{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ●Spectral Analysis 3 libtfr by Python 3.6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# #Spectral analysis of EEG during general anesthesia with sevoflurane"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・・In this section, we will perform spectrum analysis by Python using EEG Analyzer and digital EEG data file eeg_bis.tsv acquired from a patient under general anesthesia of sevoflurane (during the transition phase from anesthesia to arousale). The influence of window functions, the application of the multitaper method, and the development into spectrograms will be shown."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# EEG analysis during the transition from anesthesia to arousal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt \n",
    "from scipy.fftpack import fft\n",
    "from scipy import signal as sig #Signal function import from SciPy package\n",
    "\n",
    "from IPython.display import set_matplotlib_formats\n",
    "set_matplotlib_formats('svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・First, the EEG data from the digital EEG data file eeg_bis_10_20_2.tsv acquired from the BIS monitor through the EEG Analyzer are imported into the Pandas DataFrame df_tsv."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_tsv = pd.read_table('../eeg_bis_20220629_sev_EME.tsv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Let's display the first five items of the imported data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>.Ch</th>\n",
       "      <th>Time</th>\n",
       "      <th>ch[0]</th>\n",
       "      <th>ch[1]</th>\n",
       "      <th>ch[2]</th>\n",
       "      <th>ch[3]</th>\n",
       "      <th>ch[4]</th>\n",
       "      <th>ch[5]</th>\n",
       "      <th>ch[6]</th>\n",
       "      <th>ch[7]</th>\n",
       "      <th>ch[8]</th>\n",
       "      <th>ch[9]</th>\n",
       "      <th>ch[10]</th>\n",
       "      <th>ch[11]</th>\n",
       "      <th>ch[12]</th>\n",
       "      <th>ch[13]</th>\n",
       "      <th>ch[14]</th>\n",
       "      <th>ch[15]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ch1:</td>\n",
       "      <td>12:15:17</td>\n",
       "      <td>6.70</td>\n",
       "      <td>3.80</td>\n",
       "      <td>1.75</td>\n",
       "      <td>-1.75</td>\n",
       "      <td>-1.95</td>\n",
       "      <td>1.10</td>\n",
       "      <td>5.15</td>\n",
       "      <td>10.30</td>\n",
       "      <td>15.70</td>\n",
       "      <td>19.65</td>\n",
       "      <td>20.60</td>\n",
       "      <td>17.55</td>\n",
       "      <td>12.90</td>\n",
       "      <td>12.75</td>\n",
       "      <td>18.00</td>\n",
       "      <td>23.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ch1:</td>\n",
       "      <td>12:15:17</td>\n",
       "      <td>26.30</td>\n",
       "      <td>26.60</td>\n",
       "      <td>25.60</td>\n",
       "      <td>23.00</td>\n",
       "      <td>17.85</td>\n",
       "      <td>8.90</td>\n",
       "      <td>0.20</td>\n",
       "      <td>-0.95</td>\n",
       "      <td>4.10</td>\n",
       "      <td>7.10</td>\n",
       "      <td>7.00</td>\n",
       "      <td>6.20</td>\n",
       "      <td>7.05</td>\n",
       "      <td>10.10</td>\n",
       "      <td>13.05</td>\n",
       "      <td>13.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>ch1:</td>\n",
       "      <td>12:15:17</td>\n",
       "      <td>10.45</td>\n",
       "      <td>4.45</td>\n",
       "      <td>-2.90</td>\n",
       "      <td>-12.30</td>\n",
       "      <td>-24.95</td>\n",
       "      <td>-35.85</td>\n",
       "      <td>-38.35</td>\n",
       "      <td>-30.90</td>\n",
       "      <td>-17.70</td>\n",
       "      <td>-5.70</td>\n",
       "      <td>4.10</td>\n",
       "      <td>11.35</td>\n",
       "      <td>11.60</td>\n",
       "      <td>6.05</td>\n",
       "      <td>-4.35</td>\n",
       "      <td>-20.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>ch1:</td>\n",
       "      <td>12:15:17</td>\n",
       "      <td>-39.00</td>\n",
       "      <td>-52.55</td>\n",
       "      <td>-64.65</td>\n",
       "      <td>-76.25</td>\n",
       "      <td>-83.35</td>\n",
       "      <td>-82.55</td>\n",
       "      <td>-75.25</td>\n",
       "      <td>-64.40</td>\n",
       "      <td>-52.55</td>\n",
       "      <td>-42.90</td>\n",
       "      <td>-36.65</td>\n",
       "      <td>-32.25</td>\n",
       "      <td>-29.05</td>\n",
       "      <td>-24.50</td>\n",
       "      <td>-19.45</td>\n",
       "      <td>-20.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>ch1:</td>\n",
       "      <td>12:15:17</td>\n",
       "      <td>-27.60</td>\n",
       "      <td>-34.85</td>\n",
       "      <td>-38.25</td>\n",
       "      <td>-35.30</td>\n",
       "      <td>-26.20</td>\n",
       "      <td>-15.60</td>\n",
       "      <td>-7.65</td>\n",
       "      <td>-3.50</td>\n",
       "      <td>-2.55</td>\n",
       "      <td>-4.50</td>\n",
       "      <td>-7.75</td>\n",
       "      <td>-12.00</td>\n",
       "      <td>-20.40</td>\n",
       "      <td>-28.80</td>\n",
       "      <td>-30.85</td>\n",
       "      <td>-27.15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    .Ch      Time  ch[0]  ch[1]  ch[2]  ch[3]  ch[4]  ch[5]  ch[6]  ch[7]  \\\n",
       "0  ch1:  12:15:17   6.70   3.80   1.75  -1.75  -1.95   1.10   5.15  10.30   \n",
       "1  ch1:  12:15:17  26.30  26.60  25.60  23.00  17.85   8.90   0.20  -0.95   \n",
       "2  ch1:  12:15:17  10.45   4.45  -2.90 -12.30 -24.95 -35.85 -38.35 -30.90   \n",
       "3  ch1:  12:15:17 -39.00 -52.55 -64.65 -76.25 -83.35 -82.55 -75.25 -64.40   \n",
       "4  ch1:  12:15:17 -27.60 -34.85 -38.25 -35.30 -26.20 -15.60  -7.65  -3.50   \n",
       "\n",
       "   ch[8]  ch[9]  ch[10]  ch[11]  ch[12]  ch[13]  ch[14]  ch[15]  \n",
       "0  15.70  19.65   20.60   17.55   12.90   12.75   18.00   23.80  \n",
       "1   4.10   7.10    7.00    6.20    7.05   10.10   13.05   13.15  \n",
       "2 -17.70  -5.70    4.10   11.35   11.60    6.05   -4.35  -20.85  \n",
       "3 -52.55 -42.90  -36.65  -32.25  -29.05  -24.50  -19.45  -20.40  \n",
       "4  -2.55  -4.50   -7.75  -12.00  -20.40  -28.80  -30.85  -27.15  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_tsv.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Let's display the first five items of the imported data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>.Ch</th>\n",
       "      <th>Time</th>\n",
       "      <th>ch[0]</th>\n",
       "      <th>ch[1]</th>\n",
       "      <th>ch[2]</th>\n",
       "      <th>ch[3]</th>\n",
       "      <th>ch[4]</th>\n",
       "      <th>ch[5]</th>\n",
       "      <th>ch[6]</th>\n",
       "      <th>ch[7]</th>\n",
       "      <th>ch[8]</th>\n",
       "      <th>ch[9]</th>\n",
       "      <th>ch[10]</th>\n",
       "      <th>ch[11]</th>\n",
       "      <th>ch[12]</th>\n",
       "      <th>ch[13]</th>\n",
       "      <th>ch[14]</th>\n",
       "      <th>ch[15]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4678</th>\n",
       "      <td>ch1:</td>\n",
       "      <td>12:25:18</td>\n",
       "      <td>5.65</td>\n",
       "      <td>-1.30</td>\n",
       "      <td>-5.40</td>\n",
       "      <td>-1.50</td>\n",
       "      <td>10.25</td>\n",
       "      <td>13.10</td>\n",
       "      <td>13.4</td>\n",
       "      <td>8.70</td>\n",
       "      <td>9.85</td>\n",
       "      <td>17.95</td>\n",
       "      <td>16.30</td>\n",
       "      <td>5.70</td>\n",
       "      <td>10.60</td>\n",
       "      <td>21.15</td>\n",
       "      <td>13.30</td>\n",
       "      <td>-5.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4679</th>\n",
       "      <td>ch1:</td>\n",
       "      <td>12:25:18</td>\n",
       "      <td>6.65</td>\n",
