Labor_Rechneruebung_zur_Signaluebertragung_II/Versuch 3 - Leistungsdichtespektrum/Versuch3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c2d0642c-26b7-4f52-b03c-a80e9513f92c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "cd ~/Downloads/Labor_Rechnerübung_zur_Signalübertragung_II/'Versuch 3 - Leistungsdichtespektrum'/"
   ]
  },
  {
   "attachments": {
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T1fTUDSBr9VXm3lRRa+atXTnFsX8ZL6qdNG0V2D70sgpsdUY0V53JhWBbBBCg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\nziuZYfqQcuK5A7UNAVxglYWqnavSyZT5545Xku7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AAQQQQAABBBBAYA4KkKiG60WPpETV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\nPWcdk/zf1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tRWoJ86PITI0aNbhvfNdddz3//PONWiDMU5bDvrFaEhMV3YuXfGIvv/zyicef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\ngg==\n"
    }
   },
   "cell_type": "markdown",
   "id": "b850f0db-001c-4fd2-a1c1-3600143bff7e",
   "metadata": {},
   "source": [
    "<img src=\"attachment:media/image1.emf\" style=\"width:2.42083in;height:0.56944in\" /><img src=\"attachment:media/image2.png\" style=\"width:8.26778in;height:1.87209in\" />\n",
    "\n",
    "**Rechnerübung zur Signalübertragung II**\n",
    "\n",
    "***Versuch 3: Leistungsdichtespektrum, Autokorrelationsfunktion***\n",
    "\n",
    "**Hinweis**: Die Untersuchungen erfolgen in diesem Dokument numerisch an\n",
    "Hand von Abtastwerten. Ein derartiges Vorgehen wird immer dann\n",
    "verwendet, wenn in einem Rechner eine Systemsimulation durchgeführt\n",
    "wird. Die Fouriertransformation wird beispielsweise durch einen\n",
    "FFT-Algorithmus durchgeführt. Dieser erhält $N$ Abtastwerte und gibt\n",
    "$2N$ Werte zurück (bei manchen anderen FFT-Algorithmen auch nur $N$).\n",
    "Folgende Grafik, in der die Zusammenhänge zwischen Signalen und Spektren\n",
    "im kontinuierlichen Fall und im abgetasteten Fall dargestellt sind, soll\n",
    "helfen, die Berechnungsweise in dieser Matlab-Aufgabe zu verstehen.\n",
    "\n",
    "<img src=\"attachment:media/image3.png\" style=\"width:6.13954in;height:5.2899in\" />\n",
    "\n",
    "**  \n",
    "**\n",
    "\n",
    "**Teil 3.1 Berechnung der Autokorrelationsfunktion**\n",
    "\n",
    "Weißes Rauschen wird auf einen idealen Bandpass der Bandbreite\n",
    "$f_{\\mathrm{\\Delta}}$ und der Mittenfrequenz $f_{0}$ gegeben.\n",
    "\n",
    "Zunächst einige Matlab-Definitionen:\n",
    "\n",
    "Öffnen Sie die Datei „Versuch3.m“ und führen Sie das Programm aus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8d6021d1-8de3-41b1-9a5b-614ae2d581a4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Versuch3;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8232f6d1-2018-4479-a68c-60e7ba6f62b6",
   "metadata": {},
   "source": [
    "In dem Matlab-Code können Sie die Anzahl der Messwerte ändern, indem Sie\n",
    "den Wert für e ändern. In der Grundeinstellung: Anzahl der Messwerte:\n",
