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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Yn5//22+/jRs3jhDCMExRUZGPjw83pa+vb0FBgekiBQAA0+tg6gDUmD59+s2bNydOnEgIEQgEcXFxY8aMIYTU1dU1NDSIRCJuSpFIVF1dbbJAAQDADJh7VluzZs0PP/zwzTffiMXi3377bd68eZ06dQoPD9d2OWKxmB3gx8/iAQDQwTWelsKss9qzZ8927doVFxfn6elJCBk2bFhYWNiOHTvCw8Pt7OxsbGzkcjk3sVwut7e3b2tRSGYAADpQbDwtIsOZ9Xs1gUBgbW2tWMIwjJWVFTvK09MzLy+PG5Wbm+vt7U07RAAAMCfmntVGjRq1ffv2oqKihoaG3Nzc/fv3s+/VCCHR0dFZWVlSqbSmpmbbtm2lpaUREREmjRcAAExMwDCMqWNQpa6ubv369adOnbp3717v3r3Hjx8/e/bszp07s2OlUqlEIrlz546Tk1NsbGxgYGCrCxGLxXgCCeZMEHeGSQowdRQAalhEW2ruWc0gLGJPQHuGrAYWwSLaUrN+AgkAAKAVZDUAAOAPZDUAAOAPZDUAAOAPZDUAAOAPZDUAAOAPZDUAAOAPZDUAAOAPZDUAAOAPZDUAAOAPZDUAAOAPZDUAAOAPZDUAAOAPZDUAAOAPZDUAAOCPDjRX9vDhw9zc3PLy8tra2m7duvXv33/YsGHdu3enGQMAAPAYpaxWWFi4devWM2fOPHv2rFu3bt26dautra2trbWysgoICIiOjvb29qYTCQAA8BiNrDZ//vzs7OwxY8b8+9//9vLyEgqFbHlNTU1hYeH3338fHR09cuTIdevWUQgGAAB4jEZWc3R0/PHHH1s+aRQKhSNHjhw5cmR8fPxXX31FIRIAAOA3Glnto48+Uj1B9+7dFy5cSCESAADgN/SBBAAA/kAfSAAA4A/0gQQAAP5AH0gAAOAP9IEEAAD+QB9IAADgD6q9RQghTU1N169ff/DggWLhkCFDKIcBAAC8RDWrFRYWzps3r7KyUqm8rKysrVmCgoLKy8sVS0aNGiWRSNhhqVQqkUju3Lnj5OQUGxsbGBho8JgBAMCCUM1qK1asGDp06KxZs7gOI2odP36cGy4vLw8KCgoKCmL/lMlk8fHxCQkJAQEBGRkZMTExBw4ccHNzM3zcAABgIahmtStXrqSnp+v8AbUDBw507979jTfeYP9MS0vz9/cPCQkhhERFRWVmZm7fvj0xMdFg4QIAgKWh+t0iDg4OT5480W3e5ubmI0eOTJgwoXPnzoQQhmGKiop8fHy4CXx9fQsKCgwTKAAAWCaqWS04OHjz5s0Mw+gw748//njv3r2wsDD2z7q6uoaGBpFIxE0gEomqq6sNEygAAFgmqk8gCwoKzp07l5WV5ezsrJjb0tPT1c6bkZHh5eU1cOBA3VYtFovZARU9UwAAQAnXeFoKqlnNwcFh3LhxOsxYVVWVnZ39+eefcyV2dnY2NjZyuZwrkcvl9vb2bS0ByQwAQAeKjadFZDiqWS0pKUm3GQ8dOtSlS5exY8dyJQKBwNPTMy8vLzw8nC3Jzc3Fl0kCALRzlvFLNBkZGRMmTOjatatiYXR0dFZWllQqramp2bZtW2lpaUREhIkCBAAAs0Ajq+3fv7+5uVnFBM3Nzfv3729rbH5+/o0bN95++22lcj8/v4SEBIlEMnz48IyMjJSUFHxYDQCgnRPo1iNRKxMnTqytrQ0LCxszZswLL7ygOKq8vPzYsWMHDx7s3r37oUOHjBSAWCzGezUwZ4K4M0xSgKmjAFDDItpSGu/VMjIyDh8+nJaWlpiYKBKJ+vTpY2dnV1dXd+vWrfv377u4uMydO5f9MDUAAIA+aGQ1Kyur0NDQ0NDQoqKic+fOsb+F/fzzzwcFBfn6+uKxIQAAGArVPpCenp6enp401wgAAO2KKftANjU1mXDtAADAP1Sz2u3bt9etW8cOp6SkeHh4BAYGXrt2jWYMAADAY1SzWmJioqurKyHkzp07mzdvXrp0qYeHx9q1a2nGAAAAPEY1q+Xm5vr6+hJCcnJyhg8fPm3atPj4+Pz8fJoxAAAAj1HNak+ePGE/Hnf+/PmhQ4cSQmxtbR8/fkwzBgAA4DGqWW3QoEEbN27Myck5fvy4n58fIaSsrGzQoEE0YwAAAB6jmtUWLlx45MiRyMjIsWPHssls586d06dPpxkDAADwGNXPq3l5ef3yyy+PHj0SCoVsyezZs1988UWaMQAAAI9RzWqEEGtray6lEUJcXFwoBwAAADxmAd/ZDwAAoCEaWW3fvn1BQUFbt269efOm0qjy8vLU1NQ33nhj3759FCIBAAB+w3f2AwAAf+A7+wEAgD+o9haxtbWdNWsWzTUCAEC7QvXzauPGjaO5OgAAaG+oZrVevXrdu3eP5hoBAKBdoZrVJk6cmJKS8vTpU5orBQCA9oPqe7XCwsL8/PxTp07179+/U6dOXHl6ejrNMAAAgK+oZrXevXvj1RoAABgP1ayWlJREc3UAANDeUH2vdvnyZZqrAwCA9gY9+wEAgD/Qsx8AAPgDPfsBAIA/LKBn/927d5OSkrKzswUCwfjx4xcsWNC1a1d2lFQqlUgkd+7ccXJyio2NDQwMNO4GAACAeaN6r8b27B82bFjv3r17KlAxy8OHD6dMmVJTU3Po0KEzZ84MGDDg7Nmz7CiZTBYfH//BBx/k5OSEhobGxMSUlJRQ2Q4AADBTAoZhTB2DKomJiVKp9NSpUzY2NkqjIiIibG1tJRIJ+2doaOiAAQMSExNbLkQsFpeVlRk9VgBdCeLOMEkBpo4CQA2LaEup3quxKioqZDKZTCarqKhQO/EPP/wwatSolimNYZiioiIfHx+uxNfXt6CgwMCxAgCARaH6Xq2xsXHZsmWHDh3iSiZOnLhs2bLOnTu3Ncvt27d79uw5c+bM3NzcXr16jRkzZt68eV27dq2rq2toaBCJRNyUIpGourq6reWIxWJ2wPwvNAAAzAfXeFoKqlktOTlZJpMlJCQMHjyYEFJYWJiUlJScnLx48eK2ZmEYZuvWrYmJievXr//zzz9jYmJqa2tXrlyp7aqRzAAAdKDYeFpEhqP6BDIzMzMpKSk0NNTZ2dnZ2fmtt95au3ZtZmamill69erl5+c3duzYrl27enh4hIeHHz9+nBBiZ2dnY2Mjl8u5KeVyub29vdG3AQAAzBjVrCaXy93c3BRLXnrpJcXM1BJ7V6fIysqKECIQCDw9PfPy8rjy3Nxcb29vwwULAACWh2pWc3R0lMlkiiXZ2dmOjo4qZomKivr555+PHTvW0NDw+++/79ixg/varejo6KysLKlUWlNTs23bttLS0oiICOMFDwAA5o/qe7V33nlnyZIlxcXF3t7ez549Kyws3LVr14IFC1TM4uHhsWHDhuTk5IULFz733HMTJkyYO3cuO8rPzy8hIUEikSxdutTJySklJUXpRhAAANobqp9XYxjm66+/Tk1NffDgASGkR48ec+bMmTFjhkAgMOp6LeIzFtCe4fNqYBEsoi2leq8mEAjCw8PDw8OrqqoIIQ4ODjTXDgAAvEf1vVpjY+PPP/9MCHFwcGBTmkwma2xspBkDAADwGNWsJpFIiouLFUtKSkr+/e9/04wBAAB4jGpWk0qlb731lmLJW2+9deTIEZoxAAAAj1HNavfv3+/Q4b/e5FlZWbHv2AAAAPRHNau5uLgcPXpUseTo0aMDBw6kGQMAAPAY1T6QERERixcvvn79uq+v77Nnz86dO7dv375WfzsGAABAB1Sz2vjx42tqalJSUnbv3k0I6dmz5yeffBIcHEwzBgAA4DGqWY0QMm3atKlTp96+fVsgEDg6OrJf6ggAAGAQVJNKQ0MDIcTKyuqFF17o27cvm9LQWwQAAAyFalabMmXKtWvXFEtyc3P//ve/04wBAAB4jGpW69mz58SJE0+cOEEIYRhGIpFERkaOHj2aZgwAAMBjVN+rpaenb9iw4Z///Oe0adPKy8sLCwu//PJL9BYBAABDoZrVrKys5s+f37Fjxw0bNlhZWX3zzTceHh40AwAAAH6j3QVx27Ztqamp48aN69evX2xsbElJCeUAAACAx6hmtblz5yYnJ//rX/9KSko6ePCgu7t7WFjY3r17acYAAAA8RjWrlZWV7d+/PzQ0lBBiZ2e3bt26xYsXr1y5kmYMAADAY1Tfqx06dKhbt26KJdOnT8erNQAAMBSq92pKKY2FrAYAAIaCL6wCAAD+QFYDAAD+QFYDAAD+QFYDAAD+QFYDAAD+oP37ak1NTdevX3/w4IFi4ZAhQyiHAQAAvEQ1qxUWFs6bN6+yslKpvKysjGYYAADAV1Sz2ooVK4YOHTpr1iyhUKjhLBKJZMOGDdyfdnZ258+f5/6USqUSieTOnTtOTk6xsbGBgYEGjhgAACwK1ax25cqV9PT07t27azWXh4fHgQMHWpbLZLL4+PiEhISAgICMjIyYmJgDBw64ubkZKFgAALA8VHuLODg4PHnyxFBLS0tL8/f3DwkJEQqFUVFRrq6u27dvN9TCAQDAElHNasHBwZs3b2YYRqu5Ll686OXlNWzYsJkzZ166dIktZBimqKjIx8eHm8zX17egoMCQ4QIAgKWh+gSyoKDg3LlzWVlZzs7OirktPT29rVkcHBwSEhJGjhxZU1Ozdu3aKVOmHD161NHRsa6urqGhQSQScVOKRKLq6mrjbgAAAJg3qlnNwcFh3LhxWs0yefJkdkAoFK5evTogIGD//v3z58/XdtVisZgdQH9LAADNcY2npaCa1ZKSkvSZvWPHjk5OTtevXyeE2NnZ2djYyOVybqxcLre3t29rXiQzAAAdKDaeFpHhTPDdIhUVFTKZTCaTVVRUaDUj+wnu3r17E0IEAoGnp2deXh43Njc319vb28CxAgCARaGa1RobG5csWeLv7//ee++99957/v7+S5YsaWxsVDFLTExMfn5+XV3drVu3Fi1aVFtbyz2TjI6OzsrKkkqlNTU127ZtKy0tjYiIoLEZAABgrqg+gUxOTpbJZAkJCYMHDyaEFBYWJiUlJScnL168uK1ZIiMjJRJJUVGRjY0N+8G1AQMGsKP8/PwSEhIkEsnSpUudnJxSUlLwYTUAgHZOoG0/e334+fl9+eWXr776KleSl5cXFxcnk8mMul6xWIz3amDOBHFnmKQAU0cBoIZFtKVUn0DK5XKl26mXXnpJsccHAACAPqhmNUdHR6XbsuzsbEdHR5oxAAAAj1F9r/bOO+8sWbKkuLjY29v72bNnhYWFu3btWrBgAc0YAACAx6hmtYiICCsrq9TU1K1btxJCevToERcXN2PGDJoxAAAAj1HNagKBIDw8PDw8vKqqihDi4OBAc+0AAMB7tH8Lm4V8BgAAxmCC7xYBAAAwEhr3alOnTiWE7N27lx1oae/evRTCAAAA3qOR1VxcXJQGAAAAjIFGVlu+fLnSAAAAgDFQfa+2bt06DQsBAAB0QDWrbdq0ScNCAAAAHZi4D+Tdu3eFQqFpYwAAAN6g9Hm1d999V2mAENLc3FxeXj506FA6MQAAAO9Rymr9+vUjhOTl5bEDrI4dOwYEBISFhdGJAQAAeI9SVlu5ciUhxMbGZunSpUqjSkpK8GufAABgEFTfq/32228NDQ2KJVevXo2OjqYZAwAA8BjVrNahQ4eFCxdyv759+/btyMjI119/nWYMAOZJEHfG1CEA8AHVrCaRSC5evLh69WpCSFVVVUREhLu7+6pVq2jGAAAAPEb1O/tFItGWLVvCwsLs7e2/++67Pn36rF271trammYMAADAY7Q/r9a/f/+UlJT169d36dIlNTW1c+fOlAMAAAAeo3GvFhUVpVQiFAoZhpk7dy77Z3p6OoUwAACA92hktZ49eyqV+Pr6UlgvAAC0NzSyWlJSEoW1AAAA4LewAQCAP6j2gSSENDU1Xb9+/cGDB4qFQ4YMoRwGAADwEtWsVlhYOG/evMrKSqXysrIymmEAAABfUc1qK1asGDp06KxZs3T49ZkdO3YkJCSMGTNmw4YNXKFUKpXkhe6wAAAfVklEQVRIJHfu3HFycoqNjQ0MDDRovAAAYGGoZrUrV66kp6d3795d2xlLS0u3b9/+8ssvKxbKZLL4+PiEhISAgICMjIyYmJgDBw7gi5IBANozqr1FHBwcnjx5ou1c9fX1sbGxy5YtE4lEiuVpaWn+/v4hISFCoTAqKsrV1XX79u0GixUAACwQ1awWHBy8efNm7tuNNbRs2bLhw4ePHDlSsZBhmKKiIh8fH67E19e3oKDAMIECAIBlovoEsqCg4Ny5c1lZWc7Ozoq5TcV3i3z77bd//PHHoUOHlMrr6uoaGhoU795EIlF1dXVbyxGLxewAeqYAAGiOazwtBdWs5uDgMG7cOM2nv3Xr1sqVK9PT021sbPRcNZIZAIAOFBtPi8hwVLOatl8ycuHChQcPHkycOFGxUCwWnzlzxtHR0cbGRi6Xc+Vyudze3t4wgQIAgGWi/SlsrYwePVrxMuEf//hHly5duJ79np6eeXl54eHh7J+5ubne3t4miBIAAMwG1ax27dq1VsudnZ11WFp0dPSsWbOkUmlAQMDBgwdLS0uXL1+uT3gAAGDpqGa1MWPGtFqu20svPz+/hIQEiUSydOlSJyenlJQUfFgNAKCdo5rVMjIyuGGGYa5evbp27dr3339fw9m/+uorpZKQkJCQkBCDxQcAABaOalZT+nIQDw8PR0fHjRs3Tp06lWYYAADAVyb+JZqXX365tLTUtDEAAABvmDirFRYW6v9ZNAAAABbVJ5CLFi1S/LOmpkYmk3Fd8wEAAPRENatVVVUp/tmjR49PP/00NDSUZgwAAMBjNLLaihUrli5dSghZsGCBUocRAAAAA6LxXm3nzp3sdxlPmjSJwuoAAKDdopHVevXqdf78eQorAgCAdo7GE8iwsLBp06ZZWVkRQlxdXVtOcOHCBQphAAAA79HIavPmzQsMDLx27VpsbOzq1asprBEAANonSn0g3dzc3NzcTp06NWHCBDprBACAdojqp7CTk5MV/2xqaqK5dgAA4D2qWe327dvr1q1jh1NSUjw8PNgnkzRjAAAAHqOa1RITE9neInfu3Nm8efPSpUs9PDzWrl1LMwYAAOAxqlktNzfX19eXEJKTkzN8+PBp06bFx8fn5+fTjAEAAHiMalZ78uQJ+3Hs8+fPDx06lBBia2v7+PFjmjEAAACPUc1qgwYN2rhxY05OzvHjx/38/AghZWVlgwYNohkDAADwGNWstnDhwiNHjkRGRo4dO5ZNZjt37pw+fTrNGAAAgMeofme/l5fXL7/88ujRI6FQyJbMnj37xRdfpBkDAADwGNWsRgixtrbmUhohxMXFhXIAAADAY7SzWlNT0/Xr1x88eKBYOGTIEMphAAAAL1HNaoWFhfPmzausrFQqLysroxkGAADwFdWstmLFiqFDh86aNUvxISQAAIChUM1qV65cSU9P7969O82VAgBA+0G1Z7+Dg8OTJ09orhEAANoVqlktODh48+bN7NeLAAAAGBzVJ5AFBQXnzp3LyspydnZWzG3p6eltzVJVVfXVV1+dOnXq/v37zs7OUVFRir/QJpVKJRLJnTt3nJycYmNjAwMDjbsBAABg3qhmNQcHh3Hjxmk1y+7du8Vi8XvvvWdra/v9999/9NFHIpFoxIgRhBCZTBYfH5+QkBAQEJCRkRETE3PgwAE3NzfjxA4AABZAYFnPA0eOHDlp0qSYmBhCSEREhK2trUQiYUeFhoYOGDAgMTGx5VxisRgfHgBzJog7QwhhkgJMHQiAKhbRllJ9r8aqqKiQyWQymayiokLzuerr6w8fPvzw4cOAgABCCMMwRUVFPj4+3AS+vr4FBQWGDxcAACwH1SeQjY2Ny5YtO3ToEFcyceLEZcuWde7cWcVcly9fZp9bdurUaeXKlewzxrq6uoaGBpFIxE0mEomqq6uNFjsAAFgAqlktOTlZJpMlJCQMHjyYEFJYWJiUlJScnLx48WIVcw0cOLCsrKympubYsWNLliyxtbXVoVeIWCxmB8z/9hkAwHxwjaeloJrVMjMzk5KSXn31VfZPZ2fnPn36xMXFqc5qLKFQGBYWlp2dvW/fvsDAQDs7OxsbG7lczk0gl8vt7e3bmh3JDABAB4qNp0VkOKrv1eRyuVIfxZdeekkxM6nV1NTEDggEAk9Pz7y8PG5Ubm6ut7e3QeIEAAALRTWrOTo6ymQyxZLs7GxHR0cVs8TExPz66691dXXV1dXbtm2TyWShoaHsqOjo6KysLKlUWlNTs23bttLS0oiICOMFDwAA5o/qE8h33nlnyZIlxcXF3t7ez549Kyws3LVr14IFC1TMEh4evmnTpqKioo4dOw4cOHDTpk3+/v7sKD8/v4SEBIlEsnTpUicnp5SUFHxYDQCgnaP6eTWGYb7++uvU1FT299V69OgxZ86cGTNmCAQCo67XIj5jAe0ZPq8GFsEi2lKq92oCgSA