       "      <td>20.25</td>\n",
       "      <td>17.00</td>\n",
       "      <td>10.60</td>\n",
       "      <td>12.55</td>\n",
       "      <td>10.20</td>\n",
       "      <td>20.5</td>\n",
       "      <td>18.85</td>\n",
       "      <td>12.50</td>\n",
       "      <td>22.15</td>\n",
       "      <td>33.80</td>\n",
       "      <td>22.90</td>\n",
       "      <td>14.50</td>\n",
       "      <td>12.85</td>\n",
       "      <td>21.85</td>\n",
       "      <td>22.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4680</th>\n",
       "      <td>ch1:</td>\n",
       "      <td>12:25:18</td>\n",
       "      <td>17.05</td>\n",
       "      <td>14.30</td>\n",
       "      <td>15.10</td>\n",
       "      <td>16.15</td>\n",
       "      <td>29.15</td>\n",
       "      <td>29.00</td>\n",
       "      <td>31.9</td>\n",
       "      <td>36.95</td>\n",
       "      <td>32.90</td>\n",
       "      <td>28.40</td>\n",
       "      <td>36.15</td>\n",
       "      <td>34.20</td>\n",
       "      <td>36.05</td>\n",
       "      <td>48.30</td>\n",
       "      <td>41.95</td>\n",
       "      <td>39.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4681</th>\n",
       "      <td>ch1:</td>\n",
       "      <td>12:25:18</td>\n",
       "      <td>53.75</td>\n",
       "      <td>55.75</td>\n",
       "      <td>49.75</td>\n",
       "      <td>58.85</td>\n",
       "      <td>65.15</td>\n",
       "      <td>69.65</td>\n",
       "      <td>70.7</td>\n",
       "      <td>72.40</td>\n",
       "      <td>82.45</td>\n",
       "      <td>87.25</td>\n",
       "      <td>85.80</td>\n",
       "      <td>93.45</td>\n",
       "      <td>95.95</td>\n",
       "      <td>91.35</td>\n",
       "      <td>89.50</td>\n",
       "      <td>94.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4682</th>\n",
       "      <td>ch1:</td>\n",
       "      <td>12:25:18</td>\n",
       "      <td>105.20</td>\n",
       "      <td>113.00</td>\n",
       "      <td>104.95</td>\n",
       "      <td>99.35</td>\n",
       "      <td>108.80</td>\n",
       "      <td>111.40</td>\n",
       "      <td>109.3</td>\n",
       "      <td>112.30</td>\n",
       "      <td>111.55</td>\n",
       "      <td>108.90</td>\n",
       "      <td>111.80</td>\n",
       "      <td>113.35</td>\n",
       "      <td>107.90</td>\n",
       "      <td>110.50</td>\n",
       "      <td>114.30</td>\n",
       "      <td>111.75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       .Ch      Time   ch[0]   ch[1]   ch[2]  ch[3]   ch[4]   ch[5]  ch[6]  \\\n",
       "4678  ch1:  12:25:18    5.65   -1.30   -5.40  -1.50   10.25   13.10   13.4   \n",
       "4679  ch1:  12:25:18    6.65   20.25   17.00  10.60   12.55   10.20   20.5   \n",
       "4680  ch1:  12:25:18   17.05   14.30   15.10  16.15   29.15   29.00   31.9   \n",
       "4681  ch1:  12:25:18   53.75   55.75   49.75  58.85   65.15   69.65   70.7   \n",
       "4682  ch1:  12:25:18  105.20  113.00  104.95  99.35  108.80  111.40  109.3   \n",
       "\n",
       "       ch[7]   ch[8]   ch[9]  ch[10]  ch[11]  ch[12]  ch[13]  ch[14]  ch[15]  \n",
       "4678    8.70    9.85   17.95   16.30    5.70   10.60   21.15   13.30   -5.60  \n",
       "4679   18.85   12.50   22.15   33.80   22.90   14.50   12.85   21.85   22.60  \n",
       "4680   36.95   32.90   28.40   36.15   34.20   36.05   48.30   41.95   39.25  \n",
       "4681   72.40   82.45   87.25   85.80   93.45   95.95   91.35   89.50   94.80  \n",
       "4682  112.30  111.55  108.90  111.80  113.35  107.90  110.50  114.30  111.75  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_tsv.tail(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Create a new Pandas DataFrame df_eeg and set the column names as \"Time\" and \"eeg\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "cols = ['Time', 'eeg']\n",
    "df_eeg = pd.DataFrame(data=None, index=[], columns=cols)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Of the df_tsv (line 109611), copy the voltage µV data corresponding to the status under deep sevoflurane anesthesia (line 97,000-99,048) to df_eeg."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#for row in range(len(df_tsv)):　\n",
    "for row in range(0, 4682): \n",
    "    # Import only 1024 lines of data. Since 8 lines / second, 128 seconds = 2 minutes 8 seconds \n",
    "    #Number of data = 16,384\n",
    "    #By playing with the range here, you can change which brain waves you can take out.\n",
    "    \n",
    "    t_tmp = df_tsv.iat[row,1]\n",
    "    for column in range(2, 18):\n",
    "              eeg_tmp = df_tsv.iat[row, column]\n",
    "              data_tmp = pd.Series( [t_tmp, eeg_tmp], index=df_eeg.columns )\n",
    "              df_eeg = df_eeg.append(data_tmp, ignore_index=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Let's confirm and display 1,024 rows x 16 = 16,383 µV data (for 128 seconds) captured in df_eeg."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>Time</th>\n",
       "      <th>eeg</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12:15:17</td>\n",
       "      <td>6.70</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12:15:17</td>\n",
       "      <td>3.80</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12:15:17</td>\n",
       "      <td>1.75</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12:15:17</td>\n",
       "      <td>-1.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12:15:17</td>\n",
       "      <td>-1.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>74907</th>\n",
       "      <td>12:25:18</td>\n",
       "      <td>93.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74908</th>\n",
       "      <td>12:25:18</td>\n",
       "      <td>95.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74909</th>\n",
       "      <td>12:25:18</td>\n",
       "      <td>91.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74910</th>\n",
       "      <td>12:25:18</td>\n",
       "      <td>89.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74911</th>\n",
       "      <td>12:25:18</td>\n",
       "      <td>94.80</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>74912 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           Time    eeg\n",
       "0      12:15:17   6.70\n",
       "1      12:15:17   3.80\n",
       "2      12:15:17   1.75\n",
       "3      12:15:17  -1.75\n",
       "4      12:15:17  -1.95\n",
       "...         ...    ...\n",
       "74907  12:25:18  93.45\n",
       "74908  12:25:18  95.95\n",
       "74909  12:25:18  91.35\n",
       "74910  12:25:18  89.50\n",
       "74911  12:25:18  94.80\n",
       "\n",
       "[74912 rows x 2 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_eeg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Save the data imported to df_eeg as a csv file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_eeg.to_csv(\"data_eeg/eeg_linealized_04.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Transfer the df_eeg time and µV data to the new Python arrays Time and eeg, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Place brain wave data in the data frame\n",
    "time = df_eeg['Time'].values\n",
    "eeg = df_eeg['eeg'].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Display the data captured in the array eeg using Matplotlib function plot()."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "#Time-series graph display of EEG data\n",
    "fig, ax = plt.subplots(figsize=(18,6))\n",
    "plt.plot(eeg)\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_1.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data preprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Let's calculate the mean and standard deviation of eeg."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-9.047095925886374, 25.190010135621716)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m=np.mean(eeg)\n",
