add notebook V01.2.ipynb

sys2-jupyter-notebooks/exam_examples/V01.2.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "04105e65-6705-4c92-a009-48c54bd38ad4",
+   "metadata": {},
+   "source": [
+    "# <span style='color:OrangeRed'>V1 DIE GEWICHTFOLGE </span>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ffe7d73f-7986-44b6-a9fd-a678b9aaa182",
+   "metadata": {},
+   "source": [
+    "<div style=\"font-family: 'times'; font-size: 13pt; text-align: justify\">\n",
+    "\n",
+    "In dieser Aufgabe wird die Gewichtsfunktion g(t) linearer, zeitkontinuierlicher Systeme bzw. die Gewichtsfolge g(k)\n",
+    "linearer, zeitdiskreter Systeme thematisiert. g(k) ergibt sich aus g(t) durch eine Abtastung mit der Abtastzeit Ts:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "b7d82b1f-1a44-44a1-a235-e5556d641592",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "clear all"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "53866cc1-a0ea-4d77-8d9c-c8345704d874",
+   "metadata": {},
+   "source": [
+    "<div style=\"font-family: 'times'; font-size: 13pt; text-align: justify\">\n",
+    "Das folgende Eingangssignal ist gegeben:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "a0b9d775-f176-483e-aaca-43da284aa2e4",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "u =\n",
+      "\n",
+      "   4   2  -3   3   1\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "u = [4 2 -3 3 1]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1cb98bc6-138b-45bc-9178-74f8493d4171",
+   "metadata": {},
+   "source": [
+    "<div style=\"font-family: 'times'; font-size: 13pt; text-align: justify\">\n",
+    "\n",
+    "Die Gewichtsfolge lautet:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "03459a21-1072-416b-a04b-5de7b9a30813",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "g =\n",
+      "\n",
+      "   1   0   2  -1   0\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "g = [1 0 2 -1 0]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "071800da-0e16-4189-bb65-5746c0415165",
+   "metadata": {},
+   "source": [
+    "<div style=\"font-family: 'times'; font-size: 13pt; text-align: justify\">\n",
+    "\n",
+    "Der erste Wert des Ausgangssignals wird so berechnet:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "5adb101b-4286-428a-a4bd-eeb57e860e9c",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "y =  4\n"
+     ]
+    }
+   ],
+   "source": [
+    "y(1) = g(1)*u(1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eae75561-2795-400d-802d-f649281ff316",
+   "metadata": {},
+   "source": [
+    "<div style=\"font-family: 'times'; font-size: 13pt; text-align: justify\">\n",
+    "Der zweite Wert wird sein:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "acf57137-23eb-4be3-87ef-eb9d08076f07",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "y =\n",
+      "\n",
+      "   4   2\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "y(2) = g(1)*u(2)+g(2)*u(1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ab36a55a-6239-4214-9d36-85f4d111c61e",
+   "metadata": {},
+   "source": [
+    "<div style=\"font-family: 'times'; font-size: 13pt; text-align: justify\">\n",
+    "Und der dritte Wert:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "c4c1fce4-7677-40d3-813e-5a5e4758f00f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "y =\n",
+      "\n",
+      "   4   2   5\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "y(3) = g(1)*u(3)+g(2)*u(2)+g(3)*u(1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c5fb33ea-47d7-49bf-a8ce-f1d81917a1d0",
+   "metadata": {},
+   "source": [
+    "<div style=\"font-family: 'times'; font-size: 13pt; text-align: justify\">\n",
+    "Und schließlich der vierte Wert (und so weiter...):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "14c39a24-fc50-4924-8075-84125990776f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "y =\n",
+      "\n",
+      "   4   2   5   3\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "y(4) = g(1)*u(4)+g(2)*u(3)+g(3)*u(2)+g(4)*u(1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "25ea2215-45ca-4980-a862-372d0eccf237",
+   "metadata": {},
+   "source": [
+    "<div style=\"font-family: 'times'; font-size: 13pt; text-align: justify\">\n",
+    "Wir können unsere Berechnungen auch mit der Faltungssumme-Funktion überprüfen, die direkt in Octave verfügbar ist:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "5d66f64a-7857-470c-a708-2645a70a9e3f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "y2 =\n",
+      "\n",
+      "   4   2   5   3  -7   9  -1  -1   0\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "y2 = conv(g,u)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9e1a668f-07ac-442a-bb62-950dacd49832",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f68f7a0c-84ff-4c18-9d68-3dc540fc8f07",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Octave",
+   "language": "octave",
+   "name": "octave"
+  },
+  "language_info": {
+   "file_extension": ".m",
+   "help_links": [
+    {
+     "text": "GNU Octave",
+     "url": "https://www.gnu.org/software/octave/support.html"
+    },
+    {
+     "text": "Octave Kernel",
+     "url": "https://github.com/Calysto/octave_kernel"
+    },
+    {
+     "text": "MetaKernel Magics",
+     "url": "https://metakernel.readthedocs.io/en/latest/source/README.html"
+    }
+   ],
+   "mimetype": "text/x-octave",
+   "name": "octave",
+   "version": "5.2.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}