005_ee_basic_Proba-V_NDVI_Time-Series_Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# author: René Kopeinig\n",
    "# script: Basic Proba-V Time-Series Analysis\n",
    "# description: Basic Proba-V NDVI (Normalized Difference Vegetation Index) Time-Series Analysis with \n",
    "#              help of Google Earth Engine Python API.\n",
    "#              Note: Please make sure you have all dependencies in Python installed and you are signed up for Google Earth Engine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Add IPython-specific directive to display plots directly below the notebook cell\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import Dependencies\n",
    "import ee, datetime\n",
    "import pandas as pd\n",
    "import matplotlib.dates as mdates\n",
    "from IPython.display import Image\n",
    "from matplotlib import dates\n",
    "from pylab import *\n",
    "\n",
    "ee.Initialize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set start and end date\n",
    "startTime = datetime.datetime(2015, 2, 3)\n",
    "endTime = datetime.datetime(2015, 4, 15)\n",
    "\n",
    "# Create image collection\n",
    "collection = ee.ImageCollection('VITO/PROBAV/C1/S1_TOC_100M').filterDate(startTime, endTime)\n",
    "# Create point in Luxembourg (Proba-V Footprint: X18Y02)\n",
    "point = {'type':'Point', 'coordinates':[6.134136, 49.612485]};"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Retrieve information over image collection\n",
    "info = collection.getRegion(point,500).getInfo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reshape image collection \n",
    "header = info[0]\n",
    "data = array(info[1:])\n",
    "\n",
    "iTime = header.index('time')\n",
    "time = [datetime.datetime.fromtimestamp(i/1000) for i in (data[0:,iTime].astype(int))]\n",
    "\n",
    "# List of used image bands\n",
    "band_list = ['RED',u'NIR']\n",
    "\n",
    "iBands = [header.index(b) for b in band_list]\n",
    "yData = data[0:,iBands].astype(np.float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate NDVI\n",
    "red = yData[:,0]\n",
    "nir = yData[:,1]\n",
    "ndvi = (nir - red) / (nir + red)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reshape NDVI array into Pandas Dataframe\n",
    "df = pd.DataFrame(data=ndvi, index=list(range(len(ndvi))), columns=['NDVI'])\n",
    "df = df.interpolate()\n",
    "df['DateTime'] = pd.Series(time, index=df.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>NDVI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>71.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.121775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.105253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.006887</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.025716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.088106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.227011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.331023</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            NDVI\n",
       "count  71.000000\n",
       "mean    0.121775\n",
       "std     0.105253\n",
       "min     0.006887\n",
       "25%     0.025716\n",
       "50%     0.088106\n",