    "sd=np.std(eeg)\n",
    "m, sd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Count the number of null (NA) data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_eeg['eeg'].isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Outlier removal: Change the data that exceeds 3 times the standard deviation from the mean value to None."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/teijisw/opt/anaconda3/envs/Python36_2/lib/python3.6/site-packages/ipykernel_launcher.py:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(eeg)):\n",
    "    if  df_eeg['eeg'][i] > m+3*sd:\n",
    "      df_eeg['eeg'][i] = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/teijisw/opt/anaconda3/envs/Python36_2/lib/python3.6/site-packages/ipykernel_launcher.py:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(eeg)):\n",
    "    if  df_eeg['eeg'][i] < m-3*sd:\n",
    "      df_eeg['eeg'][i] = None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・After removing the outliers, count the number of null (NA) data again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1154"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_eeg['eeg'].isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Make a copy of df_eeg and perfrom spline interpolation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_eeg_copy = df_eeg.copy()\n",
    "df_eeg_copy.interpolate(inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Count the number of null (NA) data in the copy of df_eeg."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_eeg_copy['eeg'].isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Save the data with spline completion to a csv file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_eeg.to_csv(\"data_eeg/eeg_linealized_04_ip.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Copy the eeg data to the array eeg_ip."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "eeg_ip = df_eeg_copy['eeg'].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Plot and display eeg data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
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   ],
   "source": [
    "#Time-series graph display of EEG data that complements and corrects missing values\n",
    "fig, ax = plt.subplots(figsize=(18,6))\n",
    "plt.plot(eeg_ip)\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_2.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・From the eeg data, 512 cases (4 seconds, eeg_512) and 8,192 cases (64 seconds, eeg_8192) are extracted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "eeg_512 = eeg_ip[5000:5512]\n",
    "time_512 = time[5000:5512]\n",
    "eeg_8192 = eeg_ip[5000:13192]\n",
    "time_8192 = time[5000:13192]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Let's display of eeg_512"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "#Time-series graph display of EEG data that complements and corrects missing values\n",
    "fig, ax = plt.subplots(figsize=(18,6))\n",
    "plt.ylim(-100, 100)\n",
    "plt.plot(eeg_512, linewidth =0.5)\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_3.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Display 128 samples for 1 second of eeg_512"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "#Time-series graph display of EEG data that complements and corrects missing values\n",
    "fig, ax = plt.subplots(figsize=(18,6))\n",
    "plt.ylim(-100, 100)\n",
    "plt.plot(eeg_512[0:128], linewidth =0.5)\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_3_1.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
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       "       -2.950e+01, -3.325e+01])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eeg_512"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savetxt('data_eeg/eeg_512_2.csv', eeg_512, delimiter=',', fmt='%d')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Let's display of eeg_8192 data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
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     },
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     "output_type": "display_data"
    }
   ],
   "source": [
    "#Time-series graph display of EEG data that complements and corrects missing values\n",
    "fig, ax = plt.subplots(figsize=(18,6))\n",
    "plt.plot(eeg_8192, linewidth =0.5)\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_3_2.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savetxt('data_eeg/eeg_8192_2.csv', eeg_8192, delimiter=',', fmt='%d')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Set the parameters of the FFT function. Here, the sampling frequency is 128 Hz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Parameter set of FFT function\n",
    "N=len(eeg_512) #Total number of data points\n",
    "N2=len(eeg_8192) #Total number of data points\n",
    "f_s = 128 #Sampling frequency\n",
    "T = 1.0/f_s  #Data width (seconds)\n",
    "s_rate = 1/f_s #Sampling rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Define a decibel conversion formula as a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "#dB conversion　\n",
    "def db(x, dBref):\n",
    "    y = 20 * np.log10(x / dBref)     #Conversion formula\n",
    "    return y                         #Returns a dB value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(64.0, 256.0)"
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     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Check the operation of the contents of the FFT function\n",
    "1.0/(2.0*T), N/2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Let's perform FFT of the eeg_512 (4 seconds) data with Scipy's fft () function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.fftpack import fft\n",
    "#FFT transform with FFT function\n",
    "xfft = np.linspace(0, int(1.0/(2.0*T)), int(N/2)) \n",
    "yfft=fft(eeg_512)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Display the power spectrum with a simple FFT."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "#Power spectrum display of each split EEG\n",
    "plt.plot(xfft, 2.0/N*abs(yfft[0:int(N/2)]), linewidth =0.5)\n",
    "plt.grid()\n",
    "plt.yscale(\"log\")\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_4.svg')"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Convert to decibels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "dBref = 1\n",
    "yfft_db = db(2.0/N*abs(yfft[0:int(N/2)]), dBref)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Display SPD by simple FFT (periodogram) in decibel transform."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Power spectrum display of each split EEG\n",
    "plt.plot(xfft, yfft_db[0:int(N/2)], linewidth =0.5, label=\"Periodogram\")\n",
    "plt.legend(bbox_to_anchor=(1, 1), loc='upper right', borderaxespad=1, fontsize=12)\n",
    "#plt.yscale(\"log\")\n",
    "plt.grid()\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_4_1.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Create a Hann window using Scipy's Signal module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Prepare window function apply with scipy.\n",
    "han = sig.hann(N)    #Creating the Hann window"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "acf_han: 2.0039138943248536\n"
     ]
    }
   ],
   "source": [
    "acf_han = 1/(sum(han)/N) #Calculate Amplitude Correction Factor\n",
    "print(\"acf_han:\", acf_han)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Adapt the Hann window to eeg_512 and perform FFT calculation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Window function correction\n",
    "fft_data_acf_han = acf_han*np.abs(fft(eeg_512*han)/(N/2)) #data is time waveform, FFT, normalization, amplitude correction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Display the PSD by the periodogram to which the Hann window function is applied."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "#EEG power spectrum display\n",
