{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import supporting package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import copy\n",
    "import glob\n",
    "from datetime import datetime\n",
    "\n",
    "# The package for data structure\n",
    "import xarray as xr\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# The packages for working with uncertainties\n",
    "from uncertainties import ufloat\n",
    "from uncertainties import unumpy as unp\n",
    "from uncertainties import umath\n",
    "\n",
    "# The package for plotting\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['font.size'] = 18 # Set the global font size\n",
    "\n",
    "# -------------- The modules written by us --------------\n",
    "\n",
    "# The packages for read data\n",
    "from DataContainer.ReadData import read_hdf5_file, read_hdf5_global, read_hdf5_run_time, read_csv_file\n",
    "\n",
    "# The packages for data analysis\n",
    "from Analyser.ImagingAnalyser import ImageAnalyser\n",
    "from Analyser.FitAnalyser import FitAnalyser\n",
    "from Analyser.FitAnalyser import ThomasFermi2dModel, DensityProfileBEC2dModel, Polylog22dModel\n",
    "from Analyser.FFTAnalyser import fft, ifft, fft_nutou\n",
    "from ToolFunction.ToolFunction import *\n",
    "\n",
    "# Add errorbar plot to xarray package\n",
    "from ToolFunction.HomeMadeXarrayFunction import errorbar, dataarray_plot_errorbar\n",
    "xr.plot.dataarray_plot.errorbar = errorbar\n",
    "xr.plot.accessor.DataArrayPlotAccessor.errorbar = dataarray_plot_errorbar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Start a client for parallel computing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "    <div style=\"width: 24px; height: 24px; background-color: #e1e1e1; border: 3px solid #9D9D9D; border-radius: 5px; position: absolute;\"> </div>\n",
       "    <div style=\"margin-left: 48px;\">\n",
       "        <h3 style=\"margin-bottom: 0px;\">Client</h3>\n",
       "        <p style=\"color: #9D9D9D; margin-bottom: 0px;\">Client-f2bef319-3533-11ee-93d0-80e82ce2fa8e</p>\n",
       "        <table style=\"width: 100%; text-align: left;\">\n",
       "\n",
       "        <tr>\n",
       "        \n",
       "            <td style=\"text-align: left;\"><strong>Connection method:</strong> Cluster object</td>\n",
       "            <td style=\"text-align: left;\"><strong>Cluster type:</strong> distributed.LocalCluster</td>\n",
       "        \n",
       "        </tr>\n",
       "\n",
       "        \n",
       "            <tr>\n",
       "                <td style=\"text-align: left;\">\n",
       "                    <strong>Dashboard: </strong> <a href=\"http://127.0.0.1:8787/status\" target=\"_blank\">http://127.0.0.1:8787/status</a>\n",
       "                </td>\n",
       "                <td style=\"text-align: left;\"></td>\n",
       "            </tr>\n",
       "        \n",
       "\n",
       "        </table>\n",
       "\n",
       "        \n",
       "\n",
       "        \n",
       "            <details>\n",
       "            <summary style=\"margin-bottom: 20px;\"><h3 style=\"display: inline;\">Cluster Info</h3></summary>\n",
       "            <div class=\"jp-RenderedHTMLCommon jp-RenderedHTML jp-mod-trusted jp-OutputArea-output\">\n",
       "    <div style=\"width: 24px; height: 24px; background-color: #e1e1e1; border: 3px solid #9D9D9D; border-radius: 5px; position: absolute;\">\n",
       "    </div>\n",
       "    <div style=\"margin-left: 48px;\">\n",
       "        <h3 style=\"margin-bottom: 0px; margin-top: 0px;\">LocalCluster</h3>\n",
       "        <p style=\"color: #9D9D9D; margin-bottom: 0px;\">6feafb41</p>\n",
       "        <table style=\"width: 100%; text-align: left;\">\n",
       "            <tr>\n",
       "                <td style=\"text-align: left;\">\n",
       "                    <strong>Dashboard:</strong> <a href=\"http://127.0.0.1:8787/status\" target=\"_blank\">http://127.0.0.1:8787/status</a>\n",
       "                </td>\n",
       "                <td style=\"text-align: left;\">\n",
       "                    <strong>Workers:</strong> 6\n",
       "                </td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                <td style=\"text-align: left;\">\n",
       "                    <strong>Total threads:</strong> 60\n",
       "                </td>\n",
       "                <td style=\"text-align: left;\">\n",
       "                    <strong>Total memory:</strong> 55.88 GiB\n",
       "                </td>\n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "    <td style=\"text-align: left;\"><strong>Status:</strong> running</td>\n",
       "    <td style=\"text-align: left;\"><strong>Using processes:</strong> True</td>\n",
       "</tr>\n",
       "\n",
       "            \n",
       "        </table>\n",
       "\n",
       "        <details>\n",
       "            <summary style=\"margin-bottom: 20px;\">\n",
       "                <h3 style=\"display: inline;\">Scheduler Info</h3>\n",
       "            </summary>\n",
       "\n",
       "            <div style=\"\">\n",
       "    <div>\n",
       "        <div style=\"width: 24px; height: 24px; background-color: #FFF7E5; border: 3px solid #FF6132; border-radius: 5px; position: absolute;\"> </div>\n",
       "        <div style=\"margin-left: 48px;\">\n",
       "            <h3 style=\"margin-bottom: 0px;\">Scheduler</h3>\n",
       "            <p style=\"color: #9D9D9D; margin-bottom: 0px;\">Scheduler-d874d42b-af02-44f9-8b31-e393671fca42</p>\n",
       "            <table style=\"width: 100%; text-align: left;\">\n",
       "                <tr>\n",
       "                    <td style=\"text-align: left;\">\n",
       "                        <strong>Comm:</strong> tcp://127.0.0.1:62557\n",
       "                    </td>\n",
       "                    <td style=\"text-align: left;\">\n",
       "                        <strong>Workers:</strong> 6\n",
       "                    </td>\n",
       "                </tr>\n",
       "                <tr>\n",
       "                    <td style=\"text-align: left;\">\n",
       "                        <strong>Dashboard:</strong> <a href=\"http://127.0.0.1:8787/status\" target=\"_blank\">http://127.0.0.1:8787/status</a>\n",
       "                    </td>\n",
       "                    <td style=\"text-align: left;\">\n",
       "                        <strong>Total threads:</strong> 60\n",
       "                    </td>\n",
       "                </tr>\n",
       "                <tr>\n",
       "                    <td style=\"text-align: left;\">\n",
       "                        <strong>Started:</strong> Just now\n",
       "                    </td>\n",
       "                    <td style=\"text-align: left;\">\n",
       "                        <strong>Total memory:</strong> 55.88 GiB\n",
       "                    </td>\n",
       "                </tr>\n",
       "            </table>\n",
       "        </div>\n",
       "    </div>\n",
       "\n",
       "    <details style=\"margin-left: 48px;\">\n",
       "        <summary style=\"margin-bottom: 20px;\">\n",
       "            <h3 style=\"display: inline;\">Workers</h3>\n",
       "        </summary>\n",
       "\n",
       "        \n",
       "        <div style=\"margin-bottom: 20px;\">\n",
       "            <div style=\"width: 24px; height: 24px; background-color: #DBF5FF; border: 3px solid #4CC9FF; border-radius: 5px; position: absolute;\"> </div>\n",
       "            <div style=\"margin-left: 48px;\">\n",
       "            <details>\n",
       "                <summary>\n",
       "                    <h4 style=\"margin-bottom: 0px; display: inline;\">Worker: 0</h4>\n",
       "                </summary>\n",
       "                <table style=\"width: 100%; text-align: left;\">\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Comm: </strong> tcp://127.0.0.1:62591\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Total threads: </strong> 10\n",
       "                        </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Dashboard: </strong> <a href=\"http://127.0.0.1:62595/status\" target=\"_blank\">http://127.0.0.1:62595/status</a>\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Memory: </strong> 9.31 GiB\n",
       "                        </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Nanny: </strong> tcp://127.0.0.1:62560\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\"></td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td colspan=\"2\" style=\"text-align: left;\">\n",
