FFT practice.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.50000000+0.j        ,  2.08155948-1.65109876j,\n",
       "       -1.83155948+1.60822041j, -1.83155948-1.60822041j,\n",
       "        2.08155948+1.65109876j])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.fftpack import fft, ifft\n",
    "x = np.array([1.0, 2.0, 1.0, -1.0, 1.5])\n",
    "y = fft(x)\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.0+0.j,  2.0+0.j,  1.0+0.j, -1.0+0.j,  1.5+0.j])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yinv = ifft(y)\n",
    "yinv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "//anaconda/lib/python2.7/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n",
      "  warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.fftpack import fft\n",
    "N = 600\n",
    "T = 1.0 / 800.0\n",
    "x = np.linspace(0.0, N*T, N)\n",
    "y = np.sin(50.0 * 2.0*np.pi*x) + 0.5*np.sin(80.0 * 2.0*np.pi*x)\n",
    "yf = fft(y)\n",
    "xf = np.linspace(0.0, 1.0/(2.0*T), N/2)\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(xf, 2.0/N * np.abs(yf[0:N/2]))\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.fftpack import fft\n",
    "N = 600\n",
    "T = 1.0 / 800.0\n",
    "x = np.linspace(0.0, N*T, N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "//anaconda/lib/python2.7/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n",
      "  warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1088c2810>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cluster</th>\n",
       "      <th>depth</th>\n",
       "      <th>Latitude</th>\n",
       "      <th>Longitude</th>\n",
       "      <th>mag</th>\n",
       "      <th>startday</th>\n",
       "      <th>startmonth</th>\n",
       "      <th>startyear</th>\n",
       "      <th>type</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>57.09</td>\n",
       "      <td>-153.48</td>\n",
       "      <td>8.3</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>1900</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>-135.0</td>\n",
       "      <td>7.1</td>\n",
       "      <td>18</td>\n",
       "      <td>1</td>\n",
       "      <td>1901</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>-160.0</td>\n",
       "      <td>6.6</td>\n",
       "      <td>30</td>\n",
       "      <td>12</td>\n",
       "      <td>1901</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>51.45</td>\n",
       "      <td>-171.02</td>\n",
       "      <td>7.8</td>\n",
       "      <td>31</td>\n",
       "      <td>12</td>\n",
       "      <td>1901</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>52.38</td>\n",
       "      <td>-167.45</td>\n",
       "      <td>7.8</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1902</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>50.85</td>\n",
       "      <td>-175.16</td>\n",
       "      <td>7.0</td>\n",
       "      <td>17</td>\n",
       "      <td>1</td>\n",
       "      <td>1903</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>175.0</td>\n",
       "      <td>6.8</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>1903</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>61.56</td>\n",
       "      <td>-158.54</td>\n",
       "      <td>8.3</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>1903</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>64.62</td>\n",
       "      <td>-148.23</td>\n",
       "      <td>7.8</td>\n",
       "      <td>27</td>\n",
       "      <td>8</td>\n",
       "      <td>1904</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>50.73</td>\n",
       "      <td>-178.55</td>\n",
       "      <td>7.7</td>\n",
       "      <td>14</td>\n",
       "      <td>2</td>\n",
       "      <td>1905</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>51.28</td>\n",
       "      <td>174.83</td>\n",
       "      <td>7.2</td>\n",
       "      <td>22</td>\n",
       "      <td>3</td>\n",
       "      <td>1905</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>52.06</td>\n",
       "      <td>171.45</td>\n",
       "      <td>7.4</td>\n",
       "      <td>15</td>\n",
       "      <td>9</td>\n",
       "      <td>1905</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>53.88</td>\n",
       "      <td>-161.68</td>\n",
       "      <td>7.0</td>\n",
       "      <td>10</td>\n",
       "      <td>12</td>\n",
       "      <td>1905</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>50.77</td>\n",
       "      <td>179.73</td>\n",
       "      <td>8.0</td>\n",
       "      <td>17</td>\n",
       "      <td>8</td>\n",
       "      <td>1906</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>-165.0</td>\n",
       "      <td>7.6</td>\n",
       "      <td>23</td>\n",
       "      <td>12</td>\n",
       "      <td>1906</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>5</td>\n",
       "      <td>120.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>-161.0</td>\n",
       "      <td>6.5</td>\n",
       "      <td>22</td>\n",
       "      <td>8</td>\n",
       "      <td>1907</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>52.44</td>\n",
       "      <td>170.28</td>\n",
       "      <td>7.7</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>1907</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>5</td>\n",
       "      <td>25.0</td>\n",
