simple-signals.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generating Simple Audio Signals\n",
    "\n",
    "[back to main page](index.ipynb)\n",
    "\n",
    "We create a simple sine wave as an introductory example using Python and NumPy, using a Jupyter/IPython notebook.\n",
    "\n",
    "Let's start very simple. We create ~~three~~ four numbers and give each of them a name.\n",
    "\n",
    "> Sometimes these are called *variables*, but that is actually misleading.\n",
    "> Think about objects and names. An object is created (in our case a number) and we specify a name by which we want to access this object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dur = 1.5  # duration in seconds\n",
    "amp = 0.3  # amplitude (full scale: +-1.0)\n",
    "freq = 440.  # frequency in Hertz\n",
    "fs = 44100  # sampling frequency in Hertz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Everything following a `#` sign is a comment.\n",
    "You don't have to comment everything, but sometimes it helps other people (and future you) to understand what you did in your code.\n",
    "\n",
    "There is no output. If you want to see which object a certain name refers to, just type the name:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dur"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Python, *everything* is an object. And every object has a *type*. Let's see ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(float, float, float, int)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(dur), type(amp), type(freq), type(fs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we didn't specify any types explicitly, we just got Python's default types. Numbers with a comma are by default of type `float`, numbers without comma are of type `int`.\n",
    "\n",
    "There are many more built-in types in Python (strings, tuples, lists, dictionaries, ...), but let's ignore them for now.\n",
    "If you *really* want to know more, you can have a look at my [Introduction to Python](intro-python.ipynb).\n",
    "\n",
    "If you want an overview about all the objects you have defined up to now, use `%who` or its more verbose cousin `%whos`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variable   Type     Data/Info\n",
      "-----------------------------\n",
      "amp        float    0.3\n",
      "dur        float    1.5\n",
      "freq       float    440.0\n",
      "fs         int      44100\n"
     ]
    }
   ],
   "source": [
    "%whos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's bring NumPy into the game. The canonical way to do that is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this, we'll have to prepend \"`np.`\" to all NumPy functions, types etc.\n",
    "\n",
    "Now let's create the most basic signal, a sine. This is kind of the \"Hello, world!\" of signals.\n",
    "\n",
    "In order to create a sine tone, we need first a series of time instances to represent our sampling times. The distance between those instances is the *sampling interval* $\\tau = \\frac{1}{f_s}$, where $f_s$ is the *sampling frequency*.\n",
    "\n",
    "To create a series of regularly ascending (or descending) values, NumPy provides the function [numpy.arange()](http://docs.scipy.org/doc/numpy/reference/generated/numpy.arange.html). Let's use that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.00000000e+00,   2.26757370e-05,   4.53514739e-05, ...,\n",
       "         1.49993197e+00,   1.49995465e+00,   1.49997732e+00])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = np.arange(np.ceil(dur * fs)) / fs\n",
    "t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, this creates an array of numbers from 0 to just below the value specified in `dur`. These are a lot of numbers, so to avoid flooding us with heaps of useless output, IPython just shows the first and last few values. Very handy.\n",
    "\n",
    "> Note that in Python 2 and before, the division operator works a little differently then in Python 3. Here we assume we're using the latter, where the division of two `int`s returns a `float` value (and not an `int` with the truncated result!).\n",
    "> To make sure this also works as expected in Python 2, you can convert one operand to `float` before the division or use a special `import` statement:\n",
    ">\n",
    "> ```python\n",
    "> 1. / fs\n",
    "> ```\n",
    ">\n",
    "> or\n",
    ">\n",
    "> ```python\n",
    "> 1 / float(fs)\n",
    "> ```\n",
    ">\n",
    "> or\n",
    ">\n",
    "> ```python\n",
    "> from __future__ import division\n",
    "> 1 / fs\n",
    "> ```\n",
    "\n",
    "If you want to get help about `np.arange()` (or any other function/object), just write its name (without the parentheses) followed (or preceded) by a question mark:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.arange?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This will open a help screen at the bottom of your browser window with an explanation of all parameters and with a few usage examples.\n",
    "\n",
    "Now let's check the type of `t`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `ndarray` is the single most important type of NumPy. It can handle arrays with an arbitrary number of dimensions. All values stored in an `ndarray` have the same data type. This makes most operations on them faster then on Python's built-in `list`s.\n",
    "\n",
    "Let's get some information about our brand new array named `t`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(66150, dtype('float64'), 1)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(t), t.dtype, t.ndim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, NumPy stores floating point numbers as `float64`, i.e. each number using 64 bits. This is sometimes called *double precision*. If you want *single precision*, you can use `float32`. The length of our array can be obtained with the built-in `len()` function and `t.ndim` shows how many dimensions the array has. This one has only one. Boring.\n",