       "                            <strong>Local directory: </strong> C:\\Users\\data\\AppData\\Local\\Temp\\dask-worker-space\\worker-z88tts4o\n",
       "                        </td>\n",
       "                    </tr>\n",
       "\n",
       "                    \n",
       "\n",
       "                    \n",
       "\n",
       "                </table>\n",
       "            </details>\n",
       "            </div>\n",
       "        </div>\n",
       "        \n",
       "        <div style=\"margin-bottom: 20px;\">\n",
       "            <div style=\"width: 24px; height: 24px; background-color: #DBF5FF; border: 3px solid #4CC9FF; border-radius: 5px; position: absolute;\"> </div>\n",
       "            <div style=\"margin-left: 48px;\">\n",
       "            <details>\n",
       "                <summary>\n",
       "                    <h4 style=\"margin-bottom: 0px; display: inline;\">Worker: 1</h4>\n",
       "                </summary>\n",
       "                <table style=\"width: 100%; text-align: left;\">\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Comm: </strong> tcp://127.0.0.1:62587\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Total threads: </strong> 10\n",
       "                        </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Dashboard: </strong> <a href=\"http://127.0.0.1:62588/status\" target=\"_blank\">http://127.0.0.1:62588/status</a>\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Memory: </strong> 9.31 GiB\n",
       "                        </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Nanny: </strong> tcp://127.0.0.1:62561\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\"></td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td colspan=\"2\" style=\"text-align: left;\">\n",
       "                            <strong>Local directory: </strong> C:\\Users\\data\\AppData\\Local\\Temp\\dask-worker-space\\worker-dnlgjo01\n",
       "                        </td>\n",
       "                    </tr>\n",
       "\n",
       "                    \n",
       "\n",
       "                    \n",
       "\n",
       "                </table>\n",
       "            </details>\n",
       "            </div>\n",
       "        </div>\n",
       "        \n",
       "        <div style=\"margin-bottom: 20px;\">\n",
       "            <div style=\"width: 24px; height: 24px; background-color: #DBF5FF; border: 3px solid #4CC9FF; border-radius: 5px; position: absolute;\"> </div>\n",
       "            <div style=\"margin-left: 48px;\">\n",
       "            <details>\n",
       "                <summary>\n",
       "                    <h4 style=\"margin-bottom: 0px; display: inline;\">Worker: 2</h4>\n",
       "                </summary>\n",
       "                <table style=\"width: 100%; text-align: left;\">\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Comm: </strong> tcp://127.0.0.1:62590\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Total threads: </strong> 10\n",
       "                        </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Dashboard: </strong> <a href=\"http://127.0.0.1:62593/status\" target=\"_blank\">http://127.0.0.1:62593/status</a>\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Memory: </strong> 9.31 GiB\n",
       "                        </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Nanny: </strong> tcp://127.0.0.1:62562\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\"></td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td colspan=\"2\" style=\"text-align: left;\">\n",
       "                            <strong>Local directory: </strong> C:\\Users\\data\\AppData\\Local\\Temp\\dask-worker-space\\worker-jid5c__l\n",
       "                        </td>\n",
       "                    </tr>\n",
       "\n",
       "                    \n",
       "\n",
       "                    \n",
       "\n",
       "                </table>\n",
       "            </details>\n",
       "            </div>\n",
       "        </div>\n",
       "        \n",
       "        <div style=\"margin-bottom: 20px;\">\n",
       "            <div style=\"width: 24px; height: 24px; background-color: #DBF5FF; border: 3px solid #4CC9FF; border-radius: 5px; position: absolute;\"> </div>\n",
       "            <div style=\"margin-left: 48px;\">\n",
       "            <details>\n",
       "                <summary>\n",
       "                    <h4 style=\"margin-bottom: 0px; display: inline;\">Worker: 3</h4>\n",
       "                </summary>\n",
       "                <table style=\"width: 100%; text-align: left;\">\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Comm: </strong> tcp://127.0.0.1:62578\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Total threads: </strong> 10\n",
       "                        </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Dashboard: </strong> <a href=\"http://127.0.0.1:62585/status\" target=\"_blank\">http://127.0.0.1:62585/status</a>\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Memory: </strong> 9.31 GiB\n",
       "                        </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Nanny: </strong> tcp://127.0.0.1:62563\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\"></td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td colspan=\"2\" style=\"text-align: left;\">\n",
       "                            <strong>Local directory: </strong> C:\\Users\\data\\AppData\\Local\\Temp\\dask-worker-space\\worker-g6ne7ypa\n",
       "                        </td>\n",
       "                    </tr>\n",
       "\n",
       "                    \n",
       "\n",
       "                    \n",
       "\n",
       "                </table>\n",
       "            </details>\n",
       "            </div>\n",
       "        </div>\n",
       "        \n",
       "        <div style=\"margin-bottom: 20px;\">\n",
       "            <div style=\"width: 24px; height: 24px; background-color: #DBF5FF; border: 3px solid #4CC9FF; border-radius: 5px; position: absolute;\"> </div>\n",
       "            <div style=\"margin-left: 48px;\">\n",
       "            <details>\n",
       "                <summary>\n",
       "                    <h4 style=\"margin-bottom: 0px; display: inline;\">Worker: 4</h4>\n",
       "                </summary>\n",
       "                <table style=\"width: 100%; text-align: left;\">\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Comm: </strong> tcp://127.0.0.1:62592\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Total threads: </strong> 10\n",
       "                        </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Dashboard: </strong> <a href=\"http://127.0.0.1:62596/status\" target=\"_blank\">http://127.0.0.1:62596/status</a>\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Memory: </strong> 9.31 GiB\n",
       "                        </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Nanny: </strong> tcp://127.0.0.1:62564\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\"></td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td colspan=\"2\" style=\"text-align: left;\">\n",
       "                            <strong>Local directory: </strong> C:\\Users\\data\\AppData\\Local\\Temp\\dask-worker-space\\worker-q9ez95ng\n",
       "                        </td>\n",
       "                    </tr>\n",
       "\n",
       "                    \n",
       "\n",
       "                    \n",
       "\n",
       "                </table>\n",
       "            </details>\n",
       "            </div>\n",
       "        </div>\n",
       "        \n",
       "        <div style=\"margin-bottom: 20px;\">\n",
       "            <div style=\"width: 24px; height: 24px; background-color: #DBF5FF; border: 3px solid #4CC9FF; border-radius: 5px; position: absolute;\"> </div>\n",
       "            <div style=\"margin-left: 48px;\">\n",
       "            <details>\n",
       "                <summary>\n",
       "                    <h4 style=\"margin-bottom: 0px; display: inline;\">Worker: 5</h4>\n",
       "                </summary>\n",
       "                <table style=\"width: 100%; text-align: left;\">\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Comm: </strong> tcp://127.0.0.1:62599\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Total threads: </strong> 10\n",
       "                        </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Dashboard: </strong> <a href=\"http://127.0.0.1:62600/status\" target=\"_blank\">http://127.0.0.1:62600/status</a>\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Memory: </strong> 9.31 GiB\n",
       "                        </td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td style=\"text-align: left;\">\n",