    "$N = 2^{10}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8f335f06-267b-4554-a94c-787f414ee13d",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "e = 10;\n",
    "N = 2^e;\n",
    "\n",
    "s = rand(1,N) - 0.5;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f1c47ea-d814-4eef-a170-1bd7a83cb25b",
   "metadata": {},
   "source": [
    "-   Erzeugung der Musterfunktion des Eingangsprozesses:\n",
    "    $s = \\text{rand}\\left( 1,N \\right) - 0.5$\n",
    "\n",
    "Mit der Funktion $s = \\text{rand}\\left( 1,N \\right) - 0.5$ erzeugt\n",
    "Matlab einen Vektor mit $N$ Elementen, dessen Werte Abtastwerte eines\n",
    "gleichverteilten, weißen Rauschprozesses sind.\n",
    "\n",
    "“Figure 1“ zeigt eine Musterfunktion des Eingangsprozesses. Zunächst\n",
    "soll die Autokorrelationsfunktion und auch das Leistungsdichtespektrum\n",
    "des Eingangsprozesses bestimmt werden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "18c2201b-05fe-4d00-839e-acb850d521ab",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure(1)\n",
    "plot(s)\n",
    "axis([0 N -0.5 0.5]);\n",
    "title('Abbildung 1: Eine Musterfunktion des Eingangsprozesses')\n",
    "xlabel('n')\n",
    "ylabel('s(n)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88b05e41-f002-4bd2-9442-ed82048ca63d",
   "metadata": {},
   "source": [
    "-   Bestimmung der Autokorrelationsfunktion:\n",
    "    $\\varphi_{\\text{ss}} = \\text{xcorr}(s)$\n",
    "\n",
    "$$\\Phi_{\\text{ss}} = \\text{abs}\\left( \\text{ffts}h\\text{ift}\\left( \\text{fft}\\left( \\varphi_{\\text{ss}},\\ 2^{e + 1} \\right) \\right) \\right)$$\n",
    "\n",
    "-   Bereich der Werte: $0\\ldots 2^{e + 1}$\n",
    "\n",
    "“Figure 2“ zeigt den Verlauf der Autokorrelationsfunktion\n",
    "$\\varphi_{\\text{ss}}$des Eingangsprozesses nach „Figure 1“."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "460c2940-baf8-4b4a-b09a-833579ba82d8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%  Autokorrelationsfunktion berechnen\n",
    "Autocorr = xcorr(s);\n",
    "figure(2)\n",
    "plot(Autocorr)\n",
    "axis([0 2.*N+1 min(Autocorr) max(Autocorr)]);\n",
    "title('Abbildung 2: Autokorrelationsfunktion des Eingangsprozesses')\n",
    "xlabel('m')\n",
    "ylabel('Autokorrelationsfunktion xcorr(s(n))')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d90ee22a-8769-4a56-9107-f1686df5f9d5",
   "metadata": {},
   "source": [
    "Die Autokorrelationsfunktion von weißem Rauschen ist nach der Theorie\n",
    "gleich einem Dirac-Impuls zur Zeit $\\tau = 0$, der mit der spektralen\n",
    "Leistungsdichte $N_{0}$ multipliziert wird. „Figure 2“ zeigt einen\n",
    "Impuls zum Zeitpunkt $\\tau = 0$ in der Mitte des dargestellten\n",
    "Bereiches. Der hier dargestellte Verlauf wurde aus der Musterfunktion\n",
    "bestimmt.\n",
    "\n",
    "Über eine FFT-Routine wurde oben das Leistungsdichtespektrum\n",
    "Φ<sub>ss</sub> des Eingangsprozesses berechnet.Dieses ist in „Figure 3“\n",