    "\n",
    "Now that we have our time instances, we can compute the sine for each of them, according to the equation\n",
    "\n",
    "$$x(t) = A\\sin(\\omega t),$$\n",
    "\n",
    "where $A$ is the amplitude, $\\omega = 2\\pi f$ and $f$ is the desired frequency of the resulting sine tone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.0187945 ,  0.03751516, ..., -0.05608843,\n",
       "       -0.03751516, -0.0187945 ])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sig = amp * np.sin(2 * np.pi * freq * t)\n",
    "sig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we didn't have to explicitly loop over the array elements. Most NumPy functions - including `np.sin()` - work element-wise. If an array is multiplied by a scalar, the multiplication is also applied element-wise.\n",
    "\n",
    "> This is called \"broadcasting\", but more about that later ...\n",
    "\n",
    "To check if this actually worked, we plot the signal, but first we'll set up inline plotting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAD7CAYAAABuSzNOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDAZJUsNgkCQ1DAZJUuP/ANj5+d2GfVndAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff22089aa20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sig)\n",
    "plt.ylim(-1.1, 1.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hmmm ... maybe we recognize something if we only plot the first 200 values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAEKCAYAAAAb7IIBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff21e5d51d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sig[:200])\n",
    "plt.xlabel(\"time / samples\")\n",
    "plt.ylim(-1.1, 1.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Better.\n",
    "\n",
    "If we want to show the time in milliseconds instead of samples, we have to specify the time instances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEZCAYAAACZwO5kAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff21e438208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t[:200] * 1000, sig[:200])\n",
    "plt.title(\"sine tone\")\n",
    "plt.xlabel(\"time / milliseconds\")\n",
    "plt.ylim(-1.1, 1.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we can *see* our signal, wouldn't it also be nice to hear it?\n",
    "\n",
    "There are several 3rd-party libraries for Python that allow audio playback, let's try one of them: the [sounddevice](http://python-sounddevice.rtfd.org/) module.\n",
    "\n",
    "Follow the [installation instructions](http://python-sounddevice.rtfd.org/#Installation), then re-start the IPython kernel and re-evaluate this notebook (with the menu commands \"Kernel\" $\\to$ \"Restart\" and \"Cell\" $\\to$ \"Run All Above\") and continue here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sounddevice as sd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sd.play(sig, fs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Did it work? No?\n",
    "\n",
    "Don't despair, if you can't play the signal directly, you can save it to a sound file and play that in an external sound file player.\n",
    "I've written a separate [description how to read and write audio files in Python](audio-files/index.ipynb), have a look there.\n",
    "\n",
    "OK, now we know how to create a *mono* signal, but what about *stereo*?\n",
    "\n",
    "For now, we were using one-dimensional arrays, but for stereo signals we need two-dimensional arrays.\n",
    "The 2 channels can be either stored as rows or as columns of such a two-dimensional array.\n",
    "Both ways are possible, but it's more common to store the channels as columns.\n",
    "\n",
    "Let's create two sine signals with different frequencies, one on the left channel and one on the right.\n",
    "\n",
    "There are several possibilities:\n",
    "\n",
    "1. Create two separate mono signals like above, and combine them with [numpy.column_stack()](http://docs.scipy.org/doc/numpy/reference/generated/numpy.column_stack.html)\n",
    "\n",
    "1. Duplicate the time array `t` and the array with the two frequencies with [numpy.tile()](http://docs.scipy.org/doc/numpy/reference/generated/numpy.tile.html) and use those larger two-dimensional arrays in the calculations (this is not recommended)\n",
    "\n",
    "1. Use [broadcasting](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html) and do everything at once\n",
    "\n",
    "1. For sure, there are more ways to do this ...\n",
    "\n",
    "In this case, let's use *broadcasting*!\n",
    "\n",
    "This means that we use arrays of different (but compatible) shapes in our calculations and the singular dimensions are internally repeated.\n",
    "This sounds complicated, let's just see it in an example.\n",
    "\n",
    "Remember our time array `t`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.00000000e+00,   2.26757370e-05,   4.53514739e-05, ...,\n",
       "         1.49993197e+00,   1.49995465e+00,   1.49997732e+00])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This array is one-dimensional (note that there is only one pair of brackets).\n",
    "\n",
    "To be completely obvious, we could also check the number of dimensions explicitly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t.ndim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But we can re-shape it, for example into a two-dimensional array with one column.\n",
    "We can specify the concrete shape, or we can set one component to `-1`, which means this dimension is determined automatically, based on the given data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.00000000e+00],\n",
       "       [  2.26757370e-05],\n",
       "       [  4.53514739e-05],\n",
       "       ..., \n",
       "       [  1.49993197e+00],\n",
       "       [  1.49995465e+00],\n",