       "                            <strong>Nanny: </strong> tcp://127.0.0.1:62565\n",
       "                        </td>\n",
       "                        <td style=\"text-align: left;\"></td>\n",
       "                    </tr>\n",
       "                    <tr>\n",
       "                        <td colspan=\"2\" style=\"text-align: left;\">\n",
       "                            <strong>Local directory: </strong> C:\\Users\\data\\AppData\\Local\\Temp\\dask-worker-space\\worker-52yeb577\n",
       "                        </td>\n",
       "                    </tr>\n",
       "\n",
       "                    \n",
       "\n",
       "                    \n",
       "\n",
       "                </table>\n",
       "            </details>\n",
       "            </div>\n",
       "        </div>\n",
       "        \n",
       "\n",
       "    </details>\n",
       "</div>\n",
       "\n",
       "        </details>\n",
       "    </div>\n",
       "</div>\n",
       "            </details>\n",
       "        \n",
       "\n",
       "    </div>\n",
       "</div>"
      ],
      "text/plain": [
       "<Client: 'tcp://127.0.0.1:62557' processes=6 threads=60, memory=55.88 GiB>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from dask.distributed import Client\n",
    "client = Client(n_workers=6, threads_per_worker=10, processes=True, memory_limit='10GB')\n",
    "client"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## With 10 Hz Modulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;CH1&#x27; (x: 1200)&gt;\n",
       "array([0.59 , 0.648, 0.62 , ..., 0.612, 0.576, 0.638])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'CH1'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 1200</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-3d9b8fab-33e7-4742-9d89-f17a9b75d35e' class='xr-array-in' type='checkbox' checked><label for='section-3d9b8fab-33e7-4742-9d89-f17a9b75d35e' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>0.59 0.648 0.62 0.668 0.638 0.686 ... 0.582 0.544 0.612 0.576 0.638</span></div><div class='xr-array-data'><pre>array([0.59 , 0.648, 0.62 , ..., 0.612, 0.576, 0.638])</pre></div></div></li><li class='xr-section-item'><input id='section-d831cd50-e001-4e67-a945-46e6819ab05c' class='xr-section-summary-in' type='checkbox'  checked><label for='section-d831cd50-e001-4e67-a945-46e6819ab05c' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.002 0.004 ... 2.396 2.398</div><input id='attrs-4ea7da9f-9ac8-4e87-bf65-f7b2c1e7c37e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-4ea7da9f-9ac8-4e87-bf65-f7b2c1e7c37e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-9cc66621-0f93-4c99-9378-a76ddd5ec51b' class='xr-var-data-in' type='checkbox'><label for='data-9cc66621-0f93-4c99-9378-a76ddd5ec51b' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-fc6402cb-311b-4051-ae36-9ffadb3b61c0' class='xr-section-summary-in' type='checkbox'  ><label for='section-fc6402cb-311b-4051-ae36-9ffadb3b61c0' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-66ac611d-5c7d-457a-869f-a193fc0be7cb' class='xr-index-data-in' type='checkbox'/><label for='index-66ac611d-5c7d-457a-869f-a193fc0be7cb' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Float64Index([                 0.0,                0.002,                0.004,\n",
       "                             0.006,                0.008,                 0.01,\n",
       "                             0.012,                0.014,                0.016,\n",
       "              0.018000000000000002,\n",
       "              ...\n",
       "                              2.38,                2.382,                2.384,\n",
       "                             2.386,                2.388,                 2.39,\n",
       "                             2.392,                2.394,                2.396,\n",
       "                             2.398],\n",
       "             dtype=&#x27;float64&#x27;, name=&#x27;x&#x27;, length=1200))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-5d6ab24f-78cf-4c34-afcb-c0e2a68a3b47' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-5d6ab24f-78cf-4c34-afcb-c0e2a68a3b47' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'CH1' (x: 1200)>\n",
       "array([0.59 , 0.648, 0.62 , ..., 0.612, 0.576, 0.638])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filePath = r'F:\\Jianshun\\AccordionLatticeShorTermStability\\withModulation.csv'\n",
    "\n",
    "data = read_csv_file(filePath, csvEngine='pandas', csvKwargs=dict(header=[0], skiprows=[1], encoding = \"ISO-8859-1\",))\n",
    "dataWithModulation = xr.DataArray(\n",
    "    data=data.CH1[0,:],\n",
    "    dims=['x'],\n",
    "    coords=dict(\n",
    "        x=data.X[0,:].to_numpy() * 2e-3\n",
    "    )\n",
    ")\n",
    "dataWithModulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 68176 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dataWithModulation.plot.errorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataWithModulation = dataWithModulation - dataWithModulation.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 66168 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "dataWithModulation.plot.errorbar(ax=ax)\n",
    "# ax.set_xlim([0.5, 1])\n",
    "# ax.set_ylim([0, 0.25])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataWithModulationFFT = fft(dataWithModulation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 31892 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "abs(dataWithModulationFFT).plot.errorbar(ax=ax, x='freq_x')\n",
    "# ax.set_xlim([0.5, 1])\n",
    "# ax.set_ylim([0, 0.25])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Without Modulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;CH1&#x27; (x: 1200)&gt;\n",
       "array([0.59 , 0.74 , 0.75 , ..., 0.744, 0.738, 0.586])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'CH1'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 1200</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-65679b30-5eaa-4ff9-89cf-4715fd8d6c7a' class='xr-array-in' type='checkbox' checked><label for='section-65679b30-5eaa-4ff9-89cf-4715fd8d6c7a' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>0.59 0.74 0.75 0.576 0.732 0.572 ... 0.746 0.582 0.744 0.738 0.586</span></div><div class='xr-array-data'><pre>array([0.59 , 0.74 , 0.75 , ..., 0.744, 0.738, 0.586])</pre></div></div></li><li class='xr-section-item'><input id='section-a1bba0ba-f579-40b0-8093-c842e7b8d880' class='xr-section-summary-in' type='checkbox'  checked><label for='section-a1bba0ba-f579-40b0-8093-c842e7b8d880' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.002 0.004 ... 2.396 2.398</div><input id='attrs-aa45aff3-be45-4059-83ea-5bd56f52a536' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-aa45aff3-be45-4059-83ea-5bd56f52a536' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-a97847ea-34db-47e0-b996-5f5211691cc7' class='xr-var-data-in' type='checkbox'><label for='data-a97847ea-34db-47e0-b996-5f5211691cc7' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-dbe21854-f811-459a-a2d5-ae5c51125ab8' class='xr-section-summary-in' type='checkbox'  ><label for='section-dbe21854-f811-459a-a2d5-ae5c51125ab8' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-6546220e-51f0-4d35-97ee-f550fac4cb28' class='xr-index-data-in' type='checkbox'/><label for='index-6546220e-51f0-4d35-97ee-f550fac4cb28' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Float64Index([                 0.0,                0.002,                0.004,\n",
       "                             0.006,                0.008,                 0.01,\n",
       "                             0.012,                0.014,                0.016,\n",
       "              0.018000000000000002,\n",
       "              ...\n",
       "                              2.38,                2.382,                2.384,\n",
       "                             2.386,                2.388,                 2.39,\n",
       "                             2.392,                2.394,                2.396,\n",
       "                             2.398],\n",
       "             dtype=&#x27;float64&#x27;, name=&#x27;x&#x27;, length=1200))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-e2fb5382-c7a6-4e5a-85fb-639cd98052a4' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-e2fb5382-c7a6-4e5a-85fb-639cd98052a4' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'CH1' (x: 1200)>\n",
       "array([0.59 , 0.74 , 0.75 , ..., 0.744, 0.738, 0.586])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filePath = r'F:\\Jianshun\\AccordionLatticeShorTermStability\\withoutModulation.csv'\n",
    "\n",