       "      <td>59.0</td>\n",
       "      <td>-141.0</td>\n",
       "      <td>7.1</td>\n",
       "      <td>15</td>\n",
       "      <td>5</td>\n",
       "      <td>1908</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>175.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>10</td>\n",
       "      <td>4</td>\n",
       "      <td>1909</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5</td>\n",
       "      <td>90.0</td>\n",
       "      <td>52.5</td>\n",
       "      <td>-169.0</td>\n",
       "      <td>7.4</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>1909</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>-149.5</td>\n",
       "      <td>7.4</td>\n",
       "      <td>19</td>\n",
       "      <td>9</td>\n",
       "      <td>1909</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>5</td>\n",
       "      <td>100.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>-160.0</td>\n",
       "      <td>6.7</td>\n",
       "      <td>13</td>\n",
       "      <td>5</td>\n",
       "      <td>1910</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>42.0</td>\n",
       "      <td>-127.0</td>\n",
       "      <td>6.8</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>1910</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>5</td>\n",
       "      <td>25.0</td>\n",
       "      <td>50.75</td>\n",
       "      <td>179.38</td>\n",
       "      <td>7.3</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>1910</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>-135.0</td>\n",
       "      <td>6.8</td>\n",
       "      <td>6</td>\n",
       "      <td>11</td>\n",
       "      <td>1910</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>37.25</td>\n",
       "      <td>-121.75</td>\n",
       "      <td>6.6</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>1911</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>7.1</td>\n",
       "      <td>17</td>\n",
       "      <td>9</td>\n",
       "      <td>1911</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>5</td>\n",
       "      <td>60.0</td>\n",
       "      <td>60.5</td>\n",
       "      <td>-149.0</td>\n",
       "      <td>6.9</td>\n",
       "      <td>22</td>\n",
       "      <td>9</td>\n",
       "      <td>1911</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>173.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>13</td>\n",
       "      <td>11</td>\n",
       "      <td>1911</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>5</td>\n",
       "      <td>25.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>-179.0</td>\n",
       "      <td>7.1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1912</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617829</th>\n",
       "      <td>11</td>\n",
       "      <td>591.48</td>\n",
       "      <td>-21.541</td>\n",
       "      <td>-179.1091</td>\n",
       "      <td>4.6</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617830</th>\n",
       "      <td>11</td>\n",
       "      <td>6.56</td>\n",
       "      <td>-21.3093</td>\n",
       "      <td>168.6738</td>\n",
       "      <td>4.9</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617831</th>\n",
       "      <td>13</td>\n",
       "      <td>10.0</td>\n",
       "      <td>39.5984</td>\n",
       "      <td>73.068</td>\n",
       "      <td>4.2</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617832</th>\n",
       "      <td>7</td>\n",
       "      <td>9.1</td>\n",
       "      <td>29.6131</td>\n",
       "      <td>143.3523</td>\n",
       "      <td>4.6</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617833</th>\n",
       "      <td>6</td>\n",
       "      <td>43.29</td>\n",
       "      <td>-2.1018</td>\n",
       "      <td>138.966</td>\n",
       "      <td>4.4</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617834</th>\n",
       "      <td>3</td>\n",
       "      <td>93.55</td>\n",
       "      <td>-20.6978</td>\n",
       "      <td>-69.1784</td>\n",
       "      <td>4.7</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617835</th>\n",
       "      <td>0</td>\n",
       "      <td>31.94</td>\n",
       "      <td>16.6123</td>\n",
       "      <td>-97.8297</td>\n",
       "      <td>4.3</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617836</th>\n",
       "      <td>7</td>\n",
       "      <td>35.0</td>\n",
       "      <td>46.8062</td>\n",
       "      <td>152.8785</td>\n",
       "      <td>4.4</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617837</th>\n",
       "      <td>3</td>\n",
       "      <td>11.2</td>\n",
       "      <td>-20.1948</td>\n",
       "      <td>-70.9115</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617838</th>\n",
       "      <td>0</td>\n",
       "      <td>9.11</td>\n",
       "      <td>36.1518</td>\n",
       "      <td>-89.6965</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617839</th>\n",
       "      <td>8</td>\n",
       "      <td>98.55</td>\n",
       "      <td>24.8082</td>\n",
       "      <td>95.2124</td>\n",
       "      <td>4.4</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617840</th>\n",
       "      <td>6</td>\n",
       "      <td>35.0</td>\n",
       "      <td>-0.2665</td>\n",
       "      <td>125.5466</td>\n",