8PDw8PLyqqooQ4uDgQHPtAADAe7R/C5uFfAYAAMZAI6tNnTqVELJ37152oKW9e/dSCAMAAHiPRlZzcXFRGgAAADAGGllt+fLlSgMAAADGQPXzauvWrdOwEAAAQAdUs9qmTZs0LAQAANCBCX6JRtHdu3eFQqFpYwAAAN6g1LP/3XffVRoghDQ3N5eXlw8dOpRODAAAwHuUslq/fv0IIXl5eewAq2PHjgEBAWFhYXRiAAAA3qOU1VauXEkI6dChA7pBAgCA8VB9r4aUBgAARmXi3iIAAAAGRPt7II8dO/bdd9/dvn376dOnXGFmZiblMAAAgJeo3qvt3bv3448/fv755y9evOjn52dra/vnn396eHjQjAEAAHiM6r3arl27kpKS/P39d+/evXjxYkLImjVr7ty5QzMGAADgMar3ajdu3Bg2bBghxNrauqGhgRASGRmZk5NDMwYAAOAxqlntyZMnNjY2hBB7e/tbt24RQqysrNj0BgAAoD/T/Gqoj4/P6tWrp06deuTIkZdeeskkMQAAAP9QvVebO3cuOxAbG3vv3r05c+b88ccfn3zyCc0YAACAx6jeq8XExLADffr0kUql9fX1Xbt2pRkAAADwmyk/hY2UBgAAhkXjXm3q1KmqJ9i7dy+FMAAAgPdoZDUXFxcKawEAAKCR1fClxgAAQIcJ3qvdvHnz5MmTX3/9NSHk7t279AMAAAC+otoHsqGh4bPPPvv222+tra2fPn06Y8aM5cuXv/322/7+/jTDAAAAvqJ6r/bFF1+UlZXt3bv3999/Z0vCw8PT0tJUzFJSUjJ//vzhw4f7+PhERUWVlJQojpVKpaNHj3Z3dw8ODj59+rQRQwcAAEtANasdO3YsKSnJy8vL2tqaLXF1deUyXKvWr18fFBR05MiRY8eOOTo6RkREcA8tZTJZfHz8Bx98kJOTExoaGhMTo5TzAACgvaGa1err6x0cHBRLmpubraxUxfDVV18FBQU5ODjY29t/8sknjx49+vnnn9lRaWlp/v7+ISEhQqEwKirK1dV1+/btxgseAADMH9Ws5uLicuDAAcWSc+fOaf49kLW1tc3NzUKhkBDCMExRUZGPjw831tfXt6CgwIDRAgCAxaHaWyQyMvLDDz/8/fffR44cSQjJyMhITExMSEjQcPYVK1Y4OjqOGDGCEFJXV9fQ0CASibixIpGourq6rXnFYjE7UFZWpvsGAAC0M1zjaSmoZrXx48c3NDSsW7fuxIkThJAvv/xy4cKFgYGBmsy7du3a7OzsHTt2sL9loy0kMwAAHSg2nhaR4Wj/Es3kyZPffvvtioqKZ8+e9enTR/VLNU5KSsrOnTu3bNni4eHBltjZ2dnY2Mjlcm4auVxub29vlKABAMBCUH2vdvnyZUKIQCDo06fPCy+8oHlKS09P37Jly5AhQ7hCgUDg6emZl5fHleTm5np7exs8ZgAAsCBUs9q4ceO0nSU1NbVlSmNFR0dnZWVJpdKamppt27aVlpZGREQYJlAAALBMVLNar1697t27p9Usqamp9fX106ZNE/9HSkoKO8rPzy8hIUEikQwfPjwjIyMlJcXNzc0IUQMAgMWg+l5t4sSJKSkpn3zySYcOmq63uLhYxdiQkJCQkBBDhAYAAHxANasVFhbm5+efOnWqf//+nTp14srT09NphgEAAHxFNav17t1bh1drAAAAGqKa1WbPnj1w4ECaawQAgHbF3PtAAgAAaM7c+0ACAABojmpWY/tAPn36lOZKAQCg/UAfSAAA4A/0gQQAAP6gmtWSkpJorg4AANob2t/ZTwipqKi4cuUKIeR//ud/HB0d6QcAAAB8RTWrNTY2Llu27NChQ1zJxIkTly1b1rlzZ5phAAAAX1HtA5mcnCyTyRISEk6cOHHixIkvvvhCJpMlJyfTjAEAAHiM6r1aZmZmUlLSq6++yv7p7Ozcp0+fuLi4xYsX0wwDAAD4iuq9mlwuV/qxmJdeeknx96wBAAD0QTWrOTo6ymQyxZLs7Gx0GAEAAEOh+gTynXfeWbJkSXFxsbe397NnzwoLC3ft2rVgwQKaMQAAAI9RzWoRERFWVlapqalbt24lhPTo0SMuLm7GjBk0YwAAAB6jmtUEAkF4eHh4eHhVVRUhxMHBgebaAQCA96i+V6uurmYHHBwcuJRWUlJCMwYAAOAxqllt9uzZDQ0NiiVXr16Njo6mGQMAAPAY1azWoUOHhQsXMgzD/nn79u3IyMjXX3+dZgwAAMBjVLOaRCK5ePHi6tWrCSFVVVURERHu7u6rVq2iGQMAAPAY1d4iIpFoy5YtYWFh9vb23333XZ8+fdauXWttbU0zBgAA4DGq92qEkP79+6ekpKxfv75Lly6pqan4XmMAADAgGvdqUVFRSiVCoZBhmLlz57J/4rewAQDAIGhktZ49eyqV+Pr6UlgvAAC0NzSymj4/gV1fX3/06NE9e/ZcuHAhMTFxwoQJimOlUqlEIrlz546Tk1NsbGxgYKDewQIAgAWj/V6NEFJRUSGTyWQyWUVFhdqJDx069Ntvv61cubLlKJlMFh8f/8EHH+Tk5ISGhsbExOAD3QAA7Zy5/xb29OnT2xqVlpbm7+8fEhJCCImKisrMzNy+fXtiYqJhYwYAAAtiqb+FzTBMUVGRj48PV+Lr61tQUGC4YAEAwPJY6m9h19XVNTQ0iEQirkQkEnHfMwkAAO0T1axmwt/CFovF7EBZWRmF1QEA8APXeFoKqlmN/S3ssWPHciU6/xa2nZ2djY2NYkaUy+X29vZtTY9kBgCgA8XG0yIynKX+FrZAIPD09MzLywsPD2dLcnNzvb29DRovAABYGAv+Lezo6OhZs2ZJpdKAgICDBw+WlpYuX77coPECAICFEXC/C0OT5r+FnZOTExkZqVgyadIk7uNrGn4KWywW4wkkmDNB3BlCCJMUYOpAAFSxiLaU6r3aunXr5s+fT/47n3GFrRo+fLiKSgwJCWE/rwYAAEAof15t06ZNGhYCAADowATfmKXo7t27QqHQtDEAAABvUHoC+e677yoNEEKam5vLy8uHDh1KJwYAAOA9SlmtX79+hJC8vDx2gNWxY8eAgICwsDA6MQAAAO9Rympsr8UOHTqg8z20c4K4M5r3ddRqYgAglN+rIaUBAIBRUe3Zf+3atVbLnZ2daYYB7RBuevSB2gMLQjWrjRkzptVy8/9YHwAAWASqWS0jI4MbZhjm6tWra9euff/992nGAECfQe51cMMEoAmqWe3ll19W/NPDw8PR0XHjxo1Tp06lGQaAaWmSn5DDAHRj4k9hv/zyy6WlpaaNAXiJ/WZFMAbULZgzE2e1wsJCGxsb08YAFKAdBD3hEAINUX0CuWjRIsU/a2pqZDIZ9wNpACbXDp/7tcNNBn6jeq9W9d9sbGw+/fTT2NhYmjGAJdL8Ot3crugNHo+pNrCt9VrurgG+onqvlp6eTnN1wDMa3lWomMxI9yU6LFa3SFQnBmNsneplapiocDsINJn4vRohpKmpydQhgMm0h+t3xW1sD9urD9QP6M+UWa20tHTlypUjRowwYQy8x/tmwthPwIxXgSqWbKSVUjgY+H288XvreMMEWe3+/fs7duz4+9///tZbbx0/fjw4OJh+DAActqniGixzS35GXbtBth3ArNDLas3NzVlZWfPmzfPz80tMTLx48eK+fft++umnTz/9lFoMwDKrxsuEwRh21WZVqzrQKrdZ+sZqoj1sIy/RyGpXrlxZs2bNyJEjZ8+eXVlZ+fHHH+fk5BBCvLy8BAIBhQDMmQHPHD49X1K7IpoJqdWx5tzk0X+2qcOKzCcSs1q+OR9XloJGVnvzzTelUunkyZNPnDixb9++qVOnCoVCCuulxlIORArP1iylKvRh2N4fSksw7AJ5szv0/1yBbtO3nMucq9ScY6OJRlZ7/vnnq6urz507l5eXV1tbS2GNloLOUUj/WG+rFdAnEh1up/RcBY/bCGNsmqF2UMspWz2EsHegLTSyWlZW1tatW5977rnPP/98+PDh//znP0+fPk1hvRbEJB9lpdCIm+o+j+sEYdQGwkg3ambeqJn8OFGayxwuaAxyK2nm+92C0MhqVlZWfn5+ycnJZ8+ejY+Pv3379pw5cwghGzZsuHz5MoUAKDPeHYnaGam959dhRebzBlGHVz4G2RbKvSvVxmzsV1/GezxI7aUdhRWZpLngN6o9+4VC4dSpUzMyMo4ePRoZGblv375x48a9+eabNGPQB4WUo2IJOsyu/yxqI9eh5VLRvGrbL0P/LN4erqb1zKbaPkM27I2OwW+b9L9A0W0W/U9/Q13f8J5pPoU9cODAxYsXy2Sy1NRUZ2dnk8RgttQevi1bGUNlL93m1WEJfKJh0tVnH2mys1QfCSZ5xK0/PcOmecnCnbYaLscinjZbKFN+t4i1tXVgYGBqaqoJY9CNVgeuhrNolWZ0vmQ26ozaMtRlsvk0DYpXJHRe6el5E6DV1zPq9jjOgPfKetLhGayG0+g5o5Gyr/mcF5SZ/nsg9SGVSkePHu3u7h4cHGzYHihKV1JqmyqlKzXdLplbPevaara0XYVWF/h6tpVKy9TzCZgxZqHz3MmASzZ2C2Xa7GLsGTVclKHun9S2ElrN0lYh97+KsFs9DXl/m2jBWU0mk8XHx3/wwQc5OTmhoaExMTElJSX6LFCrq2y1T7qNcYmq4f0cV67hN9zrtnbFcm03R/VVs+odYaizkcdnNTHE8zTNpzHIrYbBj0O111X6Xyxqcvq3PDu0vYjRYdUanpJ0nivQZ8FZLS0tzd/fPyQkRCgURkVFubq6bt++XfUsbTWdbQ23Oq8Ox6hu02s4JeV7CBVngg6RtMy7elZvqyiftPrf6XJUX5eYf2Okfw4zRgDGOMa0WpQmd0uGvXpr60ZN8Vav1dbP/I+xliw1qzEMU1RU5OPjw5X4+voWFBSonVFx52nylEzPFkqTZw7GOG6Md96qXWyrhUb6VTO1620ZgyWepSqorViDbK+2a9Hzgsw89xGFc0rtMvVsTLRNuua5I9Sy1KxWV1fX0NAgEom4EpFIVF1d3erEl8ZtamsPGXa3mcNBYCk/z2gOdcVqtcbMJzwDUszrZr6B+jzVpLBpWj3ktyytPoPR/KmmObDUrGYM1A5QEx4clv5EizKDPGU1EvOJxBzwL7sQ89vFllLJlprV7OzsbGxs5HI5VyKXy+3t7Vud2OXo++S/d4mGu0dpMkvZqYp021KdpzSfKuLBvqPPUIeBJVLaorYepJvbhreMR22EGs6iQ4NpJiw1qwkEAk9Pz7y8PK4kNzfX29u7rem5vdLqcalYqHqXq20rae5+FevSIQx9Im9ZLVotzbLOGf4xk/o3+DFjqiRtJvXJaisYtrythpEbq6JhNFuWmtUIIdHR0VlZWVKptKamZtu2baWlpREREapnaXW3tZxAw0bZJCnN4KugdrAathkyCLWXqO0KhQ3XuSdRq20rndtx1VnBHOjcEKloA3VYmvmw4Kzm5+eXkJAgkUiGDx+ekZGRkpLi5uam1RIMsreMsct1eIagYiw/nsVZ4hUDz5jJcwidpzRUGBrevmh4FmuyNMq1YeknggVnNUJISEjIyZMni4uLMzMzAwMDdVuIJoemtpeTmicSbmIV54+GtxTU2v22bnDbmt4YMZiWGb5fUWLA58m6LVzxqDDIsaHbFtHZTS0zk4qbS62ylyZNR1uTKa2a+9f2dpjFyaU/y85qRqX5kwf986KK5ypqA9D/yZ7Oh7LxzhDdnuYb+5w0w4eoKlZqni2U2tNKk+PfUIlBqyl1qE8D3mNpciGl+bab57FhKMhqmtL/sZ5WV6+qL/pUTKY5Uz2s0LwJ1ur1gIpy8zyHDfLESf91GXYJhk38dO7nWi5Bn6Naw/NU7YWstmcEzcPJzCGr6cJ4R4lWN22qZ9dz7QZckVbnp0FuzszqEtWAKzWr+E11VaThMjVPw9TOmpaz0GlJ2htkNSNS+0DAeBetejLIw0Nj0/n2zkiXCxq2j9rerBskNn2m13ZpNI9VC2q7dc6ypq1hS4SsZiwWcW5TyF6qH6sagz6BabVYc2tc2qpew2ZxPR8n6BCDDoeNSS7LLOKUbw+Q1dojI50ShrpPUns3Y8CGta21UGu7TbWKtu4sDZgP1KZGwx4wmlBcr9q5kDksFLKaydA/Z/S8CDWrk9xI70IM0oZy1aX/O5tWF86o/DSIDgtUsSJDLdPkB49FPFQ34Rr5BFnNuAx7OUz5it6yTi3zj5bOfkcTbG4Mu99R22ohq/GWnj1TzPDkMeqtifHWaNH0rwHzrENtD3L9X1UCNchqoIbxTmCzevlv7J6BBmdWARvj7ZfBIRW1E8hqYO4sojEyXu6kkG+oMatggK+Q1dopM2xfzDAkQ9Gqc4o+PVkslBlumhmGBBpCVgONmPlJbozwzHyT9dHeqsucYwODQ1YDVdAcGKObQKvLNEZveDPsYW9yqAHeQ1YDoIFPr8cAzBmyGpiYUdtrJAPDMnZ9Yn+B/pDVAACAP5DVAACAP5DVAACAP5DVAPSCV0EAZgVZDQAA+ANZDQAA+ANZDQAA+ANZDcCU8BMnAIaFrAZaEIvFpg7BHOmQigxek+02HeKYNCB+VCayGgAA8AeyGgAA8AeyGgAA8IeAYRhTx2B0/HhYDGbo0rhNLkffN3UU/8fc4gH+KSsrM3UIarSLrAYAAO0EnkACAAB/IKsBAAB/IKsBAAB/IKsBAAB/IKsBAAB/IKsBAAB/IKsBAAB/8DyrSaXS0aNHu7u7BwcHnz592tThmDWJRCJWMHjwYG6UimpEDbPq6+v3798fEhIiFou//fZbpbE6VGC7rVgVNaniECWoyRZKSkrmz58/fPhwHx+fqKiokpISxbF8PiYZ/vrpp59cXV0PHz788OHDtLQ0V1fX4uJiUwdlvjZu3Dhp0qSW5SqqETXM2blzZ3x8fHFxsYuLy5EjRxRH6VCB7bliVdRkW4cog5pszcyZM48dO1ZZWXnv3r2PP/54yJAhf/31FzuK38ckn7NaeHj4nDlzuD8nTpz44YcfmjAeM9dWk6GiGlHDLbVsi3WoQFQs01pNqshqqEnVHj9+7OrqmpGRwf7J72OSt08gGYYpKiry8fHhSnx9fQsKCkwYkvm7ePGil5fXsGHDZs6ceenSJaKyGlHDmtChAlGxKrQ8RAlqUgO1tbXNzc1CoZC0g2OSt1mtrq6uoaFBJBJxJSKRqLq62oQhmTkHB4eEhITs7OyMjIxu3bpNmTKloqJCRTWihjWhQwWiYtvS6iFKUJMaWLFihaOj44gRI0g7OCZ5m9VAW5MnTx4/frxQKOzbt+/q1attbW33799v6qAA/g8OUd2sXbs2Ozt7/fr1NjY2po6FBt5mNTs7OxsbG7lczpXI5XJ7e3sThmRBOnbs6OTkdP36dRXViBrWhA4ViIrVBHeIEtSkSikpKTt37tyyZYuHhwdbwvtjkrdZTSAQeHp65uXlcSW5ubne3t4mDMmCNDU1Xb9+vXfv3iqqETWsCR0qEBWrCe4QJajJtqWkpKSnp2/ZsmXIkCFcIf+PSRP1UqFBsStqenq6OXdFNQdz587Ny8urra29efPmggULXnnllStXrjAqqxE13JLqnv0aViAqlmmtJts6RBnUZGskEomnp2d+fn7LUfw+Jvmc1RiGOXz48KhRo9zc3N58881Tp06ZOhyzdv78+aioKG9v79dee+3999+/dOkSN0pFNaKGWWfPnnX5b/Hx8dxYHSqw3VasippUcYgyqMkW3NzclGpyw4YN3FgeH5P4LWwAAOAP3r5XAwCAdghZDQAA+ANZDQAA+ANZDQAA+ANZDQAA+ANZDQAA+ANZDQAA+ANZDQAA+ANZDQAA+ANZDQAA+ANZDQAA+KODqQMAaI/i4uIqKysHDRr0448//vXXX2KxePny5VevXt20adONGzf69u27aNEif39/U4cJYHlwrwZgGnl5eVZWVt98880PP/xACImIiNi9e/f69evz8vICAgJiY2Pv379v6hgBLA+yGoBp9O3bd/HixSKR6G9/+9vkyZNramo+/fTTgQMHdu3aNTo6ur6+vri42NQxAlgeZDUA03B2dhYIBOywUCgkhPTv35/9s0ePHoSQmpoaU8UGYLmQ1QBMo+VPG1pZ4XwE0BfOIgAA4A9kNQAA4A9kNQAA4A9By4f7AAAAFgr3agAAwB/IagAAwB/IagAAwB/IagAAwB/IagAAwB/IagAAwB/IagAAwB/IagAAwB//D0G8s3DVOs7RAAAAAElFTkSuQmCC"
     },