    "wiedergegeben."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a48b5474-10ab-47a7-b366-5b6b685c6f0f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%  Leistungsdichtespektrum aus Autokorrelationsfunktion berechnen\n",
    "Y = fftshift(fft(Autocorr,2^(e+1)));\n",
    "psd_eingang = abs(Y);\n",
    "\n",
    "%  plot(Pyy)\n",
    "figure(3)\n",
    "plot(psd_eingang);\n",
    "axis([0 length(psd_eingang) min(psd_eingang) max(psd_eingang)]);\n",
    "title('Abbildung 3: Leistungsdichtespektrum des Eingangsprozesses')\n",
    "xlabel('m')\n",
    "ylabel('Leistungsdichtespektrum')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebe6432a-e764-4ddb-8e4b-9241dee39fe8",
   "metadata": {},
   "source": [
    "Auf den ersten Blick fällt in „Figure 3“ auf, dass das\n",
    "Leistungsdichtespektrum nicht konstant ist, was man der Theorie nach bei\n",
    "weißem Rauschen nicht erwarten würde. Das liegt an der hier durch den\n",
    "Parameter$N$zeitlich begrenzten Musterfunktion des Eingangsprozesses.\n",
    "Würde man die Anzahl der Messwerte $N$ deutlich erhöhen, so würde das\n",
    "Leistungsdichtespektrum einen immer gleichmäßigeren Verlauf annehmen.\n",
    "\n",
    "Verändern Sie den Parameter $N$ auf einen höheren Wert (indem Sie in dem\n",
    "Matlab-Code den Wert von e ändern) und betrachten Sie das\n",
    "Leistungsdichtespektrum!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "acdab80a-a793-4a01-9944-9513b2399870",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "e = 22;\n",
    "N = 2^e;\n",
    "\n",
    "s = rand(1,N) - 0.5;\n",
    "Autocorr = xcorr(s);\n",
    "Y = fftshift(fft(Autocorr,2^(e+1)));\n",
    "psd_eingang = abs(Y);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13455eca-e97c-43b5-bbea-6066709c5c19",
   "metadata": {},
   "source": [
    "Sie werden sehen, dass das sich das Leistungsdichtespektrum immer weiter\n",
    "einem konstanten Verlauf annähert. Sollten die Rechenzeiten zu lang\n",
    "sein, können Sie die Berechnung durch Drücken von „Strg + C“ beenden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "00caf201-6ad2-425d-8873-a24200da3aee",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%  plot(Pyy)\n",
    "figure(3)\n",
    "plot(psd_eingang);\n",
    "axis([0 length(psd_eingang) min(psd_eingang) max(psd_eingang)]);\n",
    "title('Abbildung 3: Leistungsdichtespektrum des Eingangsprozesses')\n",
    "xlabel('m')\n",
    "ylabel('Leistungsdichtespektrum')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fb06439-b108-4d9b-aa58-356a0ffcb6c9",
   "metadata": {},
   "source": [
    "**Teil 3.2 Einfluss des Bandpasses**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8e31cfce-8419-4793-a2e9-1d8c09cfb7de",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "e = 10;\n",
    "N = 2^e;\n",
    "\n",
    "s = rand(1,N) - 0.5;\n",
    "Autocorr = xcorr(s);\n",
    "Y = fftshift(fft(Autocorr,2^(e+1)));\n",
    "psd_eingang = abs(Y);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a830561b-1c6a-45bc-a934-25f85fdee2b2",
   "metadata": {},
   "source": [
    "Der untersuchte Eingangsprozess soll nun durch einen idealen Bandpass\n",