    "plt.plot(xfft, fft_data_acf_han[0:int(N/2)], linewidth =0.5, label=\"hann\")\n",
    "plt.legend(bbox_to_anchor=(1, 1), loc='upper right', borderaxespad=1, fontsize=12)\n",
    "plt.yscale(\"log\")\n",
    "plt.grid()\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_5.svg')"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Perform decibel conversion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "dBref = 1\n",
    "yfft_acf_db_han = db(fft_data_acf_han[0:int(N/2)], dBref)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Display a decibel PSD with a periodogram adapted to the Hann window function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
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     "output_type": "display_data"
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   ],
   "source": [
    "#Display SPD by simple FFT (periodogram) in decibel transform.\n",
    "plt.plot(xfft, yfft_acf_db_han[0:int(N/2)], linewidth =0.5, label=\"hann\")\n",
    "plt.legend(bbox_to_anchor=(1, 1), loc='upper right', borderaxespad=1, fontsize=12)\n",
    "#plt.yscale(\"log\")\n",
    "plt.grid()\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_6.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Compare PSD with simple periodogram and Hann window adaptation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
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      "needs_background": "light"
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     "output_type": "display_data"
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   ],
   "source": [
    "#EEG power spectrum display\n",
    "plt.plot(xfft, yfft_db, linewidth =0.5, label=\"periodogram\", alpha=0.8)\n",
    "plt.plot(xfft, yfft_acf_db_han, linewidth =0.5, label=\"hann\", alpha=0.8)\n",
    "plt.legend(bbox_to_anchor=(1, 1), loc='upper right', borderaxespad=1, fontsize=12)\n",
    "plt.grid()\n",
    "#plt.yscale(\"log\")\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_7.svg')"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Create Hann windows, Hamming windows, and Blackman windows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Prepare multiple window functions This time, with numpy.\n",
    "window_n = np.hanning(N)\n",
    "window_m = np.hamming(N)\n",
    "window_b = np.blackman(N)\n",
    " \n",
    "x = np.arange(0,N,1) #Horizontal axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Window function correction value\n",
    "acf_bm=1/(sum(window_b)/N)\n",
    "F_abs_amp_bm = acf_bm*np.abs(fft(eeg_512*window_b)/(N/2)) #Blackman window: OK if you multiply the value after FFT\n",
    "\n",
    "dBref = 1\n",
    "yfft_acf_db_bm = db(F_abs_amp_bm[0:int(N/2)], dBref)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Display a graph comparing the PSD with the Blackman window function applied to the Hann window."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
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     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "#Power spectrum display of each split EEG\n",
    "plt.plot(xfft, yfft_acf_db_han, linewidth =0.5, label=\"hann\", alpha=0.7)\n",
    "plt.plot(xfft, yfft_acf_db_bm, linewidth =0.5, label=\"blackman\", alpha=0.7)\n",
    "plt.legend(bbox_to_anchor=(1, 1), loc='upper right', borderaxespad=1, fontsize=12)\n",
    "\n",
    "plt.legend(bbox_to_anchor=(1, 1), loc='upper right', borderaxespad=1, fontsize=12)\n",
    "plt.grid()\n",
    "#plt.yscale(\"log\")\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_8.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Practice of power spectrum of multiple analysis segments of EEG"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Let's allow you to select window functions. Here, let's choose the Hann window. The analysis data window consists of 512 samples, and the windows overlap by 50%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Select Hanning\n"
     ]
    }
   ],
   "source": [
    "dt = 1/128   #Sampling rate\n",
    "split = 512/N2  #Overall data ratio of analysis frame data\n",
    "overlap = 0.5 #Overlap rate\n",
    "\n",
    "window = \"hanning\" #Window function selection: Hann, Hamming, Blackman\n",
    "#窓の用意\n",
    "if window == \"hanning\":\n",
    "    window_select = \"hanning\"         # Hann window\n",
    "    print(\"Select Hanning\")\n",
    "elif window == \"hamming\":\n",
    "    window_select = \"hamming\"          # Hamming window\n",
    "    print(\"Select Hamming\")\n",
    "elif window == \"blackman\":\n",
    "    window_select = \"blackman\"         # Blackman window\n",
    "    print(\"Select Blackman\")\n",
    "else:\n",
    "    window_select = \"hanning\"          # Select Hann window\n",
    "    print(\"Select Hanning\")\n",
    "\n",
    "#fq_ave, F_abs_amp_ave, time, freq, power = FFT_main(time, eeg, dt, split, overlap, window_select)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Define a function data_split () that allows the EEG record to be split and analyzed for each analysis segment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "#A function that splits data into FFT analysis widths and returns the split data as an array.\n",
    "\n",
    "def data_split(_t, _x, _split, _overlap):\n",
    " \n",
    "    split_data = []\n",
    "    one_frame_cnt = int(len(_t)*_split) #Number of samples per frame\n",
    "    overlap_cnt = int(one_frame_cnt*_overlap) #Number of overlapping samples\n",
    "    print(\"Number of frame samples:  \", one_frame_cnt)\n",
    "    print(\"Number of overlapping samples: \", overlap_cnt)\n",
    "    \n",
    "    start_S = 0\n",
    "    end_S = start_S + one_frame_cnt\n",
    " \n",
    "    while True:\n",
    "        t_cnt = _t[start_S:end_S]\n",
    "        x_cnt = _x[start_S:end_S]\n",
    "        split_data.append([t_cnt, x_cnt])\n",
    " \n",
    "        start_S = start_S + (one_frame_cnt - overlap_cnt)\n",
    "        end_S = start_S + one_frame_cnt\n",
    " \n",
    "        if end_S > len(_t):\n",
    "            break\n",
    " \n",
    "    return np.array(split_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Define the FFT function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "#FFT function\n",
    "def FFT(_data_input, _dt, _window_select):\n",
    " \n",
    "    data_cnt_adj = len(_data_input[0])\n",
    " \n",
    "    #Window function processing\n",
    "    if _window_select == \"hanning\":\n",
    "        window_select = np.hanning(data_cnt_adj)    #Hanning\n",
    "    elif _window_select == \"hamming\":\n",
    "        window_select = np.hamming(data_cnt_adj)    #Hamming\n",
    "    elif _window_select == \"blackman\":\n",
    "        window_select = np.blackman(data_cnt_adj)   #Blackman\n",
    "    else:\n",
    "        window_select  = np.hanning(data_cnt_adj)   #Hanning\n",
    " \n",
    "    #Signal after window function\n",
    "    x_windowed = _data_input[1]*window_select\n",
    " \n",
    "    #FFT calculation\n",
    "    F = np.fft.fft(x_windowed)\n",
    "    F_abs = np.abs(F)\n",
    "    F_abs_amp = F_abs / data_cnt_adj * 2\n",
    "    fq = np.linspace(0, 1.0/dt, data_cnt_adj)\n",
    " \n",
    "    #Window function correction\n",
    "    acf=1/(sum(window_select)/data_cnt_adj)\n",
    "    F_abs_amp = acf*F_abs_amp\n",
    " \n",
    "    #Extract up to Nyquist constant\n",
    "    fq_out = fq[:int(data_cnt_adj/2)+1]\n",
    "    F_abs_amp_out = F_abs_amp[:int(data_cnt_adj/2)+1]\n",
    " \n",
    "    return [fq_out, F_abs_amp_out]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Define a function plot_TTF that plots FFT results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Graph display of FFT results (used to display average value)\n",