     "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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ZDQAApANZDQAApANZDQAApANZDQAApANZDQAApANZDQAApANZDQAApANZDQAApANZDQAApANZDQAApENwWa26unrfvn1BQUFKpfLQoUP6FqupqYmLixs0aJCHh8eQIUOSkpJqa2vNGSeAqSiiTtb5GgAMILislpWVdfHixbi4OO7FNm7ceOTIkZSUlHPnzq1Zs2b37t3bt283T4QAACBYjSwdgLYpU6bwWay4uPj99993d3cnhPj5+fn4+Fy5coVyaAAAIHSCO1fjaeTIkXl5ecXFxS9fviwsLLx48WJgYKClgwIAAAsT3LkaT1OmTLl7925wcDAhRKFQREVFDRs2zNJBAQCAhYk1q61fv/7777//+uuvlUrlxYsXIyMjmzRpEhISom95pVLJvCgtLTVXjAAAoscePMVClFnt7du36enpUVFRXl5ehJC+fftOnDhx9+7dHFkNyQwAwACaB09RZDhR3ldTKBTW1taaJWq12spKlNsCAAAmJKZMoFKpfHx8CCEKhWLo0KG7du26cOFCTU3NmTNn9u3bh/tqAAAguKyWn5+vVCqZ89zo6GilUhkTE6O72IoVK4YOHTp37lw/P7+lS5dOnjw5MjLS7MECAICwKNRqtaVjoE6pVOK+GggT8zARdcJgRdRJ9l9LBwVQN1EcSwV3rgYAAGAwZDUAAJAOZDUAAJAOZDUAAJAOZDUAAJAOZDUAAJAOZDUAAJAOZDUAAJAOZDUAAJAO6s/sf/369Z07dx4/fqxZ2Lt3b9r1AgCADNHNakVFRZGRkQ8fPtQqF/4zVwAAQIzoZrXVq1f7+vrOnDnT1taWakUAosY8DRIAjEc3q924cSMtLa1169ZUawEAAGDQnS3i4ODw6tUrqlUAAACw6Ga1UaNGff7553L4sRsAABACulcgz58/X1BQkJub6+Liopnb0tLSqNYLAADyRDerOTg4BAYGUq0CAACARTerJSQkUF0/AACAJjxbBAAApIP6s0UIIQ8ePLhx4wYhpGvXrk5OTmaoEQAA5IluVnv58mVsbGxWVhZbEhwcHBsb27RpU6r1AgCAPNG9ApmYmJiXlxcfH3/06NGjR4+uXbs2Ly8vMTGRaqUAACBbdM/VDh8+nJCQ0KdPH+ZPFxcXZ2fnqKioRYsWUa0XAADkie65WmVlpbu7u2ZJjx49KisrqVYKAACyRTerOTk55eXlaZacOnUKE0YAAIASulcgP/zww8WLF1+5csXb2/vt27dFRUXp6elz586lWikAAMgW3awWGhpqZWWVkpKyfft2QkibNm2ioqKmTZvG8Zbq6urvvvtu7969JSUlGzZsGDNmjL4ly8rKEhISTp06pVAoRo8ePXfu3ObNm5t+GwAAQDzoZjWFQhESEhISElJeXk4IcXBwqPctWVlZJSUlcXFxwcHBHIs9efLkgw8+UCqVWVlZbdu2/eabb06fPh0QEGCy0AHMDr+yBmA8c3wLm/DLZ4wpU6bwWWzbtm2vXr1KTEy0sbEhhEyaNMnw4AAAQCqoZDUmx2RkZOhLNhkZGUZW8f333w8dOpRJaQAAAAwqWc3V1VXrhcndv3+/bdu2M2bMOHPmTLt27YYNGxYZGYn7agAAMkclq61cuVLrhcmp1ert27dv2LAhKSnp119/jYiIePr0aVxcnL7llUol86K0tJRSSAAA0sMePMWC7vfVNm3axLOwodq1azdw4MARI0Y0b97c09MzJCTkyJEjHMuX/sn4qgEA5KNUg6Vj4YVuVtu6dSvPwoby8fHRKrGywq/qAADInbkzQVlZma2trWHvValUbDKbPn36jz/+mJOTU1NTc+nSpd27d+NHtwEAgNbM/qlTp2q9IITU1tbeunXL19eX4435+flhYWHM6+jo6Ojo6HHjxuneMPP09Ny8eXNiYmJ0dHT79u3HjBkze/Zsk24BAACIj0KtVtNYb0xMDCEkMzNz3LhxbGHjxo07duw4ceLEVq1a0ahUH6VSKZYrwiA3ut+8VicMtkgkAPUSxbGU1rkac3bVqFEjetMgAQAAtNC9rxYZGalbWFxcTLVSAACQLbpZbdasWTU1NZolN2/eDA8Pp1opAADIFt2s1qhRo+joaPbW3f3798PCwt5//32qlQIAgGzRzWrJycnXrl1bt24dIaS8vDw0NNTDw2PNmjVUKwUAANmi+8x+Ozu71NTUiRMn2tvbf/vtt87Ozhs3brS2tqZaKQAAyBb1b2F36dJFpVIlJSU1a9YsJSWladOmtGsEAADZonKuNn36dK0SW1tbtVrNflE6LS2NRr0AACBzVLJa27ZttUr69etHoyIAAABNVLJaQkICjdUCAABwoztbhBDy+vXrO3fuPH78WLOwd+/etOsFAAAZopvVioqKIiMjHz58qFUu/CeJAdCmiDqp75GPHP8FANzoZrXVq1f7+vrOnDnT4F+fAQAA4I9uVrtx40ZaWlrr1q2p1gIAAMCg+301BweHV69eUa0CAACARTerjRo16vPPP6f0E24AAABa6F6BPH/+fEFBQW5urouLi2Zuw7ewAUhdPxkKAEaim9UcHBwCAwOpVgEAAMCim9XwdWwAADAn6k83BgAAMBu652q3b9+us9zFxYVqvQAAIE90s9qwYcPqLMezRQAAgAa6WS0zM5N9rVarb968uXHjxo8//phqpQAAIFt0s1rPnj01//T09HRyctqyZcukSZOo1gsAAPJk7tkiPXv2vHr1qpkrBQAAmTB3VisqKrKxsTFzpQAAIBN0r0AuXLhQ88+qqqq8vLyQkBCOt1RXV3/33Xd79+4tKSnZsGHDmDFjuKvYvXt3fHz8sGHDNm/ebIKIAQBAzOhmtfLycs0/27Rps3z58rFjx3K8JSsrq6SkJC4uLjg4uN71X716ddeuXVp37wAAQLaoZLXVq1cvXbqUEDJ37tyGppwpU6bwXLK6unrevHmxsbFffvllg0MEAAAponJfbc+ePcyzjMeNG0dj/YzY2Nj+/fsPGjSIXhUAACAuVM7V2rVrd+7cud69e9NYOePQoUOXL1/OysriubxSqWRe4AvgAAD8sQdPsaCS1SZOnDh58mQrKytCiJubm+4CJSUlxqz/3r17cXFxaWlp/KdTIpkBABhA8+ApigxHJatFRkYOGTLk9u3b8+bNW7duncnXX1JS8vjxY63pJEql8uTJk87OziavDgAAxILWHEh3d3d3d/fjx4/XOzXfAAEBAZofH/71r381a9YMM/sBAIDut7ATExM1/3z9+rUxa1OpVD4+PsZFBAAAUkY3q92/f3/Tpk3Ma5VK5enpyVyZ5HhLfn6+Uqlkrt5GR0crlcqYmBiqQQIAgGQomCn4lMyZM2fEiBHDhg37/fffAwICFi9e/PPPP9fW1pr5aqFSqcRsERAaRdTJOsvVCYMVUSfVCYPNHA9AvURxLKV7rnbmzJl+/foRQvLz8/v37z958uQlS5YUFhZSrRQAAGSLblZ79eoVcy547tw5X19fQkiLFi1evHhBtVIAAJAtulnt3Xff3bJlS35+/pEjRwYOHEgIKS0tfffdd6lWCgAAskU3q0VHR3/zzTdhYWEjRoxgktmePXv4P+kRAACgQeg+s79Xr14//fTT8+fPbW1tmZJZs2Z169aNaqUAACBbdLMaIcTa2ppNaYQQV1dX2jUCAIBsUc9qr1+/vnPnzuPHjzULqT74GAAAZItuVisqKoqMjHz48KFWufC/8QAAAGJEN6utXr3a19d35syZmhchAQAAKKGb1W7cuJGWlta6dWuqtQAAADDozux3cHB49eoV1SoAAABYdLPaqFGjPv/8c6qPmgQAAGDRvQJ5/vz5goKC3NxcFxcXzdyWlpZGtV4AAJAnulnNwcEhMDCQahUAkoTH9gMYhm5WS0hIoLp+AAAATdS/hU0IefDgwY0bNwghXbt2dXJyMkONAAAgT3Sz2suXL2NjY7OystiS4ODg2NjYpk2bUq0XAADkie4cyMTExLy8vPj4+KNHjx49enTt2rV5eXmJiYlUKwUQL+aHsC0dBYCI0T1XO3z4cEJCQp8+fZg/XVxcnJ2do6KiFi1aRLVeAACQJ7rnapWVle7u7polPXr0qKyspFopAADIFt2s5uTklJeXp1ly6tQpTBgBAABK6F6B/PDDDxcvXnzlyhVvb++3b98WFRWlp6fPnTuXaqUAACBbdLNaaGiolZVVSkrK9u3bCSFt2rSJioqaNm0a1UoBAEC26GY1hUIREhISEhJSXl5OCHFwcKBaHQAAyJw5voVNkM8AAMAs6M4WMUB1dfW+ffuCgoKUSuWhQ4f0LVZcXDxnzpz+/fv7+flNnz69uLjYnEECAIAwUTlXmzRpEiEkIyODeaErIyND33uzsrJKSkri4uKCg4M5qkhKSgoODo6JibGyskpMTAwNDf3uu+8cHR2NjBwAAESNSlZzdXXVesHflClT+Cy2bds29vWyZcuysrJ+/PHHsWPHNrQ6AACQEipZbeXKlVovqHr69Gltba2tra0Z6gIAACGje19t06ZNPAuNsXr1aicnpwEDBph2tQAAIDp0s9rWrVt5Fhps48aNp06dSkpKsrGx4VhM+ScTVg0AIHlKDZaOhRczzexnlZWVmfBSoUql2rNnT2pqqqenJ/eSpaWlpqoUAEA+NA+eokhstLLa1KlTtV4QQmpra2/duuXr62uSKlQqVVpaWmpqau/evU2yQgAjKaJOMj8lo04YLNUaAQSOVlbr1KkTIeTs2bPMC0bjxo0HDx48ceJEw9apUql27dp17tw5QkhKSgpSGgAAaKGV1eLi4gghjRo1aug0yPz8/LCwMOZ1dHR0dHT0uHHjmLVpSklJef369eTJk9mS2bNnR0REGBc1AACIG937agbM7O/fv7++e2ARERFs3rpy5YpRkQEAgBRRny2Sk5Pz7bff3r9//82bN2zh4cOHadcLIHmKqJOWDgFAcOjO7M/IyIiJienQocO1a9cGDhzYokWLX3/9td75igAAAIahe66Wnp6ekJDg7+//5ZdfLlq0iBCyfv3633//nWqlAAAgW3TP1X777be+ffsSQqytrWtqagghYWFh+fn5VCsFAADZopvVXr16xTzyw97e/t69e4QQKysrJr0BAACYnJmeLeLn57du3bpJkyZ98803PXr0ME+lAAAgN3TP1WbPns28mDdvXkVFxSeffHL58uVly5ZRrRTAIjAjEUAI6J6rsV8vc3Z2zs7Orq6ubt68OdUaAQBAzuieq2lBSgMAAKqonKtNmjSJe4GMjAwa9QIAgMxRyWqurq40VgsAAMCNSlYz4PGPAAAAxjPrfTUAAACqzJHV7t69e+zYsS+++IIQUlZWZoYaAeQD3ygA0ER3Zn9NTc2KFSsOHTpkbW395s2badOmrVy5cvz48f7+/lTrBQAAeaJ7rrZ27drS0tKMjIxLly4xJSEhITt27KBaKQAAyBbdc7WcnJy9e/d269aNLXFzc2MzHAAAgGnRPVerrq52cHDQLKmtrbWywhQVAACggm6CcXV13b9/v2ZJQUEBnm4MwE2dMNjSIQCIFd0rkGFhYfPnz7906dKgQYMIIZmZmRs2bIiPj6daKQAAyBbdrDZ69OiamppNmzYdPXqUEPLZZ59FR0cPGTKEaqUAACBbdLPaL7/8MmHChPHjxz948ODt27fOzs64qQYAAPTQzTGBgYGEEIVC4ezs/Ne//hUpDQAAqKKbZtq1a1dRUUG1CgAAABbdrBYcHKxSqd68eUO1FgDLUkSdFMJjq4QQA4DF0b2vVlRUVFhYePz48S5dujRp0oQtT0tLo1ovAADIE92s5ujoyNxao6G6uvq7777bu3dvSUnJhg0bxowZQ6kiAAAQC7pZbdasWd27d6e08qysrJKSkri4uODgYEpVABhMEXVS35epOf7LtGsAkCG6WS0wMLC0tJTSyqdMmUJpzQAAIFKYAwkAANKBOZAAACAdcpkDqVQqmRf0rogCEEyvB8lhD55iIeI5kA2CZAYAYADNg6coMhzKvF7VAAAgAElEQVTdrJaQkEB1/QCyhZNCgDrRzWqMBw8e3LhxgxDStWtXJycnM9QIAADyRHe2yMuXLxcvXuzv7//RRx999NFH/v7+ixcvfvnypUlWnp+fr1QqmTPi6OhopVIZExNjkjUDCAROyAAaiu65WmJiYl5eXnx8vI+PDyGkqKgoISEhMTFx0aJFxq+8f//+uFsGAACa6Ga1w4cPJyQk9OnTh/nTxcXF2dk5KirKJFkNAABAC90rkJWVle7u7polPXr0qKyspFopAADIFt2s5uTklJeXp1ly6tQpTBgBAABK6F6B/PDDDxcvXnzlyhVvb++3b98WFRWlp6fPnTuXaqUAACBbdLNaaGiolZVVSkrK9u3bCSFt2rSJioqaNm0a1UoBAEC26GY1hUIREhISEhJSXl5OCHFwcKBaHQAAyBzd+2qPHj1iXjg4OLAprbi4mGqlAMKHL6IBUEI3q82aNaumpkaz5ObNm+Hh4VQrBQAA2aKb1Ro1ahQdHa1Wq5k/79+/HxYW9v7771OtFAAAZItuVktOTr527dq6desIIeXl5aGhoR4eHmvWrKFaKQAAyBbd2SJ2dnapqakTJ060t7f/9ttvnZ2dN27caG1tTbVSAACQLbrnaoSQLl26qFSqpKSkZs2apaSkNG3alHaNAAAgW1TO1aZPn65VYmtrq1arZ8+ezfxp/t/CBgAAOaCS1dq2batV0q9fPxoVAQiQOmEwJu4DWAqVrIafwAYAAIugfl8NAPhQJwy2dAgAUkB3DiTjwYMHN27cIIR07doVD+wHAAB66Ga1ly9fxsbGZmVlsSXBwcGxsbGYCQkAADTQvQKZmJiYl5cXHx9/9OjRo0ePrl27Ni8vLzExkWqlAAAgW3TP1Q4fPpyQkNCnTx/mTxcXF2dn56ioqEWLFlGtFwAA5InuuVplZaW7u7tmSY8ePSorK6lWCgAAskU3qzk5OeXl5WmWnDp1ChNGAACAErpXID/88MPFixdfuXLF29v77du3RUVF6enpc+fOpVopAADIFt2sFhoaamVllZKSsn37dkJImzZtoqKipk2bRrVSAACQLbpZTaFQhISEhISElJeXE0LYn8MGAACgge59tU2bNjEvHBwc2JTGFgIAAJgW3ay2detWnoWasrOzAwICPDw8Ro0adeLEiTqXqampiYuLGzRokIeHx5AhQ5KSkmpra00QMQAAiJm5nwNZVlZma2vLsUBeXt6SJUs+/fTT/Pz8sWPHRkREFBcX6y62cePGI0eOpKSknDt3bs2aNbt372Zu3QHIE34lAIBB677a1KlTtV4QQmpra2/duuXr68vxxh07dvj7+wcFBRFCpk+ffvjw4V27dm3YsEFrseLi4vfff5/5Mpyfn5+Pj8+VK1dMvA0AACA2tM7VOnXq1KlTJ/YFw9XVNTw8fN26dfrepVarL1y44Ofnx5b069fv/PnzukuOHDkyLy+vuLj45cuXhYWFFy9eDAwMpLEhAAAgIrTO1eLi4gghjRo1WrlyJf93PXv2rKamxs7Oji2xs7N79OiR7pJTpky5e/ducHAwIUShUERFRQ0bNoxjzUqlknlRWlrKPx4AAJljD55iQXdmf1hY2O3bt3XLXVxcjFzz+vXrv//++6+//lqpVF68eDEyMrJJkyYhISH6lkcyAxoUUSeF9rtoAgwJRE3z4CmKDEc3q+k7f9KXY1q2bGljY6P5oMjKykp7e3utxd6+fZuenh4VFeXl5UUI6du378SJE3fv3s2R1QAAQA7oZrXMzEz2tVqtvnnz5saNGz/++GN9yysUCi8vr7Nnz7L56cyZM97e3rqLWVtba5ao1WorK/yuNwCA3NHNBD01eHp6BgUFffbZZzk5ORxvCQ8Pz83Nzc7Orqqq2rlz59WrV0NDQ5n/UqlUPj4+hBCFQjF06NBdu3ZduHChpqbmzJkz+/bt476vBgAAckD3XE1Xz549r169yrHAwIED4+Pjk5OTly5d2rlzZ5VKpfVbNowVK1YkJSXNnTu3oqLC0dFx8uTJs2bNohY1AACIg7mzWlFRkY2NDfcyQUFBzPfVtERERERERDCvW7ZsGRMTExMTY/oQAQBAtOhmtYULF2r+WVVVlZeXhzkdAABACd2sxjyqn9WmTZvly5ePHTuWaqUA5oRHVQEICt2slpaWRnX9AAAAmiwwG/7169fmrxQAAOTArFnt6tWrcXFxAwYMMGelAAAgH+aYA/nf//730KFDWVlZ165da9++/ahRo8xQKYDF4eFVAOZHMavV1tb+8MMPBw8ePHnyJCHk9evXX331lZeXl0KhoFcpAADIGZWsduPGjQMHDhw6dKi8vLxXr14xMTGjRo3y9fXt1asXjeoAAAAYVLLayJEj7e3tP/jggzFjxhj/eH4AAACeqGS1Dh06/PHHHwUFBR06dLC3t2/VqhWNWgAAALRQmQOZm5u7ffv29u3br1q1qn///v/+979PnDhBoyIAAABNVM7VrKysBg4cOHDgwKqqqsOHDx84cOCTTz4hhGzevHnEiBHdu3enUSkAAADd76vZ2tpOmjQpMzPzu+++CwsL++qrrwIDA0eOHEm1UgAAkC0zfQu7e/fuixYtysvLS0lJwfwRAACgxKy/RGNtbT1kyJAhQ4aYs1IAAJAPCzwHEgAAgBJkNQCKTP47NfjhGwBuyGoAVOAJkAAWQTer/fLLL1TXDyBeSHsANNDNaoGBgVTXDwAAoIluVmvXrl1FRQXVKgAAAFh0s1pwcLBKpXrz5g3VWgBEBD+6BkAV3e+rFRUVFRYWHj9+vEuXLk2aNGHL09LSqNYLYBHqhMGYowhgWXSzmqOjI26tAQCA2dDNagkJCVTXDwAAoMkc31e7e/fusWPHvvjiC0JIWVlZvctnZ2cHBAR4eHiMGjWK4ydsysrKFixY0KdPn759+8bFxVVXV5syaACxYa9/4iooyBndrFZTU7NgwYKAgIA5c+bExcURQlauXJmbm8vxlry8vCVLlnz66af5+fljx46NiIgoLi7WXezJkycffPBBVVVVVlbWyZMn33nnndOnT9PaDAAAEAm6WW3t2rWlpaUZGRmXLl1iSkJCQnbs2MHxlh07dvj7+wcFBdna2k6fPt3NzW3Xrl26i23btu3Vq1eJiYnOzs7NmzefNGlSQEAAjU0AAAARoZvVcnJyEhISevXqZW1tzZS4ubmxGU6XWq2+cOGCn58fW9KvX7/z58/rLvn9998PHTrUxsbG5DEDCBwuMAJwoJvVqqurHRwcNEtqa2utrPRW+uzZs5qaGjs7O7bEzs7u0aNHukvev3+/bdu2M2bM6Nmzp7+//9q1a3FfDQAA6GY1V1fX/fv3a5YUFBT06NHD+DWr1ert27cHBwcXFBQkJSXl5OQw9+30Uf7J+KoBAORDqcHSsfBCd2Z/WFjY/PnzL126NGjQIEJIZmbmhg0b4uPj9S3fsmVLGxubyspKtqSystLe3l53yXbt2nl4eIwYMYIQ4unpGRISkpyczJHYSktLjdoSAABZ0jx4iiKx0c1qo0ePrqmp2bRp09GjRwkhn332WXR0NMdvYSsUCi8vr7Nnz4aEhDAlZ86c8fb21l3Sx8fn5cuXmiUcFzYBAEAmqGeCCRMmnD59+uTJk8ePH8/Pzx83bhz38uHh4bm5udnZ2VVVVTt37rx69WpoaCjzXyqVysfHh3k9ffr0H3/8MScnp6am5tKlS7t378ZDTAAAgO65GkOhUDg7O/NceODAgfHx8cnJyUuXLu3cubNKpXJ3d9ddzNPTc/PmzYmJidHR0e3btx8zZszs2bNNGjUAAIgPlax248YN7gW6du3K8b9BQUFBQUG65REREREREeyf/v7+/v7+hkUIYDZ4SD+AOVHJaiNHjuReAHM3AACABipZ7eDBg8yLoqKixMTEjz76iJnxcf78+dTU1Hnz5tGoFAAAgEpWY7+RtnTp0g0bNrDXCf38/JRK5ZYtWyZPnkyjXgAAkDm6cyCvX7/u6+urWeLr64vLjwAAQAndrNaqVauCggLNkoKCgtatW1OtFAAAZIvuzP6JEydGR0eHhYX16tWLEFJUVLRz586wsDCqlQIAgGzRzWqRkZEtW7ZMTU3dsmULIaRNmzazZ89GVgMAAEroZjUrK6uPPvroo48+Kisrs7Ky0np+P4CR8FUwYcJ+AQsyx7NFCCGOjo7mqQgAAOQMTwQGAFPCj5qCZSGrgbFwFAOBQFcEgqwGIoXjl/BhH4FFIKsBGELgh2yBhwdAD7IamAYOo2BB6H7AojsHss6fpGnatKmjo2Pjxo2pVg3mh/ncYHHohEA3q+n7SZqmTZuOGzduyZIljRqZ6asFAAAgB3SvQC5fvrx169bz58/fs2fPF198MX/+fFtb24ULFy5evPjIkSM7duygWjvIhIiuPhkQqki3TkRhg8TQPVU6cODAxo0bBwwYwPzZp08fV1fXzZs3HzhwoEOHDhs2bJg5cybVAADES50wGLkBoKGo/xIN83uhLB8fH+aXaHx9fR88eEC1dqCNPeaa+eCLYz1wQw+RM+q/RFNYWKhZUlhYaGtrSwipqKj4y1/+QrV2AGkQ0TFaRKGCVNG9Ajl+/Pj58+eHhoZ6enoqFIpLly7t2LFj6tSphJCsrKzg4GCqtQOADCGzyhzdrDZnzpxWrVpt27atqqqKENK6detZs2aFh4cTQkaPHv3OO+9QrR1Ahti7cZjjDvJE/ZdoZsyYMWPGjLKyMvJ/n9zfvXt3qlUDAIAMmenZIo6OjvgxGoYi6qQAr5Cwn+4tGwDImaX6gMU7PwdhRiVw1L8EnZOT8+23396/f//Nmzds4eHDh2nXC5bS0AtfBl8ow4CXJLP1H5AquudqGRkZMTExHTp0uHbt2sCBA1u0aPHrr796enpSrRSkzTzJTFwp04DDutk2UEQtKaJQgQPdrJaenp6QkLB8+XJCyKJFi/bt2xceHv7ixQvud2VnZwcEBHh4eIwaNerEiRPcC+/evVupVEZGRposaGowZnShTQDqhWHSIHSz2m+//da3b19CiLW1dU1NDSEkLCwsPz+f4y15eXlLliz59NNP8/Pzx44dGxERUVxcrG/hq1ev7tq1q2fPniaPHAwjq+En9o0VVPzGByOozQELopvVXr16ZWNjQwixt7e/d+8eIcTKyopJb/rs2LHD398/KCjI1tZ2+vTpbm5uu3btqnPJ6urqefPmxcbG2tnZUYgdzIf/M0pMcuTinh0gt4NjndvLNhGu94LomGkOpJ+f37p1606cOLFy5coePXroW0ytVl+4cMHPz48t6dev3/nz5+tcODY2tn///oMGDTJ9uGaBkQwA+uD4YDC6WW327NnMi3nz5lVUVHzyySeXL19etmyZvuWfPXtWU1Ojee5lZ2f36NEj3SUPHTp0+fLl6Ohok8cscxhLYGbocmBadGf2Dx8+nHnh7OycnZ1dXV3dvHlz41d77969uLi4tLQ05vImH0qlknnBPFvZUjCABQhTwzWhNUALe/AUC7rnaoGBgZp/1pvSWrZsaWNjU1lZyZZUVlba29trLVZSUvL48ePg4GClUqlUKk+dOnX06FGlUnn//n19ay79U8M3QuJklWgbet9Oko1jwK+gSbId9JHVxvJRqsHSsfBCN6u1a9euoqKC//IKhcLLy+vs2bNsyZkzZ7R+y4YQEhAQoNnQgwYNGjZsWGlpqbOzs2nipk/II8c8RzqBtIClfkxHaIS2+bLqhLoEG5go0M1qwcHBKpVK86ki9QoPD8/Nzc3Ozq6qqtq5c+fVq1dDQ0OZ/1KpVD4+PlQChf8LM98AQKTo3lcrKioqLCw8fvx4ly5dmjRpwpanpaXpe8vAgQPj4+OTk5OXLl3auXNnlUrl7u5ONUhRwN0O4+kmUaRVTehjhGaXQPOaDd2s5ujoqHVrjY+goKCgoCDd8oiIiIiICN3ybdu2GRKcCAlnYAgwHxjfOALcKLEwVc807S7gHxXVXS+cYSsTdLNaQkIC1fUDgEBwfJvbDFWzvyoHQPe+2qZNm3gWghjhUCJh2LMmhyY1D7pZbevWrTwLpc2Evdnkl2hMuDYQO/QHQZHD90xoMNMTs1hlZWW2trZmrhQkDwO+QRrUXGhbEBda99WmTp2q9YIQUltbe+vWLV9fX0qVgnAYcIcc92CgQWS1E2W1sUaida7WqVOnTp06sS8Yrq6u4eHh69ato1SpJMmwNwtqkwUVjMTQnnlIb+XGEGxgkkHrXC0uLo4Q0qhRo5UrV1KqQs4wV1gyZH7iKO1tN/k4xcDng+59NaS0ekl7VAsEGtkkBNWMggqGP/P8gqDMmWO2yN27d48dO/bFF18QQsrKysxQo7RR6vcGr1Y4Hx4FfkTQ90FbOA0IQiDwbix8dLNaTU3NggULAgIC5syZw1yTXLlyZW5uLtVKQVZ4XpPBkQJAJuhmtbVr15aWlmZkZFy6dIkpCQkJ2bFjB9VKgQ9F1Emqj7wz+H9pvFGwFcmHYU1qwR2BPiBedLNaTk5OQkJCr169rK2tmRI3Nzc2w4FANPQWtEUGPI4yIC7osZZCN6tVV1c7ODholtTW1lpZmfur3+Ilt4Eh8wmBDSWKG3LYp2BmdBOMq6vr/v37NUsKCgp69OhBtVIQPuEf5oR5LMbEbl0GN4g5968A+5KE0c1qYWFhGzZsiIyMPHDgACEkMzNzxYoV4eHhVCuVKvw8mBghCckQBqZl0c1qo0ePXrVq1c8//7xkyRJCyGeffRYdHT1kyBCqlQqTGDu6GGOmQTLtYOYNEXJGl8w+BV10f1+NEDJhwoTx48c/ePDg7du3zs7OuKkGJmSq64QNfTiklB4mKZkNERQ0qQWZI8coFApnZ2eFQnHnzh21Wm2GGsF4lh2WOCjIGfY+GINWVsvMzJw5c+aMGTNycnJqa2vnzJkzZMiQ4cOH//Of/6yoqKBUKRhAyJeJRATNKATS2ws4kzYAlayWnp4eExNTXl7+6NGjOXPmrF69uri4ODY2NjY29unTpyqVikalwkS7R6LHs6ge0fS1s/QOoyBwGPL1onJfbe/evatWrZowYQIhZN++fcuWLdu/f7+npych5N13342KiqJRKYgaPpNaltDan2o8gtpSA+ALHtyonKvdvXs3MDCQec28cHNzY/7s0aMHHnDMR4OeaCXYUSrYwMRO5gc1wV4CkcCYlQAqWe3Vq1fNmzdnXjMvGjduzPzZtGnTN2/e0KhUjHj2bLl9NJPVxgI3qkd/oZ2hgklgnn2DMcNAOINBOJGYlpS2y1RfPzB+JQKJwZj1CKEd+DP4I6nxn+2EdqQyG1rfV/Py8uL4E/jDx0mQJOH0auEPMeFHKChUstqMGTNorFYITN63mP5qkmtuwr9QaYYItargUyMOGVq4v2NuQAubJB6qVRhJ+BHKCpWsNn/+fGPenp2dnZyc/Pvvv3fu3HnevHl1PmGruLg4NTX17Nmzb9688fDwiIqKcnd3N6bSBmEHvBh7s5ExIwGImqV2nwk/vTWUMfXyf6+gxoUYj0smJLj7anl5eUuWLPn000/z8/PHjh0bERFRXFysu1hSUtLw4cO/+eabnJwcJyen0NBQ2lMrBdVrgQP2FA0yP1CKjtYokNWgEFxW27Fjh7+/f1BQkK2t7fTp093c3Hbt2qW72LZt24YPH+7g4GBvb79s2bLnz5//+OOPtGOTVc8AfUTUDcwTqogaRA6wO4SV1dRq9YULF/z8/NiSfv36nT9/nvtdT58+ra2ttbW1pRydgSh9yNW3Wqp9ukErr3NhDDmBs/gJmWkDMLi/8bzbiv4sQMLKas+ePaupqbGzs2NL7OzsHj16xP2u1atXOzk5DRgwgGMZ5Z9ME6ipmXZsSG+kmWoiuMUP2SZX7xYJqjMIKhiezBYzjYpMsk6lBuPXZgbCymoG2Lhx46lTp5KSkmxsbDgWK/2T2QKjSnpHZ/NDG4qIGNMhB3FtTqkGS8fCi7CyWsuWLW1sbCorK9mSyspKe3t7fcurVKo9e/akpqYyD5k0s3q7pvHX6ygxvi7dlEAvSYjrECBJWjsXewSETFhZTaFQeHl5nT17li05c+aMt7d3nQurVKq0tLTU1NTevXubK0AAA8kqE8j2PBjffRQCYWU1Qkh4eHhubm52dnZVVdXOnTuvXr0aGhrK/JdKpfLx8WFep6SkmC2libSbCids4UQCRFQpRzdU4fQl4UTCnxhjNoDgstrAgQPj4+OTk5P79++fmZmpUqnq/Hp1SkpKdXX15MmT2duYFvzZNuH0FSMjEeDxzrJtK8AGMRjVL5w1aM3CGS8Go7QJRq6W+4c+JNDsPNF6DqQxgoKCgoKCdMsjIiIiIiKY11euXDFnSMLvENxPObI4jkOqkMMG4ZBYJzHbw1ZkOL4Ed64GUiWWocV9oBHLVgiWCRtQIGfS6BJCg6xGl6UGnklGmgw/5XFgm0IgB9MGMWw/8vkynBhbw1REtPlsnHIY0chqFiOW8WAkOYwiAZJJ7xImtvGxFyxC1lnNzA+XEmkXF2ZaEmljgjkxnUTrkoMw+3NDcU8MMcn66a2cNvlmNcHuNsEG1iCm+sU4i7y3oWSYYqXRSy2OTU40LmbKsFsy5JjVTPsbDQIf3pgZbxHmmdvGczFhTkO3CONjFuNWN4gEzmvlmNUI770l0p2qD/PBULaZxngS6w/An5R2vZS2pU4yzWos0z7L0XiCfW63MQy7eW6R7Gt8peYPGx9TTEvIDzShTRpbKvesJh8N6q/iPVAK5PEZBr/Fgqs1npGBcXxP3/iVm5AEDv3cmyD2DURWo4JStxDOwG4ozcjFuxXiIsB2ppT2ADTJK6tRfUia0D7g1DtNwMzHCHNWJ/DnhzWIoM4+LUX4164tjk9vN+y5OaIbR/LKakQMe0jsh2NJHlMsvlHGT/Ox+CaImu6obGh7Crz9RX3M0SK7rFYn6Z2ogQG47+sY/HbzMKb2Bk3nMeFmWrDFhFM1/0+xHDEbmXH5rFNEkNXq1qB+JvBPYXImkG+2ireHCO2MhN6Iq3OdovhAYxjxJq16IavpZeaHU5jqwiON4ziN56wzm2yq1RpJaMduU6F6O8o8jSCopjbD1z0Ftb0ihawmXPz7t3BGgm4kQogNMUgJ1ZYUwm6qNwYhBClkyGr/p4vUeVIiuj5U59dIjdwK4VyvMGzMG7z5VL+X3dBQTRiMcHq12SIRTh8WCLZB9LWMSGeuySWrGb9vdO/xNmh5I6vjuVrhHKoswiKHbJPcadO9XSSKG3imusslkNufxtQl3qHH59hI+ycCTEsuWY3Ut/PYTyW095957ifxTLoNioQ54TNJ8AafTmmGbVgOkMYUPm6mDcywGRMN7WC0r13TeLaO+TuAyUcfx1maaSs1JxllNV2UzreMSYoG1Mj/7M2YsWrywEy1NpPMaAcTEv4sEmnsd5FeHjQDWWS164FbTbg2jsMr//M8sXwUojqJzszEOPuGNmm0Cf+zfJ4Lm4TxHwT5rEFc1wbNQxZZzYQMOMqbKoHRG411RtigsA0YjcYsbzwhH6MFwiJNZEzP4dNLdZfnvwaTDF5TpToaly4kA1nt/6B3Pd2Cvc1UVdPYBIsPTpkcBUx+zk11hoioJ48YhtLdENM2siLqpGmve1GCrGY4kw/LBt0wN/L0SCwEOL/OSEae7lsWvblCgsX/NrMBp31G7l/zfzJw/e5j066WBmS1ugn/jrcxFRk5H0QsNwVBhgz7tMdzREjvEoIFt5EemWY1Ue85UQdvTmgoStCw/ImlrcQSJx8yzWp14rgaUO9/cZcYFonxS5q8pyqVStOuUFyMbE/Ntze0JYU5z0ggzNwtTTXoTLtfOCak1DvBRGgXuo0ki6ymeS1YXdf3iE2YhwTeM0wYHqUtFc4lEYHvSmMIZ+6SeWb2CmdVJqd5QDM+Tt3bZkLedn1kkdVIA+/KinFHSpJYPisAH7gdKzTGfI9CyOSS1XTVm+fENX0fAGTLtPlJ7BckFWq12tIxUCf2u0HXA7eKYkItAHCQxkAuLS21dAj1kEVWAwAAmZDvFUgAAJAeZDUAAJAOZDUAAJAOZDUAAJAOZDUAAJAOZDUAAJAOZDUAAJAOiWe17OzsgIAADw+PUaNGnThxwtLhCFpycrJSg4+PD/tfHM2IFmZUV1fv27cvKChIqVQeOnRI638NaEDZNixHS3J0UYKW1FFcXDxnzpz+/fv7+flNnz69uLhY83+l3CfV0vXDDz+4ubkdPHjwyZMnO3bscHNzu3LliqWDEq4tW7aMGzdOt5yjGdHCrD179ixZsuTKlSuurq7ffPON5n8Z0IBybliOltTXRdVoybrMmDEjJyfn4cOHFRUVMTExvXv3/uOPP5j/knaflHJWCwkJ+eSTT9g/g4OD58+fb8F4BE7fIYOjGdHCunSPxQY0IBpWXVdLcmQ1tCS3Fy9euLm5ZWZmMn9Ku09K9gqkWq2+cOGCn58fW9KvX7/z589bMCThu3btWq9evfr27Ttjxozr168TzmZEC/NhQAOiYTnodlGCluTh6dOntbW1tra2RAZ9UrJZ7dmzZzU1NXZ2dmyJnZ3do0ePLBiSwDk4OMTHx586dSozM7NVq1YffPDBgwcPOJoRLcyHAQ2IhtWnzi5K0JI8rF692snJacCAAUQGfVKyWQ0aasKECaNHj7a1te3YseO6detatGixb98+SwcF8P+hixpm48aNp06dSkpKsrGxsXQs5iDZrNayZUsbG5vKykq2pLKy0t7e3oIhiUjjxo07d+58584djmZEC/NhQAOiYflguyhBS3JSqVR79uxJTU319PRkSiTfJyWb1RQKhZeX19mzZ9mSM2fOeHt7WzAkEXn9+vWdO3ccHR05mhEtzIcBDYiG5YPtogQtqZ9KpUpLS0tNTe3duzdbKP0+aaFZKuagORU1LS1NyFNRhWD27Nlnz559+vTp3bt3586d++BR3A8AAAG0SURBVLe//e3GjRtqzmZEC+vintnPswHRsOq6WlJfF1WjJeuSnJzs5eVVWFio+1/S7pNSzmpqtfrgwYNDhw51d3cfOXLk8ePHLR2OoJ07d2769One3t7vvffexx9/fP36dfa/OJoRLcw4ffq06/+1ZMkS9n8NaEDZNixHS3J0UTVaUoe7u7tWS27evJn9Xwn3SfwWNgAASIdk76sBAIAMIasBAIB0IKsBAIB0IKsBAIB0IKsBAIB0IKsBAIB0IKsBAIB0IKsBAIB0IKsBAIB0IKsBAIB0IKsBAIB0NLJ0AADyFRUVVV5e7u3tffjw4fLy8m7dui1fvpz9HSwAMADO1QAsqaCgoKqqKiMjIzc3t2PHjrNnz37z5o2lgwIQMWQ1AEtydnZeunRpu3bt2rZtO2vWrLKystu3b1s6KAARQ1YDsKTOnTtbWf3vMGzdujUh5PHjxxaNCEDckNUALEmhUFg6BABJQVYDAADpQFYDAADpQFYDAADpUKjVakvHAAAAYBo4VwMAAOlAVgMAAOlAVgMAAOlAVgMAAOlAVgMAAOlAVgMAAOlAVgMAAOlAVgMAAOn4f+YNcukl67aLAAAAAElFTkSuQmCC"