    "data = read_csv_file(filePath, csvEngine='pandas', csvKwargs=dict(header=[0], skiprows=[1], encoding = \"ISO-8859-1\",))\n",
    "dataWithoutModulation = xr.DataArray(\n",
    "    data=data.CH1[0,:],\n",
    "    dims=['x'],\n",
    "    coords=dict(\n",
    "        x=data.X[0,:].to_numpy() * 2e-3\n",
    "    )\n",
    ")\n",
    "dataWithoutModulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 81732 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dataWithoutModulation.plot.errorbar(fmt='o-')\n",
    "plt.xlim([0, 0.15])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataWithoutModulation = dataWithoutModulation - dataWithoutModulation.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 37900 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "dataWithoutModulation.plot.errorbar(ax=ax)\n",
    "# ax.set_xlim([0.5, 1])\n",
    "# ax.set_ylim([0, 0.25])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataWithModulationFFT = fft(dataWithModulation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataWithoutModulationFFT = fft(dataWithoutModulation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 52872 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "abs(dataWithoutModulationFFT).plot.errorbar(ax=ax, x='freq_x')\n",
    "ax.set_xlim([0.5, 250])\n",
    "ax.set_ylim([0, 0.05])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
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       ".xr-attrs dd {\n",
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       "\n",
       ".xr-attrs dt {\n",
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       "}\n",
       "\n",
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       "\n",
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;CH1&#x27; (x: 1200)&gt;\n",
       "array([-0.0376, -0.0336, -0.0328, ..., -0.0328, -0.0336, -0.0388])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'CH1'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 1200</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-a50e155f-54b3-4d46-84cc-f7448f5df969' class='xr-array-in' type='checkbox' checked><label for='section-a50e155f-54b3-4d46-84cc-f7448f5df969' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>-0.0376 -0.0336 -0.0328 -0.0374 ... -0.038 -0.0328 -0.0336 -0.0388</span></div><div class='xr-array-data'><pre>array([-0.0376, -0.0336, -0.0328, ..., -0.0328, -0.0336, -0.0388])</pre></div></div></li><li class='xr-section-item'><input id='section-f8b92283-d7f4-4964-a2fd-32ab92f5418c' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f8b92283-d7f4-4964-a2fd-32ab92f5418c' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.002 0.004 ... 2.396 2.398</div><input id='attrs-d7c0c185-49ed-4015-92b8-2d517b52d676' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d7c0c185-49ed-4015-92b8-2d517b52d676' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-9d8ba920-afa3-4ca4-9a06-1a2e970bfa5b' class='xr-var-data-in' type='checkbox'><label for='data-9d8ba920-afa3-4ca4-9a06-1a2e970bfa5b' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-4b26487b-960f-419d-bfcf-b0d20b84bf91' class='xr-section-summary-in' type='checkbox'  ><label for='section-4b26487b-960f-419d-bfcf-b0d20b84bf91' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-4333720f-1d9a-4942-a55b-c46bdaa92ab6' class='xr-index-data-in' type='checkbox'/><label for='index-4333720f-1d9a-4942-a55b-c46bdaa92ab6' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Float64Index([                 0.0,                0.002,                0.004,\n",
       "                             0.006,                0.008,                 0.01,\n",
       "                             0.012,                0.014,                0.016,\n",
       "              0.018000000000000002,\n",
       "              ...\n",
       "                              2.38,                2.382,                2.384,\n",
       "                             2.386,                2.388,                 2.39,\n",
       "                             2.392,                2.394,                2.396,\n",
       "                             2.398],\n",
       "             dtype=&#x27;float64&#x27;, name=&#x27;x&#x27;, length=1200))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-3901bc48-674e-4f94-a591-7ee2dbb7e636' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-3901bc48-674e-4f94-a591-7ee2dbb7e636' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'CH1' (x: 1200)>\n",
       "array([-0.0376, -0.0336, -0.0328, ..., -0.0328, -0.0336, -0.0388])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filePath = r'F:\\Jianshun\\AccordionLatticeShorTermStability\\dark.csv'\n",
    "\n",
    "data = read_csv_file(filePath, csvEngine='pandas', csvKwargs=dict(header=[0], skiprows=[1], encoding = \"ISO-8859-1\",))\n",
    "dataDark = xr.DataArray(\n",
    "    data=data.CH1[0,:],\n",
    "    dims=['x'],\n",
    "    coords=dict(\n",
    "        x=data.X[0,:].to_numpy() * 2e-3\n",
    "    )\n",
    ")\n",
    "dataDark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 45644 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dataDark.plot.errorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataDark = dataDark - dataDark.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataDarkFFT = fft(dataDark)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 25592 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "abs(dataDarkFFT).plot.errorbar(ax=ax, x='freq_x')\n",
    "ax.set_xlim([0.5, 250])\n",
    "ax.set_ylim([0, 0.05])\n",
    "plt.show()"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Only One Beam"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;CH1&#x27; (x: 1200)&gt;\n",
       "array([0.229, 0.242, 0.241, ..., 0.225, 0.225, 0.235])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'CH1'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 1200</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-b7e78c7c-7134-42a6-824b-0b53f19ef2e5' class='xr-array-in' type='checkbox' checked><label for='section-b7e78c7c-7134-42a6-824b-0b53f19ef2e5' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>0.229 0.242 0.241 0.227 0.242 0.227 ... 0.237 0.237 0.225 0.225 0.235</span></div><div class='xr-array-data'><pre>array([0.229, 0.242, 0.241, ..., 0.225, 0.225, 0.235])</pre></div></div></li><li class='xr-section-item'><input id='section-29d4fd3a-d80c-4f9b-8f5d-691555f92266' class='xr-section-summary-in' type='checkbox'  checked><label for='section-29d4fd3a-d80c-4f9b-8f5d-691555f92266' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.002 0.004 ... 2.396 2.398</div><input id='attrs-3758bcb0-96ee-4102-bc8a-ee79c06b8f6d' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3758bcb0-96ee-4102-bc8a-ee79c06b8f6d' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f9a571ca-d791-4c7c-a423-3ffc606f3fbc' class='xr-var-data-in' type='checkbox'><label for='data-f9a571ca-d791-4c7c-a423-3ffc606f3fbc' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-78831768-94ae-40a1-a66e-7e9b555e379c' class='xr-section-summary-in' type='checkbox'  ><label for='section-78831768-94ae-40a1-a66e-7e9b555e379c' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-93558b68-c74f-476f-a4e4-22959b390fc9' class='xr-index-data-in' type='checkbox'/><label for='index-93558b68-c74f-476f-a4e4-22959b390fc9' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Float64Index([                 0.0,                0.002,                0.004,\n",
       "                             0.006,                0.008,                 0.01,\n",
       "                             0.012,                0.014,                0.016,\n",
       "              0.018000000000000002,\n",
       "              ...\n",
       "                              2.38,                2.382,                2.384,\n",
       "                             2.386,                2.388,                 2.39,\n",
       "                             2.392,                2.394,                2.396,\n",
       "                             2.398],\n",
       "             dtype=&#x27;float64&#x27;, name=&#x27;x&#x27;, length=1200))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-fbe5da7b-c284-457c-adae-1b70667478a7' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-fbe5da7b-c284-457c-adae-1b70667478a7' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'CH1' (x: 1200)>\n",
       "array([0.229, 0.242, 0.241, ..., 0.225, 0.225, 0.235])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filePath = r'F:\\Jianshun\\AccordionLatticeShorTermStability\\onlyOneBeam.csv'\n",
    "\n",
    "data = read_csv_file(filePath, csvEngine='pandas', csvKwargs=dict(header=[0], skiprows=[1], encoding = \"ISO-8859-1\",))\n",
    "dataOnlyOneBeam = xr.DataArray(\n",