    "mit der Mittenfrequenz $f_{0}$ und der Bandbreite $f_{\\mathrm{\\Delta}}$\n",
    "übertragen werden. Dazu zunächst wieder einige Matlab-Definitionen:\n",
    "\n",
    "-   Mittenfrequenz des Bandpasses: $f_{0} = f_{\\text{mf}} = 100$\n",
    "\n",
    "-   Bandbreite des Bandpasses:\n",
    "    $f_{\\mathrm{\\Delta}} = f_{\\text{bb}} = 35$\n",
    "\n",
    "-   Dargestellter Bereich:\n",
    "    $n = 1:\\text{lengt}h\\left( \\Phi_{\\text{ss}} \\right)$\n",
    "\n",
    "-   Übertragungsfunktion des Bandpasses:\n",
    "    $H_{\\text{BP}} = h_{\\text{bp}} = \\text{heaviside}\\left( n - f_{\\text{mf}} + \\frac{f_{\\text{bb}}}{2} \\right) - h\\text{eaviside}\\left( n - f_{\\text{mf}} - \\frac{f_{\\text{bb}}}{2} \\right) + \\text{heaviside}\\left( n + f_{\\text{mf}} + \\frac{f_{\\text{bb}}}{2} - 2^{e + 1} \\right) - h\\text{eaviside}(n + f_{\\text{mf}} - \\frac{f_{\\text{bb}}}{2} - 2^{e + 1})$\n",
    "\n",
    "($f_{\\text{mf}}$, $f_{\\text{bb}}$ und $h_{\\text{bp}}$ sind die\n",
    "entsprechenden Variablen-Namen in dem Matlab-Code.)\n",
    "\n",
    "„Figure 4“ stellt die Übertragungsfunktion $H_{\\text{BP}}$des Bandpasses\n",
    "dar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "798d77d1-1d91-4747-a301-9bbf9eba937d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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A5CDVAABykGoAADlINQCAHKQaAEAOUg0AIAepBgCQg1QDAMhBqgEA5CDVAABykGoAADlINQCAHKQaAEAOUg0AIAepBgCQg1QDAMhBqgEA5CDVAABykGoAADlINQCAHKQaAEAOUg0AIAepBgCQg1QDAMhBqgEA5CDVAABykGoAADlINQCAHKQaAEAOUg0AIAepBgCQg1QDAMhBqgEA5CDVAABykGoAADlINQCAHKQaAEAOUg0AIAepBgCQg1QDAMjhw6lWUVGxadMmm81mtVq3bdvm7XIAAN7nw6m2ZcuW/fv3z58/39uFAADMopW3C6i7xMREb5cAADAXH36tBgBAFaQaAEAOHz4DWStWq1W7UFxc7OEmlmmf1rhcXTSoYWoCgEZW/+cx/cnTVzSXVPM8zJxVv+NdTREAMKd6Po85P3n6RMJxBhIAIAepBgCQw4dTLScnx2q1aq+IZ8yYYbVaZ82a5e2iAADe5MPvq/Xv379u75YBAKTy4ddqAABUQaoBAOQg1QAAcpBqAAA5SDUAgBykGgBADlINACAHqQYAkINUAwDIQaoBAOQg1QAAcpBqAAA5SDUAgBykGgBADlINACAHqQYAkINUAwDIQaoBAOQg1QAAcpBqAAA5SDUAgBykGgBADlINACAHqQYAkINUAwDIQaoBAOQg1QAAcpBqAAA5SDUAgBykGgBADlINACAHqQYAkINUAwDIQaoBAOQg1QAAcpBqAAA5SDUAgBykGgBADlINACAHqQYAkINUAwDIQaoBAOQg1QAAcpBqAAA5SDUAgBykGgBADlINACAHqQYAkINUAwDIYcZUy8jISEhICAsLGz58eGZmZo1jKisr58+f/8ADD4SFhQ0ePHjp0qU3btxo4joBAGZjulTLzs5OSUmZMGFCTk7OqFGj7HZ7YWFh9WGLFy/+6KOPli9fvm/fvgULFqxdu/btt99u+moBAKZiulRbtWpVfHy8zWYLCAhITk4OCQlJT0+vPqywsPD+++8PDQ1t06ZNTExMVFTUgQMHmrxYAIC5mCvVVFUtKCiIiYnRl8TGxubn51cf+cgjj2RnZxcWFl65ciUvL2///v2PPvpoE1YKADCjVt4u4H9cvHixsrIyMDBQXxIYGHju3LnqIxMTE0+cODFy5EhFUSwWy7Rp04YOHWqwZ6vVql0oLi5u0JIBQDL9ydNXmCvVPLdw4cKPP/74nXfesVqt+/fvnzRpUuvWrceNG+dqPGEGAHXg/OTpEwlnrjOQ/v7+fn5+paWl+pLS0tKgoKAqw27evLl+/fqkpKTw8HA/P79+/fqNHj167dq1TVssAMB0zJVqFoslPDx87969+pLc3NzIyMjqw1q2bOm8RFXVFi3MdSwAgKZnuiQYP358VlZWRkZGeXn5mjVrioqKkpKStFUOhyMqKkpRFIvFMmTIkPT09IKCgsrKytzc3E2bNhm/rwYAaA5M975aXFxcampqWlra7Nmzg4ODHQ5HaGho9WGvvvrq0qVLp0yZcvbs2a5du44dO/b5559v+moBAKZiulRTFMVms9lsturL7Xa73W7XLvv7+8+aNWvWrFlNWxoAwNRMdwYSAIA6I9UAAHKQagAAOUg1AIAcpBoAQA5SDQAgB6kGAJCDVAMAyEGqAQDkINUAAHKQagAAOUg1AIAcpBoAQA5SDQAgB6kGAJCDVAMAyEGqAQDkINUAAHKQagAAOUg1AIAcpBoAQA5SDQAgB6kGAJCDVAMAyEGqAQDkINUAAHKQagAAOUg1AIAcpBoAQA5SDQAgB6kGAJCDVAMAyEGqAQDkINUAAHKQagAAOUg1AIAcpBoAQA5SDQAgB6kGAJCDVAMAyNGqUff+008/LVq0qLi4+O67754+fXqHDh0a9eYAAM1c475We+211w4dOvTQQw8dPHhw7ty5jXpbAAA07mu1nJycLVu2dO/e/ZFHHhk1alSj3hYAAI37Wu38+fPdu3dXFKV79+4//fRTo94WAACN+1pNUZRt27bVeHnEiBGNfdMAgOamcVOtV69eb731VvXLCqkGAGgEjZtq27dvb9T9AwDgjO+rAQDkaNJU++GHH7Zv315cXGw8LCMjIyEhISwsbPjw4ZmZma6GnTp16qWXXrrvvvv69es3f/78ioqKhq4XAOBjGjfVDh06NGLEiNDQ0Keeeurrr78ePnx4amqqzWbLyMhwtUl2dnZKSsqECRNycnJGjRplt9sLCwurDysrKxszZkx5efmWLVs+/fTTnj177tmzpzEPBQDgAxr9W9jR0dEbN27s3bv3c889t2DBgj179ixevHjFihWuNlm1alV8fLzNZgsICEhOTg4JCUlPT68+bMWKFVevXl2yZEn37t3btWv35JNPJiQkNOKRAAB8QeOmWlFR0dSpU/v27Tt16tSysrIHH3xQUZRBgwYdP368xvGqqhYUFMTExOhLYmNj8/Pzq4/8+OOPhwwZ4ufn1ziFAwB8UuOmWmVlpb+/v6Io2r9t2rTR/r127VqN4y9evFhZWRkYGKgvCQwMPHfuXPWR//nPfzp27PjMM8/cc8898fHxr7/+Ou+rAQC89i3selJV9e23337jjTeWLl363Xff2e32CxcuzJ8/39V4q9WqXXD7WRUAgE5/8vQV3vkWdq9evWoc7+/v7+fnV1paqi8pLS0NCgqqPrJTp05hYWEPP/ywoih9+/YdN25cWlqaQaoRZgBQB85Pnj6RcOb6FrbFYgkPD9+7d++4ceO0Jbm5uZGRkdVHRkVFXblyxXlJixZ89w4AmjvTJcH48eOzsrIyMjLKy8vXrFlTVFSUlJSkrXI4HFFRUdrl5OTkzz//fMeOHZWVlf/617/Wrl376KOPeq1oAIA5NPr7arUVFxeXmpqalpY2e/bs4OBgh8MRGhpafVjfvn2XLVu2ZMmSGTNmdOnSZcSIERMnTmz6agEAptIAqfbLX/7SeMD7779fqx3abDabzVZ9ud1ut9vt+tX4+Pj4+Pha7RkAIFsDpFpwcLDz1Z07dw4dOrT+uwUAoLYaINWWLVvmfNVqtVZZAgBA0zDdp0UAAKgzUg0AIAepBgCQg1QDAMjRAJ8WCQ8PN15SUFBQ/1sBAMCtBki1xMTE+u8EAID6a4BUmz59ev13AgBA/fG+GgBADlINACAHqQYAkINUAwDIQaoBAOQg1QAAcpBqAAA5SDUAgBykGgBADlINACAHqQYAkINUAwDIQaoBAOQg1QAAcpBqAAA5SLXaURcNskz71NtVAIB7lmmfqosGebuKpkaqAQDkINUAAHKQagAAOUg1AIAcpBoAQA5SDQAgB6kGAJCDVAMAyEGqAQDkINUAAHKQagAAOUg1AIAcpBoAQA5SDQAgB6kGAJCDVAMAyEGqAQDkINUAAHKQagAAOUg1AIAcpBoAQA5SDQAgB6kGAJDDjKmWkZGRkJAQFhY2fPjwzMxM48Fr1661Wq2TJk1qmtoAAGZmulTLzs5OSUmZMGFCTk7OqFGj7HZ7YWGhq8FFRUXp6en33HNPU1YIADAt06XaqlWr4uPjbTZbQEBAcnJySEhIenp6jSMrKiqmTp06Z86cwMDApq0RAGBS5ko1VVULCgpiYmL0JbGxsfn5+TUOnjNnTv/+/R944IGmqg4AYHatvF3A/7h48WJlZaXza6/AwMBz585VH7lt27Zvvvlmy5YtTVgdAMDszJVqHiopKZk/f/7q1av9/Pw83MRqtWoXiouLG60uAJBGf/L0FeZKNX9/fz8/v9LSUn1JaWlpUFBQlWEHDx48f/78yJEjnRdardZPP/20e/fuNe6ZMAOAOnB+8vSJhDNXqlkslvDw8L17944bN05bkpubGxkZWWVYQkKCc6OfffbZtm3bLlu2rOkKBQCYkrk+LaIoyvjx47OysjIyMsrLy9esWVNUVJSUlKStcjgcUVFRXq0OAGBqpku1uLi41NTUtLS0/v37b9682eFwhIaGersoAIBvMNcZSI3NZrPZbNWX2+12u91effmKFSsavygAgA8w3Ws1AADqjFQDAMhBqgEA5CDVAABykGoAADlINQCAHKQaAEAOUg0AIAepBgCQg1QDAMhBqgEA5CDVAABykGoAADlINQCAHKQaAEAOUg0AIAepBgCQg1QDAMhBqgEA5CDVAABykGoAADlINQCAHKQaAEAOUg0AIAepBgCQg1QDAMhBqgEA5CDVAABykGoAADlINQCAHKQaAEAOUg0AIAepBgCQg1QDAMhBqgEA5CDVAABykGoAADlINQCAHKQaAEAOUg0AIAepBgCQg1QDAMhBqgEA5CDVAABykGoAADlINQCAHKQaAEAOUg0AIAepBgCQw4yplpGRkZCQEBYWNnz48MzMzBrHFBYWTp48uX///jExMcnJyYWFhU1cJADAhEyXatnZ2SkpKRMmTMjJyRk1apTdbq8xsZYuXTps2LD3339/x44d3bp1S0pKOnXqVNNXCwAwFdOl2qpVq+Lj4202W0BAQHJyckhISHp6evVhK1asGDZsWOfOnYOCgl5++eVLly59/vnnTV4sAMBczJVqqqoWFBTExMToS2JjY/Pz8423unDhwo0bNwICAhq5OgCA2bXydgH/4+LFi5WVlYGBgfqSwMDAc+fOGW81b968bt26DRw40GCM1WrVLhQXF9e/TgBoJvQnT19hrlSrg8WLF+/evXvt2rV+fn4GwwgzAKgD5ydPn0g4c52B9Pf39/PzKy0t1ZeUlpYGBQW5Gu9wONatW7dy5cq+ffs2SYEAAFMzV6pZLJbw8PC9e/fqS3JzcyMjI2sc7HA4Vq9evXLlyujo6KYqEABgauZKNUVRxo8fn5WVlZGRUV5evmbNmqKioqSkJG2Vw+GIiorSLi9fvpxIAwBUYbr31eLi4lJTU9PS0mbPnh0cHOxwOEJDQ6sPW758+bVr18aOHasvmThxot1ub8JKAQCmY7pUUxTFZrPZbLbqy+12u55bBw4caNqiAAA+wHRnIAEAqDNSDQAgB6kGAJCDVAMAyEGqAQDkINUAAHKQagAAOUg1AIAcpBoAQA5SDQAgB6kGAJCDVAMAyEGqAQDkINUAAHKQagAAOUg1AIAcpBoAQA5SDQAgB6kGAJCDVAMAyEGqAQDkINUAAHKQagAAOUg1AIAcpBoAQA5SDQAgB6kGAJCDVAMAyEGqAQDkINUAAHKQagAAOUg1AIAcpBoAQA5SDQAgB6kGAJCDVAMAyEGqAQDkINUAAHKQagAAOUg1AIAcpBoAQA5SDQAgB6kGAJCDVAMAyEGqAQDkINUAAHKQagAAOUg1AIAcvp1qGRkZCQkJYWFhw4cPz8zM9HY5AAAv8+FUy87OTklJmTBhQk5OzqhRo+x2e2FhobeLEs5qtXq7BCHoZAOimQ1FRid9ONVWrVoVHx9vs9kCAgKSk5NDQkLS09O9XRQAwJt8NdVUVS0oKIiJidGXxMbG5ufne7EkAIDX+WqqXbx4sbKyMjAwUF8SGBh47tw5L5YEAPC6Vt4uoCkcfvQvlmmf1mHDms8y13VvEjTnY29YdLIB0UzXavck5q6TfRqoqkblq6nm7+/v5+dXWlqqLyktLQ0KCqpxsLpoUB1vZlFxHTcEADNo2CcxX3hK9NUzkBaLJTw8fO/evfqS3NzcyMhIL5YEAPA6X001RVHGjx+flZWVkZFRXl6+Zs2aoqKipKQkbxcFAPAmi6qq3q6h7jIyMtLS0n744Yfg4OCpU6cOHjzY2xUBALzJt1MNAABnPnwGEgCAKkg1AIAcpBoAQA7hqcaP+nsuLS3N6iQqKkpfZdBGOqypqKjYtGmTzWazWq3btm2rsrYODWy2jTXopMEUVehkNYWFhZMnT+7fv39MTExycnKVH3+XPCdVuT777LOQkJCtW7eWlZWtWrUqJCTkwIED3i7KvN58883HHnus+nKDNtJh3bp161JSUg4cONCnT5/333/feVUdGticG2vQSVdTVKWTNXnmmWd27Nhx+vTps2fPzpo1Kzo6+scff9RWyZ6TklOxg+g/AAADDUlEQVRt3LhxL774on515MiR06dP92I9JufqKcOgjXS4uurPxXVoII1Va+qkQarRSWOXL18OCQnZvHmzdlX2nBR7BlLlR/1r79ChQxEREf369XvmmWcOHz6sGLaRDnuiDg2ksQaqT1GFTnrgwoULN27cCAgIUJrBnBSbavyof2117tw5NTV19+7dmzdvvvXWW8eMGXPy5EmDNtJhT9ShgTTWlRqnqEInPTBv3rxu3boNHDhQaQZzUmyqobaeeOKJX/ziFwEBAT169PjjH//Yvn37TZs2ebso4P8wRetm8eLFu3fvXrp0qZ+fn7draQpiU61WP+qPKm655Zbg4OBjx44ZtJEOe6IODaSxntCnqEInDTkcjnXr1q1cubJv377aEvFzUmyq8aP+9XHt2rVjx4517drVoI102BN1aCCN9YQ+RRU66ZrD4Vi9evXKlSujo6P1hfLnpJc+pdIUnD+Kunr1ajN/FNUMJk6cuHfv3gsXLpw4cWLKlCn33nvvv//9b9WwjXS4OuNP9nvYQBqr1tRJV1NUpZM1SUtLCw8Pz8vLq75K9pyUnGqqqm7dunXIkCGhoaGPPPLIJ5984u1yTG3fvn3JycmRkZEDBgx44YUXDh8+rK8yaCMd1uzZs6fP/0pJSdHX1qGBzbaxBp00mKIqnawmNDS0SieXLVumrxU8J/nNfgCAHGLfVwMANEOkGgBADlINACAHqQYAkINUAwDIQaoBAOQg1QAAcpBqAAA5SDUAgBykGgBADlINACBHK28XADRf06ZNO3PmTGRk5Pbt28+cOdOrV69XXnlF/3+wANQBr9UAb/ryyy/Ly8s3btyYlZXVo0ePiRMnXr9+3dtFAT6MVAO8qXv37rNnz+7UqVPHjh2ff/75U6dOHT161NtFAT6MVAO8KTg4uEWL//8w7NChg6Io58+f92pFgG8j1QBvslgs3i4BEIVUAwDIQaoBAOQg1QAAclhUVfV2DQAANAxeqwEA5CDVAABykGoAADlINQCAHKQaAEAOUg0AIAepBgCQg1QDAMjx/wDNktmtMejqhQAAAABJRU5ErkJggg=="
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%  Dargestellter Bereich\n",
    "n = 1:length(psd_eingang);\n",
    "\n",
    "%  Übertragungsfunktion des Bandpasses\n",
    "h_bp = heaviside(n-f_mf+f_bb/2)-heaviside(n-f_mf-f_bb/2)...\n",
    "      +heaviside(n+f_mf+f_bb/2-2^(e+1))-heaviside(n+f_mf-f_bb/2-2^(e+1));\n",
    "figure(4)\n",
    "plot(n,h_bp);\n",
    "axis([0 length(h_bp) 0 1.2]);\n",
    "title('Abbildung 4: Übertragungsfunktion des Bandpasses')\n",
    "xlabel('n')\n",
    "ylabel('H_B_P')\n",
    "\n",
    "% zoomed in\n",
    "figure(1)\n",
    "plot(n,h_bp);\n",
    "%axis([f_mf-f_bb f_mf+f_bb 0 1.2]);\n",
