{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ThinkDSP\n",
    "\n",
    "This notebook contains an implementation of an algorithm to generate pink noise.\n",
    "\n",
    "Copyright 2015 Allen Downey\n",
    "\n",
    "License: [Creative Commons Attribution 4.0 International](http://creativecommons.org/licenses/by/4.0/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get thinkdsp.py\n",
    "\n",
    "import os\n",
    "\n",
    "if not os.path.exists('thinkdsp.py'):\n",
    "    !wget https://github.com/AllenDowney/ThinkDSP/raw/master/code/thinkdsp.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from thinkdsp import decorate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating pink noise\n",
    "\n",
    "The Voss algorithm is described in this paper:\n",
    "\n",
    "Voss, R. F., & Clarke, J. (1978). \"1/f noise\" in music: Music from 1/f noise\". *Journal of the Acoustical Society of America* 63: 258–263. Bibcode:1978ASAJ...63..258V. doi:10.1121/1.381721.\n",
    "\n",
    "And presented by Martin Gardner in this *Scientific American* article:\n",
    "\n",
    "Gardner, M. (1978). \"Mathematical Games—White and brown music, fractal curves and one-over-f fluctuations\". *Scientific American* 238: 16–32.\n",
    "\n",
    "McCartney suggested an improvement here:\n",
    "\n",
    "http://www.firstpr.com.au/dsp/pink-noise/\n",
    "\n",
    "And Trammell proposed a stochastic version here:\n",
    "\n",
    "http://home.earthlink.net/~ltrammell/tech/pinkalg.htm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fundamental idea of this algorithm is to add up several sequences of random numbers that get updated at different rates.  The first source should get updated at every time step; the second source every other time step, the third source ever fourth step, and so on.\n",
    "\n",
    "In the original algorithm, the updates are evenly spaced.  In the stochastic version, they are randomly spaced.\n",
    "\n",
    "My implementation starts with an array with one row per timestep and one column for each of the white noise sources.  Initially, the first row and the first column are random and the rest of the array is Nan."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.54878587, 0.80870645, 0.64066175, 0.63762133, 0.36665185],\n",
       "       [0.58319314,        nan,        nan,        nan,        nan],\n",
       "       [0.84357289,        nan,        nan,        nan,        nan],\n",
       "       [0.18418847,        nan,        nan,        nan,        nan],\n",
       "       [0.2622209 ,        nan,        nan,        nan,        nan],\n",
       "       [0.2106998 ,        nan,        nan,        nan,        nan]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nrows = 100\n",
    "ncols = 5\n",
    "\n",
    "array = np.full((nrows, ncols), np.nan)\n",
    "array[0, :] = np.random.random(ncols)\n",
    "array[:, 0] = np.random.random(nrows)\n",
    "array[0:6]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step is to choose the locations where the random sources change.  If the number of rows is $n$, the number of changes in the first column is $n$, the number in the second column is $n/2$ on average, the number in the third column is $n/4$ on average, etc.\n",
    "\n",
    "So the total number of changes in the matrix is $2n$ on average; since $n$ of those are in the first column, the other $n$ are in the rest of the matrix.\n",
    "\n",
    "To place the remaining $n$ changes, we generate random columns from a geometric distribution with $p=0.5$.  If we generate a value out of bounds, we set it to 0 (so the first column gets the extras)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 2, 4, 1, 2, 1, 2, 1, 3, 3, 1, 1, 2, 2, 4, 1, 4, 2, 1, 4, 2, 1,\n",
       "       2, 1, 2, 2, 1, 4, 1, 1, 0, 1, 1, 1, 1, 1, 2, 0, 1, 4, 3, 1, 2, 1,\n",
       "       3, 1, 1, 4, 1, 2, 1, 1, 3, 2, 1, 0, 1, 1, 1, 2, 4, 1, 3, 1, 4, 2,\n",
       "       2, 2, 1, 3, 3, 1, 1, 1, 1, 2, 2, 3, 2, 0, 3, 1, 2, 1, 1, 2, 1, 3,\n",
       "       2, 4, 1, 1, 1, 3, 4, 1, 1, 1, 2, 1])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = 0.5\n",
    "n = nrows\n",
    "cols = np.random.geometric(p, n)\n",
    "cols[cols >= ncols] = 0\n",
    "cols"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Within each column, we choose a random row from a uniform distribution.  Ideally we would choose without replacement, but it is faster and easier to choose with replacement, and I doubt it matters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([79, 54, 81, 56, 89, 39, 70, 24, 47, 68, 18, 17, 84, 40, 35, 48,  5,\n",
       "       46, 98, 27, 36, 42, 28, 20, 22,  7, 49, 56, 59, 71, 78, 96, 64, 24,\n",
       "       28, 33, 77,  7, 18, 54,  3, 29, 71, 84, 54, 55, 66, 33, 13, 42, 66,\n",
       "       41, 64, 81, 19, 97, 66, 28, 55, 14, 73, 45, 39, 48, 85, 72, 50, 85,\n",