    "    data=data.CH1[0,:],\n",
    "    dims=['x'],\n",
    "    coords=dict(\n",
    "        x=data.X[0,:].to_numpy() * 2e-3\n",
    "    )\n",
    ")\n",
    "dataOnlyOneBeam"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 40804 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dataOnlyOneBeam.plot.errorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataOnlyOneBeam = dataOnlyOneBeam - dataOnlyOneBeam.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 40348 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dataOnlyOneBeam.plot.errorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataOnlyOneBeamFFT = fft(dataOnlyOneBeam)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<Figure size 640x480 with 1 Axes>"
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    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "abs(dataOnlyOneBeamFFT).plot.errorbar(ax=ax, x='freq_x')\n",
    "ax.set_xlim([0.5, 250])\n",
    "ax.set_ylim([0, 0.05])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 65896 characters]",
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       "<Figure size 640x480 with 1 Axes>"
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   ],
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    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "abs(dataOnlyOneBeamFFT).plot.errorbar(ax=ax, x='freq_x', fmt='r')\n",
    "abs(dataWithoutModulationFFT).plot.errorbar(ax=ax, x='freq_x', fmt='b')\n",
    "\n",
    "ax.set_xlim([0.5, 250])\n",
    "ax.set_ylim([0, 0.02])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Without Modulation # 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;CH1&#x27; (x: 1200)&gt;\n",
       "array([0.49 , 0.53 , 0.533, ..., 0.522, 0.498, 0.454])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 1e-05 2e-05 3e-05 ... 0.01197 0.01198 0.01199</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'CH1'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 1200</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-2eac37f6-45e8-4b9b-b071-de4d23748327' class='xr-array-in' type='checkbox' checked><label for='section-2eac37f6-45e8-4b9b-b071-de4d23748327' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>0.49 0.53 0.533 0.491 0.531 0.494 ... 0.506 0.47 0.522 0.498 0.454</span></div><div class='xr-array-data'><pre>array([0.49 , 0.53 , 0.533, ..., 0.522, 0.498, 0.454])</pre></div></div></li><li class='xr-section-item'><input id='section-bafcc823-32fc-4b66-a0be-415973ff983e' class='xr-section-summary-in' type='checkbox'  checked><label for='section-bafcc823-32fc-4b66-a0be-415973ff983e' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 1e-05 2e-05 ... 0.01198 0.01199</div><input id='attrs-524aeb8b-5119-4d6b-86ab-4df0403179f4' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-524aeb8b-5119-4d6b-86ab-4df0403179f4' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-32bfc995-c1a9-4df2-b8a1-12ed02736afd' class='xr-var-data-in' type='checkbox'><label for='data-32bfc995-c1a9-4df2-b8a1-12ed02736afd' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.000e+00, 1.000e-05, 2.000e-05, ..., 1.197e-02, 1.198e-02, 1.199e-02])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-760ccdad-011a-453e-852b-f16468d1d9bd' class='xr-section-summary-in' type='checkbox'  ><label for='section-760ccdad-011a-453e-852b-f16468d1d9bd' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-a8acc7d0-2f36-4da7-9855-d81ca29b5558' class='xr-index-data-in' type='checkbox'/><label for='index-a8acc7d0-2f36-4da7-9855-d81ca29b5558' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Float64Index([                   0.0,                  1e-05,\n",
       "                               2e-05, 3.0000000000000004e-05,\n",
       "                               4e-05,                  5e-05,\n",
       "               6.000000000000001e-05,  7.000000000000001e-05,\n",
       "                               8e-05,                  9e-05,\n",
       "              ...\n",
       "                              0.0119,                0.01191,\n",
       "                0.011920000000000002,   0.011930000000000001,\n",
       "                0.011940000000000001,                0.01195,\n",
       "                             0.01196,   0.011970000000000001,\n",
       "                0.011980000000000001,                0.01199],\n",
       "             dtype=&#x27;float64&#x27;, name=&#x27;x&#x27;, length=1200))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-d7ab66d7-d847-4bd2-9bca-641fad4acbfb' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-d7ab66d7-d847-4bd2-9bca-641fad4acbfb' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'CH1' (x: 1200)>\n",
       "array([0.49 , 0.53 , 0.533, ..., 0.522, 0.498, 0.454])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 1e-05 2e-05 3e-05 ... 0.01197 0.01198 0.01199"
      ]
     },
     "execution_count": 27,
     "metadata": {},
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    }
   ],
   "source": [
    "filePath = r'F:\\Jianshun\\AccordionLatticeShorTermStability\\withoutModulation_2.csv'\n",
    "\n",
    "data = read_csv_file(filePath, csvEngine='pandas', csvKwargs=dict(header=[0], skiprows=[1], encoding = \"ISO-8859-1\",))\n",
    "dataWithoutModulation2 = xr.DataArray(\n",
    "    data=data.CH1[0,:],\n",
    "    dims=['x'],\n",
    "    coords=dict(\n",
    "        x=data.X[0,:].to_numpy() * 1e-05\n",
    "    )\n",
    ")\n",
    "dataWithoutModulation2"
   ]
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  {
   "cell_type": "code",
   "execution_count": 28,
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       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dataWithoutModulation2.plot.errorbar(fmt='o')\n",
    "# plt.xlim([0, 0.0075])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataWithoutModulation2 = dataWithoutModulation2 - dataWithoutModulation2.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataWithoutModulationFFT2 = fft(dataWithoutModulation2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 56224 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "abs(dataWithoutModulationFFT2).plot.errorbar(ax=ax, x='freq_x')\n",
    "ax.set_xlim([1, 40000])\n",
    "ax.set_ylim([0, 0.00005])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Only One Beam # 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;CH1&#x27; (x: 1200)&gt;\n",
       "array([0.215, 0.197, 0.195, ..., 0.194, 0.218, 0.198])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 1e-05 2e-05 3e-05 ... 0.01197 0.01198 0.01199</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'CH1'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 1200</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-a7a0b230-0379-4f74-a464-a3fc5c3e347e' class='xr-array-in' type='checkbox' checked><label for='section-a7a0b230-0379-4f74-a464-a3fc5c3e347e' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>0.215 0.197 0.195 0.214 0.218 0.194 ... 0.214 0.218 0.194 0.218 0.198</span></div><div class='xr-array-data'><pre>array([0.215, 0.197, 0.195, ..., 0.194, 0.218, 0.198])</pre></div></div></li><li class='xr-section-item'><input id='section-0602ccf9-903e-4368-bc85-d089b2719e12' class='xr-section-summary-in' type='checkbox'  checked><label for='section-0602ccf9-903e-4368-bc85-d089b2719e12' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 1e-05 2e-05 ... 0.01198 0.01199</div><input id='attrs-1a981a2e-a56c-42a1-9ac1-63ae1cf4e068' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1a981a2e-a56c-42a1-9ac1-63ae1cf4e068' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-988b4bde-e74a-45ff-a356-1f4653df312e' class='xr-var-data-in' type='checkbox'><label for='data-988b4bde-e74a-45ff-a356-1f4653df312e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.000e+00, 1.000e-05, 2.000e-05, ..., 1.197e-02, 1.198e-02, 1.199e-02])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f136a99c-5f01-46fc-991f-dcc0674540b9' class='xr-section-summary-in' type='checkbox'  ><label for='section-f136a99c-5f01-46fc-991f-dcc0674540b9' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-911abc08-a315-446d-9789-794c48cb5b1f' class='xr-index-data-in' type='checkbox'/><label for='index-911abc08-a315-446d-9789-794c48cb5b1f' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Float64Index([                   0.0,                  1e-05,\n",
       "                               2e-05, 3.0000000000000004e-05,\n",
       "                               4e-05,                  5e-05,\n",
       "               6.000000000000001e-05,  7.000000000000001e-05,\n",
       "                               8e-05,                  9e-05,\n",
       "              ...\n",
       "                              0.0119,                0.01191,\n",