    "axis([0 f_mf+f_bb 0 1.2]);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d64d0e5f-f23b-4a8a-953d-40ad761309ca",
   "metadata": {},
   "source": [
    "Das Leistungsdichtespektrum des Ausgangsprozesses ist laut Theorie\n",
    "gleich dem Produkt aus Energiedichtespektrum des Bandpasses und\n",
    "Leistungsdichtespektrum des Eingangsprozesses:\n",
    "\n",
    "-   Leistungsdichtespektrum des Ausgangsprozesses:\n",
    "    $\\Phi_{\\text{gg}} = \\Phi_{\\text{ss}} \\bullet {|H_{\\text{BP}}|}^{2}$\n",
    "\n",
    "„Figure 5“ stellt das Leistungsdichtespektrum $\\Phi_{\\text{gg}}$ des\n",
    "Ausgangsprozesses dar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "8655d4b7-3fcb-4a08-a3f1-df9f216e2cce",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "psd_ausgang = psd_eingang.*abs(h_bp).^2;\n",
    "figure(5)\n",
    "plot(psd_ausgang);\n",
    "title('Abbildung 5: Leistungsdichtespektrum des Ausgangsprozesses')\n",
    "axis([0 length(psd_eingang) min(psd_eingang) max(psd_ausgang)]);\n",
    "xlabel('n')\n",
    "ylabel('Leistungsdichtespektrum')\n",
    "\n",
    "% zoomed in\n",
    "figure(1)\n",
    "plot(psd_ausgang);\n",
    "%axis([f_mf-f_bb f_mf+f_bb min(psd_eingang) max(psd_ausgang)]);\n",
    "axis([0 f_mf+f_bb min(psd_eingang) max(psd_ausgang)]);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b524015-988d-4667-8c5e-fd0a7bb90377",
   "metadata": {},
   "source": [
    "Aus dem Leistungsdichtespektrum kann über die Fourier-Rücktransformation\n",
    "die Autokorrelationsfunktion des Ausgangsprozesses bestimmt werden.\n",
    "\n",
    "-   Berechnung der Autokorrelierten\n",
    "    $\\varphi_{\\text{gg}} = |\\text{ffts}h\\text{ift}(\\text{ifft}\\left( \\Phi_{\\text{gg}} \\right))|$\n",
    "\n",
    "Die so berechnete Autokorrelationsfunktion $\\varphi_{\\text{gg}}$ ist\n",
    "eine komplexe Funktion von $\\tau$. Der Verlauf des Betrages ist in\n",
    "„Figure 6“ dargestellt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "725b2e37-ef2c-401f-b554-dd66cdab8cd6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%  Autokorrelationsfunktion des Ausgangssignals\n",
    "Autocorr_ausgang = abs(fftshift(ifft(psd_ausgang)));\n",
    "figure(6)\n",
    "plot(n,Autocorr_ausgang)\n",
    "title('Abbildung 6: Betrag der Autokorrelationsfunktion des Ausgangssignals')\n",
    "axis([0 length(Autocorr_ausgang) min(Autocorr_ausgang) max(Autocorr_ausgang)]);\n",
    "xlabel('n')\n",
    "ylabel('Betrag der Autokorrelationsfunktion')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac3faba7-259e-4b93-8e8e-c0e755e4e895",
   "metadata": {},
   "source": [
    "„Figure 7“ zeigt dagegen den theoretischen Verlauf des Betrages der\n",
    "Autokorrelationsfunktion. Die Gleichung für die Autokorrelationsfunktion\n",
    "lässt sich recht einfach herleiten. Es ist:\n",
    "\n",
    "-   Spektrale Leistungsdichte: $N_{0} = 1.0$\n",
    "\n",
    "-   Autokorrelationsfunktion:\n",
