From e0936ccdb7a7e0a59eddf580d2f0442672c8931b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lukas=20M=C3=BCller?= <muellerl@mv.uni-kl.de>
Date: Tue, 14 Jul 2020 18:12:37 +0200
Subject: [PATCH] added notebook
---
"\303\234bung 11.ipynb" | 149 ++++++++++++++++++++++++++++++++++++++++
1 file changed, 149 insertions(+)
create mode 100644 "\303\234bung 11.ipynb"
diff --git "a/\303\234bung 11.ipynb" "b/\303\234bung 11.ipynb"
new file mode 100644
index 0000000..c3ba598
--- /dev/null
+++ "b/\303\234bung 11.ipynb"
@@ -0,0 +1,149 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Übung 11 - Abtastung & Aliasing\n",
+ "\n",
+ "In dieser Übung betrachten wir ein Signal $x(t)=\\cos(2\\pi\\cdot f\\cdot t)$ mit der Frequenz $f=10\\,\\text{Hz}$ , welches mit einer Frequenz $f_T$ abgetastet werden soll.\n",
+ "\n",
+ "Um die bei diesem Unterfangen möglicherweise auftretenden Probleme zu visualisieren, setzen wir in diesem Notebook eine variierende Abtastfrequenz $f_T$ ein, die durch einen Slider variiert werden kann.\n",
+ "## Berechnung und Definition"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from numpy import cos, pi, abs\n",
+ "import numpy\n",
+ "from scipy.fft import fft, fftshift\n",
+ "\n",
+ "\n",
+ "f = 10 # Hz\n",
+ "ft = 40 # Hz\n",
+ "duration = 1 # s\n",
+ "\n",
+ "t = numpy.linspace(0, duration, 5000)\n",
+ "n = numpy.arange(0, duration*ft)\n",
+ "zeropadding = 2**10\n",
+ "Omega = numpy.linspace(-pi, pi, zeropadding)\n",
+ "\n",
+ "def x_continuous(t, f):\n",
+ " return cos(2*pi*f*t)\n",
+ "\n",
+ "def x_discrete(n, ft):\n",
+ " return cos(2*pi*f/ft*n)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Visualisierung"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "scrolled": false
+ },
+ "outputs": [],
+ "source": [
+ "from IPython.display import display\n",
+ "from ipywidgets import IntSlider, FloatSlider\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib notebook\n",
+ "\n",
+ "ft_slider = IntSlider(min=1, max=f*5, layout={'width':'100%'}, value=2)\n",
+ "\n",
+ "figure, (axis1, axis2) = pyplot.subplots(2, 1)\n",
+ "pyplot.tight_layout()\n",
+ "figure.set_figwidth(13)\n",
+ "figure.set_figheight(13)\n",
+ "x_result = x_continuous(t, f)\n",
+ "\n",
+ "def slider_update_plot(changes):\n",
+ " ft = ft_slider.value # get the sampling frequency from the slider\n",
+ " n = numpy.arange(0, duration*ft)\n",
+ " dft = abs(fftshift(fft(x_discrete(n, ft), zeropadding)))/ft/duration\n",
+ " max_index = numpy.argmax(dft[0:int(zeropadding/2)])\n",
+ " omega_max = abs(Omega[max_index])\n",
+ " \n",
+ " # visualize\n",
+ " axis1.cla()\n",
+ " axis1.set_xlim((0, 1))\n",
+ " axis1.plot(t, x_result)\n",
+ " axis1.plot(t, x_continuous(t, omega_max*ft/(2*pi)))\n",
+ " axis1.stem(n/ft, x_discrete(n, ft))\n",
+ " axis1.set_xlabel('$t$ in s', fontsize=22)\n",
+ " axis1.set_yticks([-1, 0, 1])\n",
+ " axis2.cla()\n",
+ " axis2.set_xlim((-12, 12))\n",
+ " axis2.set_ylim((0, 1.1))\n",
+ " axis2.plot(Omega*ft/(2*pi), dft)\n",
+ " axis2.set_xticks(numpy.arange(-12, 13, 1))\n",
+ " axis2.set_ylabel('DFT{x[n]}', fontsize=22)\n",
+ " axis2.set_xlabel('$f$ in Hz', fontsize=22)\n",
+ "\n",
+ "ft_slider.observe(slider_update_plot)\n",
+ "slider_update_plot(None)\n",
+ "display(ft_slider)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.3"
+ },
+ "varInspector": {
+ "cols": {
+ "lenName": 16,
+ "lenType": 16,
+ "lenVar": 40
+ },
+ "kernels_config": {
+ "python": {
+ "delete_cmd_postfix": "",
+ "delete_cmd_prefix": "del ",
+ "library": "var_list.py",
+ "varRefreshCmd": "print(var_dic_list())"
+ },
+ "r": {
+ "delete_cmd_postfix": ") ",
+ "delete_cmd_prefix": "rm(",
+ "library": "var_list.r",
+ "varRefreshCmd": "cat(var_dic_list()) "
+ }
+ },
+ "types_to_exclude": [
+ "module",
+ "function",
+ "builtin_function_or_method",
+ "instance",
+ "_Feature"
+ ],
+ "window_display": false
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
--
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