       "      <td>4.5</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617841</th>\n",
       "      <td>7</td>\n",
       "      <td>10.0</td>\n",
       "      <td>35.5119</td>\n",
       "      <td>129.8661</td>\n",
       "      <td>4.8</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617842</th>\n",
       "      <td>6</td>\n",
       "      <td>35.0</td>\n",
       "      <td>-0.3386</td>\n",
       "      <td>125.4749</td>\n",
       "      <td>4.4</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617843</th>\n",
       "      <td>5</td>\n",
       "      <td>10.0</td>\n",
       "      <td>43.3325</td>\n",
       "      <td>-126.6572</td>\n",
       "      <td>3.1</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617844</th>\n",
       "      <td>1</td>\n",
       "      <td>36.21</td>\n",
       "      <td>21.8613</td>\n",
       "      <td>145.3276</td>\n",
       "      <td>5.2</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617845</th>\n",
       "      <td>13</td>\n",
       "      <td>155.4</td>\n",
       "      <td>38.2305</td>\n",
       "      <td>73.6797</td>\n",
       "      <td>4.3</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617846</th>\n",
       "      <td>0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>36.2626</td>\n",
       "      <td>-97.5821</td>\n",
       "      <td>3.5</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617847</th>\n",
       "      <td>3</td>\n",
       "      <td>39.51</td>\n",
       "      <td>-41.6855</td>\n",
       "      <td>-74.0542</td>\n",
       "      <td>4.3</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617848</th>\n",
       "      <td>11</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-32.927</td>\n",
       "      <td>-177.8664</td>\n",
       "      <td>5.2</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617849</th>\n",
       "      <td>6</td>\n",
       "      <td>192.36</td>\n",
       "      <td>2.0851</td>\n",
       "      <td>128.3228</td>\n",
       "      <td>4.3</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617850</th>\n",
       "      <td>0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>37.3679</td>\n",
       "      <td>-98.2025</td>\n",
       "      <td>3.5</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617851</th>\n",
       "      <td>13</td>\n",
       "      <td>10.0</td>\n",
       "      <td>39.489</td>\n",
       "      <td>73.4459</td>\n",
       "      <td>4.4</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617852</th>\n",
       "      <td>7</td>\n",
       "      <td>29.15</td>\n",
       "      <td>29.7514</td>\n",
       "      <td>142.1428</td>\n",
       "      <td>4.6</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617853</th>\n",
       "      <td>5</td>\n",
       "      <td>10.0</td>\n",
       "      <td>44.1651</td>\n",
       "      <td>-128.9059</td>\n",
       "      <td>4.3</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617854</th>\n",
       "      <td>7</td>\n",
       "      <td>21.26</td>\n",
       "      <td>35.7802</td>\n",
       "      <td>140.9868</td>\n",
       "      <td>4.4</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617855</th>\n",
       "      <td>11</td>\n",
       "      <td>257.05</td>\n",
       "      <td>-18.8947</td>\n",
       "      <td>169.4241</td>\n",
       "      <td>4.8</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617856</th>\n",
       "      <td>4</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-56.8016</td>\n",
       "      <td>-142.1336</td>\n",
       "      <td>5.9</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617857</th>\n",
       "      <td>5</td>\n",
       "      <td>10.0</td>\n",
       "      <td>53.4488</td>\n",
       "      <td>-163.4493</td>\n",
       "      <td>3.8</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617858</th>\n",
       "      <td>14</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0.166</td>\n",
       "      <td>-79.8907</td>\n",
       "      <td>4.3</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>2016</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>617859 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       cluster   depth  Latitude  Longitude  mag startday startmonth  \\\n",
       "0            5     0.0     57.09    -153.48  8.3       10         10   \n",
       "1            5     0.0      60.0     -135.0  7.1       18          1   \n",
       "2            5     0.0      52.0     -160.0  6.6       30         12   \n",
       "3            5     0.0     51.45    -171.02  7.8       31         12   \n",
       "4            5     0.0     52.38    -167.45  7.8        1          1   \n",
       "5            5     0.0     50.85    -175.16  7.0       17          1   \n",
       "6            5     0.0      52.0      175.0  6.8        5          2   \n",
       "7            5     0.0     61.56    -158.54  8.3        2          6   \n",
       "8            5     0.0     64.62    -148.23  7.8       27          8   \n",
       "9            5     0.0     50.73    -178.55  7.7       14          2   \n",
       "10           5     0.0     51.28     174.83  7.2       22          3   \n",
       "11           7     0.0     52.06     171.45  7.4       15          9   \n",
       "12           5     0.0     53.88    -161.68  7.0       10         12   \n",