       "                0.011920000000000002,   0.011930000000000001,\n",
       "                0.011940000000000001,                0.01195,\n",
       "                             0.01196,   0.011970000000000001,\n",
       "                0.011980000000000001,                0.01199],\n",
       "             dtype=&#x27;float64&#x27;, name=&#x27;x&#x27;, length=1200))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-e6ce165b-ceec-4e2d-8287-814dbc8264f2' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-e6ce165b-ceec-4e2d-8287-814dbc8264f2' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'CH1' (x: 1200)>\n",
       "array([0.215, 0.197, 0.195, ..., 0.194, 0.218, 0.198])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 1e-05 2e-05 3e-05 ... 0.01197 0.01198 0.01199"
      ]
     },
     "execution_count": 32,
     "metadata": {},
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    }
   ],
   "source": [
    "filePath = r'F:\\Jianshun\\AccordionLatticeShorTermStability\\onlyOneBeam_2.csv'\n",
    "\n",
    "data = read_csv_file(filePath, csvEngine='pandas', csvKwargs=dict(header=[0], skiprows=[1], encoding = \"ISO-8859-1\",))\n",
    "dataOnlyOneBeam2 = xr.DataArray(\n",
    "    data=data.CH1[0,:],\n",
    "    dims=['x'],\n",
    "    coords=dict(\n",
    "        x=data.X[0,:].to_numpy() * 1e-05\n",
    "    )\n",
    ")\n",
    "dataOnlyOneBeam2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
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       "<Figure size 640x480 with 1 Axes>"
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     "metadata": {},
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   "source": [
    "dataOnlyOneBeam2.plot.errorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataOnlyOneBeam2 = dataOnlyOneBeam2 - dataOnlyOneBeam2.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataOnlyOneBeamFFT2 = fft(dataOnlyOneBeam2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
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     "metadata": {},
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   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "abs(dataOnlyOneBeamFFT2).plot.errorbar(ax=ax, x='freq_x')\n",
    "ax.set_xlim([1, 40000])\n",
    "ax.set_ylim([0, 0.00005])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 58208 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "abs(dataOnlyOneBeamFFT2).plot.errorbar(ax=ax, x='freq_x', fmt='r')\n",
    "abs(dataWithoutModulationFFT2).plot.errorbar(ax=ax, x='freq_x', fmt='b')\n",
    "\n",
    "ax.set_xlim([1, 40000])\n",
    "ax.set_ylim([0, 0.00005])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data analyse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transform intensity to phase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Analyser.FitAnalyser import NewFitModel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sine_with_offset(x, amplitude=1.0, frequency=1.0, shift=0.0, offset=0.0):\n",
    "    \"\"\"Return a sinusoidal function.\n",
    "\n",
    "    sine(x, amplitude, frequency, shift) =\n",
    "        amplitude * sin(x*frequency + shift)\n",
    "\n",
    "    \"\"\"\n",
    "    return amplitude*np.sin(x*frequency + shift) + offset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "fitModel = NewFitModel(sine_with_offset)\n",
    "fitAnalyser = FitAnalyser(fitModel, fitDim=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = fitAnalyser.fitModel.make_params()\n",
    "params.add(name=\"amplitude\", value=  0.1, max=np.inf, min=-np.inf, vary=True)\n",
    "params.add(name=\"frequency\", value=  63, max=np.inf, min=-np.inf, vary=True)\n",
    "params.add(name=\"shift\", value=  0.11, max=np.inf, min=-np.inf, vary=True)\n",
    "params.add(name=\"offset\", value=  0.6, max=np.inf, min=-np.inf, vary=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# param = fitAnalyser.guess(dataWithModulation)\n",
    "fitResult = fitAnalyser.fit(dataWithModulation, params)\n",
    "fitCurve = fitAnalyser.eval(fitResult, x=dataWithModulation.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 108324 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "dataWithModulation.plot.errorbar(ax=ax)\n",
    "fitCurve.plot.errorbar(ax=ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:    ()\n",
       "Data variables:\n",
       "    amplitude  float64 0.09749\n",
       "    frequency  float64 62.83\n",
       "    shift      float64 0.162\n",
       "    offset     float64 -5.246e-07</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-f3c1a267-ba98-4ae8-843d-ada6023f2ab3' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-f3c1a267-ba98-4ae8-843d-ada6023f2ab3' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-51aca2a7-52be-44c2-9677-ed6ed0b5a184' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-51aca2a7-52be-44c2-9677-ed6ed0b5a184' class='xr-section-summary'  title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-9cb03ce1-4f97-418f-a5ca-164e3fa46bef' class='xr-section-summary-in' type='checkbox'  checked><label for='section-9cb03ce1-4f97-418f-a5ca-164e3fa46bef' class='xr-section-summary' >Data variables: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>amplitude</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.09749</div><input id='attrs-92e9e314-c94e-4bca-b282-675db789cb13' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-92e9e314-c94e-4bca-b282-675db789cb13' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-7e48f35e-ac9b-4e8e-8933-e721ade1f14d' class='xr-var-data-in' type='checkbox'><label for='data-7e48f35e-ac9b-4e8e-8933-e721ade1f14d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.09749395)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>frequency</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>62.83</div><input id='attrs-86e9a2c0-f534-47c4-bcff-7afecb25bfb4' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-86e9a2c0-f534-47c4-bcff-7afecb25bfb4' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-bf381a99-293d-4396-9dc7-ac2e9731d14c' class='xr-var-data-in' type='checkbox'><label for='data-bf381a99-293d-4396-9dc7-ac2e9731d14c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(62.83446818)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>shift</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.162</div><input id='attrs-260cfbfc-5fcb-4d36-84ab-104198c7a1e0' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-260cfbfc-5fcb-4d36-84ab-104198c7a1e0' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b177d131-c41f-436b-889a-12bbe265d096' class='xr-var-data-in' type='checkbox'><label for='data-b177d131-c41f-436b-889a-12bbe265d096' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.16204272)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>offset</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-5.246e-07</div><input id='attrs-bf7a18ed-ad73-4eb5-bf29-9bc6b6073ee1' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-bf7a18ed-ad73-4eb5-bf29-9bc6b6073ee1' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-13f6a155-f270-4815-972a-8659e0a72401' class='xr-var-data-in' type='checkbox'><label for='data-13f6a155-f270-4815-972a-8659e0a72401' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(-5.24574535e-07)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-54b45105-5610-4da0-bde4-9d5072a08546' class='xr-section-summary-in' type='checkbox' disabled 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      ],
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:    ()\n",
       "Data variables:\n",
       "    amplitude  float64 0.09749\n",
       "    frequency  float64 62.83\n",
       "    shift      float64 0.162\n",
       "    offset     float64 -5.246e-07"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val = fitAnalyser.get_fit_value(fitResult)\n",
    "val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def voltage_to_phase(voltage):\n",
    "    voltage = (voltage - val.offset)\n",
    "    # voltage = xr.where(voltage > val.amplitude, voltage % val.amplitude, voltage % val.amplitude - val.amplitude)\n",
    "    voltage = voltage / val.amplitude\n",
    "    voltage_frac, b= np.modf(voltage.to_numpy())\n",
    "    voltage = xr.where(np.abs(voltage) > 1, np.arcsin(voltage_frac) + np.trunc(voltage) * np.pi, np.arcsin(voltage))\n",
    "    return voltage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\data\\AppData\\Roaming\\Python\\Python39\\site-packages\\xarray\\core\\computation.py:760: RuntimeWarning: invalid value encountered in arcsin\n",
      "  result_data = func(*input_data)\n"
     ]
    }
   ],
   "source": [