       "       [  1.49997732e+00]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t.reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is two-dimensional (note the two levels of brackets!).\n",
    "\n",
    "Let's now create an array for our two frequencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([500, 600])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freq = np.array([500, 600])\n",
    "freq"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, this two-element array is one-dimensional.\n",
    "\n",
    "The interesting part comes when we multiply those two arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.00000000e+00,   0.00000000e+00],\n",
       "       [  1.13378685e-02,   1.36054422e-02],\n",
       "       [  2.26757370e-02,   2.72108844e-02],\n",
       "       ..., \n",
       "       [  7.49965986e+02,   8.99959184e+02],\n",
       "       [  7.49977324e+02,   8.99972789e+02],\n",
       "       [  7.49988662e+02,   8.99986395e+02]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freq * t.reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wow, the result is a two-dimensional array with two columns!\n",
    "The left column holds the time array element-wise multiplied with the left frequency, the right column used the right frequency value for multiplication.\n",
    "\n",
    "Isn't this great?\n",
    "Now we can use this for creating our *stereo* sine signal:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  0.        ],\n",
       "       [ 0.02135331,  0.02561443],\n",
       "       [ 0.0425983 ,  0.05104179],\n",
       "       ..., \n",
       "       [-0.0636272 , -0.07609638],\n",
       "       [-0.0425983 , -0.05104179],\n",
       "       [-0.02135331, -0.02561443]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sig = amp * np.sin(2 * np.pi * freq * t.reshape(-1, 1))\n",
    "sig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we have an array with two columns, one for each channel.\n",
    "\n",
    "The plt.plot() function can handle two-dimensional arrays and just plots each column with a new color. How convenient!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD7CAYAAABjVUMJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xe8XFXV//HPIgGkKSLSuwLSS+hECNUEkF4lNOkYQKTX\nc48+0qSpKFJCEUMoUhJ6TQRF6aEIKDwSH9DQQSk/kOD6/bF2wiW592bunTNzZu75vl+v+8otZ87Z\nOTOz1+y2trk7IiJSPTOVXQARESmHAoCISEUpAIiIVJQCgIhIRSkAiIhUlAKAiEhFDSy7AFOYmeaj\nioj0gbtbXx7XMgEA+v6fkM8zsw537yi7HP2F7mexdD+LVc+HZ3UBiYhUlAKAiEhFKQD0T+PLLkA/\nM77sAvQz48sugASrNxeQmV0KbAm87u4rdXPMz4BhwIfA3u7+RBfHuMYARER6p566s4gWwGXA0O7+\naGZbAF9396WBA4ALCrimiIjUqe4A4O4PAO/0cMjWwBXp2IeAuc1s/nqvKyIi9WnGGMDCwMudfn4F\nWKQJ1xURkR40axB42v4pLfoSESlZMxaC/QNYtNPPi6TfTcfMOjr9ON7dxzeuWCIi7cfMhgBDCjlX\nETuCmdkSwM1dzQJKg8Aj3H0LM1sHOM/d1+niOM0CEhHppXrqzrpbAGY2GtgQmNfMXgYyYGYAd7/Q\n3W8zsy3M7EXgA2Cfeq8pIiL1K6QFUAS1AEREeq/sdQAiItKGFABERCpKAUBEpKIUAEREKkoBQESk\nohQAREQqSgFARKSiFABERCpKAUBEpKIUAEREKkoBQESkohQAREQqSgFARKSiFABERCpKAUBEpKIU\nAEREKkoBQESkohQAREQqSgFARKSiFABERCpKAUBEpKIUAEREKkoBQESkohQAREQqSgFARKSiFABE\nRCpKAUBEpKIUAEREKkoBQESkohQAREQqSgFARKSiFABERCpKAUBEpKIUAEREKkoBQESkohQAREQq\nSgFARKSiFABERCpKAUBEpKIUAEREKkoBQESkohQAREQqqu4AYGZDzex5M3vBzI7t4u9DzOxfZvZE\n+jqp3muKiEj9BtbzYDMbAJwPbAr8A3jEzMa6+3PTHPo7d9+6nmuJiEix6m0BrAW86O4T3f0T4Gpg\nmy6OszqvIyIiBas3ACwMvNzp51fS7zpzYF0zm2Bmt5nZ8nVeU0REClBXFxBRuc/I48Bi7v6hmQ0D\nbgKW6epAM+vo9ON4dx9fZ/lERPoVMxsCDCnkXO611OHdFmQdoMPdh6afjwf+6+5n9PCYl4BB7v72\nNL93d1dXkYhIL9RTd9bbBfQosLSZLWFmswC7AGOnKdz8Zmbp+7WIoPP29KcSEZFmqqsLyN0nm9kI\n4E5gADDS3Z8zswPT3y8EdgQONrPJwIfArnWWWUREClBXF1CR1AUkItJ7ZXYBiYhIm1IAEBGpKAUA\nEZGKUgAQEakoBQARkYpSABARqSgFABGRilIAEBGpKAUAEZGKUgAQEakoBQARkYpSABARqSgFABGR\nilIAEBGpKAUAEZGKqndP4LZjuS0BbASsBiwKzMqnM0/mzWX/w0sbf8qjB33Cm8vNCcwOfAy8C/wN\neBJ40J1Xyym59JbltjCwObAKsBgwB/A+8E9iN7txnvn/FX5dYxHgm8AKwBLAPMSHrY/Stf83Xf9h\nd/5f0devovRcbwSsQTzXXwD+A/wdeAa4yzP/e3kl7BszBhB11RrA8sCCwBeJ/dhPc+d3dZ2/ChvC\nWG4Dge8ABwJLA/fy8ZxP8Pi+izJp0LpMnnUFFpwwiSXu+4QFJyzCR3NP5KWNxjBm5MNMnv3LwFLA\n6sC6wEvAdcDlCgatJz3XOwCHEm+Yu4DHiOftA2BOIvCvCWwKvAD8ArjGM5/c5+saSwJ7ATsDXwUe\nAJ4iPjy8DUwGZgMWApYF1krlGwdcCYx15z99vX4VWW4zEc/1wUSQHwf8iaj0PwBmBZYk3rubAxOB\nC4BRnnnL3mszDNgY2APYGpgE/BH4M/EB4t/p0AnuTKqn7uz3AcBy2xb4CfAKcA6XPPgQr6x7GHAQ\n8BBwBXCbO++n42cmbvoPgLmBoz3z26KMDCQ+2X2H2OryFuDH7jxfdLml9yy3LYGzgTeAc4BbPPNP\nejh+ZmAocBSwMHCEZ35zr65prA6cTLwuRgGjiU/2/63hsfMAWwH7AN8AzgN+6c57vSlDFVlumxHP\n8YfAWcBYz/zjHo4fQDzX3yc+0B0PXOdZi1SATK1fhgNHA58ClwHXufNKz49TAJj+fLl9FbgIWA4Y\nQYffDxwGHAfcCJzuzv/28HgDtiTelA8Bh3r22Wb2ZnwJGAEcns53sjuvF1V+qZ3lNg/wS+KT3hHA\nbb19Y6cK5efAs8ABnvmbPR5vLEZUPIOB04GR7nzQh+JPOd/KRKU0BMiAS2oJIlVjuX2JeJ42IN57\nY/vwXG8E/IxoFR7omU8qvKC9ZMYwPvvw8kPgPndq+n9pS8hpWG7fBB4H/gKsQoe/mX7eGFjPnf17\nqvwBPHP3zG8BVgbeBB633NaY+nfnX+78mGjOfwg8bcZOjfkfSXcstzWBCcCrwCqe+a19+VTnmd9N\ndCP8DZhgua3f5fUMM+NQ4AkiWHzdnZ/VU/kDuPOUO7sRHzr2BMaZsVQ95+xvLLfVie68D4AVPPMx\nfXyuxwGDiHG9xyy3DYstae3M+KoZ1xFB7WhgiDv31lr5183dW+IrilLAeTrYiw5eo4Nh4APAjwZ/\nA3w4uNVx3h3o4HU62Knr8vta4H8BvxJ87rLvZxW+6GC39JxsW/B5t0zn3XOa53g+8FvBHwZfumH/\nr3jd/iC9bg+q53XbX77oYFs6eIMOdin4vJvRwat0sH/T/0/4RuCvgJ8JPlvfz4P39bH9qgvIcjse\n2B/Ykg5/C7gGGADs6c7EusuY2ypEv/+ZnvnPp/u7MQdwJtGvu4M7j9Z7Tema5XY40Xc/zDN/pgHn\nXx64FfiFZ36WGZsR40WXAR3udDu2UFgZjOWAXwMvE6/h9xt9zVZkuR0InAJs45kX/p6y3L4O3EEM\nxv+w0eMCqa8/A/YF9nbnrvrOV/ExgNRfnxMDs5vQ4fMQFfUoIHPn08LKmdviwL3ABZ752V0eY2xH\njD8c7M5vi7q2BMvtOOC7wGaNnNpnuS0C3MNftnqB0TcPAr7jzvhGXa/LMhizEjNXVge2caftpjLW\nw3I7jJiQsYln3mO3bZ3XmQ+4mwj6JzYqCJjxRWIW4UzAHl7ATEKNAcQnwR2AIXT4ysR0sFPcOanI\nyh8gVThDgIPTi3P6Y5wbiWln55pxQprWJQWw3H5AfHIa0vB53R0+iZ8/P475ntmcEcte1OzKH8Cd\nj4n/7xXAH81Yr9llKIvl9l1iUH/DRlb+AJ7568AmwBZARyOuYcZCwP3E4POwIir/erV9ALDchhOz\ncb5Fh29BvFF2cOfKRl3TM3+FeLEca7nt0OUxzhPA2sD2wIVm7X+vy2a57UbM/NjYM/9nQ69lfAG4\njreW/Qavrrom8/51v3T9pkvdtecSgeAmM75VRjmaKU3pPRUY2qwFXGnm1+bA7pbb/kWe24wViLn8\nVxM9A31ec1Kktu4Cstw2J/rtNqbD1yfmY2/qzl8aUcYurr860Xe4rWf+YJfHGHMR3VEvAfsW3SKp\nCsttMHAD0RXwdEOvFZX/TcSCmz3c+dhyWwm4B9jTM7+