       "75%     0.227011\n",
       "max     0.331023"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Obtain statistical information over all elements of the Time-Series\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Introduce Maple's auto correlation\"\n",
    "def maple_auto_correlation(x):\n",
    "    x = np.asarray(x)\n",
    "    y = x-x.mean()\n",
    "    result = np.correlate(y, y, mode='full')\n",
    "    result = result[len(result)//2:]\n",
    "    result /= result[0]\n",
    "    return result "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Apply auto correlation algorithm on dataframe\n",
    "macf = maple_auto_correlation(df['NDVI'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_macf = pd.DataFrame(data=macf, index=list(range(len(macf))), columns=['Maple Auto Correlation'])\n",
    "df_macf.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reshape data for discrete Fourier Transformation\n",
    "df_as_matrix = df['NDVI'].as_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/site-packages/numpy/core/numeric.py:492: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": 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t17U4ONI8sGfj9qZ2zCbFsNjePW4LbQ4X7c7OAX28YAwb3N5SiSNAqQS6Vk8OJK01JfYmbBYTTe1O2chKiAhSUtOMzTOVuKRmYEudNY0dpMbZMHnWmHh17ck9eAOUxg9uz6yS7jNKvNIToqhtah/Qq08cae6goc3JqeNTga5PcCGEsWmtKbY3he29a2/qO4cbuhYGDmad28DB7SmVeOZxByqVuDQcbRm4UyJvXXvh5Ez3bQluISJCdWM7zR2dLJiYjsWkBnyMqvdydy9vp3IwZ5YYOLh7rpzsvvjGKxzL3r0zSuZPSCPKYgr5dKvD6eLB1fuolsupCTEgtNb89cP9HDzSEtLxRZ6BydzMBLJTY33v5YHib9UkdC0MHMy53IYP7vpWB50uHbBUAgMb3MU1zVjNitHDYshJiwu5x/3a9gruX13IG9sPDVhbhPhvVlzTzF/eK+D/3tkT0vHemSTj0uMYlxY3oDNLtNbUSKmkf95SSa1nZNjf4KT3tGUgByiL7U2MSY3DYja5gzuEJ9/l0jy6tgiAgsrGAWuLEP/NCj3vpXd3Vfp608EU25uJtprISoxmXHo8JbXNAzb+Vd/qwNGpDVMq6Vt/MAhvj9sbyv5q3N5Pv8qGNvZXN7KzooEdFfUkRFu4+awJvp9xLEpqmslJiwPcn9yrdlfR4XT5Rqr9eX9PFcX2ZmKsZgqrJLiFGAgFVY0o5V7T8fjHxfzxkhODHl9sbyInLR6TSZGTFkeH08WhulZGp8Qe82O/s+Mwn+yvYXJWAlNHJmE1ud///kslg38xBcMHd61ntZK/UkmczUy01cSf3y3gz+8WAGCzmOhwuthzuIGHr5gVNHB763RpDtS2cPakDADGpcXT6dIcPNrC+PR4v9+jtbu3PTolhrPzMnghvxyXS/eZMjSYGtocvLuzkktnjRrSdojI9On+GlLjbUzKShzSdhRWNTImJZb5E9N4YXM5dyzKJSMxOuDxxTXNTBuZBODrfJXUNB9zcD+7oZRfvb6LKIuJ9l6bVfXeYAog2mrGZjENaqnEwMHtLZW4e9z+BieVUtyxKJdDdW1MG5nEtJGJTEiP55kNB/jdW7u56bkt/O1bs3rscRJMxdFWOjpdjEvv6nGD+xQsUHBvKjnCtrI6/vfiqdgsJlodnRw82sKY1Lhj/j8PlLvf2s0L+eWMTI7htAlpQ9YOEXk6nC5ufHYLybFWVt9xRsjvnXDYW9lIXlYCy04fz/Mby/jHpyXcuWSy32M7nC4OHmnh4ukjgO7v3SYW5KaH/JhPrCvm7rf3cM7kDB65cha1zR3srKhnZ0U99sZ2Zo4e5vf73PuVDN7gZEjBrZRaDDwImIEntNZ/DGur6Nvj9lcqAVi2YHyf+66bn0O01cwvX9vBd/+Zz/KrTyLW1v9/tdgzgyQnzR3S4zx/u5fRZvr9nkfXFpEaZ+Oy2aN9m1MVVDYOWXBvLTvKC/nlAKzeUyXBLY7JxpJamtqdNLU7+dtHRdyxKHdI2tHm6KS0ppkLTxhOdmos558wnOc/K+Pmsyb4PfsuO9KMS0OOJ7DT46OIj7Ic0wDlIx/s455VhZx/QhYPXD4Tm8XEyOQYRibHcN7UrKDfmxhjGdRSSb91BKWUGfgrsASYAlyhlJoS7oZ11bgDl0qCuXJuNvdcOp31RTVc8+Rm2hz9L0f1Psne06ykWCupcbaAT/7eygY+LLBzzaljibaamZiZABCwzl1Z38Y97xXwyAf7eGZDKa9uK2dtoT3oAEq7s5PNpUdCWnrf6dL8z+s7yUyMYm5OCmv2VAf8vre+OMTt/97O69srqG8JzwtOa80zG0r5/du7ZeuAfrz5+SF+88ausL35HZ0uPt1fw2/f3BV0lsaaPdVEWUycNzWTR9cWcaA2tODbX93E4frWoMfsrKjnjc8PsWLjAR5dW8Rf3tvLhqJav8cW2ZtwacjNcr+nbjpjPI3tTlZ8VhbgeM+MEk9nSykV8uQCgAdWF3LPqkK+PnMkDy2deUwlVhj8HQJD6XHPAfZrrYsBlFL/Ai4GdoezYd5SyRFPqSTBzyZT/bnkpFEA/OjFz3lvVyUXzxgZ9PhiezMJUZYedaxx6YGnBD62tphYm5mr5o0B3NefGzUshoIq/yPgz2wo5W8fFfW5/8YF47jzfP+ngH94Zy9Pry/lqWtO5ixP7T2Q5zeVsbOigYevmEldq4NfvbaT/dVNvg8UL5dL84d39nKovpVXt1VgMSlOHpvCkhOyuHJOtu8K1sfD3tjOT176nI8K7ACcMzmTueNSj/vnfhW1OTr5zRu7qG3uYPWeKh5cOpOTxvg/JT9Wn+yr4d/5B/mooJrGNidKgdbwjVkj+9Swtda+s7TfXTyNs+/5iN++uZsnrzk56GPUtzq45O/rSYmzser2BX4nBXxWXMvS5Z/1uX/17mreu31Bn/u9nZ88z2t32sgkTp+YxpOflnDtaWP7lHC871Fvjxvc79380qNB2w5Q3+LgwTX7uPDE4dxz2XTMX2JcKCnGSt0ALgTsTyjv0JHAwW63yz339aCUWqaUyldK5dvt9uNumFIKi0nh0u5A/LJhcvGMEcTazGwrq+v32JKaZsalx6FU1xPn/tTuG8TlR1t44/NDXDEnm+Rum87kZSZQUOl/L+BNJUeYmZ1Mwd2Lyb/rHD788Zl8bfoInlpfSvnRvosMympbWLHxAAB/fq8AV5CeeW1TO/e8V8Cp41O58MThLPSE/Go/F4P4rKSWirpW7v/mDF75/qksWzCOI80d/M/ru7jv/cKAjxGqtYV2ljy4jvVFtfzqwimkxNl4fF1JwON///Zurnz8M5Y9k88dL2zn16/vZMXGAxHbS/+suJbfvbmbn770Od9fsYWr/rGR657eHPCN/eq2CmqbO/jF+ZMA+OZjG3h4zb7jnsq2oaiWq5/cyPr9NSyZlsXyq07ik5+djdWseHlLeZ/jC6uaKD/aysLJGWQmRnPbObl8sLea1burgj7OY2uLqG91UFLTzAv5B/t83eXS/N87exieFM17ty3gszsXsuu353HHolwKqhr9/l72VjZiNSvGpnUF8U1njMfe2M6r2yr6HF9S00RafFSPM/OctDgO1bf2e7a9vbwOreGKOdlfKrQBz3UnDVbjDoXWejmwHGD27NkD8o6zmk04XZ1+t3QNlcVs4sRRSWwt6/+Tt6SmmZPH9uzpjEuP54X88j47FP5zfSkKuH5+To/j87ISWFto7zOFsM3RyefldVx3Wg5RFjNR8WbS4qO4c8kk3ttVyX2rCrnv8hk9fta97xdgNil+fG4ef/jPXt7acZiLPIMvvf353QKa25389qKpKKUYkRzDlOGJrNlTxffO7DkO8PKWChKiLCyelkW01cys7GH8dPEk7nxlB3/7qIiZ2cNYNKVvTX/lpjJ2H2rgZ0smER/V9zlxdLr487t7eXxdCbmZ8az47lzyshJoaHX3aIrsTX0GedcW2n3HH2nuoKndSUOrg4Y2J/uqmvj116b0+CAFcHa6eHRtEXsqG4mzmYmLshBns5Aca2ViZgJ5mQlkJkb1+b5j0dDmYF9VIwWVTVQ1tNHc7qS5o5OWDicxVjN3nJtLRkLfGQ6rd1fxvRVbfLvIxUdZiIuy8EV5HQ+s3sdvLpra43iXS/P4umJOGJnEDaePY+mcbO56dSf3vl/IJ/treHDpTLKS+j6O1prnPjvA/uom7jx/cp8eaFVDG7eu3MbYtDhev/k0EroF2ll5Gby67RA/WzypR4do9R53QC+c5H7urzltLC/kH+Q3b+5i/sQ0vwOV1Q1tPPVpKV+bPoLDda08sHofX585sseY0ts7DvNFeT33XDadvKyus7+5OSkAbC492uf1VljZyPj0+B6991PHp3LCyCSeWFfM0pNH93h+i+3NvgFJr5y0OLSGA7UtPR63t60HjqIUnDgqKeAx/UmMthiuVFIBjO52e5TnvrCzmBU4/C++ORazsoex/ONi2hydAUfJ2xydVNS18s200T3uH9dtWtGM0cm+Y1/cUs65UzMZkRzT4/i8rAScLk1JTXOPF8v2g3U4OjVzPC9WrxHJMVx72liWf1zM9afnMHWE+8Wzs6Ke17cf4uazxnPD6eN4dVsF964qYMm0rD6notvKjvLv/IPccHpOj7LIOZMzeOTD/Rxp7iAlzn1W0Nzu5D873R8AvX8Xv/7aFHZU1HHHC9t569b5vgFWrTX3rirkkQ/3A+4e5WNXncS4biF8uL6VW57fxpYDR/n2KdncdcEU38+/at4Y/r62iCfWlfCHb5zg+x5np4u739rNmNRY3rx1PlEWs+/x7n57D//4pASTUvzqwsm+N2l9i4NbVm5l3b4axqTG0u5weULVSfcOamK0hbysBKaNTGLG6GSmj0pmTGqs3zCvbWrni/J6th+s44vyOgoqGzlU33PrglibmVibhfgoM4fr21hbaGf5VbM5odub/cO91Xx/xVYmD0/k2evn9vig/+WrO3j2swN8+5RsJmR0PUcf7K2m2N7MQ1fMdF8xPNrKg0tncEZuOr96fScXPLSOB5fOZP7ErkHm1o5Ofv7KF7zuWaW7p7KRx6+e7Xs8R6eLW57fSnO7k+dvmNsjtMFdQly1u4p1+2p6lN/W7Kli2shE3weF1WzidxdP44rHP+PvHxVxu5+Byoc/2I+j08WPFuVS09TOpY9u4MlPSrjl7ImAe7bHX94rYFJWAl+f2fNEffroZGxmE5tLj/QN7qomZvfqRCmluHreGH7y0hdsLDnCKd1Kb8U1zZw3tefP8HYSSmqaggd32VHyMhP6/J6ORVKM+2IKWuvj6jCEKpTg3gxMVErl4A7spcCVYW2Vh/diCsc6MNnbrOxhOF2aHRX1nDw2xe8x3ZfLducNp2J7ky+4391ZSV2Lg2/NHdPn5+R6grOgqrHHi2VTyRGUgtlj+j7+98+cwL83H+SP/9nLs9fPBeBP7+4lOdbKjWeMx2RS/HRxHtc9nc+/Nx/k26d0PW6xvYlbnt9GRkIUPzyn5xtr4eRMHvpgPx/urfbV+/+zs5KWjk7f7e6irWb+/q2TuPDhT7jpua28+v1TsZgUd722k39tPsjSk0dz/gnD+eG/tnHxI59y3+UzWDQlk48L7dz27+20Ozp55MqZXHhiz7OCtPgoLpk1ipe3lvOjc3N9q89WbipjX3UTj111ki+0wf0GveuCybi05slPS7CYFXcumUSRvYnv/jOfirpW/nTJCVx+crbve7TWHG1