       "       19,  0, 35, 98,  0, 77, 33, 98, 34, 13, 50, 99, 73, 15,  7, 52, 55,\n",
       "       36, 95, 24, 45, 10,  0, 13, 42, 86, 26, 60,  9, 97, 36, 70])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rows = np.random.randint(nrows, size=n)\n",
    "rows"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can put random values at rach of the change points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.54878587, 0.51221941, 0.64066175, 0.15579406, 0.36665185],\n",
       "       [0.58319314,        nan,        nan,        nan,        nan],\n",
       "       [0.84357289,        nan,        nan,        nan,        nan],\n",
       "       [0.18418847,        nan,        nan, 0.38864791,        nan],\n",
       "       [0.2622209 ,        nan,        nan,        nan,        nan],\n",
       "       [0.2106998 ,        nan,        nan,        nan, 0.99871071]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array[rows, cols] = np.random.random(n)\n",
    "array[0:6]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we want to do a zero-order hold to fill in the NaNs.  NumPy doesn't do that, but Pandas does.  So I'll create a DataFrame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.548786</td>\n",
       "      <td>0.512219</td>\n",
       "      <td>0.640662</td>\n",
       "      <td>0.155794</td>\n",
       "      <td>0.366652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.583193</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.843573</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.184188</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.388648</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.262221</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4\n",
       "0  0.548786  0.512219  0.640662  0.155794  0.366652\n",
       "1  0.583193       NaN       NaN       NaN       NaN\n",
       "2  0.843573       NaN       NaN       NaN       NaN\n",
       "3  0.184188       NaN       NaN  0.388648       NaN\n",
       "4  0.262221       NaN       NaN       NaN       NaN"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.DataFrame(array)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then use `fillna` along the columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
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       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.548786</td>\n",
       "      <td>0.512219</td>\n",
       "      <td>0.640662</td>\n",
       "      <td>0.155794</td>\n",
       "      <td>0.366652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.583193</td>\n",
       "      <td>0.512219</td>\n",
       "      <td>0.640662</td>\n",
       "      <td>0.155794</td>\n",
       "      <td>0.366652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.843573</td>\n",
       "      <td>0.512219</td>\n",
       "      <td>0.640662</td>\n",
       "      <td>0.155794</td>\n",
       "      <td>0.366652</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.184188</td>\n",
       "      <td>0.512219</td>\n",
       "      <td>0.640662</td>\n",
       "      <td>0.388648</td>\n",
       "      <td>0.366652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.262221</td>\n",
       "      <td>0.512219</td>\n",
       "      <td>0.640662</td>\n",
       "      <td>0.388648</td>\n",
       "      <td>0.366652</td>\n",
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      ],
      "text/plain": [
       "          0         1         2         3         4\n",
       "0  0.548786  0.512219  0.640662  0.155794  0.366652\n",
       "1  0.583193  0.512219  0.640662  0.155794  0.366652\n",
       "2  0.843573  0.512219  0.640662  0.155794  0.366652\n",
       "3  0.184188  0.512219  0.640662  0.388648  0.366652\n",
       "4  0.262221  0.512219  0.640662  0.388648  0.366652"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filled = df.fillna(method='ffill', axis=0)\n",
    "filled.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we add up the rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    2.224113\n",
       "1    2.258520\n",
       "2    2.518900\n",
       "3    2.092369\n",
       "4    2.170402\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total = filled.sum(axis=1)\n",
    "total.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we put the results into a Wave, here's what it looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from thinkdsp import Wave\n",
    "\n",
    "wave = Wave(total)\n",
    "wave.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the whole process in a function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def voss(nrows, ncols=16):\n",
    "    \"\"\"Generates pink noise using the Voss-McCartney algorithm.\n",
    "    \n",
    "    nrows: number of values to generate\n",
    "    rcols: number of random sources to add\n",
    "    \n",
    "    returns: NumPy array\n",
