{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import csv\n",
    "\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import scipy.fftpack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.genfromtxt('data/Netzfrequenz_Sekundenwerte_2012_KW37.csv', delimiter=',')[1:,1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "36f1f4d7970e41afa4737b6f63b7c449",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f952a6e4580>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(data[:3600*24, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02051102806199375"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(data[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d7fe0512f4254efeb15235a5617ef064",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(1e-06, 0.5)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Number of samplepoints\n",
    "N = len(data[:,0])\n",
    "# sample spacing\n",
    "T = 1.0\n",
    "x = np.linspace(0.0, N*T, N)\n",
    "yf = scipy.fftpack.fft(data[:,0])\n",
    "xf = np.linspace(0.0, 1.0/(2.0*T), N//2)\n",
    "\n",
    "yf = 2.0/N * np.abs(yf[:N//2])\n",
    "\n",
    "#yf = sum(yf[s::10] for s in range(10)) / 10\n",
    "#xf = sum(xf[s::10] for s in range(10)) / 10\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.loglog(xf, yf)\n",
    "ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: f'{1/x:.1f}'))\n",
    "ax.set_xlabel('T in s')\n",
    "ax.set_ylabel('Amplitude Δf')\n",
    "ax.grid()\n",
    "ax.set_xlim([1/1000000, 0.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fd94bc97a276400db0539b703c4eeeac",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(1.6666666666666667e-05, 0.5)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Number of samplepoints\n",
    "N = len(data[:,0])\n",
    "# sample spacing\n",
    "T = 1.0\n",
    "x = np.linspace(0.0, N*T, N)\n",
    "yf = scipy.fftpack.fft(data[:,0])\n",
    "xf = np.linspace(0.0, 1.0/(2.0*T), N//2)\n",
    "\n",
    "yf = 2.0/N * np.abs(yf[:N//2])\n",
    "\n",
    "average_from = lambda val, start, average_width: np.hstack([val[:start], [ np.mean(val[i:i+average_width]) for i in range(start, len(val), average_width) ]])\n",
    "\n",
    "average_width = 20\n",
    "average_start = 100\n",
    "yf = average_from(yf, average_start, average_width)\n",
    "xf = average_from(xf, average_start, average_width)\n",
    "yf = average_from(yf, 300, average_width)\n",
    "xf = average_from(xf, 300, average_width)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.loglog(xf, yf)\n",
    "ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: f'{1/x:.1f}'))\n",
    "ax.set_xlabel('T in s')\n",
    "ax.set_ylabel('Amplitude Δf')\n",
    "ax.grid()\n",
    "ax.set_xlim([1/60000, 0.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "object of type <class 'float'> cannot be safely interpreted as an integer.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m~/safety-reset/lab-windows/env/lib/python3.8/site-packages/numpy/core/function_base.py\u001b[0m in \u001b[0;36mlinspace\u001b[0;34m(start, stop, num, endpoint, retstep, dtype, axis)\u001b[0m\n\u001b[1;32m    116\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 117\u001b[0;31m         \u001b[0mnum\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moperator\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnum\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    118\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: 'float' object cannot be interpreted as an integer",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-7-75728c9461c4>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mys\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconvolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mys\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mones\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmode\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'valid'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mxs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m2.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0;31m#xs = np.linspace(len(data)/2, 1, len(data)/2)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<__array_function__ internals>\u001b[0m in \u001b[0;36mlinspace\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
      "\u001b[0;32m~/safety-reset/lab-windows/env/lib/python3.8/site-packages/numpy/core/function_base.py\u001b[0m in \u001b[0;36mlinspace\u001b[0;34m(start, stop, num, endpoint, retstep, dtype, axis)\u001b[0m\n\u001b[1;32m    117\u001b[0m         \u001b[0mnum\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moperator\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnum\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    118\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 119\u001b[0;31m         raise TypeError(\n\u001b[0m\u001b[1;32m    120\u001b[0m             \u001b[0;34m\"object of type {} cannot be safely interpreted as an integer.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    121\u001b[0m                 .format(type(num)))\n",
      "\u001b[0;31mTypeError\u001b[0m: object of type <class 'float'> cannot be safely interpreted as an integer."
     ]
    }
   ],
   "source": [
    "ys = scipy.fftpack.fft(data[:,0])\n",
    "ys = 2.0/len(data) * np.abs(ys[:len(data)//2])\n",
    "s = 60\n",
    "\n",
    "ys = np.convolve(ys, np.ones((s,))/s, mode='valid')\n",
    "\n",
    "xs = np.linspace(0, 1.0/2.0, len(data)/2)\n",
    "#xs = np.linspace(len(data)/2, 1, len(data)/2)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.loglog(xs[s//2:-s//2+1], ys)\n",
    "ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: 1/x))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ys = scipy.fftpack.fft(data[:,0])\n",
    "ys = 2.0/len(data) * np.abs(ys[:len(data)//2])\n",
    "s = 1\n",
    "\n",
    "ys = np.convolve(ys, np.ones((s,))/s, mode='valid')\n",
    "\n",
    "xs = np.linspace(0, 1.0/2.0, len(data)/2)\n",
    "#xs = np.linspace(len(data)/2, 1, len(data)/2)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.loglog(xs[s//2:-s//2+1 if s > 1 else None], ys)\n",
    "ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: 1/x))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ys = scipy.fftpack.fft(data[:,0])\n",
    "ys = 2.0/len(data) * np.abs(ys[:len(data)//2])\n",
    "s = 1\n",
    "\n",
    "ys = np.convolve(ys, np.ones((s,))/s, mode='valid')\n",
    "\n",
    "xs = np.linspace(0, 1.0/2.0, len(data)/2)\n",
    "\n",
    "ys *= 2*np.pi*xs\n",
    "#xs = np.linspace(len(data)/2, 1, len(data)/2)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.loglog(xs[s//2:-s//2+1 if s > 1 else None], ys)\n",
    "ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: 1/x))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ys = scipy.fftpack.fft(data[:,0])\n",
    "ys = 2.0/len(data) * np.abs(ys[:len(data)//2])\n",
    "s = 30\n",
    "\n",
    "ys = np.convolve(ys, np.ones((s,))/s, mode='valid')\n",
    "\n",
    "xs = np.linspace(0, 1.0/2.0, len(data)/2)\n",
    "\n",
    "ys *= 2*np.pi*xs[s//2:-s//2+1]\n",
    "\n",
    "#xs = np.linspace(len(data)/2, 1, len(data)/2)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9,5))\n",
    "ax.loglog(xs[s//2:-s//2+1], ys)\n",
    "ax.xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _pos: 1/x))\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "1/0.0628"
   ]
  }
 ],
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