xUFjVSGFVIwWVjeytbGTlpjKe+rQUcL+5hidF93hjNbQ6qKhr9TwuTMyIZ05OCrlZ7p57bmYCI5JjepxC7zpUz7JntnDpo+v5y2XTuWj6CD4qqObGZ7eQmxXPs9fN7TML6o5Fubyx/RC/f3sPT107x3f/8nXFjEyO4fxpXbMWlFJcctIopo9O4nvPbeWqJzdy28Jcbj17AuVHW1n2bD4FVY385Lw8Rg2L4ccvfs7lj23gmevmkJEYzZ/+s5fNpUd5cOkM3+uxu7PyMhgWa+WlLeW+4K5pamfbwTp+4Alcr3njU7lo+gj++uF+xmfE9zjjO1DbzMpNZSydM5qxaXGMTYtj0ZRMHl1bzJVzx5ASZ2PFxgOUHWnh6WtP7lOGiLaamT46iU0lR3rc39jmfk6uzMymtwtPHMH/vrWb5zeW+YK7rqWDI80dvoFJL2+ZpSjIthUul2b7wbo+r9ljlRhjxenStDo6Q5rBdrz6fQSttVMpdQvwHu7pgE9qrXeFvWV0zSw53h73jGx34G49cLTf4M5J6xnc2SmxmE2qxwDlio0HGJsayzw/g23j0uMwm5R7ue70rvs3lx4hLzOBpNi+/5ekGCu3nDWBu9/ew7p9dhSKdftquOuCyb4PrbPyMpg9ZhgPrdnHJbNGEWMzs7Oinu88uQmAf143p0/54oSRSWQkRLFmb5UvqF/eUs6Y1FhmBxj8Gp0SywOXz+Dapzfzi1d20NTuZNXuKm45awI/OjcXpRRv3jqf7z23lRueyWfhpAw+KKgmNyOBv317VsD57tfPz2HlpjKe3XCA2xflUt/i4L73C5k3LpVz/ZRllFL8z4VT6HRpln9czOH6Nj7cW0201cTKG05hdq/nUSlFSpyNU8ZACJEwAAAQcElEQVSl9uiJOTtdFFY18Xm5uzftnaXkFZ0Rz9XzxjB9dDLTRib5LQH1NnVEEq/fchrff24rP1i5jY/2VvPWjsNMyIjnuevn+n2OU+Oj+MHCifz+nT18VFDNmXkZfH6wjk0lR7jrgsl+x3AmZCTw+i2n8YtXdnD/6kI+Larxbanw1DUnc2aeO3SHxdq46bktXPLoeq4+ZSxPfFLC1fPGBByMt1lMXDxjJM9vLKO+xUFSrJUP91ajNX5LZHd/fRqV9W388F/baGh1+DoO979fiMWseoT9T8/L47wHPuaRD/Zz26KJPPzBfk6bkMoZAeZSnzw2heUfF9PS4fQFXqFncD/Pz4dOjM3MN2aNYsXGA9Q2TSE1Pso3c6T3ezc+ykJmYlTQKYFF9iYa25zM9GTEl9W17N1pjOAG0Fq/A7wT5rb0YbW4P6H9Lb45FmnxUYxJjQ1a5w4U3DaLidHDYnxfL6xqZHPpUe5cMsnvqsQoi5lxaXHs7bZnibPTxZYDR7nUTy/X66p5Y3h6fSl/eGcvZpNiZHKMb7YKuIPpZ0smcdmjG3h6fSmzspP57j/zSYyx8uz1c3qULbxMJsXCyRm8+flhOpwuqhvb2FBcy+3n5AY9nTtrUga3nj2Bhz9wl0Z+87UpXHNaVy1/1LBYXrxpHne9tpOXtpRzyaxR3P3/phFjC7xYY0JGPOdMzuDZzw5w0xnjefiDfdS1OrirWxmkN6UUv71oKp0uzYqNZUwdkcjyq2czsld5KhiL2cSUEYlMGZHIFXP69uC+rLT4KJ777lx+/cYuVm4qY1JWAiu+O7fHQHVv3zl1LCs2HuDut/cwf0Iaj68rJiHawtIg7Yq1Wbj/8hmcnJPCb9/Yzbj0OJZfNZvs1K7VgAty03n+hlO49qlN/P6dPcwYncwvL/A/S8nrklmjeHp9KW9+cYhvnzKGNXuqyUqMZuqIvqslE6OtPHP9HG5esZW7XttJfauDs/IyeP3zQ9x0xvgeqxknZiZw2UmjefazUl9P+M4lgZ/jOTkp/O2jIraV1fnWHHg/nAKVN741N5un15fy0pZybjxjvK9T1ftsGdzv52DB7c2EWdnHN4un+0ZT/sYkBpphV04Cvv0BjrdUAjBzdDKfFtUGrEEV2ZvITIwizk+Pa1x6vG+Tm+c3lmEzm4KGcG5WAjvK6323dx1qoKWjs099u7soi5mfnJfHD/+1HYB7L5veo3wA7t7J2ZMy+OuH7rriqGExPHv93D519u4WTspk5aaDbCypZbtnZs03ZgWfFglw2zm5dDhdzBidzJIThvf5erTVzF8uPZHbF+Uyolf5IZAbTh/H5cs/495VBfxzQymXzx7tq+kHopTify+exuJpWcwekxL0w2Gw2Swm/u/r07ho+gimjEgMuEis+/G/OH8yy57dwp/fK+CdHYe5YcG4fnv5Sim+NXcMi6ZkkhRj7fO6AJgxOpmXvncqj39czA8WTvR7THfTRiaSmxnPy1vLuWz2KNbts3PxzJEBn8doq5lHrzqJn7z4OX95r4CnPi0lIcrCTX4WwN22aCKvba/glW0VXDxjhG8Zuj8njRmGScHGkiO+4C6scg86B/qAnpiZwJyxKazcVMYNp4+j2N6ExaT8Lm3PSYvn3Z2HAz7+trI6kmKsvrGsL6tra9fBGaA07O6A0FUq6e8NEYpZY4Zhb2z31TN7K6lp7lMj88pJi6O0tpnmdicvby1n8bQsUv3sEuaVl5lA2ZEWWjrc04O8Nbw5Aco0Xl87cQSzspM5YWQS/2+m/3D9yXl5tHQ4yc1M4MWbTg0a2gCnefYVX727ile2VTA3JyWkvRvMJsWd50/2G9peSrnPDEIdjJmTk8KJo5J44pMSoixmfnRuXkjfZzIpTp+YbqjQ9lJKMW98asiv0UVTMjl1fCrLPy7GpBTXnDo25MfKSIgOGsjj0+P54yUn9vuaAE8dfdYotpXVsXJjGc0dnZwzOfg6AavZxH3fnMF35o2hpqmd7505wW9ZaHhSDDcuGEeczcyP+3mOE6KtTBmRyOZude6CykYmZiYE3WfnyrnZlNa2sL6olmJ7M9kpsX7nj49Pj+Noi4OjAa4/ubXsKDOzk497T5/B3iHQ2MHtK5UMQHB7ToW2BpjPXVLT3GPyfnfj0uNoc7h4Yl0JjW1OvjU3+Cm3d0Bon6dWt6n0CGNTY4NukAPugFq57BRevGlewPmkk4cnsur2Bbxw4zzfTJFgYmxm5k9I44X8ckpqmv0OSg4WpRQ3nD4OgO+fNd7vTmtfdUopfnXhFEwKLpo+guFJoZd9BtrXZ47EpOBP7xYQbTVx6vj+t0cwmRS