    "def plot_FFT(_t, _x, _fq, _F_abs_amp):\n",
    "    fig = plt.figure(figsize=(16, 6))\n",
    "    ax2 = fig.add_subplot(121)\n",
    "    plt.title(\"time\")\n",
    "    plt.xlabel(\"time [s]\")\n",
    "    plt.ylabel(\"amplitude\"+\"[V]\")\n",
    "    plt.plot(_t, _x, linewidth =0.5)\n",
    "    \n",
    "    ax2 = fig.add_subplot(122)\n",
    "    plt.title(\"freq\")\n",
    "    plt.xlabel('freqency(Hz)')\n",
    "    plt.ylabel(\"amplitude\"+\"[V/rtHz]\")\n",
    "    #plt.xscale(\"log\")\n",
    "    plt.yscale(\"log\")\n",
    "    plt.plot(_fq, _F_abs_amp, linewidth =0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Define a function plot_split_eeg () that displays split brain waves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Depicts split brain waves\n",
    "def plot_split_eeg(_split_data, _FFT_result_list, _frame_cnt, _FFT_result_cnt):\n",
    "\n",
    "    #Split EEG data\n",
    "    fig3 = plt.figure(figsize=(24, 8))    \n",
    "    plt.title(\"time\")\n",
    "    plt.xlabel(\"time [s]\")\n",
    "    plt.ylabel(\"amplitude\"+\"[V]\")\n",
    "    loc = 0\n",
    "    for _split_data_cnt, _FFT_result_cnt in zip(_split_data, _FFT_result_list):\n",
    "        plt.xscale(\"linear\")\n",
    "        plt.yscale(\"linear\")\n",
    "        ax3 = fig3.add_subplot(_frame_cnt, 1, 1+loc)\n",
    "        plt.plot(_split_data_cnt[0], _split_data_cnt[1])\n",
    "        loc +=1\n",
    "    plt.savefig('data_eeg/spectral_analysis_3_fig_9.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Define a function plot_FFT_all() that displays all the split brain waves together."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "#dB conversion　\n",
    "def db(x, dBref):\n",
    "    y = 20 * np.log10(x / dBref)     #Conversion formula\n",
    "    return y                         #Returns a dB value\n",
    "\n",
    "#Individual split EEG data\n",
    "def plot_FFT_all(_split_data, _FFT_result_list, _frame_cnt, _FFT_result_cnt, _overlap_cnt, _dBref):\n",
    "    \n",
    "    #Spectrum of individual split data\n",
    "    fig4 = plt.figure(figsize=(12, 4))\n",
    "    ax4 = fig4.add_subplot(122)\n",
    "    plt.title(\"freq\")\n",
    "    plt.xlabel('freqency(Hz)')\n",
    "    plt.ylabel(\"amplitude\"+\"[V/rtHz]\")\n",
    "    #plt.xscale(\"log\")\n",
    "    plt.yscale(\"log\")\n",
    "    noc=1\n",
    "    \n",
    "    for _split_data_cnt, _FFT_result_cnt in zip(_split_data, _FFT_result_list):\n",
    "        plt.plot(_FFT_result_cnt[0], _FFT_result_cnt[1], label=noc, linewidth =0.5)\n",
    "        plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0, fontsize=8)\n",
    "        noc +=1\n",
    "    \n",
    "    #DB-converted spectrum of individual split data\n",
    "    fig5 = plt.figure(figsize=(12, 4))\n",
    "    ax5 = fig5.add_subplot(122)\n",
    "    plt.title(\"freq\")\n",
    "    plt.xlabel('freqency(Hz)')\n",
    "    plt.ylabel(\"amplitude\"+\"[dB/Hz]\")\n",
    "    #plt.xscale(\"log\")\n",
    "    #plt.yscale(\"log\")\n",
    "    noc=1\n",
    "    \n",
    "    for _split_data_cnt, _FFT_result_cnt in zip(_split_data, _FFT_result_list):\n",
    "        plt.plot(_FFT_result_cnt[0], db(_FFT_result_cnt[1], _dBref), label=noc, linewidth =0.5)\n",
    "        \n",
    "        plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0, fontsize=8)\n",
    "        noc +=1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Define a function set_3D_data that arranges data three-dimensionally."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "#3D data placement\n",
    "def set_3D_data(_split_data, _FFT_result_list, _frame_cnt, _FFT_result_cnt, _overlap_cnt):\n",
    "\n",
    "    #Three-dimensional data: T = time, Y = frequency, z = power are stored in a list format array.\n",
    "    #Data placement in a time axis array\n",
    "    T_pre= np.arange(0, 64, 64/_frame_cnt)\n",
    "    T=[]\n",
    "      \n",
    "    for i in T_pre:\n",
    "        T.append([i] *(1+_overlap_cnt))\n",
    "             \n",
    "    print(\"Number of time array 2D data:\", len(T))\n",
    "    print(\"Number of time array 1D data:\", len(T[0]))\n",
    "    #print(T)\n",
    "\n",
    "    #Arrangement of data in the frequency axis array\n",
    "    Y_pre= _FFT_result_cnt[0].tolist()  \n",
    "    Y=[]    \n",
    "    \n",
    "    for i in T_pre:\n",
    "        Y.append(Y_pre) \n",
    "    \n",
    "    #print(len(Y_pre))\n",
    "    print(\"Frequency array 2D number of data:\", len(Y))\n",
    "    print(\"Frequency array 1-dimensional number of data:\", len(Y[0]))\n",
    "    #print(Y)\n",
    "    \n",
    "    #Arrangement of data in the frequency power axis array\n",
    "    Z=[]\n",
    "    for split_data_cnt, FFT_result_cnt in zip(_split_data, _FFT_result_list):\n",
    "        Z_pre=10*np.log10(FFT_result_cnt[1])\n",
    "        Z.append(Z_pre.tolist())\n",
    "   \n",
    "    print(\"Frequency power array 2D number of data:\", len(Z))\n",
    "    print(\"Frequency power array 1D number of data:\", len(Z[0]))\n",
    "    #print(Z)\n",
    "    \n",
    "    #Convert dimensional data to numpy array\n",
    "    T=np.array(T)\n",
    "    Y=np.array(Y)\n",
    "    Z=np.array(Z)\n",
    "    \n",
    "    return T, Y, Z "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Set the time axis array of 8,192 data for 64 seconds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "Time_adj= np.linspace(0, 4, N2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・The SPD calculation process is performed for the data of eeg_8192 (64 seconds). Here it is divided into 31 segments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of frame samples:   512\n",
      "Number of overlapping samples:  256\n",
      "Total number of frames:  31\n"
     ]
    }
   ],
   "source": [
    "#Overlapping division of EEG data.\n",
    "split_data = data_split(Time_adj, eeg_8192, split, overlap)\n",
    "\n",
    "frame_cnt =len(split_data)\n",
    "print(\"Total number of frames: \", frame_cnt)\n",
    " \n",
    "#Perform FFT calculation.\n",
    "FFT_result_list = []\n",
    "\n",
    "for split_data_cnt in split_data:\n",
    "    FFT_result_cnt = FFT(split_data_cnt, dt, window)\n",
    "    FFT_result_list.append(FFT_result_cnt)\n",
    "        \n",
    "one_frame_cnt = int(len(time_8192)*split)\n",
    "overlap_cnt = int(one_frame_cnt*overlap) #Number of overlapping samples\n",
    "    \n",
    "#print(\"FFT_result_list[0]: \", FFT_result_list[0])\n",
    "#print(\"FFT_result_list[1]: \", FFT_result_list[1])\n",
    "    \n",
    "#Power averaging\n",
    "fq_ave = FFT_result_list[0][0]\n",
    "F_abs_amp_ave = np.zeros(len(fq_ave))\n",
    "\n",
    "for i in range(len(FFT_result_list)):\n",
    "    F_abs_amp_ave = F_abs_amp_ave + FFT_result_list[i][1]\n",
    "F_abs_amp_ave = F_abs_amp_ave/(i+1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Display segmented EEG data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "#Drawing of split brain waves\n",
    "plot_split_eeg(split_data, FFT_result_list, frame_cnt, FFT_result_cnt)"
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  },
  {
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   "metadata": {},
   "source": [
    "・Shows the overall averaged amplitude and spectrum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
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   "source": [
    "#Averaged spectrum\n",
    "plot_FFT(Time_adj, eeg_8192, fq_ave, F_abs_amp_ave)\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_10.svg')"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・The SPDs analyzed by segmenting are displayed together on the one graph window."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