    "    \"\"\"\n",
    "    array = np.full((nrows, ncols), np.nan)\n",
    "    array[0, :] = np.random.random(ncols)\n",
    "    array[:, 0] = np.random.random(nrows)\n",
    "    \n",
    "    # the total number of changes is nrows\n",
    "    n = nrows\n",
    "    cols = np.random.geometric(0.5, n)\n",
    "    cols[cols >= ncols] = 0\n",
    "    rows = np.random.randint(nrows, size=n)\n",
    "    array[rows, cols] = np.random.random(n)\n",
    "\n",
    "    df = pd.DataFrame(array)\n",
    "    df.fillna(method='ffill', axis=0, inplace=True)\n",
    "    total = df.sum(axis=1)\n",
    "\n",
    "    return total.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test it I'll generate 11025 values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.3955119 , 5.49020141, 4.82135171, ..., 5.74383027, 6.24352434,\n",
       "       5.75793234])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ys = voss(11025)\n",
    "ys"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And make them into a Wave:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "wave = Wave(ys)\n",
    "wave.unbias()\n",
    "wave.normalize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what it looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "wave.plot()\n",
    "decorate(xlabel='Time')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, it is more random-walk-like than white noise, but more random looking than red noise.\n",
    "\n",
    "Here's what it sounds like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "                <audio  controls=\"controls\" >\n",
       "                    <source 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\" type=\"audio/wav\" />\n",
       "                    Your browser does not support the audio element.\n",
       "                </audio>\n",
       "              "
      ],
      "text/plain": [
       "<IPython.lib.display.Audio object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wave.make_audio()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's the power spectrum:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "spectrum = wave.make_spectrum()\n",
    "spectrum.hs[0] = 0\n",
    "spectrum.plot_power()\n",
    "decorate(xlabel='Frequency (Hz)',\n",
    "         xscale='log', \n",
    "         yscale='log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The estimated slope is close to -1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.9993534088150459"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spectrum.estimate_slope().slope"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can get a better sense of the average power spectrum by generating a longer sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6553600"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seg_length = 64 * 1024\n",
    "iters = 100\n",
    "wave = Wave(voss(seg_length * iters))\n",
    "len(wave)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And using Barlett's method to compute the average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from thinkdsp import Spectrum\n",
    "\n",
    "def bartlett_method(wave, seg_length=512, win_flag=True):\n",
    "    \"\"\"Estimates the power spectrum of a noise wave.\n",
    "    \n",
    "    wave: Wave\n",
    "    seg_length: segment length\n",
    "    \"\"\"\n",
    "    # make a spectrogram and extract the spectrums\n",
    "    spectro = wave.make_spectrogram(seg_length, win_flag)\n",
    "    spectrums = spectro.spec_map.values()\n",
    "    \n",
    "    # extract the power array from each spectrum\n",
    "    psds = [spectrum.power for spectrum in spectrums]\n",
    "    \n",
    "    # compute the root mean power (which is like an amplitude)\n",
    "    hs = np.sqrt(sum(psds) / len(psds))\n",
    "    fs = next(iter(spectrums)).fs\n",
    "    \n",
    "    # make a Spectrum with the mean amplitudes\n",
    "    spectrum = Spectrum(hs, fs, wave.framerate)\n",
    "    return spectrum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32769"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spectrum = bartlett_method(wave, seg_length=seg_length, win_flag=False)\n",
    "spectrum.hs[0] = 0\n",
    "len(spectrum)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's pretty close to a straight line, with some curvature at the highest frequencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "spectrum.plot_power()\n",
    "decorate(xlabel='Frequency (Hz)',\n",
    "                 xscale='log', \n",
    "                 yscale='log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the slope is close to -1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0016799964612606"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spectrum.estimate_slope().slope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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