       "13           5     0.0     50.77     179.73  8.0       17          8   \n",
       "14           5     0.0      53.0     -165.0  7.6       23         12   \n",
       "15           5   120.0      57.0     -161.0  6.5       22          8   \n",
       "16           7     0.0     52.44     170.28  7.7        2          9   \n",
       "17           5    25.0      59.0     -141.0  7.1       15          5   \n",
       "18           5     0.0      52.0      175.0  7.0       10          4   \n",
       "19           5    90.0      52.5     -169.0  7.4        8          9   \n",
       "20           5     0.0      60.0     -149.5  7.4       19          9   \n",
       "21           5   100.0      57.0     -160.0  6.7       13          5   \n",
       "22           0     NaN      42.0     -127.0  6.8        5          8   \n",
       "23           5    25.0     50.75     179.38  7.3        9          9   \n",
       "24           5     0.0      53.0     -135.0  6.8        6         11   \n",
       "25           0     NaN     37.25    -121.75  6.6        1          7   \n",
       "26           5     0.0      51.0      180.0  7.1       17          9   \n",
       "27           5    60.0      60.5     -149.0  6.9       22          9   \n",
       "28           7     0.0      52.0      173.0  7.0       13         11   \n",
       "29           5    25.0      52.0     -179.0  7.1        4          1   \n",
       "...        ...     ...       ...        ...  ...      ...        ...   \n",
       "617829      11  591.48   -21.541  -179.1091  4.6        4          7   \n",
       "617830      11    6.56  -21.3093   168.6738  4.9        4          7   \n",
       "617831      13    10.0   39.5984     73.068  4.2        4          7   \n",
       "617832       7     9.1   29.6131   143.3523  4.6        4          7   \n",
       "617833       6   43.29   -2.1018    138.966  4.4        4          7   \n",
       "617834       3   93.55  -20.6978   -69.1784  4.7        4          7   \n",
       "617835       0   31.94   16.6123   -97.8297  4.3        4          7   \n",
       "617836       7    35.0   46.8062   152.8785  4.4        4          7   \n",
       "617837       3    11.2  -20.1948   -70.9115  5.0        5          7   \n",
       "617838       0    9.11   36.1518   -89.6965  3.0        5          7   \n",
       "617839       8   98.55   24.8082    95.2124  4.4        5          7   \n",
       "617840       6    35.0   -0.2665   125.5466  4.5        5          7   \n",
       "617841       7    10.0   35.5119   129.8661  4.8        5          7   \n",
       "617842       6    35.0   -0.3386   125.4749  4.4        5          7   \n",
       "617843       5    10.0   43.3325  -126.6572  3.1        5          7   \n",
       "617844       1   36.21   21.8613   145.3276  5.2        5          7   \n",
       "617845      13   155.4   38.2305    73.6797  4.3        5          7   \n",
       "617846       0     5.0   36.2626   -97.5821  3.5        5          7   \n",
       "617847       3   39.51  -41.6855   -74.0542  4.3        5          7   \n",
       "617848      11    10.0   -32.927  -177.8664  5.2        5          7   \n",
       "617849       6  192.36    2.0851   128.3228  4.3        5          7   \n",
       "617850       0     5.0   37.3679   -98.2025  3.5        5          7   \n",
       "617851      13    10.0    39.489    73.4459  4.4        5          7   \n",
       "617852       7   29.15   29.7514   142.1428  4.6        5          7   \n",
       "617853       5    10.0   44.1651  -128.9059  4.3        5          7   \n",
       "617854       7   21.26   35.7802   140.9868  4.4        5          7   \n",
       "617855      11  257.05  -18.8947   169.4241  4.8        6          7   \n",
       "617856       4    10.0  -56.8016  -142.1336  5.9        6          7   \n",
       "617857       5    10.0   53.4488  -163.4493  3.8        6          7   \n",
       "617858      14    35.0     0.166   -79.8907  4.3        6          7   \n",
       "\n",
       "       startyear type  \n",
       "0           1900    1  \n",
       "1           1901    1  \n",
       "2           1901    1  \n",
       "3           1901    1  \n",
       "4           1902    1  \n",
       "5           1903    1  \n",
       "6           1903    1  \n",
       "7           1903    1  \n",
       "8           1904    1  \n",
       "9           1905    1  \n",
       "10          1905    1  \n",
       "11          1905    1  \n",
       "12          1905    1  \n",
       "13          1906    1  \n",
       "14          1906    1  \n",
       "15          1907    1  \n",
       "16          1907    1  \n",
       "17          1908    1  \n",
       "18          1909    1  \n",
       "19          1909    1  \n",
       "20          1909    1  \n",
       "21          1910    1  \n",
       "22          1910    1  \n",
       "23          1910    1  \n",
       "24          1910    1  \n",
       "25          1911    1  \n",
       "26          1911    1  \n",
       "27          1911    1  \n",
       "28          1911    1  \n",
       "29          1912    1  \n",
       "...          ...  ...  \n",
       "617829      2016    1  \n",
       "617830      2016    1  \n",
       "617831      2016    1  \n",
       "617832      2016    1  \n",