/uWgqb906nxsXjAt43O2LcvnsFwtD6iScPDaFrWVH6fBs6FRY1ei3vt3d4mlZDIu18vymA771F/74NpvyswK0oc3BvuqmgPuPHIvB3pPb0MFt8ZVKjr+ik5eVQLTVxDY/de4jzR3UtTgCni55e+KPfVzEBM+sg2AmeWpzBZWNuFyazaVHAg6K9hZlMfe7sc+EjIRj6n0unJxJq6OTGKuZ84P0oAfDhScO57nr57Ls9MBv+q+6ycMTeel7p/Lrr03t/+AwykiM5vSJ6bQ6Opk/IT3kDaWUUkwbmRS0l6qUCnl63dycFNqdLnZ4NnKqbe4IOn0P3KWbS08axapdVRTXNPkd44Gu4Pa3+vnzg+6FN7PGHN/AJHTb2lWCu2s64ECUSqxmEyeOSvbb4/ZenizQp7b3/paOTq6Yk91vaWB0SizRVhMFVY3sq26irsXRb9iH00LPKfDiaVkhzZoIJ6UU8yemDciy+kg2K3uY3zLDYPOegfVXJgkn7wyhTSVHupa69xPc4F7p6HRpHJ26z6QCr9EpsVhMyu8lCLceqEMp93zy4+XdkmOwVk8ae3ByAEsl4H6z/OOTvgtxfPscBKhxZyREEWcz43RpLglhYM9sUkzMSKCwqpFNpZ769hAGd2ZiNP/4zuygg0Tiv9MFJwzH2enighOH7kwsLT6K8elxbC49QpRntbG/+ee9jUuP59Txqawvqg14tmw1m8hOifU7s2Rr2VEmZsQPyOQHq9lEnM08aD1uQwe3ZQBnlQDMzE7G0anZdaiek7othPlgr3tHtFHD/NcblVIsnJxJVlJ00Ole3eVmJrBun53kWBuZiVFkf4mrcAwk71XrhejObFJ8Y9bQjXt4zclJ4a0vDpMaZyMlzub3ggX+3HTGeCrqWpnsZxqj14SMeDaVHO2xbYV34c2SacG3az0WiZ7Vk4PB0OerXQtwBubzxTdAeaCrXPLWF4f4z85KbunnUmcPXTGTXwTYwc+fSVkJVDe283GhnTk5qYOyDFaISDUnJ4XGNvdir7zMhJDfLwty01n7k7OCdu5uPmsCR1s6+N2bXRuaFtc0U9/qOO75290lRltlOiCAzVMqGYgaN7ivFzc6JcY36b66sY1fvbaT6aOS+mzEdLy8+wjXtzqYM3bgXhxCfBV5B+/rWx0h1bePxfTRydx85nhe3lrOql2VQLeFNwMwMOmVGGMZtKvgGDq4LSYTJgVxA7iEdOboYWwrq0NrzZ0v76Clo5N7vzljwAfLuk9nmpMj+1ALEcyoYbG+BTeh1LeP1S1nT2TqiER+8eoOapva2VZWR2K0JeDajS8jSUolblaziYRo64Be8HZWdjKVDW08tGY/a/ZW89PFk5iQMXBPnldmYhSJ0RaSYqxMDMPPF+Krxrulcl7WwL9fbBb34qGGVie/fHUn28qOMiN72IBmy2CWSgw9OLloSgYZiQO7SGOWZ3Ol+1cXMjcnhWuPYeXasVBKsSA3nTibRa60LkQIFk8bzvqi2rBdXT4vK4E7zs3lj//Z63m8gRuYBPec8cqGtv4PHAAqHFcZmT17ts7Pzx/wnzsQOpwuTvjNe1hMindvWxDSyi4hxFdDp0vzzcc2sOXAUf553ZyAuxYOBaXUFq317FCONXSPOxxsFhO/vGAyo4bFSGgL8V/GbFI8cPkMnvq01HcFnkj0X9fjFkIIIzqWHrehByeFEEL0JcEthBARRoJbCCEijAS3EEJEGAluIYSIMBLcQggRYSS4hRAiwkhwCyFEhAnLAhyllB048CW/PQ2oGcDmhFMktRUiq72R1FaIrPZGUlshstp7PG0do7UOaQ1+WIL7eCil8kNdPTTUIqmtEFntjaS2QmS1N5LaCpHV3sFqq5RKhBAiwkhwCyFEhDFicC8f6gYcg0hqK0RWeyOprRBZ7Y2ktkJktXdQ2mq4GrcQQojgjNjjFkIIEYRhglsptVgpVaCU2q+U+vlQt6c3pdSTSqlqpdTObvelKKXeV0rt8/xtiMu5K6VGK6U+VErtVkrtUkr90HO/UdsbrZTapJT63NPe33ruz1FKbfS8Jv6tlLINdVu9lFJmpdQ2pdRbnttGbmupUmqHUmq7Uirfc59RXwvJSqmXlFJ7lVJ7lFLzDNzWPM/v1PunQSl122C01xDBrZQyA38FlgBTgCuUUlOGtlV9PA0s7nXfz4E1WuuJwBrPbSNwAj/SWk8BTgFu9vw+jdreduBsrfV0YAawWCl1CvAn4H6t9QTgKHD9ELaxtx8Ce7rdNnJbAc7SWs/oNlXNqK+FB4F3tdaTgOm4f8eGbKvWusDzO50BnAS0AK8yGO3VWg/5H2Ae8F6323cCdw51u/y0cyyws9vtAmC459/DgYKhbmOAdr8OLIqE9gKxwFZgLu6FDBZ/r5EhbuMozxvybOAtQBm1rZ72lAJpve4z3GsBSAJK8Iy9Gbmtftp+LvDpYLXXED1uYCRwsNvtcs99RpeptT7s+XclkDmUjfFHKTUWmAlsxMDt9ZQetgPVwPtAEVCntXZ6DjHSa+IB4KeAy3M7FeO2FUADq5RSW5RSyzz3GfG1kAPYgac8ZagnlFJxGLOtvS0FVnr+Hfb2GiW4I552f7waaoqOUioeeBm4TWvd0P1rRmuv1rpTu085RwFzgElD3CS/lFIXAtVa6y1D3ZZjMF9rPQt3KfJmpdSC7l800GvBAswC/q61ngk006vMYKC2+njGMy4CXuz9tXC11yjBXQGM7nZ7lOc+o6tSSg0H8PxdPcTt8VFKWXGH9gqt9Sueuw3bXi+tdR3wIe5yQ7JSyuL5klFeE6cBFymlSoF/4S6XPIgx2wqA1rrC83c17hrsHIz5WigHyrXWGz23X8Id5EZsa3dLgK1a6yrP7bC31yjBvRmY6BmZt+E+7XhjiNsUijeA73j+/R3cteQhp5RSwD+APVrr+7p9yajtTVdKJXv+HYO7Hr8Hd4Bf6jnMEO3VWt+ptR6ltR6L+3X6gdb6WxiwrQBKqTilVIL337hrsTsx4GtBa10JHFRK5XnuWgjsxoBt7eUKusokMBjtHeqifrfi/vlAIe7a5i+Huj1+2rcSOAw4cPcMrsdd21wD7ANWAylD3U5PW+fjPj37Atju+XO+gdt7IrDN096dwP947h8HbAL24z4NjRrqtvZq95nAW0Zuq6ddn3v+7PK+twz8WpgB5HteC68Bw4zaVk9744BaIKnbfWFvr6ycFEKICGOUUokQQogQSXALIUSEkeAWQogII8EthBARRoJbCCEijAS3EEJEGAluIYSIMBLcQggRYf4/Sn5G1GWicDIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate and plot Fast Fourier Transformation\n",