    "phaseWithoutModulation = voltage_to_phase(dataWithoutModulation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 36620 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "(phaseWithoutModulation/np.pi).plot.errorbar(ax=ax, fmt='o')\n",
    "\n",
    "# ax.set_xlim([0, 0.1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "def autocorr(x):\n",
    "    result = np.correlate(x, x, mode='full')\n",
    "    return result[len(result)//2:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_noise_spectrum(data):\n",
    "    dataAutoCorr = autocorr(data)\n",
    "    dataAutoCorr = xr.DataArray(\n",
    "        data=dataAutoCorr,\n",
    "        dims=['x'],\n",
    "        coords=dict(\n",
    "            x=data.x\n",
    "        )\n",
    "    )\n",
    "    \n",
    "    dataNoiseSpec = fft(dataAutoCorr)\n",
    "    \n",
    "    return dataNoiseSpec\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "phaseWithoutModulation = phaseWithoutModulation - phaseWithoutModulation.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "phaseAutoCorrWithoutModulation = autocorr((phaseWithoutModulation/np.pi))\n",
    "phaseAutoCorrWithoutModulation = xr.DataArray(\n",
    "    data=phaseAutoCorrWithoutModulation,\n",
    "    dims=['x'],\n",
    "    coords=dict(\n",
    "        x=phaseWithoutModulation.x\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
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       ".xr-var-data,\n",
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       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data,\n",
       ".xr-index-data-in:checked ~ .xr-index-data {\n",
       "  display: block;\n",
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       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
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       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-index-name div,\n",
       ".xr-index-data,\n",
       ".xr-attrs {\n",
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       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
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       "\n",
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       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
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       "  padding-right: 10px;\n",
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       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
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       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (x: 1200)&gt;\n",
       "array([ 1.92834649e+02, -7.04156659e+01,  2.53150014e+00, ...,\n",
       "       -1.15671835e-01, -1.59932171e-01,  9.16532266e-02])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 1200</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-53c26ede-f108-4e2e-a9f9-ba989040b27b' class='xr-array-in' type='checkbox' checked><label for='section-53c26ede-f108-4e2e-a9f9-ba989040b27b' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>192.8 -70.42 2.532 4.986 15.84 ... 0.3829 -0.1157 -0.1599 0.09165</span></div><div class='xr-array-data'><pre>array([ 1.92834649e+02, -7.04156659e+01,  2.53150014e+00, ...,\n",
       "       -1.15671835e-01, -1.59932171e-01,  9.16532266e-02])</pre></div></div></li><li class='xr-section-item'><input id='section-120abb18-cf75-461d-9d28-89a366fcc21f' class='xr-section-summary-in' type='checkbox'  checked><label for='section-120abb18-cf75-461d-9d28-89a366fcc21f' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.002 0.004 ... 2.396 2.398</div><input id='attrs-fa777fe7-01da-46ba-87a5-8752bebdf97e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-fa777fe7-01da-46ba-87a5-8752bebdf97e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-98bb3468-05e8-4b68-90e7-6144a67079fc' class='xr-var-data-in' type='checkbox'><label for='data-98bb3468-05e8-4b68-90e7-6144a67079fc' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-68a9c07f-0859-4d2c-9e2b-696458ab8d89' class='xr-section-summary-in' type='checkbox'  ><label for='section-68a9c07f-0859-4d2c-9e2b-696458ab8d89' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-ba65b85a-12ac-4658-b1c6-136ea642a64b' class='xr-index-data-in' type='checkbox'/><label for='index-ba65b85a-12ac-4658-b1c6-136ea642a64b' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Float64Index([                 0.0,                0.002,                0.004,\n",
       "                             0.006,                0.008,                 0.01,\n",
       "                             0.012,                0.014,                0.016,\n",
       "              0.018000000000000002,\n",
       "              ...\n",
       "                              2.38,                2.382,                2.384,\n",
       "                             2.386,                2.388,                 2.39,\n",
       "                             2.392,                2.394,                2.396,\n",
       "                             2.398],\n",
       "             dtype=&#x27;float64&#x27;, name=&#x27;x&#x27;, length=1200))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-25f4e50b-dc59-4bca-81d3-9079b245eb13' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-25f4e50b-dc59-4bca-81d3-9079b245eb13' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray (x: 1200)>\n",
       "array([ 1.92834649e+02, -7.04156659e+01,  2.53150014e+00, ...,\n",
       "       -1.15671835e-01, -1.59932171e-01,  9.16532266e-02])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phaseAutoCorrWithoutModulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 30344 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "phaseAutoCorrWithoutModulation.plot.errorbar(ax=ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
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       ".xr-attrs dd {\n",
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       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
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       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;x&#x27; (x: 1200)&gt;\n",
       "array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'x'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 1200</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-4450e2ea-1980-4c10-8aba-aa4892e7c8f0' class='xr-array-in' type='checkbox' checked><label for='section-4450e2ea-1980-4c10-8aba-aa4892e7c8f0' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>0.0 0.002 0.004 0.006 0.008 0.01 ... 2.39 2.392 2.394 2.396 2.398</span></div><div class='xr-array-data'><pre>array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])</pre></div></div></li><li class='xr-section-item'><input id='section-5984cf45-0576-4743-b4e4-f711fdcea2b0' class='xr-section-summary-in' type='checkbox'  checked><label for='section-5984cf45-0576-4743-b4e4-f711fdcea2b0' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.002 0.004 ... 2.396 2.398</div><input id='attrs-bd5e1a55-bad7-4a80-a2c8-bcf7cce2c5cb' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-bd5e1a55-bad7-4a80-a2c8-bcf7cce2c5cb' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-38cbcdd8-69df-4ec5-9cb9-2f608380f252' class='xr-var-data-in' type='checkbox'><label for='data-38cbcdd8-69df-4ec5-9cb9-2f608380f252' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-93ef5d77-98f4-4385-a0e9-e3eecdaa0098' class='xr-section-summary-in' type='checkbox'  ><label for='section-93ef5d77-98f4-4385-a0e9-e3eecdaa0098' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-8a4a96a5-89b8-42c7-96af-4d6221b753a6' class='xr-index-data-in' type='checkbox'/><label for='index-8a4a96a5-89b8-42c7-96af-4d6221b753a6' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Float64Index([                 0.0,                0.002,                0.004,\n",
       "                             0.006,                0.008,                 0.01,\n",
       "                             0.012,                0.014,                0.016,\n",
       "              0.018000000000000002,\n",
       "              ...\n",
       "                              2.38,                2.382,                2.384,\n",
       "                             2.386,                2.388,                 2.39,\n",
       "                             2.392,                2.394,                2.396,\n",
       "                             2.398],\n",
       "             dtype=&#x27;float64&#x27;, name=&#x27;x&#x27;, length=1200))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-3485ed86-61a3-4f83-a633-7a5df6c82585' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-3485ed86-61a3-4f83-a633-7a5df6c82585' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'x' (x: 1200)>\n",