       "617833      2016    1  \n",
       "617834      2016    1  \n",
       "617835      2016    1  \n",
       "617836      2016    1  \n",
       "617837      2016    1  \n",
       "617838      2016    1  \n",
       "617839      2016    1  \n",
       "617840      2016    1  \n",
       "617841      2016    1  \n",
       "617842      2016    1  \n",
       "617843      2016    1  \n",
       "617844      2016    1  \n",
       "617845      2016    1  \n",
       "617846      2016    1  \n",
       "617847      2016    1  \n",
       "617848      2016    1  \n",
       "617849      2016    1  \n",
       "617850      2016    1  \n",
       "617851      2016    1  \n",
       "617852      2016    1  \n",
       "617853      2016    1  \n",
       "617854      2016    1  \n",
       "617855      2016    1  \n",
       "617856      2016    1  \n",
       "617857      2016    1  \n",
       "617858      2016    1  \n",
       "\n",
       "[617859 rows x 9 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "df1 = pd.read_csv('allquakes.csv', dtype=object)\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df1['mag'] = pd.to_numeric(df1['mag'])\n",
    "df2 = df1['startyear'][(df1['cluster'] == '14') &(df1['mag'] >= 5)].value_counts()\n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>startyear</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1976</th>\n",
       "      <td>116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007</th>\n",
       "      <td>116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1983</th>\n",
       "      <td>110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010</th>\n",
       "      <td>109</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014</th>\n",
       "      <td>106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005</th>\n",
       "      <td>105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1979</th>\n",
       "      <td>104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009</th>\n",
       "      <td>101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974</th>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1988</th>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1992</th>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990</th>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982</th>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991</th>\n",
       "      <td>91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012</th>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008</th>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015</th>\n",
       "      <td>86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006</th>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1985</th>\n",
       "      <td>84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995</th>\n",
       "      <td>82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004</th>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997</th>\n",
       "      <td>80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1970</th>\n",
       "      <td>79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1978</th>\n",
       "      <td>79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1984</th>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1969</th>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001</th>\n",
       "      <td>76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1965</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1977</th>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1981</th>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1968</th>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973</th>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002</th>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000</th>\n",
       "      <td>69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1989</th>\n",
       "      <td>68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1980</th>\n",
       "      <td>68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996</th>\n",
       "      <td>66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1986</th>\n",
       "      <td>63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987</th>\n",
       "      <td>63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1999</th>\n",
       "      <td>62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998</th>\n",
       "      <td>61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975</th>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1994</th>\n",
       "      <td>59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016</th>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1971</th>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1972</th>\n",
       "      <td>54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013</th>\n",
       "      <td>52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1966</th>\n",
       "      <td>51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003</th>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1967</th>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1993</th>\n",
       "      <td>49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1964</th>\n",
