10.0)\n",
    "c = 343000.0 # mm/sec \n",
    "\n",
    "# Define functions for computing responses\n",
    "\n",
    "\n",
    "def compute_distances(a, b):\n",
    "    \"\"\"a and b are 2d vecotrs of shape (n, 3) where n is the number of items, and 3 is for xyz dimensions                                                                                                          \n",
    "    So, if we have a = (n, 3) and b = (m, 3), then the output will contain                                                                                                                                         \n",
    "    an array of shape (n, m) and each element will be the distance from item a[x], b[y]\"\"\"\n",
    "    aa = a[np.newaxis, :, :]\n",
    "    bb = b[:, np.newaxis, :]\n",
    "    ss = (aa - bb)**2\n",
    "    s = np.sqrt(np.sum(ss, axis=2))\n",
    "    return s\n",
    "\n",
    "def compute_response(listener_distance, angles, speaker_locations, freqs):\n",
    "    \"\"\"This function looks at how far apart two speakers (or microphones) are, how far the listener is\n",
    "    (listener_distance), and returns the frequency response\"\"\"\n",
    "    angles_rad = np.deg2rad(angles)\n",
    "    listener_positions = np.zeros((len(angles), 3))\n",
    "    listener_positions[:, 0] = np.cos(angles_rad)\n",
    "    listener_positions[:, 1] = np.sin(angles_rad)\n",
    "    listeners = listener_positions * listener_distance\n",
    "    speakers = np.array(speaker_locations)\n",
    "\n",
    "    distances = compute_distances(speakers, listeners)  # mm                                                                                                                                                       \n",
    "    # Consider distances[0, 0] to be amplitude = 1.0, and amplitude drops as 1/r**2                                                                                                                                \n",
    "    amplitudes = 1.0/(distances / distances[0, 0])**2\n",
    "    distances = distances[np.newaxis, :, :]\n",
    "    freqs1 = freqs[:, np.newaxis, np.newaxis]\n",
    "    phase = freqs1 * distances / c * 2 * np.pi   # cycles/sec * mm * sec / mm * rad/cycle = rad                                                                                                                    \n",
    "    phasor = np.cos(phase) + 1j*np.sin(phase)\n",
    "    amplitudes = amplitudes[np.newaxis, :, :]\n",
    "    mag = np.abs(np.sum(phasor * amplitudes, axis=2))\n",
    "    mag = mag / len(speakers)\n",
    "    return mag, listeners, speakers\n",
    "\n",
    "def update_data(speaker_distance = 30.0, listener_distance=1000.0, listener_angle=45.0):\n",
    "    \"\"\"update_data:  this function calls compute_response every time a slider is moved and \n",
    "    it updates the plots\"\"\"\n",
    "    # Get current values                                                                                                                                                                                           \n",
    "    sl = np.array([[0.0,  speaker_distance/2., 0],\n",
    "                   [0.0, -speaker_distance/2., 0]])\n",
    "    mag, listeners, speakers = compute_response(\n",
    "        listener_distance = listener_distance,\n",
    "        angles            = np.array([listener_angle], dtype=float),\n",
    "        speaker_locations = sl,\n",
    "        freqs = freqs)\n",
    "    x = freqs\n",
    "    y = 20*np.log10(np.abs(mag[:,0]))\n",
    "    source.data = dict(x = x, y = y)\n",
    "    graphic_source_speakers.data = dict(x = speakers[:, 0], y = speakers[:, 1])\n",
    "    graphic_source_listeners.data = dict(x=[listeners[0, 0],], y=[listeners[0, 1],])\n",
    "    x = np.transpose(np.array([speakers[:,0], np.tile(listeners[:,0], speakers.shape[0])]))\n",
    "    y = np.transpose(np.array([speakers[:,1], np.tile(listeners[:,1], speakers.shape[0])]))\n",
    "    graphic_source_lines.data = dict(x = x, y = y)\n",
    "    push_notebook()\n",
    "\n",
    "\n",
    "def create_plots():\n",
    "    # Create data sources.  start with them empty  Sorry these are global... icky I know...\n",
    "    source = ColumnDataSource(data = dict(x=[0.0], y= [0.0]))\n",
    "    graphic_source_speakers = ColumnDataSource(data = dict(x=[0], y= [0]))\n",
    "    graphic_source_listeners = ColumnDataSource(data = dict(x=[0], y=[0]))\n",
    "    graphic_source_lines = ColumnDataSource(data = dict(x=[0], y=[0]))\n",
    "\n",
    "    plot = figure(plot_width=400, \n",
    "                plot_height=400,\n",
    "                title      = \"Interference between sources\",\n",
    "                tools      = \"crosshair,pan, reset, save, wheel_zoom\",\n",
    "                x_range    = [20, 20000],\n",
    "                y_range    = [-60, 10])\n",
    "\n",
    "    plot.yaxis.axis_label=\"Response (dB)\"\n",
    "    plot.xaxis.axis_label=\"Frequency\"\n",
    "    graphic = figure(plot_height= 400,\n",
    "                     plot_width = 400,\n",
    "                     title      = \"Source Locations\",\n",
    "                     tools      = \"crosshair,pan, reset, save, wheel_zoom\",\n",
    "                     x_range=[-1100, 1100],\n",
    "                     y_range=[-1100, 1100],\n",
    "                  )\n",
    "    graphic.yaxis.axis_label=\"y (mm)\"\n",
    "    graphic.xaxis.axis_label=\"x (mm)\"\n",
    "    plot.line('x', 'y', source=source, line_width=3, line_alpha=0.6)\n",
    "    graphic.annular_wedge(x='x', y='y', source = graphic_source_speakers, inner_radius=3, outer_radius = 30, start_angle=np.pi/2, end_angle=3*np.pi/2, color=\"green\", alpha = 0.6)\n",
    "    graphic.circle('x', 'y', source = graphic_source_listeners)\n",
    "    graphic.multi_line('x', 'y', source=graphic_source_lines)\n",
    "\n",
    "    return plot, graphic, source, graphic_source_speakers, graphic_source_listeners, graphic_source_lines\n"
   ]
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   "source": [
    "### And, finally do some plots\n",
    "On the left-hand plot below (Source Locations), the two green thingies are loudspeakers.  All units are in millimeters.  The blue dot is the listener (i.e. your ear).  As you drag the sliders around, you can see that when the speakers are some distance apart, they start interfering with each other when off axis.  When on-axis, the response is always perfectly flat.    Interference is always worst when at 90 degrees off axis."
   ]
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       "      console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
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   "source": [
    "\n",
    "# Create the plots, and their respective data sources\n",
    "plot, graphic, source, graphic_source_speakers, graphic_source_listeners, graphic_source_lines = create_plots()\n",
    "\n",
    "# Show the plots\n",
    "t = show(row(plot, graphic), notebook_handle=True)\n",
    "\n",
    "# Create the interactive sliders\n",
    "i = interact(update_data, \n",
    "         speaker_distance=(1.0, 1000.0), \n",
    "         listener_distance = (1.0, 2000.0),\n",
    "         listener_angle = (0, 360, 1))"
   ]
  },
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