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      ],
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Spectrum of individual split data\n",
    "dBref=1\n",
    "plot_FFT_all(split_data, FFT_result_list, frame_cnt, FFT_result_cnt, overlap_cnt, dBref)\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_11.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Constructing a spectrogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of time array 2D data: 31\n",
      "Number of time array 1D data: 257\n",
      "Frequency array 2D number of data: 31\n",
      "Frequency array 1-dimensional number of data: 257\n",
      "Frequency power array 2D number of data: 31\n",
      "Frequency power array 1D number of data: 257\n"
     ]
    }
   ],
   "source": [
    "#Set of 3D data: 2D array of time, frequency, frequency power: The number of data in each dimension must match.\n",
    "time2, freq, power = set_3D_data(split_data, FFT_result_list, frame_cnt, FFT_result_cnt, overlap_cnt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Spectrogram construction from a simple periodogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
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       "<Figure size 288x288 with 2 Axes>"
      ]
     },
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     "output_type": "display_data"
    }
   ],
   "source": [
    "nFFT = 512       # the length of the windowing segments\n",
    "f_s =128  # the sampling frequency\n",
    "noverlap=nFFT*0.5\n",
    "\n",
    "# Pxx: the segments x freqs array of instantaneous power, \n",
    "# freqs: frequency vector\n",
    "# bins: the centers of the time bins in which the power is computed\n",
    "# im: the matplotlib.image.AxesImage instance\n",
    "\n",
    "window = np.blackman(nFFT)\n",
    "plt.figure(figsize=(4, 4))\n",
    "Pxx, freqs, bins, im = plt.specgram(eeg_8192, NFFT=nFFT, Fs=f_s, scale='dB', window=window, noverlap=noverlap, cmap='jet')\n",
    "plt.colorbar()\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_12.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Introduce libtfr library, librosa library, etc. for more advanced spectrogram construction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Define parameters for spectrogram calculation using libtfr."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "import libtfr\n",
    "from librosa import display\n",
    "from scipy.signal import chirp\n",
    "import librosa"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Define parameters for spectrogram calculation using libtfr."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(257, 32) 1040081.6523023543 0.0\n",
      "(257, 32) 0.0 -100.0\n"
     ]
    }
   ],
   "source": [
    "#Define parameters for spectrogram calculation using libtfr.\n",
    "# libtfr\n",
    "\n",
    "nfft = 512  # analysis segment\n",
    "f_s = 128   # sampling frequency\n",
    "shift = nfft/2  #overlap data points\n",
    "K = 6         # number of tapers to use (default 6)\n",
    "tm = 6.0    # time support of tapers (default 6.0)\n",
    "flock = 1   # frequency locking parameter; power is not reassigned\n",
    "                 # more than this value (normalized frequency; default 0.01)\n",
    "tlock = 5   # time locking parameter (in frames; default 5)\n",
    "\n",
    "# load signal of dimension (npoints,)\n",
    "S = libtfr.tfr_spec(eeg_8192, nfft, shift, f_s, K, tm, flock, tlock)\n",
    "print(np.shape(S), np.max(S), np.min(S))\n",
    "\n",
    "S2 = librosa.amplitude_to_db(S, ref=np.max, top_db =100)\n",
    "print(np.shape(S2), np.max(S2), np.min(S2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・SPD spectrogram construction by frequency-time reallocation method using libtfr's tfr_spec() function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
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bJS4ZcOQylBSs3y6G9VY2MrR7V6eYrKNMtCQlm0bECioqaXQvs3x7hK2+34U7awmTldhdoMSHxC/I+Zv7H/eXwHOYszOzvy6JJa2ugIrKIl0RPvmbEvvfTgBI2/ftzb/HgS8nT9z7pBIDNzrgYeiBvEI8zGVAJ1YipMzce0t6LY0fduTw6Kjfb4YbJzujRj94Hvt0N46mgcXSw1NiwHD/BP49Qh2cNiU3xKEWhMlK0nQwnc70UoDjso5OMRAOjGO7xO6J6yekzKwL6l4xLWlj3Rw7oPtrojZ9oiyOVpB8yn8ElHdud4X1+mRk0kAQ6oqVpNndIq47bDSbU/fiBIGo+yCEv572Lk3Mk57ZK7oFzi902DcJnEuq0GZ3yaH1pi+OgiSXdbypISaNri3hgi2aB+I2taufIP4bpgjr/d4x9nKbt87w6Vu5mSKJYtG/Pte5KvCmDuJIlrThMTvZLajrzMJC75P6BiV++S/sFesIJO4zdHUgq8w0H0qUOOtEGLfTbjSfQ2JkwFmcL5dEaM+lvslaULe8JD3XuenpczpBQJImdokbygX77n3eqv8IvDtMTTOCjqsGRd/JgeSnQ4HJ7M4wllLeLJDynT3OQVzRD3XdwG89cGDg9fgy736XoiYBoN48iX1WF6k74SQf3rWOUV+jC9Qo0KY6G0nqP4I3GVUv7m18VtrAziVzXfcEXbrNkDw5LiYYKEBxqciTtkSX4wc9Y6+cxOlsSTgI0aEkqxujVrhrSdy5EvfLOffGoSTUI9inC/usZGZd8ZMz6xSUXaLYNyi5pgYeV0bB7HbOLWh0DWvqW8vizAzncpLQulFcLo6gYTwueE7oD+QDut30cM8vNPnHnLA8u1cF8okmdor9a9vNmR6DSgqBl1ZDHtkljll3dRkUlTvT6wb30ZzmOTDMT5LOBcTAKQDSnG904+5z08iDVYpuLh2tdUrE9exRd/wzODZfSshUUzeBK+IhctipEyLiX25m6ZKZPaEbB1TVb0bztv9g1pCuDYfqAyabOl4KTlzblyPaUK5+gtLRTln02hZrEeq78b0NfoldiytHxVIAl/AhX/3qWZNw7dqxbJ3IalGGUpISqiYi8/Tgm+yQDxgcX7xz3indK3GA48wN+bK2I6U0+sMOR3ZoBrXbdIEiJ0k6fFUs4tk2iE29a8Un4XTWkO6ZNq8kPT04Ql8jxcmTi0ZxtzNhuC6dTcps1VjGrZ3LQe/CFZ5hsIedHB/wISS0a+bmYmpYkk4osj9FRfsWqgNy1qJzEv16h1k6cjURSABluoZbdx84kd/AfWTJxg9mZUH+pmuWcMkoigHm5v6Gay8sxs33ogEMJmzjmdU0erfmGUaXEjJblGIeO4wHzSHcEysfJfmDaMj8urkPK+Dlu6q6ET0jHOLcG5eupcjZtX1N+GB64Dns1HU6UCuP29Tkf89pZGGp6BRRCyewrokCRw1czt0rA+H8RedmUbudxNVyQ0/mxFVCncanAPDtijVqt5QGXtdxXObo6guoWN65J2SyXGXe3LUxSLq2Pw87cZr3R1viGNpLejKKMG9Q/NCUXZR8BR19D5cQIQ05ohMHThRQOSTKdX4jmbN+KOvolMghnTnJQfGCS58n5BpcMzgWxVS+ycXP9VubHsw80JMHS5Mf6sotSVu4QE1VEXJafS4HQ+6jfqlnnITpBpuQ9r3vbnOm7qUfIru0WAv3xsEe/Z6zFqPfjYL85F4RepX8KUtU1bjyD/zuSXvfO+9KXDtvNA+VIUTkq5qMaxN68P+A4SguMFjYP97E0hs/jWv7T2ThpHaix0ZyRRsVutgTp8ojywV1Dn+lQieHDFAAV3kJK4DJQy5GPgV2brQVpfGr1vLskK/3nxR47psOMhaO6qKXj+FCsF+/GIutVo3mYI/cRUl6a1ZMaC0ay0Kf0AckwbDCQmSOen1sApfg7TsyOvXOlaHA59J1cXqoJB0/LM6DcHixO5+OsGF3ZAGVtLqPdNBYziTSYBNnTqkV6Oj+XFhPm4HGj0nSfUXe7FQY/9iLrHDIjXBDcNxMERoI4xROQmA7nZ+8al0eL3BAP8jWMVQrTWLko+6WmATIl7BWoMCn8Xk+Z+v5r8Ryy5M+ZNzTnZxERSpOQ1KZo6t9eOvuqG0kaeWEKPjn9uZZDpSudfAizbAYW+RNXWoSFOTXu9kY678cB5xPeoCTJw4+nXxatFqVT7KFSygDQyYy36+AFyBTvcwkM8bevh/yZ8GunjqG8UkKWsaey4jKrC9Grec0snM5qBrNBS0EAzpk4MFLuc7hrEuafmoVQWq/aajEtXTWx32vsf9+xTCuGyZy71MwZN/VfDvrq3+NLBeUJ0+blN/HyeGhBJMdVOTZv3O25JF/1JgIDbl2eRK4WQtMh8gRkX+ICQzdvDOCjFzhCgWiDy435xOa0t6nG2J55yklXFZJtHmPfZDf8GEUor2HvY1r7xKfQ0LFPYv6cwsc7fU3XuOSTwdRCg4+dWWjCWkM8oVcOeJBAIc90pPP4yjbwu7C/J9Fk/yFq/4L12IFHUPO0iciy4/GYnNK1snVM9SqV+B12pPPyW1M2B2iFn93qtO926Lp/cyH7COTVl//NqeGCwPZzZpDyA4P9BQ1trvuczrJSpJ0WBzcsvxxc/Lp3a/G0asXHBpx0vF0Uruk616FWQV5vi9XCbbxa9FcuKOzkMoNvzayXFDncF1CEdyxCYSHWyow+7WGWJJWX8IBzlXdorRct5YL6xtgyn6ffbkEc9lEntF3zI1xk3R/n92ezkmEDKnbRvI+Mg0tHzrGJEQuOTRG/GQiXVYOIc4lfFTr3GfiAYeSpA8i69EzeAYCBXt7HsnHG2yeFM2sM2NpintcbQD5gO4ohJo8a73NZ8V7Ln2yGtei+3Unb7LVP46Q4cZ3GC0wvcMYG2y9x1zjP+JwlMOL/O6rPvU55HefGzfJ8lkM96GPTJ2xBPVIkgjXP5YFdvjJPJB76aiIO+84g4Mv8k83v85+oeCcdNcA6yr2yKzTiABJ2rAuWpbGlebk8unMphocVzSEePa/8WU3do5TQS8vMhpyx2F8MFDdu1Fz9rmSay02do++c9Wf+d6ci7z15bhJho41GpmCNcL1XIHJ3iNjwLD+ZT5bjgRWEkanbugKX9jwIQE369ccGHafwCZyVLcoRM63VG2sweo6nP3C+vujPy1J5OG4WgusPOOl0hvRZSk1x8hpw3vIfqkhogubF7MS6XNhFPDtH7C12LqTtXr3I0Ejm8MsE/JPGqAw3s5A2AJv/nVOqe49MN2UHyI8zDDWvn9EcU60xo5lqM6VB1Lr0PCBnMxYuiNWrtXPNAI7l9kqDUe6WB9yQUMcbOPqXOr3jJaFpl1Kko6FEa2ShpVEdGn5pzm1vw1KF+qrzbvgzjFtnRsF3CWSEjomlQB/l8Ovnws3Zzb6zofYXdj4u/8TeOPO5rMpqEa1/HaW5OpZEb9xdcDrAPaSpP1LYoA6/20jAO/GhE+nCoNaXGNcjop4jUcGMzS4eRpow6NYiegX8b1VvcnJGhdnL2+McdLGZ+O3k4SBtuLpyx8RKBxJotmGyx7hQDSh/DkFRFWNFXiBTiPih2p8ij9SXa0pgD8x+m/OJ18Lbs8bWxhbJCXrgrrNC9lE1o2Ce76HBwXuf2McCFPbWIprN443glyIrBUN7NZhR1kV31sJTM5vmNuTr2vQMKqs63Jy0/13V5i1aDZj0WcOi61cjy/gI4Mxs0dmdmNnHo20XzGiC2+9y+nXQ3pzzQDNeXMPXQ4dIq/cyT1tFOzVDeXNdPkoHiuLs80K/HMUiK58mY8yS+MObe5iglmYmtppf7YAXbtHS3TuaRzsTa7mgiZCLRwKRJ0qffLGtQTUSjKYPyOGSkhDUcpwz+2MZb71R3jJ1fxjDhlIM2uMsMiyiZxoqflZhLhcKvqORzlSH352RFrWcKk0U63hQ9ZKkrrmo49bP8j4lgDLN65mTd8wLlq4yVNZYE3ZuBRLs7Vgm5nbMbgQeNsaWIbE88bV9TVwA43nlFCunGZV3D2XTwbVu8Dj88nthE26h2nrxuPaxs3woa7k39NnI4sskCTVnl2KfEzNm6KodccB0gLtT5LsB6l/CISWjaFEMlsw150K172AjzzQFM6eUe36yd34xCka6NhgUAstY0it5r18ZBqXPCHtS6NidSdfAHcTN7riJE1JmvkEtMtw7Trm8PUVsxY67l+4iut1nabe2Qj8w/jnaDbxI31N0f8aZqPQLmaB67o5Djes78rau2Rf8JHvZIF1mdn6xqhRT+80HddSZnZqTy4EWzSAfeSST0b4rYFzUUrIF8WBzPydBWMYrM/jKpf2PyMGSSsnGt+SNomxvHBshq3tnfV9xpeH/ihqi43zWC1sGlkamQVzbzzBQDjUfV8WuIqeEdl5ZTib+j6dYmS4fDGfhaLzjIBD19Zt+iYuJTdyUQ6cekmawoJM8Juzhgk58Fh3wGlyFuR4SUm+s2LloyC0FxvbWw1R+YFm7ctw/O4WA51dyNegrNry0W48bqzNnllu7g2OBpYkUVzH9VM4pXNoJ57mRK38y12NAzdyaOP9cQN3v4iDPS515fdmSpo5+2n2HqIWiBkzDo3BzNGX/AGXVm9jDBABisvMh74WeND2L0k6Il5jZE8ulauayfn+FQMB+mJggLtoCuY5xhsbuQNM3018DaoEXLCOzwXhg9l5foUmMVt946ak874l6cy1IHFmRJer7UAXxyhUHNBCWmjlLcbUxyPytKSBZzac1I2LcB9/FrBBhgulvWLmq6w/wzo1SyNq4UoinXviOkeI5t8d/e+u55lM2w38g8ffHIOn5y/gweKvnRYVTuPfGLXoUx5TxhvPMkVcZu9pdvzDLecz2qPXIbBbZoLLvsaVARd1v0v4vJGE/Faqv3jwOlMgXhtZm6cw7ukmYSpOR5X4SGVpRcx81STssggMQ91YY06NxTlibOzYWFNqAjhIJNTfZHaI0epoko3BOR1s79K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   "source": [