zkdefQdnWI6YdH+DOmLLK0UiW29rEe2Yr\nz/yhEq6/NLGQbx/P/Pa6z2esBtwOHOnOqHrPN/35KzgGYLmtRqzy3I4OXwU4BtjEnRcbVcZuyjGM\nGBjcwDP/a5fHxODwGOB1YjCvJaJ/u+j0htzTM69rwGyG1zJmIyr/t4nKf+pzlaaG3gRs1IiB51qZ\nMYjoqz7cnWvKKkcjdHqu90vTsMsqx7rEe3aoZ/54n89jrEp8SPyeO9cXVb7PX6NiAcBy+wqRS+U4\nOnw+YpBoY3deamQZeyjPfkQAWtMz/1eXx0TFcgORi2Y3BYHapEVeDxEzry5u6LWM2fksUO/V1XNk\nue1BzEhZ0zN/t5Hl6YkZKwF3EkHgurLKUSTLbQ4ilcMFnvkvW6A82xMLxtbwzHvdX9+Myj+uU6EA\nkJZ03wo8Q4c/BfwI2KDs2RGW2wXAfMCO3c0gSDM6biFylezv3qTFHm0q5XoZA7zomR/R0GsZMxOf\n7t8hKv9uu+ost58ROWa28cxLW61rxipEK3hPd0rrlipCmsn3G+ATouulJd4bltuPgPWBzXuTK8qM\n5YH7gBGNnglYtVlApwCzceq/HyDm3H+r7Mo/+T6RhbDbiirN6NgOWAk4rUnlamdHAV8hWlcNkwbo\nLyEyLO5TwzjNkUSeqFMaWa4ZcedJ4vV0ZT+YHTSCyJ56SKtU/kkHkZfnh7U+IGWDvR04utWngbdV\nALDctgD25aox5/CfuS4GtvYWScSWElHtRMwMGtztcbGYZwtgazOOblb52k1K5/EDYJeeEroV5Azg\n68DOtSzwSuXZCdg3jQGVxp0HiayRN6Z8Qm3HclsPOAnYwTP/sOzydOaZf0okfxxuuX17Rseb8WWi\n2+f8Rs5ELErbBADLbSHgUp7e9Tj+uvVFwO7uPFx2uTrzzCcSmR2vTsnouj7OeYuYbvY9M3ZvUvHa\nRlqUM5roCni5odcyjgSGAd92p+bKJ/UJDwcutdzmb1T5aipLdP8cDtxixsJllqW3LLcvE8/1vo2e\n699XnvkbwC7AJWkhaJfSON9YolvurCYVry5tMQaQ+oLv4MN5nuDMt3YEcnd+3dwS1s5yOwNYBti+\np+asGSsS/YTbufOHZpWvlaW+4FuAJz3zExp6LWN74KfAuj6DlLvdniO3U4kkcluV3XVhxgnEavgN\n2iFtRHquRwNveOaHll2eGbHcjibSvGycWgaf/S0We16Vftzdm5jJtQpjAIfhNhdnTVoHuLaVK//k\nFGKQ8Ls9HeTOM0Tz/bdmfK0ZBWsDBwLzE7lSGiZNpbyQSK/Qp8o/yYgNYEYUUrD6nEZkRr0q7STV\n6oYT42ENHeMp0DnEONFRXfztCOJD33ebWfnXq+VbAJbbyjj3ctGj45g0aGZilW/L32DLbQVgPLDO\njJq2ZhxM7FWwnjvvNKF4LclyWwZ4EBjsmTdsbCd1k8QeD5G2o77zRTKxPxKfDBu6SG2GZTFmIfqg\nn3TvfkJC2Sy3JYGHiXxOE8ouT61SF9AjwLc88ycAzNiY+PS/dhkTUvptC8By+wIwiocPvYdJg5Yh\nFua0fOUP4Jn/Gfgf4Ddpm8Luj3UuIOZ0X90mn9wKl+7RlUBHgyv/2YGbgZ8XUfkDeOYvEp9if2O5\nzVLEOftclthWcgdgSzP2LrMs3UlTua8Ezminyh+m5gI7Ahhluc2WNgYaRSQKbIXZiL3S0gEAOJl3\nF3+P28/bgJjx0/L9mtP4OfAesQvZjBxFpK7+cUNL1LpOAN4ldvZqiNRPeyGxt+qZBZ/+ciJt8/EF\nn7fXUityW+AnZqxZdnm6cDgxtfKcsgvSR1cBTzF5ljOJxZ1nu3NfyWXqk5btArLcVufTgXdx7t/h\n/YW2cudPZZavryy3xYhdjIakVkH3xxrzEs3LY925thnlawVpn4W7gdU883807DrGCGA/oqut8OmG\nltvCxE5hm3nmTxZ9/l6Xx9iWWMm6pjuvlV0emNpd9ieia7SpaVuKZCfO+RU+nfllxlz2IM9vu1mZ\nizr7XReQ5TYL/x1wBbed/wnvL3RUu1b+AJ75/xFznC+roSvoTWJhz/ntOqe7t9I9uRQ4tsGV/3pE\nssAdGlH5A6TyHwNcnjacL5U7NxF5qn6bxgZKlWbzXQyc1s6VPwCnvr8Ld5z3Ortsvxgd9oWyi9NX\nLRkAcDuWf6w5L4/tP8ady8suTgEuIrqCvj+jA92ZQNpo3ox5Gl2wFnAU8BY07nk2YwHgWmKGRqPn\nml8BTKK2br9myIn0FueWXRDgAGB24LyyC1IPMwYDGU/utQnmE2jwjLVGarkuIMttRf4z+5+44KkX\neOdr66T0CW3PcluKmPWwXndZQz93vHEWMUVui/6aQtpyWxb4A5Fsa2JDrhE5fu4Bxrk3ZqOP6a4Z\nO4k9ThNSV9dUntiF6mHgJ+6MLKUMuS1K3JMZdoW2srSpyyPAfu7cnhYBPkWsA3mknDL1ky4gy20g\n/2/u33L3mZN552tb95fKH8Az/xuRT+TS1BSekePox4PC6R5cAuSNqvyTM4AP6EUul3qlDYOOp3W6\ngv5NDAqfVsagcFrwdSHwszav/GcBfgv80p3bATzz14hZQZdZbrOWWb6+qDsAmNlQM3vezF4ws2O7\nOeZn6e9Pmtlq3Z7s3cU6eG3lJXn0wO3daWgKgJKcn/793owOTKmIdwV2TStW+5tDAAN+0agLmLEL\nsA0wvITpw5cCb9Iii5xSzqwDifGAeZt8+eHAwsDpTb5u0X4KvMb0iRxHA/9LzGRrK3V1AZnZAOAv\nwKbAP4im0W7u/lynY7YARrj7Fma2NvBTd1+ni3M5x31pMqPHnuUTNyh9Kl2jdFrstFZqFfR8vLEG\ncBuxvL8lEt/Vy3JbgnitDPbMG7J7W9qCbzywWRpXabpOM8A29MyfLaMM0zLjNGANYGgzuhYttwWI\nLpJhnvljjb5eo5ixLzFetXZqUX3+75GrbAIlzAArswtoLeBFd5/o7p8Q+11uM80xWxMDY7j7Q8Dc\nZt0kz3rk4Gf5+wZtF0V7I/X/nwFclJrGPR/vPEp8srghbS/Z1tL/+SLg7AZW/l8i5mcfWVblD1Nn\ngJ0CjEyLn1rByUTL60dNut75wMg2r/zXIlov23VV+QOkPaqPJbp4e5zt10rqDQALw+e6al5Jv5vR\nMYt0ebbHDtigIpuknAt8iRnkCprCnUuIwdJL02KmdrY3keO/IdkSU27/y4F7WiRn1IXAf4CWSHaW\nuhZ3A3ZP6wQaxnLbAViRmInUlsyYj+j337+GFvjlxIy2IxtdrqLUGwBqraynrbS6fty7Sx1hZh3p\na0g9BWtlaWehfYHTUtOxFocCSxA58tuS5bYg0fr5bm92V+qlY4AF6GFjnmZKO4btB5yUZoKVzp03\niP0MLjJjmUZcI23b+nMizfNHjbhGo6UZZNcCV6Q1FT1K2WAPAI5KM9waVC4b0qme7KjrXHWOAawD\ndLj70PTz8cB/3f2MTsf8Chjv7lenn58HNnT316Y5V5/7sdqV5ZYDqwLb1pJK2IzFiSRmu7ozvsHF\nK1Tq+rkB+LNnflJDrmFsCvwaWKvODJ+Fs9yOIvYd2LTstNFTmHEAseZk7aLTrFhuvwbe8cwPL/K8\nzWTGucCyxF4RNY+XWG6HAjsTYz8Nn3xQ5hjAo8DSZraEmc1CbJowdppjxgJ7wtSA8e60lX+FnUra\niaqWg1OyqeFEut+uu9Fa107Em6khfc8pOP6GSMrVUpV/ch4wF9EaaBUXE2kZLimyazHt3DcYOLGo\nczZb2qjp20Ru/94Olv+CqFsPLrxgBat7IZiZDSNe3AOAke5+mpkdCODuF6ZjzgeGEvOx93H3x7s4\nT+VaAACW29rEZuQreeZv1vQY4zhiXveG7bBWIu2O9hTR0nmo8PMbXwAeAK525+yiz18Uy20lYgOg\nVRuZ9qI30i5WvweudK9/ha7l9iXgGWBvz/zees9XBjNWJXJTbexOnxbyWW7fIO7roJRBtGHqqTtb\nbiVw2eUog+V2DvBVz3yPmo6PT2vXA6+6c0hDC1cAy+0qYJJn3pDBMTMuJgbVd2n1SQSWWwewOrBN\nC3UFLUG0BHZ25/66zpXbxcB/PfMDiyhbs5nxFWKK8nH1JmS03E4Avgls0cjnut+sBK6wk4H1UtN5\nhlIltzewiRl7NbJg9bLctiamC5/ckPMbBwLrAfu2euWfnErsFrdr2QWZwp2JwF7EfhS1TkqYjuW2\nGbHX9dEFFa2p0l4cVwHXF5SN9yfEhISaPtiVQS2AFmG5bUxMI1vRM+9yrvF0jzGWB34HbO7OEw0s\nXp9YbnMT3QG7e+a/K/z8xvrEwPJgd14o+vyNYrmtSWxKs1LacLwlmHESMVC9UdpYpvbH5jYX8DRw\noGd+ZyPK12hpkdyaxCK5QmapWW6rETu0rZzSRhROLYB+wDO/j3ihnDGjY6c+xnmWSCtxfYtmDj0b\nGNOgyn9hYore3u1U+QOkpGFXErn6W8mpxDz2vqzROAO4r40r/52J9RG7FlX5A6RtI0fyWRqYlqIA\n0FqOBrZKrYGapKbqjcCoVtpOMnUHbEID0iKbMSsxBvKLKUm52lAGrJG6yFpCype0JzDMjOG1Ps5y\n24hY8d+Wa1TMWJ2YubNt2pOjaD8EVrLcdmzAueuiLqAWY7kNJVaPruyZ/6umxxgDiZTH97tzSiPL\nV1N5ouvnKWA/z/yuQs8dA+AXA3MDO7VJv3+XLLcNiD7nlT3zt8suzxRmTJmttKk7Pea1sdzmIJ7r\nwz3zW5pRviKlvSIeBo5w5/qGXSdm+40hdr2bVOi51QXUf3jmdwC3EpkHa3tMNFl3AfYxY7tGla0X\nzgfGFl35JwcB6xBdP21b+QN45vcTLZkLaskL1Sxp6uNhwE0pFUJPfgL8oU0r/1mJMaSRjaz8AdL0\n54uAi1vpuVYAaE1HA+tbbjVX5mnP1+2I5f2rN6xkM2C57Uxkmyw8DXJa6dtBNNULXblaouOIfDm7\nl12QztwZTSysuzGts5iO5bYVsAURLNpKakleSGQxblZivP8BFqSFFgOqC6hFWW7rEZ9OVvXMX635\ncbF3wE+Bddxp6mKjtCn64zRgd6Q042k80e1T+KBymSy3KQuP1mj0oqHeSIn1rgE+Bvbo3OJKO2FN\nAHb2zB8oqYh9ZsaRxKr6we580LTr5rYCMXNvbc+8kO1J1QXUD3nmDxKzBy6rcQexeJxzAzGgdbMZ\nczSqfNNKZbwU+EUDKv/5gFuAo/pb5Q/gmU8gulJ+3UJpo6cMCu9FpPCYmtYhdWFcClzappX/t4mM\nnds0s/IHSDui/RgY1Qq7xSkAtLYO4Iv0fmHNGcSns9FpgLgZjgHmJKYSFialKrgJGNUi6Z0b5Wwi\nS26rbCYPgDsfEnt87N9p0eEhwHzQnD2Wi2TGukTw2tad/yupGD8ldosr9L3SF+oCanFpM+1HgR08\n89/X/LjYv3QMMIkGr5K13DYkugrWSPvhFnPeSMd7PfAesa1ja7xYGyR1oT0KDG+1PDpmLAeMY/Bp\np7PpCScC66fNjdqGGd8guhH3KXv6cEqX/QRwSL0D6OoC6sc885eJvQOustxq3ss1reTcEVie6fcw\nLUzqCx5FJP8qsvKfiegCG0g/mPFTi5QgbjjwmxQMWoY7z/G1O/ZizQvO5rltzm7Dyn8h4HYix0/p\na0c887eIhWcj09ahpVALoE1YbmcCKxEDrLXnJo/kVg8QU90KzZSZ+qvvBP7omReW6yfN0DgPGESk\nufiwqHO3A8vtRKakZMj8k7LLA1Of69v45+rvcdFjg4FN3Plz2eWqRRpDug+4yr38bpfOLLdjiNl7\nQzzzPmX2VQugGk4EZgHO7M2D3HkL+BYwwqzw6XqnE6+hjqJOmCr/HwJDgK2qVvknpwHvEgPDrSID\nZmGhx3cldlu724wVSi7TDJkxL7FI8kYa2BKuw1nAP6lxj/CiKQC0ifRJcEciVcQBvXqs8zKwEfB9\ns2K2SrTcDiKW/+/YmxZJj+eMyv90YtBxc3feLeK87SbtIrUnMNRy+17Z5bHcdiWyz+7qmU9OawSO\nIoLAiqUWrgep9XsPMYPslFbsRuz0XK8AHN/s66sLqM1YbksTXTrDPfN7evVYYzGiKXyhe98/XVpu\nw4iZFIOLm8s8tdtnMFH5v1XEeduZ5bYksanIIZ75mJLKsDEwmtjK8nObo5ixG3AO8Xz1aeOURjFj\nfiK54t3Asa1Y+XeW9gZ/CDjCM/9trx6rLqDq8MxfINI+XGW59erTV5r2NoSY0ndqGmjtFcttFeAK\nYlZSUZX/QGJV5lpE33LlK38Az/wlojV0seW2TrOvnxaoXU0s9pqugk8tge8D95ixUbPL1x0zlgYe\nJGbBtXzlD+CZ/5NoUV9gua3brOsqALShlF75cODO1CKo/bGxX+76RCAYnebZ1yRtc3cb8L20UK1u\nZsxN5D5anAp3+3THM38U2Ae4Ma0ibYrU+riVaH10u/jOnWuI2SzX9CaDaKOYsTZwP3CaOx3tUPlP\nkVJH7wnclPYRaDgFgDblmY8GTgHutdyW6dVjnTeAjYmFR/fVkPALy21Zoj/1BM/8uj4UefpzGl8H\n/gg8D2zpzntFnLe/8cxvZUqfexOCgOX2dWAc8ONauiPcuY8YY/ofM07pS8uyCGbsSmy0s587l5RR\nhnp55rcTm8nfbrk1PKeXAkAb88xHEjNwxqfmeu2PdT4CvkNU6o+Z0e0eBJbbGsQCmpM88yv6XODO\n5zS2Ivq3f+rO4UVuwtEfeeajiCBwbyO7gyy3lYnK/zTP/Jc1ly+mhK4LDAVuT2mWm8KM2cz4FZHU\n7Vvu3NqsazeCZ34Dsdr6DsttcCOvpQDQ5jzzS4lsjHdZbt/u1WOd/7pzMpGd8Eozzkwpcqey3LYl\nFtAc5JlfXm95zfiiGZcQu2Ht6M6v6j1nVXjmVwHfBW623HYo+vxpL4p7gGM88wt7XT5nErAhsan6\n42YMLbiI0zFjWaIVOTcwqBW3Ru2LFASGAzdYbg3rWtMsoH7CcluLyB56GfDD3i4gMuOrxEYriwMH\n0WGPE62LPYgB37oTvKV0zhcTMzOOVJdP31hug4gUGdcBJ3rmvdq/t4vzDQBOBg4gBnxrTjnS7Tlj\nUPjXxIeH44se2E+pTo4idiE7iZjZ1hqVWYFSl9/NxFTWYzzzj6Y7RrOAxDN/mMjDvybw+z50Cb1B\nrEg8m4UeuZm3l3qVj+daH1iz3srfjBXNGENsiDHCnQNU+fedZ/4YsUr6G8Aj9fQVp5lkDwAbAIOK\nqPwB3BlHrFz/GHjWjKN6M+GgO2YMSH39zxEbAw1y51f9sfKHqdlDBxH7CDyS0sQXRi2AfialZd6X\n2HxiLHAJPcxqAAAIhElEQVR6rdM10+DfcbhtzUOH/pE7zl0fZrqbSC/9h968ydL+xJsRA1prEyse\nz09jD1KAtHJ0D2LF8J3Aj9I04VoeuzhwArA98Qn64rQoqfhyxorhHwHrAb8i0pK83MtzfJkYszoc\neBs4IQ0+V0J6rnclnuvfAaem4FBX3akA0E9ZbvMQS/YPJjJMXkcMur4w5Y2emv5fI/pttydaEBcC\nZ3nm76YpmnsR2zDOTsyr/h2RxfDv7kxdAZwydy5OtECGAN8mMpFeBFxZ0ZQOTWG5fZHoCjkEeJLo\nHroP+JtnPjkdMxOwJPFc70QE5QuBsz3zRmyEPn05I6PoYcDOwLPEQq3fA0+78/Y0x85B7JS2FjGw\nPDgd/0ti7+vWqLiazHKbCxhBBML9PPNbFACkW2nT7q2I7p11iKbkW4ARA2eTiBWIY4h9fKerqNMq\n3RWBLYFvEk37+YF/AR8Bs3Y612PAH4Cb3anp06gUw3L7ArFwbEuiS2cB4B3gU2Be4A2iwr0NuL6r\n57op5YyJBpsAmxIzh1YABqSyQuwrMSsxPfgx4C7gLq0R+YzlNjvwX8/8IwUAqVmqJOYlKoV/9bUS\nSPvEzk28UT8G3nKnJTJXSrDcZgO+TFSub3Q1gNgK0geMOYmyOvAh8HZVP+X3lgKAiEhFaRaQiIj0\nmgKAiEhFKQCIiFSUAoCISEUpAIiIVJQCgIhIRSkAiIhUlAKAiEhFKQCIiFSUAoCISEUpAIiIVJQC\ngIhIRSkAiIhUlAKAiEhFDezrA81sHuAaYheoicDO7j7dhg1mNhH4N5F//hN3X6uv1xQRkeLU0wI4\nDrjb3ZcB7k0/d8WBIe6+mip/EZHWUU8A2Bq4In1/BbBtD8dqoxcRkRZTTwCY391fS9+/RuwR2xUH\n7jKzR81s/zquJyIiBepxDMDM7iY2lp7WiZ1/cHc3s+72llzf3SeZ2VeBu83seXd/oJvrdXT6cby7\nj++pfCIiVWNmQ4AhhZyrr3sCm9nzRN/+q2a2IDDO3b8xg8dkwPvufnYXf9OewCIivVTWnsBjgb3S\n93sBN3VRsNnNbK70/RzA5sDTdVxTREQKUk8LYB7gWmAxOk0DNbOFgIvdfUszWwq4IT1kIDDK3U/r\n5nxqAYiI9FI9dWefA0DRFABERHqvrC4gERFpYwoAIiIVpQAgIlJRCgAiIhWlACAiUlEKACIiFaUA\nICJSUQoAIiIVpQAgIlJRCgAiIhWlACAiUlEKACIiFaUAICJSUQoAIiIVpQAgIlJRCgAiIhWlACAi\nUlEKACIiFaUAICJSUQoAIiIVpQAgIlJRCgAiIhWlACAiUlEKACIiFaUAICJSUQoAIiIVpQAgIlJR\nCgAiIhWlACAiUlEKACIiFaUAICJSUQoAIiIVpQAgIlJRCgAiIhWlACAiUlEKACIiFaUAICJSUQoA\nIiIVpQAgIlJRCgAiIhWlACAiUlF9DgBmtpOZ/dnMPjWz1Xs4bqiZPW9mL5jZsX29noiIFKueFsDT\nwHbA/d0dYGYDgPOBocDywG5mtlwd1xQRkYIM7OsD3f15ADPr6bC1gBfdfWI69mpgG+C5vl5XRESK\n0egxgIWBlzv9/Er6nYiIlKzHFoCZ3Q0s0MWfTnD3m2s4v/epVCIi0nA9BgB336zO8/8DWLTTz4sS\nrYAumVlHpx/Hu/v4Oq8vItKvmNkQYEgh53Kv70O6mY0DjnL3x7r420DgL8AmwD+Bh4Hd3H26MQAz\nc3fvcUBBREQ+r566s55poNuZ2cvAOsCtZnZ7+v1CZnYrgLtPBkYAdwLPAtd0VfmLiEjz1d0CKIpa\nACIivVdKC0BERNqbAoCISEUpAPRDaZaAFET3s1i6n61DAaB/GlJ2AfqZIWUXoJ8ZUnYBJCgAiIhU\nlAKAiEhFtdQ00LLLICLSjvo6DbRlAoCIiDSXuoBERCpKAUBEpKJKDwDaMrJ+ZjbRzJ4ysyfM7OH0\nu3nM7G4z+6uZ3WVmc5ddzlZkZpea2Wtm9nSn33V778zs+PRafd7MNi+n1K2rm/vZYWavpNfnE2Y2\nrNPfdD97YGaLmtm4tP3uM2Z2WPp9Ma9Rdy/tCxgAvAgsAcwMTACWK7NM7fgFvATMM83vzgSOSd8f\nC5xedjlb8Qv4JrAa8PSM7h2xremE9FpdIr12Zyr7/9BKX93czwz4QRfH6n7O+H4uAKyavp+TyK68\nXFGv0bJbAFO3jHT3T4ApW0ZK7007C2Br4Ir0/RXAts0tTntw9weAd6b5dXf3bhtgtLt/4rHN6YvE\na1iSbu4nTP/6BN3PGXL3V919Qvr+fWI73YUp6DVadgDQlpHFcOAuM3vUzPZPv5vf3V9L378GzF9O\n0dpSd/duIT6/oZFer7UbYWZPmtnITt0Vup+9YGZLEK2rhyjoNVp2ANAc1GKs7+6DgGHA98zsm53/\n6NE21L3ugxrune7rjF0ALAWsCkwCzu7hWN3PLpjZnMD1wOHu/l7nv9XzGi07APRqy0jpmrtPSv++\nAdxINPleM7MFAMxsQeD18krYdrq7d9O+XhdJv5MeuPvrngCX8FmXhO5nDcxsZqLyv9Ldb0q/LuQ1\nWnYAeBRY2syWMLNZgF2AsSWXqa2Y2exmNlf6fg5gc+Bp4j7ulQ7bC7ip6zNIF7q7d2OBXc1sFjNb\nElia2OZUepAqqCm2I16foPs5Q2ZmwEjgWXc/r9OfCnmN9rgpfKO5+2Qzm7Jl5ABgpGvLyN6aH7gx\nXicMBEa5+11m9ihwrZntC0wEdi6viK3LzEYDGwLzpi1OTwFOp4t75+7Pmtm1xPamk4FD0qdaSbq4\nnxkwxMxWJboiXgIOBN3PGq0PDAeeMrMn0u+Op6DXqFJBiIhUVNldQCIiUhIFABGRilIAEBGpKAUA\nEZGKUgAQEakoBQARkYpSABARqSgFABGRivr/LxLqlJ9GldcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff21e16a5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sig[:200])\n",
    "plt.ylim(-1.1, 1.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course we can again plot the time in milliseconds.\n",
    "And let's add a legend in order to distinguish the two signals!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEZCAYAAACZwO5kAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XecVOX1x/HPFysqAnYQDNYkmoRYYo9iDWrE+LOBWGIh\nqKjYjXV2sGPHHrsSRbFiiVgiYizYQGPvFTU2FDvI+f3xPIsDbJnZuTN35u55v177Ynfmzr2H2dlz\n733KeWRmOOecy64OaQfgnHOusjzRO+dcxnmid865jPNE75xzGeeJ3jnnMs4TvXPOZZwneucqTNLd\nknZNOw7XfsnH0bt6JakBWN7MPIk61wK/onftlqS50o7BuWrwRO9qnqQjJb0v6StJL0vaWFJf4Chg\nJ0lTJU2M23aWdLmkyfE1J0jqEJ/7q6RHJJ0l6VMgJ2leSWdIekfSR5IukjR/wbEHSXpN0meSbpfU\nrZkY55c0UtKnkr6Q9ISkxeNz4yTtVRDDfySdLulzSW/G/0vjfpqN37m28g+Qq2mSfgkMAdYws4WB\nzYG3zewe4GRglJl1MrNV40uuAn4ElgdWjdvvXbDLNYE3gCXi608DVgB6x3+XBo6Px944brMD0A14\nBxjVTKi7AwsDPYBFgMHA9/E5i1+FMbwMLAoMBy4veK61+J0rmSd6V+t+AuYDVpE0j5m9a2ZvxucU\nv8IP0pLAFsDBZvadmX0CnAP0L9jfZDO7wMxmAD8Ag4BDzGyKmX0NnFKw/UDgcjObZGY/Eu4g1pG0\nTBNx/khI3CtaMNHMpjbzf3rHzC630EF2DdBN0hJFxu9cyeZOOwDnWmJmr0s6CGggJPuxhMT8YROb\n/wKYB/hQmpn/OwDvFmzzXsH3iwMLAE8XbC9+vgDqBjxVEMs3kj4jXPUX7hPgWqAnMEpSF2AkcIyZ\nTW8izo8K9vltPPZCwGJFxO9cyfyK3tU8M7vezP5ISORGaG6BWZtDICTxH4BFzaxr/OpsZr8t3F3B\n958C3wErF2zfJTYRAUwGejVuLGlBwlX7B03EON3MhpnZKsC6wJ+B3Ur8rxYTv3Ml80TvapqklWLn\n63yEJPg9oTkHwpVxL8XL33iVfy9wlqROkjpIWl7SBk3tOzbfXAqcU9BxurSkzeMm1wN7SOodj38y\n8LiZzXGFLamPpN/GkTxTgWkFcRal1PidK5Ynelfr5iO0m38CfEho3jgqPjc6/vuZpMYmlt2AeYEX\ngc/jNkvF52bvFAU4EngdeFzSl8B9wEoAZvYAcBxwM+Hqflmaby9fKh7ry3jscYTmnNk1FUPhzy3F\n71yb+IQp55zLOL+id865jPNE75xzGeeJ3jnnMs4TvXPOZVzNTJiS5L3CzjnXBmamlp6vmUQPrQfb\nXkhqMLOGtOOoBf5e/Mzfi5/5e/GzYi6SvenGOecyzhO9c85lnCf62jQu7QBqyLi0A6gh49IOoIaM\nSzuAelL2zFhJVwBbAf9rrviSpBGE8qvfAn81s4lNbGPeRu+cc6UpJncm0Rl7JXAeoa52U0FsCaxg\nZitKWgu4CFg7geM65zLGR9+1rK0Xw2UnejN7WFKvFjbpB1wdt50gqYukJc3s43KP7ZzLHq+/1bSC\nNQpKVo02+qWZdbGH9wnLrTnnnKuCanXGzn4q8lO2c85VSTUmTH1AWGKtUQ+aWKEHwiSIgh/Hmdm4\nyoXlnHP1R1IfoE8pr6nGFf0Y4pJqktYGpjTXPm9mDQVf46oQm3POFaVXr1488MADrW5366230rNn\nTzp16sSkSZMSj8PMxhXmymJeU3ail3Q98CjwS0nvSdpT0mBJg2NQdwNvSnoduATYr9xjOudctUkq\nqkP0sMMO48ILL2Tq1Kl06dKFDh06MGPGjCpE2LwkRt0MKGKb/cs9jnPO1Toz491332XllVee4/E0\n+cxY55wrgZlx6qmnssIKK7DYYoux00478cUXX/DDDz/QqVMnfvrpJ3r37s0KK6zAhhtuCECXLl3o\n1KkTEyZMSCVmT/TOOVckM2PEiBGMGTOG8ePH8+GHH9K1a1eGDBnCfPPNx9dffw3Ac889x+uvv874\n8eMB+PLLL5k6dSprrbVWKnF7onfO1RUpma+2uuSSSzjxxBPp3r0788wzD7lcjptuuqnJdvi0m2wa\n1VQ9eueca03aufOdd95h2223pUOHn6+T5557bj7++GO6deuWYmTN80TvnHMl6NmzJ1deeSXrrLNO\nq9uWU7YgSd5045xzJdhnn304+uijeffddwH45JNPGDNmTJPbLr744nTo0IE33nijmiHOwRO9c84V\nSRJDhw6lX79+bL755iy88MKss846PPHEE7Ns02iBBRbgmGOOYb311qNr166zbFdNZdejT4rXo3fO\nxTyQdhg1SVKTZYqLyZ1+Re+ccxnnid455zLOE71zzmWcJ3rnnMs4T/TOOZdxnuidcy7jPNE751zG\neaJ3zrmM80TvnHNt8Jvf/GZmGeLWFLsMYaV4onfOuTZ4/vnn2WCDDYratqVlCMeNG0fPnj2TDG0O\nnuidc65E06dPTzuEkniid865IvTq1Yvhw4fTu3dvFlpoIXr27DmzOea7775j9913Z5FFFmHllVdm\n+PDhc1ylT5w4kd69e9OlSxf69+/PDz/8wDfffMMWW2zB5MmT6dSpEwsvvDAfffRR4rF7onfOuSKN\nGjWKu+++mylTpjD33HPPbI7J5/O8++67vPXWW9x3332MHDlylqYaM2P06NGMHTuWt956i+eee46r\nrrqKBRdckHvuuYfu3bszdepUvvrqK5ZaaqnE4/aFR5xzdUX5ZIrcWq60KpmSOPDAA1l66aXneG70\n6NFcfPHFdO7cmc6dOzN06FAaGhrmeG1jEt96662ZNGlSiKMK1To90Tvn6kqpCTpJzXWaTp48eZbn\nevToMcc2hVfqHTt2ZPLkyckH2AxvunHOuSI1N3KmW7duvPfeezN/Lvy+rftMkid655wr04477sgp\np5zClClT+OCDDzj//POLTuBLLrkkn332GV999VXF4vNE75xzZTr++OPp0aMHyy67LJtvvjk77LAD\n8847b7PbF46r/9WvfsWAAQNYbrnlWGSRRSoy6saXEnTO1YysLCV40UUXceONN/Lggw8mtk9fStA5\n51L00Ucf8cgjjzBjxgxeeeUVzjrrLLbddtu0w5rJR90451yZfvzxR/bZZx/eeustunTpwoABA9hv\nv/3SDmsmb7pxztWMrDTdVII33TjnnGuWJ3rnnMs4T/TOOZdx3hnrnKsp1Zgp2t54onfO1QwfkFEZ\n3nTjnHMZ54neOecyzhO9c85lnCd655zLOE/0zjmXcZ7onXMu4zzRO+dcxpWd6CX1lfSypNckHdnE\n830kfSlpYvw6ttxjOuecK15ZE6YkzQWcD2wKfAA8KWmMmb0026YPmVm/co7lnHOubcq9ol8TeN3M\n3jazacAoYJsmtvPZbs45l5JyE/3SQOFy5+/HxwoZsI6kSZLulrRymcd0zjlXgnJr3RSzQsAzwDJm\n9q2kLYDbgJWa2lBSQ8GP48xsXJnxOedcpkjqA/Qp6TXlrOYiaW2gwcz6xp+PAmaY2WktvOYtYHUz\n+3y2x32FKeecK1E1Vph6ClhRUi9J8wI7AWNmC2JJxbqjktYknFw+n3NXzjnnKqGsphszmy5pf2As\nMBdwuZm9JGlwfP4SYHtgX0nTgW+B/mXG7JxzrgS+OLhzztUxXxzcOeecJ3rnnMs6T/TOOZdxnuid\ncy7jPNE751zGeaJ3zrmM80TvnHMZ54neOecyzhO9c85lnCd655zLOE/0zjmXcZ7onXMu4zzRO+dc\nxnmid865jPNE75xzGVfumrF1QXnNB/yRsM7iCkBnfppnGp+sPI1Xtp7GhAOMb5foBMwDTAXeBv4L\nPGTG2+lE7RopryWBrYDVCYvPzw98CrwIjAMet5zNSORYYmHC52Q1wmdl0fhU4+diEjDejPeTOF7W\nKa8OwBrApsCvgMWBacB7wETgLsvZh+lFWByJRQifi9WBXvz8uTjDjPtTCqtomV54RHktAhwG7A28\ngXEfL+w0L6//aX2mLbga3Z/6iOXHzmDxl7rz+fKP8NghN/LMoK8Iv8jVCL/YD4FrgCvMmJJkfK5l\nymsd4GhgfcIqZo8D7wA/EBJGb2BzYAHgPOAiy9n3JR9HzAX0A/YCNozHeQJ4lXBCmQF0BpYlJK0N\ngTeAq4Brzfi6rf/HrIoXV4OBA4DpwL8IF0//I1xg/gJYG+hLeL9Ps5w9lE60TZOYF9iOkD/+APwH\neBJ4HfgMMOA5Mz5ILUiKy52ZTPTKS8A+wDDgFn6a50xO+HEl4GTCL+c84KbGxK28FgX2BYYC1wLH\nWc6+iQngj8DfCB/I8wln8K+SiNM1TXktBZwNrEv4nV1jOfuumW1F+CM8mnBy3tdydldRxxEirHOc\nB74ALgRuNuObVl43D7AxIZGtD5wJnGfGt8UcN+uUV1/gAuAlwu/vMcs1nWiU1/zALoTf30TgQMtZ\nyomTuYA9gGOBN4GLgTvMaPIzmLZ2meiV12LASGARYA8a7BvCL2oZ4EjgTjOa+9AtAZxFuD3byXL2\n3M/x0Ytw4tgEOIhwoqiNNy9DlNfmhDuoq4BhlrOik6fy2gi4HLgXGGo5+6HZbcWvgUuBjsARwL/b\n8vuM+zmBcJIZYsa/St1HViiveQl/P1sDgyxn95bw2o7AUYSLqkGWszsqE2UrcYhVCZ+hr4EjzXgs\njThK0e4SvfJaBbgDGA0cS4NtD4wAzgDOMmNakfvZhfCB3Wv2D5zEeoQE8TSwT2tXf654yutgQlPb\nQMvZuDbuoxNwJdAD6Gc5+98sz4er+P2BHHA8cLEZZbfvS2wO/AO4DTjCjB/L3Wc9iRdYtxDujHa3\nnLWpmVN5rQeMItx1n97cnUDSJDoQ7uiPBg4lNMnVRnJsRbtK9MprTUKSP4wGu4FwO70FsJ0Zz7Zx\nf7cSmnGumDVWFgAuIlz5b2/Gy22N281sfhkObAlsYTl7N4H9DSM0y2xmOXsHZv7eLgF+B/yfGW+U\nFfjsxw0ddlcC3YCdzHgryf3XKuW1NHAf4e/vqHI7xpVXj7iv8cBBlU72EosRmmy7Ajub8WYlj5e0\ndpPolddahA/GnjTYBOB24BNg93I6UJXXSsADhCaES2eNFxE6704B9jDjzrYepz2LSflMYANCUv4i\nwX0PJVylbUiDdSBcbb8IDKpUe3r8XBwE/J1wMnmkEsepFcqrOyEhX2Y5OzXB/XYB7gGeAYZUKtlL\nLE/oKL4dOLrYu/5aUkzurPtx9MrrN4Rf0h402LOED92DwLbljpKxnL0KbATkldfWszxnmBmXAX8G\nLpMYWM6x2rHjCaObEk3yAJazc4HzmT7veBb8+BFC380ulew0jZ+Ls4HdgdsktqrUsdIWBzHcC1ye\nZJIHiE0/mwNrETpFEyexBvAwcLYZh9djki9WXSf62Hl6J3AoDfYq4Zd2uRnHJNHuCmA5ex34C3CF\n8lpjjueNCYQO2lMlhiRxzPZCee0N7EZorkk0yc/UYA/w5L6L8bc1vqZB51Wr3dWMewgXAZdL7FaN\nY1aT8poHuIkw7DXRJN/IcvYV4T3cK/abJUZiY8KV/H5mXJTkvmtR3Sb62MN/EzCSBnuKMHHmJDPO\nSPpYlrMngEHA7cqr1xzPGy8Qmh4Okjgk6eNnkfJqHDq5heXs44ocQ/wBuJcHTtmbzu+/Cpwfm4qq\nIl4EbAScLLFrtY5bJWcB3wJHVLINPU6m2go4K46qKpvE+sANhP6125LYZ62r20QPnANM4dTPLyXc\nPh5rxqWtvKbNLGe3AacDY+JQsFmfDx1vGwMHSuxZqTiyII6TvxHYIzaPJX+MMOzxDmCQTet4AzAQ\nWAc4sBLHa44ZLxGaIE6X2Laax66UeCe2GbCz5eynSh/PcvYC0B8Y1dSFVikk1iSMDtrZjJqaoFVJ\ndZnoldcgoA93XjCU77uOBUaYcWUVDn0u8AJhMs8czHiP8Ed9osR2VYin7sRb/hsI7bpFTWwq+Rii\nJ6Ej7wgzxgBYzqYSxncfpbz+WInjNseMFwlXpZdIbFbNYyctzlY+GdjGcvZltY5rOfs34ULr+vgZ\nKpnEbwkn/73MuC/J+Gpd3SV65bUycAofrDGQp/YbTZjJeGY1jh1vUQcDmyqvHZvcxniV8Ed9UWwH\ndLM6mXDLP6wSO5do7CA814xrCp+znL1NmM4+Unl1rcTxm2PG04Tp9NfFSTl1R3l1Bq4jTGh6JYUQ\nzgI+B04s9YUS3YG7gIPMSGUyVprqanhlrJ8xgRlzXciw6VsS6k3sXe2JDcprdUJHzjqWsybHYkv0\nIVy5/jEm/3ZPeW1MmPXa23L2WeL7D7VJ7gceN+OIFuI4D1gC6F+tCTkzjy22J9wRrmXG5Goeu1zK\n61rgG8vZPinGsBihVMIgy9k9Rb1GLEgYjXeLGSdVMr40ZHF45YnA2wz7cVnC5IZ905i9Zjl7GjiJ\ncBvZZAVQM8YBxwB3SFT16rEWxavBKwmzjSuR5EWor/IZYQx7S44AVgb+mnQcrTHjJsJkuzFxAldd\nUF79gTUJs0ZTYzn7lNDfcmUcddeiWLfmOuA5wt1ku1Q3iT5eDe7Mxc+MhQ47Ema8pjnNfAShdG2z\nH/w4zv4uYHQshNWenUsoSTu2Qvs/gDDmetfWhtbGAmkDgOHKa/kKxdOSUwgTt66JU+9rmvJahvB5\n39lylnrJD8vZeMKd4flFbH4SsDAwuF5KGlRCzX/IAJTXQsAVPL/TqXy0ah7oZ8anacYUb/n3Ag5