       "      <td>48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963</th>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1962</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      startyear\n",
       "1976        116\n",
       "2007        116\n",
       "1983        110\n",
       "2010        109\n",
       "2014        106\n",
       "2005        105\n",
       "1979        104\n",
       "2009        101\n",
       "1974        100\n",
       "1988         99\n",
       "1992         99\n",
       "1990         96\n",
       "1982         95\n",
       "1991         91\n",
       "2012         90\n",
       "2008         90\n",
       "2015         86\n",
       "2006         85\n",
       "1985         84\n",
       "1995         82\n",
       "2004         81\n",
       "1997         80\n",
       "1970         79\n",
       "1978         79\n",
       "1984         77\n",
       "1969         77\n",
       "2001         76\n",
       "2011         75\n",
       "1965         75\n",
       "1977         72\n",
       "1981         72\n",
       "1968         71\n",
       "1973         71\n",
       "2002         70\n",
       "2000         69\n",
       "1989         68\n",
       "1980         68\n",
       "1996         66\n",
       "1986         63\n",
       "1987         63\n",
       "1999         62\n",
       "1998         61\n",
       "1975         60\n",
       "1994         59\n",
       "2016         56\n",
       "1971         56\n",
       "1972         54\n",
       "2013         52\n",
       "1966         51\n",
       "2003         50\n",
       "1967         50\n",
       "1993         49\n",
       "1964         48\n",
       "1963         39\n",
       "1962          3"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = pd.DataFrame(df2)\n",
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df2['count'] = df2['startyear']\n",
    "del df2['startyear']\n",
    "df2.to_csv('count.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.fftpack import fft, ifft\n",
    "df = pd.read_csv('count.csv', dtype=object)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:1: FutureWarning: sort(columns=....) is deprecated, use sort_values(by=.....)\n",
      "  if __name__ == '__main__':\n"
     ]
    }
   ],
   "source": [
    "df = df.sort(['year'])\n",
    "df.index = range(len(df))\n",
    "df['year'] = pd.to_numeric(df['year'])\n",
    "df['count'] = pd.to_numeric(df['count'])\n",
    "df = df[(df['year'] >= 1963) & (df['year'] <= 2015)]\n",
    "#\n",
    "x = df['year'].values\n",
    "y = df['count'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#df = df.append({'year':1984, 'count':0}, ignore_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import scipy.fftpack\n",
    "yf = scipy.fftpack.fft(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  4.10700000e+03  +0.j        ,  -6.28756245e+01 +24.59824353j,\n",
       "        -9.74347463e+01+315.46898501j,  -1.69650495e+02+142.07542797j,\n",
       "        -5.15371647e+01 -65.93984598j,  -3.03656632e+01 -20.28761149j,\n",
       "         5.19189798e+01 -22.4691426j ,  -8.42524398e+01+186.94359159j,\n",
       "         1.11365962e+02 +40.31099278j,  -4.20239026e+01 +29.66392468j,\n",
       "         6.00289681e+01 -16.24518032j,   1.96928342e+00 +38.78138057j,\n",
       "        -2.51102465e+02 +41.41405265j,  -4.01391697e+01 +39.04414328j,\n",
       "        -1.17219328e+02 +22.03776389j,  -5.58943919e+01 +89.15663257j,\n",
       "        -9.02070827e+01 +87.01938603j,   1.21899715e+00-141.9297951j ,\n",
       "        -1.55793258e+02 +61.76076886j,  -1.79143553e+01+147.76279071j,\n",
       "        -7.48845645e+00 +40.71307114j,  -1.15146923e+02 -54.10348482j,\n",
       "        -7.82171617e+01-183.59756151j,   1.99656431e+01 +99.20669802j,\n",
       "         1.45183731e+02-103.73726814j,   6.79360253e+01 -27.16318434j,\n",
       "        -1.23249629e+01 -57.23833607j,  -1.23249629e+01 +57.23833607j,\n",
       "         6.79360253e+01 +27.16318434j,   1.45183731e+02+103.73726814j,\n",
       "         1.99656431e+01 -99.20669802j,  -7.82171617e+01+183.59756151j,\n",
       "        -1.15146923e+02 +54.10348482j,  -7.48845645e+00 -40.71307114j,\n",
       "        -1.79143553e+01-147.76279071j,  -1.55793258e+02 -61.76076886j,\n",
       "         1.21899715e+00+141.9297951j ,  -9.02070827e+01 -87.01938603j,\n",
       "        -5.58943919e+01 -89.15663257j,  -1.17219328e+02 -22.03776389j,\n",
       "        -4.01391697e+01 -39.04414328j,  -2.51102465e+02 -41.41405265j,\n",
       "         1.96928342e+00 -38.78138057j,   6.00289681e+01 +16.24518032j,\n",
       "        -4.20239026e+01 -29.66392468j,   1.11365962e+02 -40.31099278j,\n",
       "        -8.42524398e+01-186.94359159j,   5.19189798e+01 +22.4691426j ,\n",
       "        -3.03656632e+01 +20.28761149j,  -5.15371647e+01 +65.93984598j,\n",
       "        -1.69650495e+02-142.07542797j,  -9.74347463e+01-315.46898501j,\n",
       "        -6.28756245e+01 -24.59824353j])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "53"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(yf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xf = np.linspace(0.0, 0.5, 53/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1159bb7d0>]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(xf, 2.0/53 * np.abs(yf[0:53/2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}