    "fig, ax = plt.subplots(figsize=(4,4))\n",
    "display.specshow(S2, x_axis='time', y_axis='hz', cmap='jet', sr=f_s, hop_length=nfft)\n",
    "plt.colorbar()\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_14.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "list=[]\n",
    "for i in range(0, 256):\n",
    "    list.append(np.mean(S2[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "Fq= np.linspace(0, 64, 256)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Create a spectrogram using libtfr's multi-taper method mfft_dpss()."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate a transform object with size 512 samples and 5 tapers for short-time analysis\n",
    "D = libtfr.mfft_dpss(512, 12, 5)\n",
    "# complex STFT with frame shift of 10 samples\n",
    "Z = D.mtstft(eeg_8192, 64)\n",
    "# spectrogram with frame shift of 10 samples\n",
    "P = D.mtspec(eeg_8192, 64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(257, 121, 5) (485.5979889556745+41.1093200344951j) (-608.296678781169+0j)\n",
      "(257, 121) 208056.85558300026 0.0003305215220193417\n"
     ]
    }
   ],
   "source": [
    "print(np.shape(Z), np.max(Z), np.min(Z))\n",
    "print(np.shape(P), np.max(P), np.min(P))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "P = librosa.amplitude_to_db(P, ref=np.max, top_db =100)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(4,4))\n",
    "display.specshow(P, x_axis='time',  y_axis='hz', cmap='jet', sr=f_s, hop_length = nfft)\n",
    "plt.colorbar()\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_18.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Display the SPD of the first segment by the multitaper method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "list3=[]\n",
    "for i in range(0, 256):\n",
    "    list3.append(np.mean(P[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
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   "source": [
    "plt.plot(Fq, list3, linewidth =0.8)\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_19.svg')"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・For the PSD of the first segment, compare two of libtfr's two methods (time reallocation method and multitaper method)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "ename": "FileNotFoundError",
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     "output_type": "error",
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      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-69-0f11b50bab4d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;31m#plt.plot(Fq, list2)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mFq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlist3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlinewidth\u001b[0m \u001b[0;34m=\u001b[0m\u001b[0;36m0.8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msavefig\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'data_eeg/data_eeg/spectral_analysis_3_fig_20.svg'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/opt/anaconda3/envs/Python36_2/lib/python3.6/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36msavefig\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    857\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0msavefig\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    858\u001b[0m     \u001b[0mfig\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgcf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 859\u001b[0;31m     \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msavefig\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    860\u001b[0m     \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcanvas\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdraw_idle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m   \u001b[0;31m# need this if 'transparent=True' to reset colors\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    861\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mres\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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      "\u001b[0;32m~/opt/anaconda3/envs/Python36_2/lib/python3.6/site-packages/matplotlib/backend_bases.py\u001b[0m in \u001b[0;36mprint_figure\u001b[0;34m(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)\u001b[0m\n\u001b[1;32m   2215\u001b[0m                     \u001b[0morientation\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morientation\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2216\u001b[0m                     \u001b[0mbbox_inches_restore\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0m_bbox_inches_restore\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2217\u001b[0;31m                     **kwargs)\n\u001b[0m\u001b[1;32m   2218\u001b[0m             \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2219\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mbbox_inches\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mrestore_bbox\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/envs/Python36_2/lib/python3.6/site-packages/matplotlib/backends/backend_svg.py\u001b[0m in \u001b[0;36mprint_svg\u001b[0;34m(self, filename, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1315\u001b[0m             \u001b[0m__\u001b[0m \u001b[0mDC_\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1316\u001b[0m         \"\"\"\n\u001b[0;32m-> 1317\u001b[0;31m         \u001b[0;32mwith\u001b[0m \u001b[0mcbook\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mopen_file_cm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfilename\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"w\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"utf-8\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mfh\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1318\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1319\u001b[0m             \u001b[0mfilename\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfh\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'name'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/envs/Python36_2/lib/python3.6/contextlib.py\u001b[0m in \u001b[0;36m__enter__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     79\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__enter__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     80\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 81\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mnext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgen\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     82\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mStopIteration\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     83\u001b[0m             \u001b[0;32mraise\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"generator didn't yield\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/envs/Python36_2/lib/python3.6/site-packages/matplotlib/cbook/__init__.py\u001b[0m in \u001b[0;36mopen_file_cm\u001b[0;34m(path_or_file, mode, encoding)\u001b[0m\n\u001b[1;32m    421\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mopen_file_cm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpath_or_file\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmode\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"r\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    422\u001b[0m     \u001b[0;34mr\"\"\"Pass through file objects and context-manage path-likes.