X\nXr9uYdPDgR8JHUntkvLaFliP8F4kv//QwXkU4XNRVMlgy9nzhLIL/6jmkEsIk6oIw3WXJhTaq1nx\nvbkUODfeydaKHPBb5bV9cxvEARH9gR3aW+2h2dVFogdOYlrHR7lp1CGEQmIvpB0QzOzcO45wGzlX\nk9sYPxFuNbeWaLIDN8vimgAXEgpdJX41GEfYXAv0b8MiMWcT6sxXfTisGT8AOwAHSGxa7eOXYFdC\nf8bwtAMpFNcd2BM4L7bbzyIOr72YcOef6kVhLaj5RK+81sbYkRGvdQVuM+OWtGOazSWEUSTNTpQy\n4wtge+CC+AFsT04HbrKcPZr0jmPn642EyqQlj4m2nE0n1iuKNVuqKq5StQswMp6wakpsAz8d2Nty\nVnPlASxnjwH/ZLYmHIlOhLHyR8bRTu1eTSf6OPv1Mh454gGmLt2VGrzNjZX69gaObGkyhxkTCZ2E\nN0ssVJ3o0qW8+hDmFRxToUMMJ6xY1ObZ0JazZwlXfhdWuwkHwIx/E+4sboonrlpyDmHRl1pOlscB\nayivLQoeuxh42IwrmnlNu1PTiR44kq+X/JL7T9kM2LFW29ksZ28Sxvie2+J2xuWEZdMurEZcaYor\nB10CHBBrliS7/zBMsR/w1wTqGp0ErESoaZSG4cBHMY6aoLy2JHRu59KOpSWxY31/QnmLjhK7AL8n\nVC11Uc0meuW1HKaDuezRZaHDnmaUVaO8Cs4EfqW8+rWy3QHAH+IHMsuOAl6IpSMSJbEM4WS5Y2wW\nK0tciWoIcLbyWrDc/ZV8/NA5uyfQX6JvtY8/u3iSPp+wLGPNL48Yx9NPZErPUwkXXANqddm/tNRs\nosc4m8cP+pQpy11tRkWmyiepIFmcq7yaHR8dV6TqD5wda2FnjvJagfBeJF5XJo6LvhY404ynktqv\n5exB4FHCCkNVZ8ZnhI7PKySWSiOGAocDE0tZCjB1Xy19GPN/tR/L3/MPM55r/QXtS00meuW1Jd93\nXZcHTvqc0AZXFyxn9xOaZlpMFnHFqxOA62uwXTYJ5wDDLWfvV2DfRwAzKKNdvgWHAYPjgjNVFyfZ\nXQZcndb4+tjPdBAtDC6oSWe9vwdPDX6TXbZYI42+llpXc4leec3H9Pku4tar5mF6x4FmTE87phId\nCuyjvH7ZynbnEToST6h8SNWjvLYCViQk+2T3HcoOHwzsFoetJspyNpkwe/K8FJPFMGBB0ku0ZxLG\nzL+T0vFLFssO/41nd90U0QO8oODsai7RM23+I3lngy682u+gpNf0rIaYLE4ELmgpWcR22T2AgXFh\n6boX23bPBYZazhLtOI8jlf4J7B+rhFbKeYSJTP9XwWM0K17YDAQOjye2qlFemwGrUkeT+yS6EJry\nBtn/fvMesB+hr6VTupHVlppK9MprGWyuo7j39P8AV6cdTxnOBxaHlidImYV1bYErJRavRmAVdgih\nA7aoYlMlOht41IwbK7DvmeJ48dQ6ZgHMeCfGcF21huLGocwjCItx10VHZqxvdCFwd+OazbE8wr8J\nS1S6qOxEL6mvpJclvSapyXHukkbE55+V1HyJ1inLjGTC/j/yce9d67kuRZyIMwQ4I5ZvaH5b4wHC\nWqaXxw9uXVJePQnNVgcnvu+wYMfGVGnREMvZQ4Rqh6n1D8XiZ+OpQBNYMw4E3oK6KuE7EOhN6Fsp\ndCSwRyulSdqVshK9pLkIV699CdUAB0izvrmStgRWMLMVgb9BC+szytbl6cE7mvF5OXHVAsvZf2Bm\nBcvWHEdoLhhcyZgq7HTgwjinIDGxjvjFhEW9Ex+P34LDgb3T6piNhgIbVnoRG+XVjTCZ76Bql21u\nK4nlaGYopeXsI0Lz6QjvmA3KvaJfE3jdzN42s2nAKGCb2bbpR2yGMbMJQBdJSza5twkH3m5fLFup\n6oZpOAIY1FqyiBPBBgIn1GOJhDgDdh1CVcbk9htGnlwNXGDGY0nuuzVxrdJTCcNlU0kWsUDbQOBC\nhU7GShkOXFqpZR2TJjE34S745BaGUl4AdINsLN9YrnIT/dIwS8fY+/Gx1rZp+kP78jYDyoynpsRk\ncQpFJAszXiZc/V8nMV814ktCrMc/Aji0ApNrDgIWIL064iOAXoQlCFNhxhMxjqsqMeQyLqvYhxqa\nlVuE4wglwkc0t0HsazmAsKh43dT9r5RyPzjF3ubNnuSaft3nKx0tqSF+9SknsBoyAvgFxSWLS4F3\nqK8hl/sCnwA3J7lTid8TZtfuktYQ2zhy6EDgnDiiKC2nAvORcP9HrLh6HnCY5ayo8s5pmzmUsojS\nF3ES3OO0vhBNXZHUpyBPNhTzmnIT/QcwS9W9noQr9pa26REfm4OZNRR8jSsztpoQrywak0XHFrcN\nHdB7E4ZcblKN+MqhvBYnjG44MMm23bjy0nXAwWa8ldR+28Jydh9h6bqK1NIvKoYwZ2BX4Mh4AkzK\nYOALqOxIpqTMMpTS+LDIlx0G7JfSAjMVYWbjCnNlMa8pN9E/BawoqZekeYGdgDGzbTMG2A1A0trA\nFDP7uMzj1pU4Y/ZpikgWsXb2HoRb9UUrHVuZTgZGWs6SXh9gODCJMG6+FhwKHKS8fpFWALHW/kGE\npr2ymyLiSbqBhE/SldLUUMpixNnZZxCG57ZbZSV6M5tOqBw3lrA02g1m9pKkwZIGx23uBt6U9Dqh\nmuF+ZcZcrw4FDmyplHEjM+4FRgOX1OqQS+W1BvBnQrJIbr9iq7jf/WpliG1cYGYElSm7UHwcxnXA\nMyQzoekU4DrL2X8T2Fc17ELTQymLcTah4OBWyYZUP2Q1cjIvZiXzeqe8jgVWs5y1OutSYn5gAnBu\nrdXVjm27jxGGU16V2H7FkoRmkv5mjE9qv0mIzW4vEhbheCC1OERn4FnCDOGir2xn2UdeawG3Ar+2\nnH2ZZHyVEIdSTgA2aWvBsliv/jzgN3F1qswoJnfW1MzYduAMoLfy+lNrG5rxPbAzcJrEihWPrDR7\nE9bBvSapHRYMpbyi1pI8zKx7fjChDk5qC72b8SWhvf7SeGIsSTxJXwAcWSdJfh5Cf81J5VSltJz9\nC3iBeivWlhBP9FUUrySGEiZytFq1Mq6Nmwf+GT/wqYttuycAQ+LqWkk5GFiYhJuCEnY78C5h2F5q\nzHiYUOXyyjY07Q0CviOMQ68Hw4DPaGVRnyIdDBwaZ3G3K57oq8xydifwGqFjrRgXEIYvNlQqphKd\nSmjbfTapHUqsQZi2vnMtVyuNnZZDgaOVV9o144cBixJKbRQlLqI9jHCSro022xbERdN3JQylLDve\nOGv7fFLua0mDJ/p0HAQcobxmn1w2h4LVh/aU2KDikbVAea1LKHeR2PJycSHn64EhcWRJTbOcvQJc\nQTjhpReHMY0wazYnsUqRLzuZcJKu+YU5JJYgNOXtHov/JeU0YC3ltXGC+6x5nuhTYDl7nVC/pajR\nE2Z8TGgXvzaOJa66OAP2AuDwhNt2LwDGmTE6wX1W2gnApsprvTSDMON1wp3QdbHzvlnKa03CaKaa\nXgMWZumvuToW/UtMnL2del9LtXmiT88pwHqxTkyr4nKKdxA64dIYnbQvYXLN9UntMK6b+weKb8aq\nCZazqYROvUuK6WupsCuBVwgFvpoUT9IXUScdsIRE3IXKnZRuI0zsTLWvpZo80afEcvYNIcFdUsL0\n+sOA5anyBzQ2MR0P7J9U267EyoTxzf3jOrr1ZjShrG+TpbmrJTbtDQI2k9i5mc0OBj6nDjpgJdYi\nvKcDYvNU4uJn+ABCX0uvShyj1vg4+pQpr9HAa5azohaljmOKHwe2qUZFx1iM7XbCYtGJXGHFdvkn\ngOFmXJnEPtMQR29MBNa3nL2caiyiN3A/sIEZL818PCzU/jiwZtIlpJMWF995GjjAjNsrfry8/g5s\nBPSth87p5vg4+vpwALCX8i0syFLAjDcJ7fU3VGlVqv7AsiRU3TA2O10B/KeekzyA5ew9wiiWfyiv\nVP+W4oLzfwdublyVKp6k/wGcXAdJfm5CmfOR1Ujy0ZmEleB2q9LxUuOJPmVxkYQjgCuK7RwyYwxh\nEsn1lRxfr7yWIDSv7JngGrAHA8uRnfbRC4B5gX3SDoRwAn2Mn0sa7wl0ooVyvjXkBGAGVVzVKxYc\n3AsYXgPDZSvKE31tuAb4mNLae48FptFCJ1wCRgDXWM6eTGJnEn8inNS2jzN/657l7Cfgr8CwlFej\namyv3w/oTs9HziQMAd0rLm1ZsyR2IMwC3zlW6qway9lEwuSzi7K8GpUn+hoQ2wf3Bg6IdUhaf02Y\nWNQf2FSCSJrFAAAQzUlEQVRK/mpSeQ0Efk9CIx9i5+u1wA5plx5OWmyfzwEj0x6yZ8YPLPze9vzp\nkH15re9dtT5mPna+XgD0S3i8fCmGEZon90rp+BXnib5GxHKq+wL/VF6dinpNqHuyNZCX2CipWGLt\n7nOA/rHGS3n7E4sRhoYeHqfvZ9GFhJEtx6YdCIcssweLvvoc1925lcRqaYfTHIlfEIqr7RX7GFJh\nOfsBGACcorx+lVYcleSJvoZYzm4B/k2Ypl3ca8Kkmf7AqDjyoixxXPgo4ATL2aSy9yc6Ev6YbzQL\nawdnUbwr2xPYJ84gToXy+gNwIB2n/B8212DgTokV0oqnORILA3cCp5txR9rxWM5eonEpz7zqZinP\nYnmirz0HE6ZoDyz2BWY8SFgX4G6JclfSOQn4kFDStSwS8wI3EZZHPKbc/dU6y9lkGkdEpdC5p7wW\nJZykh1jO3jfjFkJRvLESNdPZGBdOuRN4iHDnWCsuBd4m4UXua4GPo69ByqtxTPQWlrOnin5daKs/\nHFi/hKXWCo+7PaFzdzXL2aelvn62WOYirBDVkdD5WpHJL7VIeTUAmwCbJDhaqbVjzg3cAzxjOTti\nlufE8cD/ARvG5r7UxIXvxwAfAXu0tu5rtSmvRQhzPIZZzhIrw11JPo6+TsXKkH8Dbi2m8NnM1xkX\nE4bY3SfRrZRjxlv+i4C/JJDkOxBq+SwB7NSeknw0DJhCZUdEze50wiiso5p47gTC1fP9EotUMaZZ\nFIyVn0pol6+pJA9gOfsc6AeckWYTXNI80dcoy9mthMR7m/Iqeo1QM04iXEk/LNGrmNcor2UI9T/2\ntpw904Zwf95XaK4ZCaxEmL2biWGUpYh1+ncBNlNef6v08ZTXX4GtgJ3jcM9Z4wnDLg8CxgEPxsqQ\nVRWba24lzDkYWOPlqF8EdgduSnOd4CR5oq9tpxAKVv0z3poXxYxTCAs1jJdocRSB8upMGBFzluWs\nrBmJEgsSyiUsCPQ1Y2o5+6tnsXjYn4EG5fWXSh0nroN6GrCN5eyLZuMJyf4Iwgn9IYkelYppdvEu\n4n7CXc5fzPihWsduq7gi1RnAXbHvo655oq9hcSTHXsB8wNVxGbjiXmucRyhE9pBE36a2UV4LE9p1\nH6LMZgaJpQl/zB8D25lR9rDMemc5e40w/PUfymvLpPevvDYhVK/sF0eNtByPYWbkCJ2OEyTWTzqm\nOWIUywL/AR4h1Javp2a8s4G7gLHKK5Xy4EnxRF/j4hjf7Qg1OW4sodIlZlwFbA9cLnFcbDsHZpY3\nuJ9QlGtoOUWdJDYDniL8UexZy7fl1WY5e5qQ7K9SXtsltV/ltTWhZPT2lrMJJcVknEW4gLhZYr9K\nlb2W2I6wqPfFZhxei23yLYl/E38HHgbG1XOZBB91Uyfi2N5rgW7ADrFGTnGvDR2zo4GvgEE0qDOh\niWUUcHxbk3xsjz+WkDR2icM8XROU12qE0SbnAme0+T0P0/SHEsplbGM5e6LNMYWhuLcRFs3e34yy\nOuEL9tuR0OyxBaEMdZtjrAXxPT8W2APYNsllNJPgo24yJF7Z9ydMqHpSeW1e9GvDUMuNYMaTrHbp\nS0zr+ATTOp5qOTuujCS/EfAMsDqwuif5lsVO7nUIv8Nb4/qtJYlD/0YREs7a5SR5ADPeANYEPgCe\nl9g7DottEwlJbA08DywCrFrvSR7Clb3l7ATgaOB+5TW43uri+BV9HYpJ/lJC2/rxlrO3i3jNqsDp\nTOu4NNfe+xnvrt8NGA5ca8a3RR033OJvShirvzzhtvamJBZubi/indmJhNK4DcDlrY21jx3xexAm\nP90AHJ1EaYpZjiFWJ9xtdCUUQxtd7IipeHLYkvB56AocbMbYJOOrFcprFUK/yDfAEUkV/CtHMbnT\nE32divVwDgeGAA8Q2mvHW84+i88L6EFYWGEXYBXCH/BFlrPpsSPuCOCPhCaFewgLVLzT2JYaE/si\nhKv2jYEdgG8JCeEaM6oyGSiL4qS404GVCXMf7gCei3duxOJovQnDJvcCXies1/t0xWIKv+/NCJ+r\n3xOGQ94DPAm833hCj9stBqwBbE7oQ/qQ8Lm4odoVKKstnnj3JjTnDLWc3ZxqPJ7osy+OBugPbEto\nGphBmJDSGfgOeJTQPn+L5WyOKzSJ7oRZk5sBqxE6fT+P+2ksrvYsMB64BZjoV/DJiQl/F0J79gqE\ndXkNWBR4AxgLXJ1E3aGS4gqjZbYhJPLVCZ+nz2JsXQiTs54h3FXeYsbz1YyvFiivjoA19XdV1Tg8\n0bcv8Sq+K7AQoeP1y1Lb4OPElq6E/puvgSme2KsjNussSnjv/1et8gnFiJ+LxvHkX6VdSsH9zBO9\nc85lnI+6cc4554neOeeyzhO9c85lnCd655zLOE/0zjmXcZ7onXMu4zzRO+dcxnmid865jPNE75xz\nGeeJ3jnnMs4TvXPOZZwneuecyzhP9M45l3Ge6J1zLuPmbusLJS1CWNbsF8DbwI5mNqWJ7d4m1Eb/\nCZhmZmu29ZjOOedKV84V/d+B+8xsJcJSdn9vZjsD+pjZqp7knXOu+spJ9P2Aq+P3VwN/aWFbX1DE\nOedSUk6iX9LMPo7ffwws2cx2Btwr6SlJg8o4nnPOuTZosY1e0n3AUk08dUzhD2Zmkppbk3A9M/tQ\n0uLAfZJeNrOHmzleQ8GP48xsXEvxOedceyOpD9CnpNe0dc1YSS8T2t4/ktQNeNDMftXKa3LA12Z2\nZhPP+ZqxzjlXokqvGTsG2D1+vztwWxMBLCCpU/x+QWBz4L9lHNM551yJyrmiXwS4EViGguGVkroD\nl5rZVpKWA26JL5kb+KeZndLM/vyK3jnnSlRM7mxzok+aJ3rnnCtdpZtunHPO1QFP9M45l3Ge6J1z\nLuM80TvnXMZ5onfOuYzzRO+ccxnnid455zLOE71zzmWcJ3rnnMs4T/TOOZdxnuidcy7jPNE751zG\neaJ3zrmM80TvnHMZ54neOecyzhO9c85lnCd655zLOE/0zjmXcZ7onXMu4zzRO+dcxnmid865jPNE\n75xzGeeJ3jnnMs4TvXPOZZwneuecyzhP9M45l3Ge6J1zLuM80TvnXMZ5onfOuYzzRO+ccxnnid45\n5zLOE71zzmWcJ3rnnMs4T/TOOZdxnuidcy7jPNE751zGeaJ3zrmM80TvnHMZ54neOecyzhO9c85l\nnCd655zLuDYnekk7SHpB0k+SVmthu76SXpb0mqQj23o855xzbVPOFf1/gW2B8c1tIGku4HygL7Ay\nMEDSr8s4pnPOuRLN3dYXmtnLAJJa2mxN4HUzeztuOwrYBniprcd1zjlXmkq30S8NvFfw8/vxMeec\nc1XS4hW9pPuApZp46mgzu6OI/VubonLOOZeYFhO9mW1W5v4/AHoW/NyTcFXfJEkNBT+OM7NxZR7f\nOecyRVIfoE9JrzEr76Jb0oPAYWb2dBPPzQ28AmwCTAaeAAaY2Rxt9JLMzFps8HfOOTerYnJnOcMr\nt5X0HrA2cJekf8XHu0u6C8DMpgP7A2OBF4EbmkryzjnnKqfsK/qk+BW9c86VrqJX9M455+qDJ3rn\nnMs4T/Q1KPaqO/y9KOTvxc/8vSiNJ/ra1CftAGpIn7QDqCF90g6ghvRJO4B64oneOecyzhO9c85l\nXE0Nr0w7Buecq0etDa+smUTvnHOuMrzpxjnnMs4TvXPOZVzqid6XGvyZpCskfSzpv2nHkiZJPSU9\nGJeqfF7SgWnHlBZJ80uaIGlSfC8a0o4pbZLmkjRRUjGl0jNL0tuSnovvxRMtbptmG31cavAVYFNC\nSeMnaaa6ZXsg6Y/A18A1ZvbbtONJi6SlgKXMbJKkhYCngb+048/FAmb2bawG+x9gqJlNSDuutEg6\nBFgd6GRm/dKOJy2S3gJWN7PPW9s27Sv6mUsNmtk0oHGpwXbJzB4Gvkg7jrSZ2UdmNil+/zVh6cnu\n6UaVHjP7Nn47LzAPMCPFcFIlqQewJXAZ4EUQi3wP0k70vtSga5GkXsCqQHu+gu0gaRLwMXCvmT2Z\ndkwpOhs4nHZ8sitgwL2SnpI0qKUN0070PrbTNSs229xEaKr4Ou140mJmM8zs90APYC1Jq6QdUxok\n/Rn4n5lNxK/mAdYzs9WBLYAhsem3SWkn+pKWGnTth6R5gJuBkWZ2W9rx1AIz+xJ4EOibdiwpWRfo\nF9umrwc2lnRNyjGlxsw+jP9+AtxKaApvUtqJ/ilgRUm9JM0L7ASMSTkmlzJJAi4HXjSzc9KOJ02S\nFpPUJX7fEdiM0GfR7pjZ0WbW08yWBfoD/zaz3dKOKw2SFpDUKX6/ILA50OxovVQTvS81OCtJ1wOP\nAitJek/SHmnHlJL1gF2AjeLQsYmS2utVbDfg35KeJay5fK+Z3Z1yTLWiPTf9Lgk8HPtuJgB3mtm9\nzW3sJRCccy7j0m66cc45V2Ge6J1zLuM80TvnXMZ5onfOuYzzRO+ccxnnid455zLOE72rCkmdJe1b\n8HN3SaMrdKx5JD3dxteuLunc+P1fJZ0Xv2+QdGj8Pi9pk+QiLo+kdlsewhVn7rQDcO1GV2A/4CIA\nM5sM7FChY61PKOdbMjN7mlAWGWadkGMF2+TaHlpF+GQY1yK/onfVciqwfJzlepqkXzQusBKvnG+T\ndK+ktyQNkXSIpGckPSapa9xueUn/itX6xkv6ZTPH6gv8a/YHJX0taXhcwOM+SWtKGifpDUlbx236\nFCxo0WThLElXSdoufn9qXCDlWUmnx8cWl3STpCfi17rx8YUkXRkXi3hW0rbx8QHxsf9KOnW2eE+M\ni448JmmJ+Piy8efnJJ1YsH23+L5MjPtav/hfj8syT/SuWo4E3jCzVc3sSOZMoqsA2wJ/AE4Cvjaz\n1YDHgMZ6Jv8ADjCzNQilai9s5lh9gHFNPL4A8ICZ/QaYCpwAbBKPO6yE/4sBJmlRwoIoq5hZ77g/\ngHOBs81sTWB7Qu10gOOAL8zsd3H7ByV1J5wENwJ+D/xBUuOaDAsAj8XKleOBQQX7v8DMfgdMLohr\nZ+AeM1sV+B0wqYT/k8swb7px1dJaWdkHzewb4BtJXwKNV9X/BX4XCzetC4wONc+AsBDHrAeRlgY+\nN7PvmzjGj2Y2tmC/35vZT5KeB3qV9L8JpgDfS7ocuDN+QVgx7dcFcXaK8W9CKNwHgJlNkbQh4f/+\nWYz/n8AGwO0x3rvi5k8TCppBeB+2jd+PBE6L3z8BXBErf95mZs+24f/kMsgTvasVPxR8P6Pg5xmE\nz2kHwtXwqq3spy9wTzPPTZvtGD9CqPcel+lrTWFbuOJJYk1CAt+eUKBvE8JJbS0z+7HwxTHxz37C\ns9keU8FxZo+3xRjN7OFYk/zPwFWSzjKza4v4f7mM86YbVy1TgU5teJ0AzGwq8Jak7SGUMpb0uya2\n/xNNtM8nQMyWpONVehcz+xdwCNA7PnUvcGDBdo2P3wcMKXi8C+EqfENJiyqsodwfeKiVWB6J2wEM\nLNjfMsAnZnYZobmotZOiayc80buqiE0Tj8ROwtOI7dyNT9PMCJfZnhsI7BVLsz4PzLIwdEyUK5jZ\nq82F0cLPTX3fWoydgDtiCeGHgYPjcwcCa8QO1xeAwfHxE4Gu8T2YBPQxs4+AvxMWFJkEPGVmdxQc\no/B4jT8PJawo9BxhLd3GxzcCJkl6BtiR0JbvnJcpdtkhaT1goJntl3YsztUST/TOOZdx3nTjnHMZ\n54neOecyzhO9c85lnCd655zLOE/0zjmXcZ7onXMu4zzRO+dcxv0/7vhRkbSY+NUAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff21e0f3f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t[:200] * 1000, sig[:200])\n",
    "plt.title(\"stereo sine\")\n",
    "plt.xlabel(\"time / milliseconds\")\n",
    "plt.legend([\"left\", \"right\"])\n",
    "plt.ylim(-1.1, 1.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to know more about plotting, have a look at my [pages about plotting](plotting/index.ipynb), especially the [matplotlib intro](plotting/matplotlib.ipynb).\n",
    "\n",
    "Like before, you can play back the signal, but this time in stereo, hooray!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sd.play(sig, fs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's it for this little example, if you want to know more, go back to the [main page](index.ipynb) and dive in!\n",
    "\n",
    "Have fun!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p xmlns:dct=\"http://purl.org/dc/terms/\">\n",
    "  <a rel=\"license\"\n",
    "     href=\"http://creativecommons.org/publicdomain/zero/1.0/\">\n",
    "    <img src=\"http://i.creativecommons.org/p/zero/1.0/88x31.png\" style=\"border-style: none;\" alt=\"CC0\" />\n",
    "  </a>\n",
    "  <br />\n",
    "  To the extent possible under law,\n",
    "  <span rel=\"dct:publisher\" resource=\"[_:publisher]\">the person who associated CC0</span>\n",
    "  with this work has waived all copyright and related or neighboring\n",
    "  rights to this work.\n",
    "</p>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1+"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}