    "sp = np.fft.fft(np.sin(df_as_matrix))\n",
    "plt.plot(sp)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>NDVI</th>\n",
       "      <th>DateTime</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.051405</td>\n",
       "      <td>2015-02-03 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.044749</td>\n",
       "      <td>2015-02-04 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.038093</td>\n",
       "      <td>2015-02-05 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.031437</td>\n",
       "      <td>2015-02-06 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.024781</td>\n",
       "      <td>2015-02-07 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.018125</td>\n",
       "      <td>2015-02-08 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.015645</td>\n",
       "      <td>2015-02-09 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.013166</td>\n",
       "      <td>2015-02-10 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.010686</td>\n",
       "      <td>2015-02-11 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.008206</td>\n",
       "      <td>2015-02-12 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.007942</td>\n",
       "      <td>2015-02-13 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.007679</td>\n",
       "      <td>2015-02-14 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.007415</td>\n",
       "      <td>2015-02-15 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.007151</td>\n",
       "      <td>2015-02-16 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.006887</td>\n",
       "      <td>2015-02-17 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.015626</td>\n",
       "      <td>2015-02-18 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.024365</td>\n",
       "      <td>2015-02-19 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.033104</td>\n",
       "      <td>2015-02-20 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.041844</td>\n",
       "      <td>2015-02-21 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.174468</td>\n",
       "      <td>2015-02-22 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.134487</td>\n",
       "      <td>2015-02-23 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.094507</td>\n",
       "      <td>2015-02-24 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.054526</td>\n",
       "      <td>2015-02-25 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.014545</td>\n",
       "      <td>2015-02-26 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.074242</td>\n",
       "      <td>2015-02-27 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.133939</td>\n",
       "      <td>2015-02-28 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.193636</td>\n",
       "      <td>2015-03-01 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.253333</td>\n",
       "      <td>2015-03-02 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.049404</td>\n",