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 423\u001b[0;31m     \u001b[0mfh\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mopened\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mto_filehandle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpath_or_file\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmode\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    424\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mopened\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    425\u001b[0m         \u001b[0;32mwith\u001b[0m \u001b[0mfh\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/envs/Python36_2/lib/python3.6/site-packages/matplotlib/cbook/__init__.py\u001b[0m in \u001b[0;36mto_filehandle\u001b[0;34m(fname, flag, return_opened, encoding)\u001b[0m\n\u001b[1;32m    406\u001b[0m             \u001b[0mfh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbz2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mBZ2File\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    407\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 408\u001b[0;31m             \u001b[0mfh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mencoding\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    409\u001b[0m         \u001b[0mopened\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    410\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'seek'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: 'data_eeg/data_eeg/spectral_analysis_3_fig_20.svg'"
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   "source": [
    "fig = plt.figure()\n",
    "plt.plot(Fq, list, linewidth =0.8)\n",
    "#plt.plot(Fq, list2)\n",
    "plt.plot(Fq, list3, linewidth =0.8)\n",
    "plt.savefig('data_eeg/data_eeg/spectral_analysis_3_fig_20.svg')"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Option Spectrogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Spectrogram construction with SPD from a simple periodogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "###option spectrogram\n",
    "nFFT = 512       # the length of the windowing segments\n",
    "f_s =128  # the sampling frequency\n",
    "noverlap=nFFT*0.5\n",
    "\n",
    "freqs, times, Sxx = sig.spectrogram(eeg_8192, fs=f_s, window='hanning', nperseg=512, noverlap=noverlap, detrend=False, scaling='spectrum')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(257, 31)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "###option spectrogram\n",
    "len(Sxx), len(Sxx[0])"
   ]
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  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/teijisw/opt/anaconda3/envs/Python36_2/lib/python3.6/site-packages/ipykernel_launcher.py:4: MatplotlibDeprecationWarning: shading='flat' when X and Y have the same dimensions as C is deprecated since 3.3.  Either specify the corners of the quadrilaterals with X and Y, or pass shading='auto', 'nearest' or 'gouraud', or set rcParams['pcolor.shading'].  This will become an error two minor releases later.\n",
      "  after removing the cwd from sys.path.\n"
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      "needs_background": "light"
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     "output_type": "display_data"
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   ],
   "source": [
    "###option spectrogram\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "fig, ax = plt.subplots(figsize=(5, 6))\n",
    "image = ax.pcolormesh(times, freqs, 10+ np.log10(Sxx), cmap='jet')\n",
    "ax.axis(\"image\")\n",
    "ax.set_ylabel('Frequency [Hz]')\n",
    "ax.set_xlabel('Time [s]')\n",
    "divider = make_axes_locatable(ax)\n",
    "ax_cb = divider.new_horizontal(size=\"8%\", pad=0.05)\n",
    "fig.add_axes(ax_cb)\n",
    "plt.colorbar(image, cax=ax_cb)\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_21.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・SPD spectrogram construction by frequency-time reallocation method using libtfr's tfr_spec() function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "###option spectrogram\n",
    "times_adj = np.append(times, 64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.,  4.,  6.,  8., 10., 12., 14., 16., 18., 20., 22., 24., 26.,\n",
       "       28., 30., 32., 34., 36., 38., 40., 42., 44., 46., 48., 50., 52.,\n",
       "       54., 56., 58., 60., 62., 64.])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "###option spectrogram\n",
    "times_adj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
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      "/Users/teijisw/opt/anaconda3/envs/Python36_2/lib/python3.6/site-packages/ipykernel_launcher.py:3: MatplotlibDeprecationWarning: shading='flat' when X and Y have the same dimensions as C is deprecated since 3.3.  Either specify the corners of the quadrilaterals with X and Y, or pass shading='auto', 'nearest' or 'gouraud', or set rcParams['pcolor.shading'].  This will become an error two minor releases later.\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
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   "source": [
    "###option spectrogram\n",
    "fig, ax = plt.subplots(figsize=(5, 6))\n",
    "image = ax.pcolormesh(times_adj, freqs, S2, cmap='jet')\n",
    "ax.axis(\"image\")\n",
    "ax.set_ylabel('Frequency [Hz]')\n",
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    "divider = make_axes_locatable(ax)\n",
    "ax_cb = divider.new_horizontal(size=\"8%\", pad=0.05)\n",
    "fig.add_axes(ax_cb)\n",
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "・Create a spectrogram using libtfr's multitaper method mfft_dpss()."
   ]
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  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "121"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "###option spectrogram\n",
    "times_adj2 = np.linspace(0, 64, 121)\n",
    "len(times_adj2)"
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   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
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     "text": [
      "/Users/teijisw/opt/anaconda3/envs/Python36_2/lib/python3.6/site-packages/ipykernel_launcher.py:3: MatplotlibDeprecationWarning: shading='flat' when X and Y have the same dimensions as C is deprecated since 3.3.  Either specify the corners of the quadrilaterals with X and Y, or pass shading='auto', 'nearest' or 'gouraud', or set rcParams['pcolor.shading'].  This will become an error two minor releases later.\n",
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   "source": [
    "###option spectrogram\n",
    "fig, ax = plt.subplots(figsize=(5, 6))\n",
    "image = ax.pcolormesh(times_adj2, freqs, P, cmap='jet')\n",
    "ax.axis(\"image\")\n",
    "ax.set_ylabel('Frequency [Hz]')\n",
    "ax.set_xlabel('Time [s]')\n",
    "divider = make_axes_locatable(ax)\n",
    "ax_cb = divider.new_horizontal(size=\"8%\", pad=0.05)\n",
    "fig.add_axes(ax_cb)\n",
    "plt.colorbar(image, cax=ax_cb)\n",
    "ax.set_ylabel('Frequency [Hz]')\n",
    "ax.set_xlabel('Time [s]')\n",
    "plt.savefig('data_eeg/spectral_analysis_3_fig_23.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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