    "    $\\varphi_{\\text{gg}2}\\left( \\tau \\right) = |N_{0} \\bullet f_{\\mathrm{\\Delta}} \\bullet \\text{sinc}\\left( f_{\\mathrm{\\Delta}} \\bullet \\tau \\right) \\bullet 2 \\bullet \\cos(2 \\bullet \\pi \\bullet f_{0} \\bullet \\tau)|$\n",
    "\n",
    "-   Dargestellter Zeitbereich: $\\tau = - 0.2:0.001:0.2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0ebd2454-a47f-4162-a9cd-8c6299007e64",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%  Autokorrelationsfunktion des Ausgangssignals (theorie)\n",
    "%  Dargestellter Zeitbereich\n",
    "tau = -0.2:0.001:0.2;\n",
    "\n",
    "%  Spektrale Leistungsdichte\n",
    "N0 = 1.0;\n",
    "\n",
    "%  Autokorreationsfunktion\n",
    "Autocorr_ausgang_theorie = abs(N0*f_bb*sinc(f_bb*tau)*2.*cos(2*pi*f_mf*tau));\n",
    "figure(7)\n",
    "plot(tau,Autocorr_ausgang_theorie)\n",
    "title('Abbildung 7: Betrag der Autokorrelationsfunktion des Ausgangssignals, theoretischer Verlauf')\n",
    "axis([-0.2 0.2 min(Autocorr_ausgang_theorie) max(Autocorr_ausgang_theorie)]);\n",
    "xlabel('tau')\n",
    "ylabel('Betrag der Autokorrelationsfuktion (Theorie)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7cddf61-e5fc-414e-ba33-3e1ac75a3480",
   "metadata": {},
   "source": [
    "Beschreiben Sie die beiden Verläufe der Autokorrelationsfunktion. Woher\n",
    "kommen die Unterschiede? (Anmerkung: Sie können sich auch einen\n",
    "Ausschnitt eines Diagramms genauer anschauen mit dem „Zoom In“-Tool.)\n",
    "\n",
    "Der Eingangsprozess wird nun gleichzeitig auf einen Tiefpass der\n",
    "Grenzfrequenz $f_{g} \\leq f_{0} - \\frac{f_{\\mathrm{\\Delta}}}{2}$gegeben.\n",
    "Wie lautet die Kreuzkorrelationsfunktion zwischen den Ausgangsprozessen\n",
    "des Tief- und Bandpasses?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "245180d0-5a43-49de-a20a-ea0dec366d23",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%  Übertragungsfunktion des Tiefpass\n",
    "h_tp = heaviside(n-0)-heaviside(n-(f_mf-f_bb/2))...\n",
    "      +heaviside(n-(2^(e+1)-f_mf+f_bb/2))-heaviside(n-(2^(e+1)));\n",
    "figure(1)\n",
    "plot(h_tp)\n",
    "axis([0 length(h_tp) 0 1.2]);\n",
    "figure(2)\n",
    "plot(h_tp)\n",
    "axis([0 f_mf+f_bb 0 1.2]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "874cc793-9a4c-49fa-a923-41e015596254",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure(1)\n",
    "psd_ausgang_tp = psd_eingang.*abs(h_tp).^2;\n",
    "plot(psd_ausgang_tp)\n",
    "axis([0 length(h_tp) 0 1.2*max(psd_ausgang_tp)]);\n",
    "figure(2)\n",
    "plot(psd_ausgang_tp)\n",
    "axis([0 f_mf+f_bb 0 1.2*max(psd_ausgang_tp)]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2fb11406-756c-4257-8115-d7cfe186d0c0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xc = xcorr(psd_ausgang, psd_ausgang_tp);\n",
    "plot(xc)\n",
    "axis([0 length(xc) 0 1.2*max(xc)]);\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "MATLAB Kernel",
   "language": "matlab",
   "name": "jupyter_matlab_kernel"
  },
  "language_info": {
   "file_extension": ".m",
   "mimetype": "text/x-matlab",
   "name": "matlab"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}