       "      <td>2015-03-03 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.065111</td>\n",
       "      <td>2015-03-04 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>0.228758</td>\n",
       "      <td>2015-03-16 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>0.235470</td>\n",
       "      <td>2015-03-17 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>0.242182</td>\n",
       "      <td>2015-03-18 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>0.248894</td>\n",
       "      <td>2015-03-19 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>0.255605</td>\n",
       "      <td>2015-03-20 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>0.014125</td>\n",
       "      <td>2015-03-21 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>0.017257</td>\n",
       "      <td>2015-03-22 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>0.020388</td>\n",
       "      <td>2015-03-23 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0.023520</td>\n",
       "      <td>2015-03-24 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>0.026651</td>\n",
       "      <td>2015-03-25 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>0.050589</td>\n",
       "      <td>2015-03-26 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>0.074527</td>\n",
       "      <td>2015-03-27 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>0.098465</td>\n",
       "      <td>2015-03-28 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>0.122403</td>\n",
       "      <td>2015-03-29 01:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>0.146341</td>\n",
       "      <td>2015-03-30 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>0.117223</td>\n",
       "      <td>2015-03-31 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>0.088106</td>\n",
       "      <td>2015-04-01 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>0.058988</td>\n",
       "      <td>2015-04-02 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>0.029870</td>\n",
       "      <td>2015-04-03 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>0.079861</td>\n",
       "      <td>2015-04-04 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>0.129852</td>\n",
       "      <td>2015-04-05 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>0.179844</td>\n",
       "      <td>2015-04-06 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>63</th>\n",
       "      <td>0.229835</td>\n",
       "      <td>2015-04-07 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>0.279826</td>\n",
       "      <td>2015-04-08 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>0.292625</td>\n",
       "      <td>2015-04-09 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>0.305424</td>\n",
       "      <td>2015-04-10 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>0.318224</td>\n",
       "      <td>2015-04-11 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>0.331023</td>\n",
       "      <td>2015-04-12 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>0.331023</td>\n",
       "      <td>2015-04-13 02:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>0.331023</td>\n",
