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+{
+ "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"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "labenv",
+ "language": "python",
+ "name": "labenv"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}