       "array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phaseAutoCorrWithoutModulation.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "powerSpecWithoutModulation = fft(phaseAutoCorrWithoutModulation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 43900 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "abs(powerSpecWithoutModulation).plot.errorbar(ax=ax, x='freq_x')\n",
    "# ax.set_xlim([0, 250])\n",
    "# ax.set_ylim([0, 0.001])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "phaseAutoCorrWithoutModulation = autocorr((dataWithoutModulation))\n",
    "phaseAutoCorrWithoutModulation = xr.DataArray(\n",
    "    data=phaseAutoCorrWithoutModulation,\n",
    "    dims=['x'],\n",
    "    coords=dict(\n",
    "        x=phaseWithoutModulation.x\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
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       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (x: 1200)&gt;\n",
       "array([ 8.13258367e+00, -3.87534581e+00, -1.52647527e-01, ...,\n",
       "       -7.66522583e-03, -1.13568061e-02,  6.45748028e-03])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 1200</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-3e184d0c-70d0-4d25-a9a9-e517ac8f0266' class='xr-array-in' type='checkbox' checked><label for='section-3e184d0c-70d0-4d25-a9a9-e517ac8f0266' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>8.133 -3.875 -0.1526 -0.002831 ... 0.02548 -0.007665 -0.01136 0.006457</span></div><div class='xr-array-data'><pre>array([ 8.13258367e+00, -3.87534581e+00, -1.52647527e-01, ...,\n",
       "       -7.66522583e-03, -1.13568061e-02,  6.45748028e-03])</pre></div></div></li><li class='xr-section-item'><input id='section-c253dbde-089a-4265-be30-c13ff8f09c05' class='xr-section-summary-in' type='checkbox'  checked><label for='section-c253dbde-089a-4265-be30-c13ff8f09c05' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.002 0.004 ... 2.396 2.398</div><input id='attrs-b11e19e2-20d9-49b5-b463-033a06457bd3' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b11e19e2-20d9-49b5-b463-033a06457bd3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-7391b73e-189d-4237-9764-71a498a530d6' class='xr-var-data-in' type='checkbox'><label for='data-7391b73e-189d-4237-9764-71a498a530d6' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-56454e00-a907-4338-a43d-e70e91fd156d' class='xr-section-summary-in' type='checkbox'  ><label for='section-56454e00-a907-4338-a43d-e70e91fd156d' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-749c9cd2-7498-4aae-b7f4-c7548e9587df' class='xr-index-data-in' type='checkbox'/><label for='index-749c9cd2-7498-4aae-b7f4-c7548e9587df' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Float64Index([                 0.0,                0.002,                0.004,\n",
       "                             0.006,                0.008,                 0.01,\n",
       "                             0.012,                0.014,                0.016,\n",
       "              0.018000000000000002,\n",
       "              ...\n",
       "                              2.38,                2.382,                2.384,\n",
       "                             2.386,                2.388,                 2.39,\n",
       "                             2.392,                2.394,                2.396,\n",
       "                             2.398],\n",
       "             dtype=&#x27;float64&#x27;, name=&#x27;x&#x27;, length=1200))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-fc26d3df-7d34-4264-9ae5-5fb9685e3c65' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-fc26d3df-7d34-4264-9ae5-5fb9685e3c65' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
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       "<xarray.DataArray (x: 1200)>\n",
       "array([ 8.13258367e+00, -3.87534581e+00, -1.52647527e-01, ...,\n",
       "       -7.66522583e-03, -1.13568061e-02,  6.45748028e-03])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398"
      ]
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     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phaseAutoCorrWithoutModulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 26644 characters]",
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       "<Figure size 640x480 with 1 Axes>"
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   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "phaseAutoCorrWithoutModulation.plot.errorbar(ax=ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
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       "array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'x'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>x</span>: 1200</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-f71cffa9-a979-4a68-b116-1f5d0e97322a' class='xr-array-in' type='checkbox' checked><label for='section-f71cffa9-a979-4a68-b116-1f5d0e97322a' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>0.0 0.002 0.004 0.006 0.008 0.01 ... 2.39 2.392 2.394 2.396 2.398</span></div><div class='xr-array-data'><pre>array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])</pre></div></div></li><li class='xr-section-item'><input id='section-9cd5dede-9b7c-4250-ba5d-cd0209fd7514' class='xr-section-summary-in' type='checkbox'  checked><label for='section-9cd5dede-9b7c-4250-ba5d-cd0209fd7514' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x</span></div><div class='xr-var-dims'>(x)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.002 0.004 ... 2.396 2.398</div><input id='attrs-3ddcac3e-1f37-41b2-b589-922a12846c36' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3ddcac3e-1f37-41b2-b589-922a12846c36' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-72fcace2-59a7-4f72-9dc2-b8672b203fa8' class='xr-var-data-in' type='checkbox'><label for='data-72fcace2-59a7-4f72-9dc2-b8672b203fa8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-c8f2ca9e-9cfd-4b1e-9b99-cb31813a1b56' class='xr-section-summary-in' type='checkbox'  ><label for='section-c8f2ca9e-9cfd-4b1e-9b99-cb31813a1b56' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-76230481-844a-42d3-a5dc-7bb87e7e1bb7' class='xr-index-data-in' type='checkbox'/><label for='index-76230481-844a-42d3-a5dc-7bb87e7e1bb7' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Float64Index([                 0.0,                0.002,                0.004,\n",
       "                             0.006,                0.008,                 0.01,\n",
       "                             0.012,                0.014,                0.016,\n",
       "              0.018000000000000002,\n",
       "              ...\n",
       "                              2.38,                2.382,                2.384,\n",
       "                             2.386,                2.388,                 2.39,\n",
       "                             2.392,                2.394,                2.396,\n",
       "                             2.398],\n",
       "             dtype=&#x27;float64&#x27;, name=&#x27;x&#x27;, length=1200))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-03ea0763-d981-42ab-91b1-bbdadaa6adf7' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-03ea0763-d981-42ab-91b1-bbdadaa6adf7' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray 'x' (x: 1200)>\n",
       "array([0.000e+00, 2.000e-03, 4.000e-03, ..., 2.394e+00, 2.396e+00, 2.398e+00])\n",
       "Coordinates:\n",
       "  * x        (x) float64 0.0 0.002 0.004 0.006 0.008 ... 2.392 2.394 2.396 2.398"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phaseAutoCorrWithoutModulation.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "powerSpecWithoutModulation = fft(phaseAutoCorrWithoutModulation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 62908 characters]",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca()\n",
    "\n",
    "abs(powerSpecWithoutModulation).plot.errorbar(ax=ax, x='freq_x')\n",
    "ax.set_xlim([0, 250])\n",
    "# ax.set_ylim([0, 0.001])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "99.99999999999999 kHz\n",
      "166.66666666666663 Hz\n"
     ]
    }
   ],
   "source": [
    "dt = 5e-6\n",
    "samplingFreq = 1/ dt\n",
    "blockLength = 1200\n",
    "df = samplingFreq / blockLength\n",
    "print(str(samplingFreq / 2 / 1e3) + ' kHz')\n",
    "print(str(df) + ' Hz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1 kHz\n",
      "0.16666666666666666 Hz\n"
     ]
    }
   ],
   "source": [
    "dt = 5e-3\n",
    "samplingFreq = 1/ dt\n",
    "blockLength = 1200\n",
    "df = samplingFreq / blockLength\n",
    "print(str(samplingFreq / 2 / 1e3) + ' kHz')\n",
    "print(str(df) + ' Hz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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