       "      <td>2015-04-14 02:00:00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>71 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        NDVI            DateTime\n",
       "0   0.051405 2015-02-03 01:00:00\n",
       "1   0.044749 2015-02-04 01:00:00\n",
       "2   0.038093 2015-02-05 01:00:00\n",
       "3   0.031437 2015-02-06 01:00:00\n",
       "4   0.024781 2015-02-07 01:00:00\n",
       "5   0.018125 2015-02-08 01:00:00\n",
       "6   0.015645 2015-02-09 01:00:00\n",
       "7   0.013166 2015-02-10 01:00:00\n",
       "8   0.010686 2015-02-11 01:00:00\n",
       "9   0.008206 2015-02-12 01:00:00\n",
       "10  0.007942 2015-02-13 01:00:00\n",
       "11  0.007679 2015-02-14 01:00:00\n",
       "12  0.007415 2015-02-15 01:00:00\n",
       "13  0.007151 2015-02-16 01:00:00\n",
       "14  0.006887 2015-02-17 01:00:00\n",
       "15  0.015626 2015-02-18 01:00:00\n",
       "16  0.024365 2015-02-19 01:00:00\n",
       "17  0.033104 2015-02-20 01:00:00\n",
       "18  0.041844 2015-02-21 01:00:00\n",
       "19  0.174468 2015-02-22 01:00:00\n",
       "20  0.134487 2015-02-23 01:00:00\n",
       "21  0.094507 2015-02-24 01:00:00\n",
       "22  0.054526 2015-02-25 01:00:00\n",
       "23  0.014545 2015-02-26 01:00:00\n",
       "24  0.074242 2015-02-27 01:00:00\n",
       "25  0.133939 2015-02-28 01:00:00\n",
       "26  0.193636 2015-03-01 01:00:00\n",
       "27  0.253333 2015-03-02 01:00:00\n",
       "28  0.049404 2015-03-03 01:00:00\n",
       "29  0.065111 2015-03-04 01:00:00\n",
       "..       ...                 ...\n",
       "41  0.228758 2015-03-16 01:00:00\n",
       "42  0.235470 2015-03-17 01:00:00\n",
       "43  0.242182 2015-03-18 01:00:00\n",
       "44  0.248894 2015-03-19 01:00:00\n",
       "45  0.255605 2015-03-20 01:00:00\n",
       "46  0.014125 2015-03-21 01:00:00\n",
       "47  0.017257 2015-03-22 01:00:00\n",
       "48  0.020388 2015-03-23 01:00:00\n",
       "49  0.023520 2015-03-24 01:00:00\n",
       "50  0.026651 2015-03-25 01:00:00\n",
       "51  0.050589 2015-03-26 01:00:00\n",
       "52  0.074527 2015-03-27 01:00:00\n",
       "53  0.098465 2015-03-28 01:00:00\n",
       "54  0.122403 2015-03-29 01:00:00\n",
       "55  0.146341 2015-03-30 02:00:00\n",
       "56  0.117223 2015-03-31 02:00:00\n",
       "57  0.088106 2015-04-01 02:00:00\n",
       "58  0.058988 2015-04-02 02:00:00\n",
       "59  0.029870 2015-04-03 02:00:00\n",
       "60  0.079861 2015-04-04 02:00:00\n",
       "61  0.129852 2015-04-05 02:00:00\n",
       "62  0.179844 2015-04-06 02:00:00\n",
       "63  0.229835 2015-04-07 02:00:00\n",
       "64  0.279826 2015-04-08 02:00:00\n",
       "65  0.292625 2015-04-09 02:00:00\n",
       "66  0.305424 2015-04-10 02:00:00\n",
       "67  0.318224 2015-04-11 02:00:00\n",
       "68  0.331023 2015-04-12 02:00:00\n",
       "69  0.331023 2015-04-13 02:00:00\n",
       "70  0.331023 2015-04-14 02:00:00\n",
       "\n",
       "[71 rows x 2 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Outlier detection based on +3 to -3 standard deviations\n",
    "df[np.abs(df.NDVI-df.NDVI.mean())<=(3*df.NDVI.std())]\n",
    "df[~(np.abs(df.NDVI-df.NDVI.mean())>(3*df.NDVI.std()))] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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