     },
     "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": 10,
   "id": "798d77d1-1d91-4747-a301-9bbf9eba937d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 10,
     "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": 11,
   "id": "8655d4b7-3fcb-4a08-a3f1-df9f216e2cce",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VAADqQaoBANSDVAMAqAepBgBQD1INAKAepBoAQD1INQCAepBqAAD1INUAAOpBqgEA1INUAwCoB6kGAFAPUg0AoB6kGgBAPUg1AIB6NItUu3LlyuLFi4OCgnx8fEJDQ/fs2SNXpaSk6Az069fPcMb09PRhw4Z5eXmFhIQcPHiw0TsOAGheWjd1B4QQ4tNPP9XpdK+88oq9vf3nn3/++uuvOzo6Dh48WKr19vbevn37g3NlZGTExcUlJCQEBwenpaXFxMRs377d09OzcfsOAGhGmsWx2syZM0eNGuXi4uLg4BAeHu7i4nL8+PFa50pNTQ0KCgoNDdVqtVFRUR4eHhs3brR8ZwEAzVezSDVZeXn5rl27bty4ERwcLBeeOnXK19d34MCBkydPPn36tFSo1+vz8vL8/f3lyQICAo4dO9bYPQYANCfN4gykEOKnn34aMWKEEKJNmzaLFy+WTyQ6OzsnJCQEBgaWlpYmJSWNHTt27969rq6uZWVlFRUVjo6O8hIcHR2vXbtW0/J1Op30orCw0JKfAwBURd55thTNJdV69+5dWFhYWlq6f//+N998097efujQoUKI8PBwaQKtVrt06dLg4OBt27bNnDmzrssnzACgHgx3ni0i4ZrXGUitVjtmzJjAwMCtW7c+WGtra+vm5lZUVCSEcHBwsLOzKykpkWtLSkqcnJwar68AgOaneaWapLKysqbyoqIiFxcXIYRGo/Hx8cnJyZFrs7Ky/Pz8GqmLAIBmqVmkWkxMzJEjR8rKyq5du7Zhw4aMjIywsDC5Kjc3t6ys7MKFC3Pnzr1586Z8TjI6OvrQoUPp6emlpaUbNmwoKCiIiIhoss8AAGgGmsV1tUmTJq1evTovL8/W1rZ3796rV68OCgqSqiIjI1NSUvLy8uzs7KQvrvXs2VOqGjJkSEJCQkpKSnx8vJubW3JyMl9WAwArp9Hr9U3dB4vT6XT1uFtEM/tr/bLg2qcDAOtQv31pI2sWZyABAFAEqQYAUA9SrW40s79u6i4AQB1Y216LVAMAqAepBgBQD1INAKAepBoAQD1INQCAepBqAAD1INUAAOpBqgEA1INUAwCoB6kGAFAPUg0AoB6kGgBAPUg1AIB6kGoAAPUg1QAA6kGqAQDUg1QDAKgHqQYAUA9SDQCgHqQaAEA9SDUAgHqQagAA9SDVAEC1NLO/buouNDZSDQCgHqQaAEA9SDUAgHqQagAA9SDVAADqQaoBANSDVAMAqAepBgBQj2aRaleuXFm8eHFQUJCPj09oaOiePXsMa9PT04cNG+bl5RUSEnLw4EEzqwAAVqhZpNqnn36q0+m2bt16+PDhl1566fXXXz98+LBUlZGRERcXN23atMzMzLCwsJiYmPz8/FqrAADWqVmk2syZM0eNGuXi4uLg4BAeHu7i4nL8+HGpKjU1NSgoKDQ0VKvVRkVFeXh4bNy4sdYqAIB1ahapJisvL9+1a9eNGzeCg4OFEHq9Pi8vz9/fX54gICDg2LFjpqsAAFartSUW+scffxQUFFy/ft2wMCQkxMQsP/3004gRI4QQbdq0Wbx4saenpxCirKysoqLC0dFRnszR0fHatWumqwAAVkv5VDt06NBrr71WXl5uVG461Xr37l1YWFhaWrp///4333zT3t5+6NChCvZKp9NJLwoLCxVcLACom7zzbCmUT7UlS5aMGzcuOjq6U6dOdZ1Xq9WOGTPmm2++2bp169ChQx0cHOzs7EpKSuQJSkpKnJychBAmqqpFmAFAPRjuPFtEwil/Xe3ixYvTp093cnKy+b/MX0JlZaX0QqPR+Pj45OTkyFVZWVl+fn6mqwAAVkv5VOvevftvv/1Wp1liYmKOHDlSVlZ27dq1DRs2ZGRkhIWFSVXR0dGHDh1KT08vLS3dsGFDQUFBRERErVUKssLf3AOgVtawQ1P+DOSUKVPi4+MXLFjg5ubWqtX/T822bdvWNMukSZNWr16dl5dna2vbu3fv1atXBwUFSVVDhgxJSEhISUmJj493c3NLTk6WbiQxXQUAsE7Kp9qjjz565syZ//qv/zIqN3Flq3///qmpqTXVhoaGhoaG1rUKAGCFlE+1+fPnu7m5hYeHa7VaxRcOAIAJyqfa6dOnDx486OLioviSAQAwTfm7RVxcXGxtbRVfLAAAtVI+1QIDA9esWaPX6xVfMgAApil/BrKwsPDIkSNfffVVjx49DLNt/fr1ircFAIAh5VPtL3/5i/RERwAAGpnyqbZs2TLFlwkAgDmUT7Vz585VW96jRw/F2wIAwJDyqfbss89WW87zhQEAlqZ8qqWlpcmv9Xr9L7/8kpSUNHXqVMUbAgDAiPKp1rdvX8O33t7erq6uK1euHDdunOJtAQBgSPnvqz2ob9++BQUFjdAQAMDKNUaqHT9+3M7OrhEaAgBYOeXPQM6dO9fwbWlpaUZGxqRJkxRvCAAAI8qn2pUrVwzfdurU6a233pJ/BRQAAMtRPtV4MhYAoKkof13tp59+UnyZAACYQ/lU4yGQAICmonyqdenS5erVq4ovFgCAWimfai+++GJycvK9e/cUXzIAAKYpf7fI8ePHc3Nzv/rqq0ceeaRNmzZyOXeRAAAsTflUc3Fx4dIaAKBJ8PtqAAD1UP662vLly80sBABAWcqn2urVq80sBABAWY3xdOPi4mKtVtsIDQEArJyS19VefvlloxdCiKqqqrNnzw4YMEDBhgAAqJaSqda9e3chRE5OjvRCYmtrGxwcPGbMGAUbAgCgWkqm2uLFi4UQrVu3XrhwoYKLBQDATMpfV5sxY8aDhfn5+Yo3BACAEeVTbcqUKRUVFYYlv/zyS3R0tOINAQBgRPlUa926dWxsrF6vl95evHgxMjLyb3/7m+INAQBgRPlUS0lJOXXq1NKlS4UQV65ciYiI8PLyeu+99xRvCAAAI8o/McvR0XHdunVjxoxxcnL6n//5n65duyYlJdnY2CjeEAAARizyLexHHnkkOTl5xYoV7dq1W7VqVdu2bS3RCgAARhQ7VouKijIq0Wq1er1++vTp0lsTv0STn5+/bt26nJyce/fueXl5zZ4929PTU6pKSUn58MMP5SkdHByOHj0qv01PT09JSfntt9/c3Nxee+21oUOHKvVxAAAtkWLHap0fEBAQ0L17d/mtiXlXrFgxfPjw3bt379+/39XVNSIiori4WK719vYu/JNhpGVkZMTFxU2bNi0zMzMsLCwmJobvDwCAlVPsWK0hP0Czdu1a+fX8+fN37tx5+PDhsLAw03OlpqYGBQWFhoYKIaKiovbt27dx48bExMR6dwMA0NJZ6unG58+fP3DgwMcffyyEMDzwqtXNmzerqqoMn4Z86tQpX1/fgQMHTp48+fTp01KhXq/Py8vz9/eXJwsICDh27JhC3QcAtEjK3wNZUVGxYMGCPXv22NjY3Lt3b+LEiQsXLhw9enRQUJA5sy9atMjV1XXw4MHSW2dn54SEhMDAwNLS0qSkpLFjx+7du9fV1bWsrKyiosLR0VGe0dHR8dq1azUtVqfTSS8KCwsb8OEAwLrIO8+WQvljtSVLlhQWFm7ZsuXEiRNSyaRJk1JTU82ZNykp6ZtvvlmxYoWdnZ1UEh4ePnLkSK1W261bt6VLl9rb22/btq0evZKvzNVjXgCwWoUGmrovZlH+WG3//v2bN2/u1auXXOLh4SEnnAnJycmbNm1at26dt7d3tRPY2tq6ubkVFRUJIRwcHOzs7EpKSuTakpISJyenBncfANCCKX+sVl5e7uzsbFhSVVXVqlUtDSUnJ69fv37dunX9+/evaZrKysqioiIXFxchhEaj8fHxycnJkWuzsrL8/Pwa1ncAQMumfKq5u7tv377dsCQ7O/uxxx4zMcuqVatqirSYmJjc3NyysrILFy7MnTv35s2b4eHhUlV0dPShQ4fS09NLS0s3bNhQUFAQERGh6EcBALQwyp+BjIyMnDNnzokTJwIDA4UQaWlpiYmJCQkJJmZZtWpVZWXl+PHj5ZLp06fHxMRIS0tJScnLy7Ozs/P29t6+fXvPnj2laYYMGZKQkJCSkhIfH+/m5pacnCx/dxsAYJ2UT7WRI0dWVFQsX778yy+/FEJ88MEHsbGxpp/6cfLkyZqq/Pz8TNxpEhoaKn1fDQAAYYlUE0KEh4ePHj360qVL9+/f79q1a60X1QAAUIRFUk0IodFounbtaqGFAwBQLYukWmlp6WefffbTTz8JIdzd3ceMGdOhQwdLNAQAgCHlzw3m5+cPGzbso48+On/+/Pnz51evXj1s2LCCggLFGwIAwIjyx2rvvvvuoEGDFi9e3L59eyFEeXn5vHnz3nnnna1btyreFgAAhpQ/Vjt58uQbb7whRZoQon379m+88Qa/EQMAaATKp5r07A9zCgEAUJbyqfbss88mJCSUlZVJb8vKyhISEp555hnFGwIAwIjy19VOnDiRm5ubkZEhPeD4zJkzt27dGjBgQFRUlDTB+vXrFW8UAABhiVRzcXEZMWKE/Pbhhx9WvAkAAKqlfKotW7ZM8WUCAGAOiz/LqrKy0tJNAAAgUT7VLl68uHz5cul1cnKyt7f30KFDz507p3hDAAAYUT7VEhMTPTw8hBC//fbbmjVr4uPjvb29k5KSFG8IAAAjyqdaVlZWQECAECIzM3PQoEHjx4+Pi4vLzc1VvCEAAIwon2p3797V6/VCiKNHjw4YMEAIYW9vf/v2bcUbAgDAiPKp1qdPn5UrV2ZmZn7xxRdDhgwRQhQWFvbp00fxhgAAMKJ8qsXGxu7evTsyMvK5556TwmzTpk0TJkxQvCEAAIwo/301X1/f77///tatW1qtViqZMmWK9JwRAAAsyiLfV7Oxsblx48aBAwc+/vhjIUTHjh1btbL4F+MAAFD+WK2iomLBggV79uyxsbG5d+/exIkTFy5cOHr06KCgIMXbAgDAkPKHUEuWLCksLNyyZcuJEyekkkmTJqWmpireEAAARpQ/Vtu/f//mzZsNL6R5eHjICQcAgOUof6xWXl7u7OxsWFJVVcV1NQBAI1A+bNzd3bdv325Ykp2d/dhjjyneEAAARpQ/AxkZGTlnzpwTJ04EBgYKIdLS0hITExMSEhRvCAAAI8qn2siRIysqKpYvX/7ll18KIT744IPY2NihQ4cq3hAAAEaUTzUhRHh4+OjRoy9dunT//v2uXbtyUQ0A0DiUzxvpx9U0Gk3Xrl0ffvhhKdLkX1wDAMBylE+11atXm1kIAICyGuPcYHFxsfxMSAAALEfJ62ovv/yy0QshRFVV1dmzZ6UfWgMAwKKUTLXu3bsLIXJycqQXEltb2+Dg4DFjxijYEAAA1VIy1RYvXiyEaN269cKFCxVcLAAAZlL+ulo9Ii0/P3/mzJmDBg3y9/ePiorKz883rE1PTx82bJiXl1dISMjBgwfNrAIAWCGL3C1SWVl55syZI/+XielXrFgxfPjw3bt379+/39XVNSIiori4WKrKyMiIi4ubNm1aZmZmWFhYTEyMnHkmqgAA1kn5b2EfP358xowZly9fNiovLCysaZa1a9fKr+fPn79z587Dhw+HhYUJIVJTU4OCgkJDQ4UQUVFR+/bt27hxY2JioukqAIB1Uj7VFi1aNGDAgFdffbV+d/PfvHmzqqpKmlev1+fl5c2aNUuuDQgI2L9/v+kqAIDVUj7Vfv755/Xr13fs2LF+sy9atMjV1XXw4MFCiLKysoqKCkdHR7nW0dHx2rVrpquqpdPppBcmDhkBAEbknWdLoXyqOTs73717t37zJiUlffPNN//93/9tZ2enbK8IMwCoB8OdZ4tIOOXvFgkJCVmzZo1er6/rjMnJyZs2bVq3bp23t7dU4uDgYGdnV1JSIk9TUlLi5ORkugoAYLUUO1aLioqSXty7dy87O/vQoUM9evQwzLb169ebmD05OXn9+vXr1q3r37+/XKjRaHx8fHJyciZNmiSVZGVl+fn5ma4CAFgtxY7VOv/J2dl5xIgRPj4+nTp16mzAxLyrVq16MNIk0dEGJ9gZAAAUR0lEQVTRhw4dSk9PLy0t3bBhQ0FBQURERK1VAADrpNix2rJly+o976pVqyorK8ePHy+XTJ8+PSYmRggxZMiQhISElJSU+Ph4Nze35ORkT09PaRoTVQAA66T83SJ37tzJzc2VbmKUZGRk+Pv7t23btqZZTp48aWKBoaGh0pfS6lQFALBCyt8tkpKSYpRS+fn5H330keINAQBgRPlUS09Pf+GFFwxLXnjhhd27dyveEAAARpRPtT/++KN16/9zYrNVq1ZXrlxRvCEAAIwon2ru7u579+41LNm7d2/v3r0VbwgAACPK3y0SERHxxhtvFBUVBQQE3L9/Pzs7e+vWrTx0GADQCJRPtZEjR5aWliYnJ3/66adCiM6dO8+fPz8kJETxhgAAMKJ8qgkhxo8fP27cuIsXL2o0GldX11atLPIrbgAAGLFIqgkhWrVq9fDDD1to4QAAVEuxVBs3bpwQYsuWLdKLB23ZskWptgAAqJZiqebu7m70AgCARqZYqi1cuNDoBQAAjYz7OAAA6qHYsdrPP/9seoJHH31UqbYAAKiWYqn2/PPPm57A8GfCAQCwBMVSbdeuXdKL48eP/+tf/3rllVekX6Y+duzYunXrXnvtNaUaAgCgJoql2mOPPSa9iI+PT0xMDAoKkt76+/vrdLqVK1ca/igoAKCpaGZ/rV8W3NS9sBTl7xY5ffr0gAEDDEsGDBjA6UcAQCNQPtU6dOiQnZ1tWJKdnd2xY0fFGwIAwIjyT8waM2ZMbGxsZGSkr6+vEOL48eMbNmyIjIxUvCEAAIwon2ozZsxwcHBYt27dypUrhRCdOnWaPn06qQYAaATKp1qrVq1eeeWVV155pbi4uFWrVs7Ozoo3AQBAtSz1zH4hhIuLixCisrLS1tbWcq0AACBT/m6RixcvLl++XHqdnJzs7e09dOjQc+fOKd4QAABGlE+1xMREDw8PIcRvv/22Zs2a+Ph4b2/vpKQkxRsCAMCI8qmWlZUVEBAghMjMzBw0aND48ePj4uJyc3MVbwgAACPKp9rdu3f1er0Q4ujRo9LXse3t7W/fvq14QwAAGFE+1fr06bNy5crMzMwvvvhiyJAhQojCwsI+ffoo3hAAAEaUT7XY2Njdu3dHRkY+99xzUpht2rRpwoQJijcEAIAR5e/s9/X1/f7772/duqXVaqWSKVOm9OrVS/GGAAAwYpHvq9nY2MiRJoRwd3e3RCsAABhRPtWq/VHstm3buri48HVsAIBFKZ9qNf0odtu2bUeNGhUXF9e6tQUfaKIszeyvm7oLAKAk1e/WlA+Yt956a8WKFZMnT3788cf1ev2JEyfWrl07depUOzu75ORkFxeXV199VfFGAQAQlki1HTt2JCUlDR48WHr7xBNPuLu7f/jhhzt27PjLX/6SmJhIqgEALMQiv4Xt5+dnWNKvXz/pt7AHDBhw6dKlB2cpLy/ftm1baGioTqfbs2ePYVVKSorOQL9+/Qxr09PThw0b5uXlFRIScvDgQcU/CwCgZbHIb2EbPR8rNzdXuiXy6tWrf/3rXx+cZefOnf/5z38WL15c7QK9vb0L/3T06FG5PCMjIy4ubtq0aZmZmWFhYTExMfn5+Yp+FABAC6P8GcjRo0fPmTMnIiLC29tbo9GcOHEiNTX15ZdfFkLs3LnzxRdffHCW+n1HOzU1NSgoKDQ0VAgRFRW1b9++jRs3JiYmNrD/AICWS/lUmzlzZocOHdauXVtaWiqE6Nix45QpU6Kjo4UQI0eO7NmzZ10XeOrUKV9f37Zt2/bt2zc2Nlb69pter8/Ly5s1a5Y8WUBAwP79+5X7HACAlsciv4U9efLkyZMnFxcXiz9/O1TSu3fvui7N2dk5ISEhMDCwtLQ0KSlp7Nixe/fudXV1LSsrq6iocHR0lKd0dHS8du2aIh8BANBCWeSrY5WVlUVFRdevXxdCnD9/Xirs379/PRYVHh4uvdBqtUuXLg0ODt62bdvMmTPruhydTie9kO5bAQCYQ955thTKp9rx48dnzJhx+fJlo/KGx4mtra2bm1tRUZEQwsHBwc7OrqSkRK4tKSlxcnKqaV7CDADqwXDn2SISTvlUW7Ro0YABA1599VXDR0EqQjoE9PLyEkJoNBofH5+cnJxJkyZJtVlZWUbfKAAAWBuLPAdy/fr1HTt2VGRpMTExEydO9PDwuH79elJS0s2bN+VzktHR0a+++mp6enpwcPCOHTsKCgoWLlyoSKMAgBZK+e+rOTs73717t06zZGZmSl+yFkLExsbqdLp58+ZJVZGRkR999FFgYODYsWNv3769fft2+S7KIUOGJCQkpKSkDBo0KC0tLTk52dPTU9nPAgBoWZQ/VgsJCVmzZs28efM0Go2ZswwaNKim615+fn6pqak1zRgaGip9Xw0AAGGJVDt27Fh2dvahQ4d69Oih1+vl8vXr1yveFgAAhpRPNWdn5xEjRii+WAAAaqV8qi1btkzxZQIAYA7l7xYBAKCpKH+sdu7cuWrLe/TooXhbjUz1vyELAC2d8qn27LPPVlvO0z0AAJamfKqlpaXJr/V6/S+//JKUlDR16lTFGwIAwIjyqda3b1/Dt97e3q6uritXrhw3bpzibQEAYKgx7hbp27dvQUFBIzQEALByjZFqx48ft7Oza4SGAABWTvkzkHPnzjV8W1pampGRIT9ZHwAAy1E+1a5cuWL4tlOnTm+99VZYWJjiDQEAYET5VON5jwCApqL8dbXly5ebWdiC8P1rAC2a9ezElE+11atXm1kIAICyGuMeyOLiYq1W2wgNAQCsnJLX1V5++WWjF0KIqqqqs2fPDhgwQMGGAAColpKp1r17dyFETk6O9EJia2sbHBw8ZswYBRsCAKBaSqba4sWLhRCtW7deuHChgosFAMBMyl9XM4q0yspKxZsAAKBayqfaxYsX5fv4k5OTvb29hw4dWtOPrgEAoCDlUy0xMdHDw0MI8dtvv61ZsyY+Pt7b2zspKUnxhgAAMKJ8qmVlZQUEBAghMjMzBw0aNH78+Li4uNzcXMUbAgDAiPKpdvfuXb1eL4Q4evSodEO/vb397du3FW8IAAAjyqdanz59Vq5cmZmZ+cUXXwwZMkQIUVhY2KdPH8UbAgCYw3oelyUskWqxsbG7d++OjIx87rnnpDDbtGnThAkTFG8IAAAjyj+z39fX9/vvv79165b8lKwpU6b06tVL8YYAADCifKoJIWxsbAwf/Oju7m6JVgAAMKJYqo0bN04IsWXLFunFg7Zs2aJUWwAAVEuxVJMPyDgyAwA0FcVSTX5QlvoeAmlVtw8BQItmqd9XO3/+/IEDBz7++GMhRHFxsYVaAQDAkPJ3i1RUVCxYsGDPnj02Njb37t2bOHHiwoULR48eHRQUpHhbAAAYUv5YbcmSJYWFhVu2bDlx4oRUMmnSpNTUVMUbAgDAiPKptn///mXLlvn6+trY2EglHh4ecsJVq7y8fNu2baGhoTqdbs+ePUa16enpw4YN8/LyCgkJOXjwoJlVAAArpHyqlZeXOzs7G5ZUVVW1amWqoZ07d/7nP/+RfnTUSEZGRlxc3LRp0zIzM8PCwmJiYvLz82utAgBYJ+VTzd3dffv27YYl2dnZjz32mIlZJkyYsHjxYk9PzwerUlNTg4KCQkNDtVptVFSUh4fHxo0ba60CAFgn5VMtMjIyMTFxxowZO3bsEEKkpaUtWLAgOjq6HovS6/V5eXn+/v5ySUBAwLFjx0xXAQCslvL3QI4cObKiomL58uVffvmlEOKDDz6IjY0dOnRoPRZVVlZWUVHh6Ogolzg6Ol67ds10FQDAalnkOZDh4eGjR4++dOnS/fv3u3btavqiWuPQ6XTSi8LCwqbtCQC0IPLOs6WwSKoJITQaTdeuXeW3GRkZ0m+t1YmDg4OdnV1JSYlcUlJS4uTkZLqqWoQZANSD4c6zRSRcIx1FvfLKK/WYS6PR+Pj45OTkyCVZWVl+fn6mqwAAVqvpzw2aFh0dfejQofT09NLS0g0bNhQUFERERNRaBQCwTs0i1TIzM3U6nXRsGxsbq9Pp5s2bJ1UNGTIkISEhJSVl0KBBaWlpycnJ8hcATFQBAKyTpa6r1cmgQYNMXPcKDQ0NDQ2taxUAwAo1i2M1AAAUodixmo+Pj1KLAgCgfhRLtQkTJii1KAAA6kexVJszZ45SiwIAoH64rgYAUA9SDQCgHqQaAEA9SDUAgHqQagAA9SDVzKWZ/XVTdwEAUAtSDQCgHqQaAEA9SDUAgHqQagAA9SDVAADqQaoBANSDVAMAqAepBgBQD1INAKAepBoAQD1INQCAepBqAGAVrORhtqQaAEA9SDUAgHqQagAA9SDVAADqQaoBANSDVAMAqAepBgBQD1INAKAepBoAQD1INQCAepBqAAD1INUAAOpBqgEA1KO5p1pKSorOQL9+/Qxr09PThw0b5uXlFRIScvDgwabqJACgmWjuqSaE8Pb2LvzT0aNH5fKMjIy4uLhp06ZlZmaGhYXFxMTk5+c3YT8BAE2uBaRaTVJTU4OCgkJDQ7VabVRUlIeHx8aNG5u6UwCAptQCUu3UqVO+vr4DBw6cPHny6dOnpUK9Xp+Xl+fv7y9PFhAQcOzYsSbqIwCgWWjd1B2ohbOzc0JCQmBgYGlpaVJS0tixY/fu3evq6lpWVlZRUeHo6ChP6ejoeO3atZqWo9PppBeFhYUW7zQAqIW882wpmnuqhYeHSy+0Wu3SpUuDg4O3bds2c+bMui6HMAOAejDcebaIhGsBZyBltra2bm5uRUVFQggHBwc7O7uSkhK5tqSkxMnJqel6BwBoei0p1SorK4uKilxcXIQQGo3Gx8cnJydHrs3KyvLz82u63gEAml5zT7WYmJjc3NyysrILFy7MnTv35s2b8jnJ6OjoQ4cOpaenl5aWbtiwoaCgICIiokk7CwBoYs39ulpkZGRKSkpeXp6dnZ23t/f27dt79uwpVQ0ZMiQhISElJSU+Pt7NzS05OdnT07NpewsAaFrNPdX8/PxSU1Nrqg0NDQ0NDW3M/gAAmrPmfgYSAADzkWoAAPUg1QAA6kGqAQDUg1QDAKgHqQYAUA9SzVz6ZcFN3QUAQC1INQBQP+v5v5xUAwCoB6kGAFAPUg0AoB6kGgBAPUg1AIB6kGoAAPUg1QAA6kGqAQDUg1QDAKgHqQYA6qSZ/bX1PFJERqoBANSDVAMAqAepVgsrPH4HoGKq36eRagAA9SDVAEDNVH9wZoRUM8XatgYAaOlINQCAepBqdaNfFqyZ/XVT9wIAUD1SzSycigTQ0lnJfoxUAwCoB6kGAFAPUg0AoB6kGgBAPUg1AIB6kGoAAPUg1QAA6kGqAQDUg1RDHeh0uqbugkowkgpiMJWijpEk1QAA6kGq1YGVPG8GgMpY1b6LVKudVW0QAFTMGvZmGr1e39R9sLh6P2Xffe/UBwtPj1jdsO4AQCNRdifmvndqYWFhw3pkcVaRagAAK8EZSACAepBqAAD1INUAAOpBqgEA1INUAwCoB6kGAFAPUg0AoB4qT7X09PRhw4Z5eXmFhIQcPHiwqbvTrKWkpOgM9OvXT64yMYyMsKS8vHzbtm2hoaE6nW7Pnj1GtfUYQKsdWBMjaWITFYzkA/Lz82fOnDlo0CB/f/+oqKj8/HzDWjVvk3r1+vbbbz08PHbt2nXjxo3U1FQPD4+TJ082daear5UrV44aNerBchPDyAjLNm3aFBcXd/LkSXd39927dxtW1WMArXlgTYxkTZuonpGszuTJk/fv33/58uWrV6/Omzevf//+v//+u1Sl7m1Szak2adKkf/7zn/LbF198cc6cOU3Yn2aupl2GiWFkhB/04L64HgPIwOqrG0kTqcZImnb79m0PD4+0tDTprbq3SdWegdTr9Xl5ef7+/nJJQEDAsWPHmrBLzd+pU6d8fX0HDhw4efLk06dPC5PDyAibox4DyMCa8OAmKhhJM9y8ebOqqkqr1Qor2CZVm2plZWUVFRWOjo5yiaOj47Vr15qwS82cs7NzQkLCN998k5aW1qFDh7Fjx166dMnEMDLC5qjHADKwNal2ExWMpBkWLVrk6uo6ePBgYQXbpGpTDXUVHh4+cuRIrVbbrVu3pUuX2tvbb9u2rak7Bfx/bKL1k5SU9M0336xYscLOzq6p+9IYVJtqDg4OdnZ2JSUlcklJSYmTk1MTdqkFsbW1dXNzKyoqMjGMjLA56jGADKw55E1UMJImJScnb9q0ad26dd7e3lKJ6rdJ1aaaRqPx8fHJycmRS7Kysvz8/JqwSy1IZWVlUVGRi4uLiWFkhM1RjwFkYM0hb6KCkaxZcnLy+vXr161b179/f7lQ/dtkE92l0hgMb0Vdv359c74VtTmYPn16Tk7OzZs3z58/P2vWrMcff/znn3/WmxxGRvhBpu/sN3MAGVh9dSNZ0yaqZySrk5KS4uPjk5ub+2CVurdJNaeaXq/ftWvX008/7enp+fzzz3/11VdN3Z1m7ejRo1FRUX5+fk8++eTUqVNPnz4tV5kYRkZY8t1337n/X3FxcXJtPQbQagfWxEia2ET1jOQDPD09jUbyww8/lGtVvE3yW9gAAPVQ7XU1AIAVItUAAOpBqgEA1INUAwCoB6kGAFAPUg0AoB6kGgBAPUg1AIB6kGoAAPUg1QAA6kGqAQDUo3VTdwCwXrNnz75y5Yqfn9++ffuuXLnSq1evt956S/4dLAD1wLEa0JSys7NLS0u3bNly6NChbt26TZ8+/d69e03dKaAFI9WAptS1a9f4+PguXbp07tx5ypQpxcXF586da+pOAS0YqQY0JTc3t1at/vfPsGPHjkKI69evN2mPgJaNVAOakkajaeouAKpCqgEA1INUAwCoB6kGAFAPjV6vb+o+AACgDI7VAADqQaoBANSDVAMAqAepBgBQD1INAKAepBoAQD1INQCAepBqAAD1+H/PVY1bH3SvwwAAAABJRU5ErkJggg=="
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 11,
     "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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4g+p1tYcPHxYXF1dXVz969Khv375Dhw4dP358v379aMYAAAA8RimrlZeX7969+8yZM21tbX379u3bt++jR48ePXpkZGTk4+MTGRmJW80AAKD7aGS1pUuXnjt3bsqUKf/85z/d3NyEQiFT3tTUVF5e/vXXX0dGRk6aNCk1NZVCMAAAwGM0spqtre23337b/kyjUCicNGnSpEmTYmNjP//8cwqRAAAAv9HIaitXrmQfoF+/fjExMRQiAQAAfkMfSAAA4A8tZLU7d+6cPHly3759hJDa2lr6AQAAAF9R7dkvkUjWrVt37NgxY2PjlpaWBQsWxMfHz5o1y9vbm2YYAADAV1SP1TZu3FhVVZWdnX3x4kWmJDQ0NDMzk2YMALpAEH2mmwMAQIeoHqsVFBQcPHhw+PDhshJHR0dZhgMwWMhhAOpC9VitubnZ2tpavqS1tdXICD1WAABAPahmFHt7+5ycHPmSkpKSkSNH0owBAAB4jOoZyPDw8BUrVly8eHHSpEmEEJFIlJSUlJiYSDMGAADgMapZbfr06RKJJDU1tbCwkBCyZcuWmJiYzl5gDQAAoCza78KePXv2rFmzampq2tra7OzscFENAADUiHZWI4QIBAI7Ozv69QIAAO/RyGohISGEkOzsbOZDe9nZ2RTCAAAA3qOR1ezt7RU+AAAAaAKNrBYfH898mDdv3ogRIyjUCAAAholqZw1/f3+a1QEAgKGhmtWsrKzq6+tp1ggAAAaFalYLDAxMS0traWmhWSkAABgOqj37y8vLy8rKTp06NXTo0J49e8rKs7KyaIYBAAB8RTWr2djY4NIaAABoDtWslpycTLM6AAAwNHhgFYBOkCb74C1rAN2nhSdm1dTU3LhxgxAybNgwW1tb+gEAAABfUc1qT58+jYuLy8vLk5UEBgbGxcX16tWLZhgAAMBXVM9ApqSkiMXixMTEwsLCwsLCjRs3isXilJQUmjEAAACPUT1WO3HiRHJy8rhx45ivQ4YMsbOzi46OXr16Nc0wAACAr6geqzU2Njo5OcmXjBw5srGxkWYMAADAY1Szmq2trVgsli85d+4cOowAAIC6UD0D+c4776xZs+bSpUvu7u5tbW3l5eUHDhxYtmwZzRgAAIDHqGa1sLAwIyOjjIyM3bt3E0L69+8fHR29YMECmjEAAACPUc1qAoEgNDQ0NDS0rq6OEGJtbU2zdgAA4D0tPFvkzp07FRUVBQUFhJDa2lr6AQAAAF9RPVaTSCTr1q07duyYsbFxS0vLggUL4uPjZ82a5e3tTTMMAADgK6rHahs3bqyqqsrOzr548SJTEhoampmZyT5WbW3typUrx40bN378+ISEhObmZtlP+fn5kydPdnZ29vPzO336tAZDBwAAfUA1qxUUFCQnJ7u5uRkbGzMljo6OsgzXoYcPH86ZM6epqSkvL+/MmTMvv/zy+fPnmZ/EYnFsbOyHH35YVFQUFBQUFRV1+fJljc8DgJrgWcYAmkA1qzU3Nyv0EGltbTUyYovh888/f/bsWUpKip2dnZmZWUhIyOTJk5mfMjMzvb29AwIChEJhRESEo6Pj3r17NRc8ADVIeAAqo5rV7O3tc3Jy5EtKSkpGjhzJMsp///d/v/HGG6ampgrlUqm0oqJi7NixshJPT88LFy6oMVoAANA7VHuLhIeHr1ix4uLFi5MmTSKEiESipKSkxMREllHu3bs3YMCAhQsXFhcXW1lZTZkyZcmSJWZmZo8fP5ZIJBYWFrIhLSwsGhoaOpuOg4MD86GqqkpNcwMAwH+ynae+oJrVpk+fLpFIUlNTCwsLCSFbtmyJiYnx9fVlGUUqle7evTspKWnbtm2//PJLVFTUo0ePEhISlK0ayQwAQAXyO0+9yHC03xo6e/bsWbNm1dTUtLW12dnZsV9UI4RYWVk5OztPmzaNEOLi4hIaGpqenp6QkGBubm5qair/ZOTGxkZLS0vNRg+gAYLoM9JkH21HAcATWrgLWyAQ2NnZvfTSS12mNELI6NGjFUqYsQQCgaura2lpqay8uLjY3d1dvaECaAKXNCZN9kGfEQAV0D5We/78+e3btx88eCBfOGbMmM6Gj4iImDt3bkFBwV//+tfr169/8cUX/v7+zE+RkZGLFi3Kz8/38fHJzc2trKyMj4/XbPQAAKDbqGa18vLyJUuW3L9/X6Gc5aKXi4vL9u3bU1JSYmJiBg4cOGPGjMWLFzM/eXl5JSYmpqenf/TRR4MHD05LS1N4eRsAABgaqlltw4YNHh4eixYtEgqF3Mfy9vbu7JFaAQEBAQEBaooOAAD0HtWsduPGjaysrH79+tGsFAAADAfV3iLW1tbPnj2jWSMAABgUqlnNz8/vs88+k0qlNCsFAADDQeMMZEREBPOhpaWlpKTk7NmzQ4YMkc9tWVlZFMIAAADeo5HVBgwYIPss65cPAACgdjSyWlhY2KhRoyhUBAAABo7GdbWZM2dSqAUAAEALT8wCAADQEGQ1AADgD0p3YX/zzTcsv06dOpVOGAAAwG+Usto//vEPll/x8jPgN7W8awYvrAHgglJW+/rrr+lUBAAAhoxSVhs2bBidigAAwJChtwgAAPAHshoAAPAHjaxWXl5OoRYAAAAaWe2rr75qbW1lGaC1tfXw4cMUIgEAAH6jkdUOHTo0derU3bt337lzR+Gn6urqjIyMN99889ChQxQiAQAAfqPRB1IkEh05ciQzMzMpKcnCwsLOzs7c3Pzx48d37979448/7O3tFy9eHBAQQCESAADgNxpZzcjIKCgoKCgoqKKioqSkpLq6+tGjRy+88MLUqVM9PT2dnJwoxAAAAIaA0v1qDFdXV1dXV5o1AgCAQUHPfgAA4A9kNQAA4A9kNQAA4A9kNQAA4A9kNQAA4A+qfSAJIc+fP799+/aDBw/kC8eMGUM5DAAA4CWqWa28vHzJkiX3799XKMdbQwEAQC2oZrUNGzZ4eHgsWrRIKBTSrBcAAAwE1ax248aNrKysfv360awUAAAMB9XeItbW1s+ePaNZIwAAGBSqWc3Pz++zzz6TSqU0KwUAAMNB9QzkhQsXSkpKzp49O2TIEPnclpWVRTMMAADgK6pZzdra2t/fn2aNADpCEH1GmuzTndHVGAwAj1HNasnJyTSrAwAAQ4NniwAAAH/QfrYIIaSmpubGjRuEkGHDhtna2tIPAAAA+IpqVnv69GlcXFxeXp6sJDAwMC4urlevXjTDAAAAvqJ6BjIlJUUsFicmJhYWFhYWFm7cuFEsFqekpNCMAQAAeIzqsdqJEyeSk5PHjRvHfB0yZIidnV10dPTq1atphgEAAHxF9VitsbHRyclJvmTkyJGNjY0so6SnpzvIGT16tPyv+fn5kydPdnZ29vPzO336tEaCBgAA/UE1q9na2orFYvmSc+fOddlhxMXFper//PTTT7JysVgcGxv74YcfFhUVBQUFRUVFXb58WSNxAwCAnqB6BvKdd95Zs2bNpUuX3N3d29raysvLDxw4sGzZMtWmlpmZ6e3tHRAQQAiJiIg4ceLE3r17k5KS1BoyAADoE6pZLSwszMjIKCMjY/fu3YSQ/v37R0dHL1iwgH2sq1evurm59erVa9SoUTExMfb29oQQqVRaUVEhnxE9PT0LCgo0Gj+AFkmTfbr5gBIAQ0A1qwkEgtDQ0NDQ0Lq6OkKItbV1l6NYW1snJiZOmjSpqalp69atc+bM+eqrr2xtbR8/fiyRSCwsLGRDWlhYNDQ0dDYdBwcH5gPeUAqUMakIj7wCPSXbeeoLLdyFTbjlM8bs2bOZD0KhcNOmTT4+PocPH166dKmyNSKZAQCoQH7nqRcZjkZWCwkJIYRkZ2czH9rLzs7mMp0ePXoMHjz49u3bhBBzc3NTU1P5/pONjY2WlpbqiBcAAPQVjazGXAmT/6Ca58+f375929nZmRAiEAhcXV1LS0tDQ0OZX4uLi93d3bsZKgAA6DUaWS0+Pl7hA3dRUVELFixwdHR88ODB1q1bHz16JDsnGRkZuWjRovz8fB8fn9zc3MrKShWmDwAAfEL1frXU1FSOhTLh4eH//Oc/J02aNGfOnCdPnuTk5Lz88svMT15eXomJienp6RMmTBCJRGlpaQq3eAMAgKGh2ltk586d7Tt6dFgo4+7unpmZ2dmvAQEBzP1qAAAAROvvV6utrRUKhdqNAQAAeIPSsdr8+fMVPhBCWltbq6urPTw86MQAAAC8RymrDRo0iBBSWlrKfGD06NHDx8cnODiYTgwAAMB7lLJaQkICIcTExATdFAEAQHOoXldbsmRJ+0I8aB8AANSFalZ77733JBKJfMnNmzcjIyNpxgAAADxGNauZmJjExMRIpVLm671798LDw19//XWaMQAAAI9RzWrp6elXr17dtGkTIaSuri4sLMzZ2fnTTz+lGQMAAPAY1buwLSwsdu3aFRwcbGlpefz4cTs7u61btxobG9OMAQAAeIz2XdhDhw5NS0vbtm1b7969MzIyevXqRTkAAADgMRrHahEREQolQqFQKpUuXryY+ZqVlUUhDAAA4D0aWW3AgAEKJZ6enhTqBQAAQ0MjqyUnJ1OoBQAAQMtPNwYAAFAjqn0gb9261WH5kCFDaIYBAAB8RTWrTZkypcPyqqoqmmEAAABfUc1qIpFI9lkqld68eXPr1q3vv/8+zRgAAIDHqGa1UaNGyX91cXGxtbXdsWNHSEgIzTAAAICvtNxbZNSoUZWVldqNAQAAeEPLWa28vNzU1FS7MQAAAG9QPQO5atUq+a9NTU1isTg0NJRmDAAAwGNUs1pdXZ381/79+3/yySdBQUE0YwAAAB6jkdU2bNjw0UcfEUKWLVum0GEEAABAjWhcV9u/fz/zptCZM2dSqA4AAAwWjaxmZWX1008/UagIAAAMHI0zkMHBwXPnzjUyMiKEODo6th/gypUrFMIAAADeo5HVlixZ4uvre+vWreXLl2/atIlCjQAAYJgo9YF0cnJycnI6derUjBkz6NQIAAAGiOpd2CkpKfJfnz9/TrN2AADgPapZ7d69e6mpqczntLQ0FxcX5swkzRgAAIDHqGa1pKQkprfIb7/99tlnn3300UcuLi5bt26lGQMAAPAY1axWXFzs6elJCCkqKpowYcLcuXNjY2PLyspoxgAAADxGNas9e/aMuR37p59+8vDwIIT06dPnyZMnNGMAoEAQfYYHVQDoI6pZ7ZVXXtmxY0dRUdE333zj5eVFCKmqqnrllVdoxgAAADxGNavFxMQcPXo0PDx82rRpTDLbv3//vHnzaMYAAAA8RvWZ/W5ubj/88MOff/4pFAqZkvfee2/48OE0YwAAAB6jmtUIIcbGxrKURgixt7enHAAAAPAY7az2/Pnz27dvP3jwQL5wzJgxlMMAAABeoprVysvLlyxZcv/+fYXyqqoqmmEAAABfUc1qGzZs8PDwWLRokfxJSAAAAHWh2gfyxo0b69atc3Bw+Mt/4jLuF1984eDgsGTJEvnC/Pz8yZMnOzs7+/n5nT59WjNRAwCA3qCa1aytrZ89e6bCiJWVlXv37h01apR8oVgsjo2N/fDDD4uKioKCgqKioi5fvqymSAEAQC9RzWp+fn6fffYZ83gR7pqbm5cvXx4XF2dhYSFfnpmZ6e3tHRAQIBQKIyIiHB0d9+7dq85wAQBA31C9rnbhwoWSkpKzZ88OGTJEPrdlZWWxjBUXFzdhwoRJkyZ9+eWXskKpVFpRUbFs2TJZiaenZ0FBgSbCBgAAfUE1q1lbW/v7+ys1yrFjx37++ee8vDyF8sePH0skEvmjNwsLi4aGhs6m4+DgwHxAf0sAAO5kO099QTWrJScnKzX83bt3ExISsrKyTE1Nu1k1khkAgArkd556keFo34VNCKmpqblx4wYhZNiwYba2tixDXrly5cGDB4GBgfKFDg4OZ86csbW1NTU1bWxslJU3NjZaWlpqKGYA7gTRZ6TJPsxfChVptAoAvUM1qz19+jQuLk7+dGJgYGBcXFyvXr06HH7y5Mny/yb8/e/CXiyyAAAgAElEQVR/79279/bt25mvrq6upaWloaGhzNfi4mJ3d3eNxQ6gQ2SJU9uBAOgcqn0gU1JSxGJxYmJiYWFhYWHhxo0bxWJxSkqKalOLjIw8e/Zsfn5+U1PTnj17Kisrw8LC1BovAADoGapZ7cSJE8nJyUFBQUOGDBkyZMjbb7+9devWEydOqDY1Ly+vxMTE9PT0CRMmiESitLQ0Jycn9QYMQBMOvwC6j+oZyMbGRoXEM3LkSPlrY+w+//xzhZKAgICAgAD1BAegDbg2BqBeVI/VbG1txWKxfMm5c+fYO4wAAABwR/VY7Z133lmzZs2lS5fc3d3b2trKy8sPHDggfyc1AABAd1DNamFhYUZGRhkZGbt37yaE9O/fPzo6esGCBTRjAAAAHqOa1QQCQWhoaGhoaF1dHSHE2tqaZu0AOgV9QwA0QQt3YRPkM4DOof8IQHfQyGohISGEkOzsbOZDe9nZ2RTCAAAA3qOR1ezt7RU+AAAAaAKNrBYfH6/wAQAAQBOo3q+WmprKsRAAAEAFVLPazp07ORYCAACogGpWa6+2tlYoFGo3BgAA4A1KPfvnz5+v8IEQ0traWl1d7eHhQScGAADgPUpZbdCgQYSQ0tJS5gOjR48ePj4+wcHBdGIAAADeo5TVEhISCCEmJiboBgnAEZ0XagPwDNXrakhpAEhUABpF+4lZBQUFx48fv3fvXktLi6xQ5ReHAgAAyKN6rJadnb127doXXnjh6tWrXl5effr0+eWXX1xcXGjGAAAAPEb1WO3AgQPJycne3t5ffvnl6tWrCSGbN2/+7bffaMYAAAA8RvVY7ddffx0/fjwhxNjYWCKREELCw8OLiopoxgAAADxGNas9e/bM1NSUEGJpaXn37l1CiJGREZPeAAAAuk8771cbO3bspk2bQkJCjh49OnLkSK3EAAAA/EP1WG3x4sXMh+XLl9fX13/wwQc///zzxx9/TDMGAADgMarHalFRUcwHOzu7/Pz85uZmMzMzmgEAAAC/afPpxkhpwD80b7JmHj5Cpy4AfaHlZ/YDAACoEY0zkCEhIewDZGdnUwgDAAB4j0ZWs7e3p1ALAAAAjayGhxoDdOcB/HggMgB3WriudufOnZMnT+7bt48QUltbSz8AAADgK6o9+yUSybp1644dO2ZsbNzS0rJgwYL4+PhZs2Z5e3vTDAMAAPiK6rHaxo0bq6qqsrOzL168yJSEhoZmZmbSjAEAAHiM6rFaQUHBwYMHhw8fLitxdHSUZTgAAIBuonqs1tzcbG1tLV/S2tpqZIR75gAAQD2oZhR7e/ucnBz5kpKSEjzdGAAA1IXqGcjw8PAVK1ZcvHhx0qRJhBCRSJSUlJSYmEgzBgAA4DGqWW369OkSiSQ1NbWwsJAQsmXLlpiYGF9fX5oxAAAAj1HNatevX589e/asWbNqamra2trs7OxwUQ0AANSIalLx9/cnhAgEAjs7u5deegkpDQAA1ItqXrGysqqvr6dZIwAAGBSqWS0wMDAtLa2lpYX7KHV1dQkJCd7e3q6urgEBAceOHZP/NT8/f/Lkyc7Ozn5+fqdPn1Z3vAAAoGeoXlcrLy8vKys7derU0KFDe/bsKSvPysrqbJQvv/zSwcHh3Xff7dOnz9dff71y5UoLC4uJEycSQsRicWxsbGJioo+Pj0gkioqKysnJcXJyojEnAACgk6geq9nY2Pj7+48fP97GxmaAHJZRli5dOnPmTBsbG3Nz89mzZ9vY2JSXlzM/ZWZment7BwQECIXCiIgIR0fHvXv30pgNAADQVVSP1ZKTk1Uet7m5ubCw8OHDhz4+PoQQqVRaUVGxbNky2QCenp4FBQVqiBIAAPQW7Z79I0aMUGEspvNkz549ExISmHOMjx8/lkgkFhYWssEsLCwaGhrUGC0AAOgdqlnN39+/qqpK2bFGjBhRVVXV1NRUUFCwZs2aPn36qHDjtoODA/NBhQAAAAyWbOepL6hmNaZnv5WVlQrjCoXC4ODgc+fOHTp0yNfX19zc3NTUtLGxUTZAY2OjpaVlZ6MjmQEPdOeF2gCqkd956kWG0/We/QqeP3/OfBAIBK6urqWlpbKfiouL3d3duxsigFohCQFQpus9+6OiokJDQ1955ZWnT58eO3ZMLBanpqYyP0VGRi5atCg/P9/Hxyc3N7eysjI+Pl7j8wAAADqMalZjevYrNUpoaOjOnTsrKip69OgxYsSInTt3ent7Mz95eXklJiamp6d/9NFHgwcPTktLw81qAAAGTtd79o8ZMyYzM7OzXwMCAgICAroXFAAA8AfVrMaoqam5ceMGIWTYsGG2trb0AwAAAL6imtWePn0aFxeXl5cnKwkMDIyLi+vVqxfNMAAAgK+o9oFMSUkRi8WJiYmFhYWFhYUbN24Ui8UpKSk0YwAAAB6jeqx24sSJ5OTkcePGMV+HDBliZ2cXHR29evVqmmEAAABfUT1Wa2xsVOimOHLkSPk7qQEAALqDalaztbUVi8XyJefOnUOHEQAAUBeqZyDfeeedNWvWXLp0yd3dva2trby8/MCBA/LP3QcAAOgOqlktLCzMyMgoIyNj9+7dhJD+/ftHR0cvWLCAZgwAAMBjVLOaQCAIDQ0NDQ2tq6sjhFhbW9OsHQAAeI/qdTXZ+8+sra1lKe3y5cs0YwAAAB6jmtXee+89iUQiX3Lz5s3IyEiaMQAAAI9RzWomJiYxMTFSqZT5eu/evfDw8Ndff51mDAAAwGNUs1p6evrVq1c3bdpECKmrqwsLC3N2dv70009pxgAAADxGtbeIhYXFrl27goODLS0tjx8/bmdnt3XrVmNjY5oxAAAAj1E9ViOEDB06NC0tbdu2bb17987IyMBzjQEAQI1oHKtFREQolAiFQqlUunjxYuYry7uwAfSUNNlHEH1GE1MWRJ+RJvtoYsoAPEAjqw0YMEChxNPTk0K9AHToSJrRkTAAtItGVlPhFdgAAAAqwLuwAQCAP/AubAAA4A+8CxsAAPgD78IGAAD+wLuwAdRAQ5349SgAAB2Bd2EDAAB/4F3YAADAH3gXNgAA8AfehQ0AAPxB9bpaamoq80H+XdiyQgAAgG6imtV27tzJsRAAAEAFtN9Eo6C2tlYoFGo3BgAA4A1K19Xmz5+v8IEQ0traWl1d7eHhQScGAADgPUpZbdCgQYSQ0tJS5gOjR48ePj4+wcHBdGIAAADeo5TVEhISCCEmJibx8fF0agQAAANE9boaUhoAAGgU1fvVbt261WH5kCFDaIYBAAB8RTWrTZkypcPyqqoqmmEA8JI02UcQfUaa7KPtQAC0iWpWE4lEss9SqfTmzZtbt259//33acYAoF5MIsEj8wF0BNWsNmrUKPmvLi4utra2O3bsCAkJoRkGAADwlZbvwh41alRlZaV2YwDQIoUThsqeP8RhIoACLWe18vJyU1NT7cYAoC7KXtbqcGBcGAPoDqpnIFetWiX/tampSSwWh4aGsoxy+fLlXbt2lZaWtrS0ODs7R0dHy79NOz8/Pz09/bfffhs8ePDy5ct9fX01FToAAOgDqsdqdf/J1NT0k08+Wb58Ocso27Ztmzp16tGjRwsKCmxtbcPCwmpra5mfxGJxbGzshx9+WFRUFBQUFBUVdfnyZSrzAQAAOorqsVpWVlb7wufPnxsbG3c2yueffy77/PHHH+fl5X3//fdBQUGEkMzMTG9v74CAAEJIRETEiRMn9u7dm5SUpIHAAQBAP2jzulplZWVCQsLEiRM5Dv/o0aPW1lbmGf9SqbSiomLs2LGyXz09PS9cuKCRQAEAQE9QPVZj/PHHH8eOHcvLy7t69erAgQP9/Pw4jrhhwwZbW1smCz5+/FgikVhYWMh+tbCwaGho0EjEAACgJ+hltdbW1u++++7IkSNnzpwhhDx//vzQoUOurq4CgYDL6Fu3bj137twXX3yhWp9JBwcH5gOeYwIAwJ1s56kvaGS1Gzdu5ObmHjt2rK6uzs3Nbe3atX5+fh4eHm5ubhynkJaWtn///l27drm4uDAl5ubmpqamjY2NsmEaGxstLS07mwKSGQCACuR3nnqR4WhktbfeesvS0nLOnDkzZsxQ4UHGaWlpWVlZu3btGjNmjKxQIBC4urqWlpbKbgwoLi52d3dXV8wAAKCPaPQWeeGFFxoaGkpKSkpLSx89eqTUuBkZGe1TGiMyMvLs2bP5+flNTU179uyprKwMCwtTW9AAGqDCbdp4dAiAUmhktbNnz+7evXvgwIHr16+fMGHCP/7xj9OnT3McNyMjo7m5ee7cuQ7/Jy0tjfnJy8srMTExPT19woQJIpEoLS1N/gZtAAAwQDTOQBoZGXl5eXl5eTU1NZ04cSI3N/eDDz4ghGzfvn3atGkjRoxgGffSpUssvwYEBDD3qwHoBRWehoXDNQClUL1fTSgUhoSEiESir776Kjw8/NChQ/7+/m+99RbNGAC0ReUHPOLJkADcaecu7BEjRqxevVosFmdkZOBF2AAAoC5auAtbxtjY2NfXF48kBgAAddHym2gAAADUCFkNAAD4A1kNAAD4g2pWu379Os3qAADA0FDNav7+/jSrAwAAQ0M1q1lZWdXX19OsEQAADArVrBYYGJiWltbS0kKzUgAAMBxU71crLy8vKys7derU0KFDe/bsKSvPysqiGQaA2uG5VgA6gmpWs7GxwaU1ALVT9lUAADxGNaslJyfTrA4AAAwN7lcDAAD+0EJWu3PnzsmTJ/ft20cIqa2tpR8AAADwFdUzkBKJZN26dceOHTM2Nm5paVmwYEF8fPysWbO8vb1phgEAAHxF9Vht48aNVVVV2dnZFy9eZEpCQ0MzMzNpxgAAADxGNasVFBQkJye7ubkZGxszJY6OjrIMBwBdQl9HAHZUs1pzc7O1tbV8SWtrq5EReqwAbyEJAVBGNaPY29vn5OTIl5SUlIwcOZJmDADycOu0AjQI6DuqvUXCw8NXrFhx8eLFSZMmEUJEIlFSUlJiYiLNGACo0dCBGo7/AFhQzWrTp0+XSCSpqamFhYWEkC1btsTExPj6+tKMAQAAeIxqViOEzJ49e9asWTU1NW1tbXZ2drioBgAAakQjq924caPD8urqaubDsGHDKIQBAAC8RyOrvfXWW+wDVFVVUQgDAAB4j0ZWO3LkCPOhvLw8JSXl3XffdXd3J4RcuHBh165dy5cvpxADAAAYAhpZTdZ3/6OPPkpKSpI9H2vs2LEODg47duyYO3cuhTAACF7awoF8E6G5QO9Q7axx7do1Dw8P+RIPDw+cfgRtYXbZuENLBjkMeIBqVuvbt29JSYl8SUlJSb9+/WjGAAAAPEa1Z39wcHBMTEx4eLibmxshpLy8fM+ePeHh4TRjAAAAHqOa1ZYsWWJubr5r164dO3YQQvr377948WJkNQAAUBeqWc3IyOjdd9999913a2trjYyMFJ50DEAHrh4B8BjtZ4swbGxstFIvAHCHfjSgj/DAKgAA4A9kNQD+UPuNCrjzAfQOshoYEC5X1JTaiev7JTpkLOAfZDUAAOAPZDUAAOAPqn0gO3wlTa9evWxsbHr06EEzEgAA4CWqWa2zV9L06tVr5syZsbGxJibaudMAgGGA15n0/dIggAKqZyA/+eSTfv36rVixYv/+/fv27VuxYoVQKFy1atWaNWu++eabzMzM9qM0NzcfPnw4ICDAwcHh2LFjCr/m5+dPnjzZ2dnZz8/v9OnTVGYCAAB0F9Vjo9zc3K1bt06cOJH5Om7cOHt7++3bt+fm5r7wwgtJSUmLFi1SGCUvL+/KlSsJCQmBgYEKP4nF4tjY2MTERB8fH5FIFBUVlZOT4+TkRGNOAABAJ9F+Ew3zvlCZ0aNHM2+i8fDwqKmpaT/KvHnzEhISOsxVmZmZ3t7eAQEBQqEwIiLC0dFx7969mgkcgBOtnMrD+UMAebTfRFNWViZfUlZWJhQKCSH19fV/+ctfuE9KKpVWVFSMHTtWVuLp6XnhwgV1hQrAQi8uv+lFkABqRzWrzZo1a8WKFenp6WKx+Pvvv8/IyFixYsXs2bMJIXl5ee3PMbJ4/PixRCKxsLCQlVhYWDQ0NKg/aOA7hcdnGM7TNBT6iaDbCPAD1etqS5cu7du37+eff97U1EQI6dev33vvvRcZGUkImT59+ssvv6y5qh0cHJgPePU2dFNnOU+LKaGzqpGooPtkO099QftNNAsXLly4cGFtbS35zyf3jxgxQqlJmZubm5qaNjY2ykoaGxstLS07Gx7JDABABfI7T73IcNp5toiNjU03X0YjEAhcXV1LS0tlJcXFxQpdUQAAwNDQvuu5oKDg+PHj9+7da2lpkRWeOHFChUlFRkYuWrQoPz/fx8cnNze3srIyPj5efZECAID+oXqslp2dvXbt2hdeeOHq1ateXl59+vT55ZdfXFxcWEYpKipycHBgDntjYmIcHBzWrl3L/OTl5ZWYmJienj5hwgSRSJSWloab1QAADBzVY7UDBw4kJyd7e3t/+eWXq1evJoRs3rz5t99+YxllwoQJLJfEAgICAgIC1B8o6AC19HTQUHcJpp+kLnfEYMLTRGdOXV4uAITysdqvv/46fvx4QoixsbFEIiGEhIeHFxUV0YwBDBb2pKoxnFsdgB+oZrVnz56ZmpoSQiwtLe/evUsIMTIyYtIbgIZgjwxgULTTB3Ls2LGbNm06ffp0fHz8yJEjtRID6D6NJiQcunWG5eBMLUsE/2eARlHNaosXL2Y+LF++vL6+/oMPPvj5558//vhjmjEA4JQaAI9R7S0SFRXFfLCzs8vPz29ubjYzM6MZAOgLzXV2AI40eiyr+91tQH9RPVa7fv26/FekNJCHHGawsOhBjahmNX9/f5rVgb7r5uGaJo4G9OsIQxPHuzq4UADkUc1qVlZW9fX1NGsEPsF/9JpA4UwvFhzQRDWrBQYGpqWlyT8rC0Cednd/OIwA4AGqvUXKy8vLyspOnTo1dOjQnj17ysqzsrJohgEAugNHcqBeVI/VbGxs/P39x48fb2NjM0AOzRhAN3V5nIR9n15jX3zo7wpqRPVYLTk5mWZ1AABgaKgeq6WmpnIsBB2nlf+s8R+9PtLi1UqsLYaJalbbuXMnx0IAmlTIl7qcYlVIJOgpA7yhnedAytTW1gqFQu3GAMrS2b05gAzWUoNF6bra/PnzFT4QQlpbW6urqz08POjEAGqk8MQjXf5PHw9nMhBYysCglNUGDRpECCktLWU+MHr06OHj4xMcHEwnBgCODCERGsJZSkNYjtAepayWkJBACDExMYmPj6dTI4A8zb0UW+3T7CYdfEoWfUhmhozqdTUmpd25c+fkyZP79u0jhNTW1tIMAFQjv0drv7/Qr/0d8Bj7qogV1UBQzWoSiWTlypWTJ09eunQpc/QWHx9/9uxZmjGAJujd//Kga/DQZFAXqllt48aNVVVV2dnZFy9eZEpCQ0MzMzNpxsB7GsouNF9LLf9Vl/Olzu5GdTYwfVmy3PFgFviHalYrKChITk52c3MzNjZmShwdHWUZDjRBZ7e6DgPjx54Ouk/tq4G6Joj1U/dRzWrNzc3W1tbyJa2trUZGWr5njk808QppzZ3b4R6n2mOQJvtwmSAvd2FcZopj+3DX2WrZ4ZLVULNr6H8mXq4keo1qRrG3t8/JyZEvKSkpGTlyJM0YADqks2ft6FBq9g38kFo277iYp5uoZrXw8PCkpKQlS5bk5uYSQkQi0bp16yIjI2nGoDs0cY6lfe9Eg90BqbDH6XB4nrVeZyd+6UeijzpcqTSxifFsraOMalabPn36+vXrf/zxx9jYWELIli1bYmJifH19acagRVhTZfBPLrAz2P/GOoSmUArta1qzZ88+f/78mTNnTp06VVRUNHPmTMoB6JTur6yGtrpjZ6ctqv0XYoD/vqBbitZpoaeGQCCws7N76aWXdLafiObWJ02ckdfW2q/1BKNU7Sq3ttZns5vk46eWY7S+Yuj1/QPtb3TRXEUamrJ2aS2v3L17t7q6WiqVaisAdhQueumjzi7ddTgknXi41Kuu4wx+LESVd/QcF7S2Fj3RgRymX703+YpSVhOJRIsWLVq4cGFBQUFra+vSpUt9fX2nTp369ttv19fX04mBBfsTobQSBsfhuYSqsEmovEdTqiO+2qcJvMesD9w3QAp3hqiwfqqwVmtlK2jflYw3GyONrHbgwIG1a9fW1dU1NDQsXbp0w4YNly9fjouLi4uLe/ToUVpaGoUYlMXX5a25GVE5Ram2x+nsPidkSvraNzjlpaDR/0TpnL+l0FyGs13QyGoHDx5cv359Xl5eXl7e+vXrDx48mJycHBISEhISsmXLFrFYTCGGLmllkStc89DEZFXA/L+s3RhAL+j1KVmV1/P2x5RqXNu1laH59B8hjax2584df39/5jPzwdHRkfk6cuRIrT+2v8vVSLXlTefchXx1HC8CKXsukfJuq/1TLViec6G57VB/d9Ycae55MSwLi/uSVbkWdjq48qt8rkITwfADjaz27NkzMzMz5jPzoUePHszXXr16tbS0UIhBK9r/Z4R3XwEAFwrbdTfP6+j1UbWydLRvPb/p8hrW/dgozB17FepK83rdO5wdhdWv+43W5RQoVKFULZpY89VyxsXQUMpqrnLaf9Ud6jpXrmt5S9neZRrdZhTC0KmG4jH1rpPMGqL2MxAGuzJoK0vxMjuaUKhj4cKFFGrhjlmK7U/xd7h0dfbculaueHVZ0v1pchmFy5Iy2P2jTlFt+aq3xs5us1OqIqWGl0/5OkW27XC5Bt/hkHqBRlZbsWIFhVpU051LtV2O2Nk61OEwaqyX97i0PJ1IDJmOLAUdP9RQapvleGqdy9RU21fobD5WisFdV6PTe0plXV4T7iwMpXqXcZwXZeeX5fo2gIao3JGSXZcJpv0Wp9TEudTSTbINUMd3empncFmN0f1rZipPQamNkGMVXCaowsav9lE0sYXo6YYH3CksX4WL38pOTYX/vThuCB2exGu/r+B+p5DK/5vqRZ8vzTHQrMZQWCc6/P9LhX/BlL3A02EtLPefqXE/rt79RZd1IQNpBbVm19yuUL3x0//fiwsue5vOrhGyDK/2vZzuM+ispsLiZNluO9xrKzV9BweH9hF2tsqqa0VUbRtuHyp3NDeh7sQpj8L1BnWFqmk04+xms6sQqrr+9+os8g7/N1UqTmUTm7J4cB2BRm8R3dH9cxcKX2UTVOMuj8uW3P26NBR8Z+Q3Zo1OHzqj0fbR3L5PPgdQW0uJmjYxtQzDrsutuPs7Or1jKFmN2r8balkhFE5gaqjro/wGrLkqeJNv9Hou9Dp4Bs21lM6GoN7EKatCQzeDE/1ZiwwlqxFNHiVobuI0aWgWKCQ2fTxJwksUtgL9XUsJrZMiap+mLGZB9Bl7tU9dAwQ6+95ONRJEn7H/6n1tRwEAoPeqqqq0HUIXDCKrAQCAgTDoPpAAAMAzyGoAAMAfyGoAAMAfyGoAAMAfyGoAAMAfyGoAAMAfyGoAAMAffMtq+fn5kydPdnZ29vPzO336dIfDXL58eenSpRMmTBg7dmxERMTly5d1J7bm5ubDhw8HBAQ4ODgcO3ZM/qf09HQHOaNHj6YSdXfD1npsLINpq0k5hqezkehUe+ry+tn98HS2SbW1F+VEyiPfffedo6PjkSNHHj58mJmZ6ejoeOnSpfaDLVy4sKCg4P79+/X19WvXrh0zZszvv/+uI7Ht378/Njb20qVL9vb2R48elf9px44dM2fO1HScCrofttZjYxlMK03KPTzdjESn2lOX10+1hKezTaqVvShHvMpqoaGhH3zwgexrYGDgihUr2Ed58uSJo6OjSCTScGhKx6YL67dUHWFrDsfYWAbThaymwkqr3Uh0qj11ef2U6udWr8t7UY74cwZSKpVWVFSMHTtWVuLp6XnhwgX2sR49etTa2ioUCnUwtvauXr3q5uY2fvz4hQsXXrt2Ta0xdkBdYWsCx9i6HIxykyobnq5FolPtqTut1yF93Op1eS/KHX+y2uPHjyUSiYWFhazEwsKioaGBfawNGzbY2tpOnDhRB2NTYG1tnZiYeO7cOZFI1Ldv3zlz5tTU1Kg70v+glrA1hGNs7IPRb1KlwtPBSHSqPXWn9Tqkj1u9Lu9FueNPVlPB1q1bz507t23bNlNTU23H0rXZs2dPnz5dKBS++OKLmzZt6tOnz+HDh7UdlH5Dk6oX2lPtdL9JdXAvqsdZ7eTJk7KuQbm5uebm5qampo2NjbIBGhsbLS0tOxs9LS1t//79u3btcnFx0bXYutSjR4/Bgwffvn1bHcH+P02HTT827rOgoSZlpzstrI/tqTut1yF92erl6dReVGV6nNUmT55c9X+CgoIEAoGrq2tpaalsgOLiYnd39w7HTUtLy8rK2rVr15gxY3QtNi6eP39++/ZtGxsbdQT7/zQdNv3YuM+ChpqUne60sD62p+60Xof0ZauXp1N7UdVpqZeKRsj3Sc3KypLvk7p9+3Z3d3fmc3p6uqura1lZmQ7GJtO+N9TixYtLS0sfPXp0586dZcuWvfrqqzdu3ND9sLUeG8tgWmlS7nOhI5EoLGidak+OMctosWe/auHpbJNqZS/KEa+ymlQqPXLkyBtvvOHk5PTWW2+dOnVKVi6/SJycnOz/0/bt23UktvPnzyvEFhsby/z0008/RUREuLu7v/baa++///61a9coxNz9sLUeG8tg2mpSBZ2FpyORtN8F61R7colZW+tn98PT2SbV1l6UC7wLGwAA+EOPr6sBAAAoQFYDAAD+QFYDAAD+QFYDAAD+QFYDAAD+QFYDAAD+QFYDAAD+QFYDAAD+QFYDAAD+QFYD0Li1a9fOnz9f21EAGARkNQAA4A9kNQDNWrdunUgkKi0tZV4Ol5qaSghJS0tjvo4aNcrPzy87O1s2fERExKpVq2Rff/75ZwcHh1u3btGPHEAfmWg7AACei4+Pb2lp+T+mxQUAAAFxSURBVPXXX/fv3y8rjIqKioqKIoQ0Nzf/8MMPMTEx/fv3nzZtmvbCBOAJHKsBaJOZmZmvr+/f/va348ePazsWAD7AsRqAFtTU1KSmphYXF9fX17e2thJCXnnlFW0HBcAHOFYD0ILFixc3NDTs3r37xx9/rKqqCg8Pb2lp6XBIvAERQCnIagAa16NHD+aAjNHc3Hz58uV33nnH3t7ezMyMEHLhwgXZr/37929qapJ9vXnzJs1QAfQdshqAxtnZ2VVXV9fW1jJfzczMbG1tjx492tDQ0NDQsHnz5n//+9+ygcePHy8Wi4uKiiQSSVlZ2bZt27QUNYBeQlYD0Ljg4GAXFxc/Pz9Zz/4dO3b8/vvvf/3rX6dOnXrv3r3AwEDZwEFBQaGhoStXrpw4ceK2bdv+/ve/ay9wAP0jwFl7AADgDRyrAQAAfyCrAQAAfyCrAQAAfyCrAQAAfyCrAQAAfyCrAQAAfyCrAQAAfyCrAQAAf/wPV1c55Jjg57QAAAAASUVORK5CYII="
     },
     "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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FxeLBQqGQTCa9Xq96t6amprm5uf1eLgBATw5ovYB7vf3229XV1cePHy9+WFlZGQ6HW1tbc7nc+fPnu7u7r1+/Xl1dnc/n19bWHA6H+okOh2N5eXmrh5VluXgjnU4/1PUDgEjUk6dR6Ktq58+fn5iYuHz5stVqLR7p6uoq3rDb7YODg21tbcPDw/39/ff7yMQMAHah9ORpiMLp6ApkJBK5cuXKxYsX6+vrN71DRUWFy+XKZDKSJNlsNqvVms1m1Wk2m3U6nfu0VgCALumlapFI5NKlSxcvXjx27NhW91lfX89kMlVVVZIkWSwWt9s9MzOjTqenpz0ez36sFQCgV7qo2nvvvbdV0oLB4OzsbD6fX1paOnPmzMrKinpNsqenZ3x8PJFI5HK5oaGh+fl5v9+/30sHAAOyvHpT6yU8LLr4udp77723vr7+/PPPq0deeumlYDAoSdKpU6ei0WgymbRarfX19VevXj18+HDxPi0tLeFwOBqNnj171uVyRSKR2tpabf4BAAB90EXV7ty5s9XI4/HEYrGtpoqiKIqyuy9qefVm4Q9tu/tcABCYoU+PurgCCQDAnqBqAABxUDUAgDioGgBAHFQNACAOqgYAEAdVAwCIg6oBAMRB1QAA4qBqAABxUDUAgDioGgBAHFQNACAOqgYAEAdVAwCIg6oBAMRB1QAA4qBqAABxUDUAgDioGgBAHFQNACAOqgYAEAdVAwCIg6oBAMShi6qlUqn+/v7m5mav1xsIBFKpVOk0kUi0t7fX1dV1dHSMjY3tcAQAMCFdVO2dd945efLkxx9/fOPGjerqar/f//XXXxdHk5OToVCor69vamqqs7MzGAyqzSszAgCYky6q9v777588ebKystLpdL711lvff//9rVu3iqNYLObz+RRFsdvtgUCgpqYmHo9vOwIAmJMuqlZqZWXlxx9/tNvtkiQVCoVkMun1etVpU1PT3Nxc+REAwLQOaL2Ae7399tvV1dXHjx+XJCmfz6+trTkcDnXqcDiWl5fLjzYly3LxRjqdflhLBwDhqCdPo9BX1c6fPz8xMXH58mWr1bq3j0zMAGAXSk+ehiicjq5ARiKRK1euXLx4sb6+vnjEZrNZrdZsNqveJ5vNOp3O8iMAgGnppWqRSOTSpUsXL148duyYetBisbjd7pmZGfXI9PS0x+MpPwIAmJYuqvbee+9tTFpRT0/P+Ph4IpHI5XJDQ0Pz8/N+v3/bEQDAnPRStdXV1eeff17+SSQSKY5aWlrC4XA0Gm1ubh4ZGYlEIrW1tduOAADmpIt3i9y5c6fMVFEURVHudwQAMCFdvFYDAGBPUDUAgDioGgBAHFQNACAOqgYAEIepq2Z59abWSwAA7CVTVw0AIBiqBgAQB1UDAIiDqgEAxEHVAADioGoAAHFQNQCAOKgaAEAcVA0AcC/j/pEKqgYAEAdVAwCIg6oBAMRB1QAA4qBqkmTkn4sCwJ4Q5jRI1QAA4qBqAABxUDUAgDio2v8R5rIyAOycYKc+XVRtdXV1eHhYURRZlkdHR0tH0WhULnH06NHSaSKRaG9vr6ur6+joGBsb299VAwB0RxdV++ijjz777LOBgYFNp/X19emf3L59Wz0+OTkZCoX6+vqmpqY6OzuDwWAqldqvJQMA9OiA1guQJEl64YUXdvFZsVjM5/MpiiJJUiAQ+POf/xyPx3//+9/v9eoAAIahi9dq5S0sLDQ0NDQ2Nvb29i4uLhYPFgqFZDLp9XrVuzU1Nc3NzWm0RgCALujitVoZlZWV4XC4tbU1l8udP3++u7v7+vXr1dXV+Xx+bW3N4XCo93Q4HMvLy1s9jizLxRvpdPqhLxoARKGePI1C71Xr6uoq3rDb7YODg21tbcPDw/39/ff7OMQMAHah9ORpiMIZ4AqkqqKiwuVyZTIZSZJsNpvVas1ms+o0m806nU7tVgcA0J6Rqra+vp7JZKqqqiRJslgsbrd7ZmZGnU5PT3s8Hu1WBwDQnt6rFgwGZ2dn8/n80tLSmTNnVlZW1GuSPT094+PjiUQil8sNDQ3Nz8/7/X5NFwsA0JguqjY1NVX8JWtJkl577TVZlt98883i6NSpU3/6059aW1u7u7t/+OGHq1evHj58uDhqaWkJh8PRaLS5uXlkZCQSidTW1mr2bwAA6IAu3i3S3Ny81bs5PB5PLBbb6hMVRSn+vhoAAJJOXqsBALAnqBoAQBxU7b8E+6vVAGBO5qoa6QKA+2K406a5qgYAEBtVAwCIg6oBAMRhlqoZ7tIwAOiHgU6hZqkaAMAMqBoAQBxUDQAgDqoGABAHVQMAiIOqAQDEYdKqGehdqgCAnTNp1QAAQqJqAABxmKhqXHUEgF0w1snTRFUDAAiPqgEANmGsl2gqM1bNoN8qAMC2zFg1AICo/31P1QAA4qBqAIDNGfH1nC6qtrq6Ojw8rCiKLMujo6P3TBOJRHt7e11dXUdHx9jY2A5HD8iI30sAgC6q9tFHH3322WcDAwMbR5OTk6FQqK+vb2pqqrOzMxgMplKpbUcAAHPSRdVeeOGFgYGB2trajaNYLObz+RRFsdvtgUCgpqYmHo9vOwIAmJMuqraVQqGQTCa9Xq96pKmpaW5urvwIAGBauq5aPp9fW1tzOBzqEYfDsby8XH4EANhzsixrvYQd0XXVAAA6kU6ntV7Cjui6ajabzWq1ZrNZ9Ug2m3U6neVHAADT0nXVLBaL2+2emZlRj0xPT3s8nvKjbR6Tt+wDgLh0XTVJknp6esbHxxOJRC6XGxoamp+f9/v9244AAOaki6pNTU3Jslz8UeRrr70my/Kbb75ZHLW0tITD4Wg02tzcPDIyEolE1F8AKDO6L7x6AwBhHNB6AZIkSc3NzWV+DqkoiqIo9zsCAJiQLl6rAQCwJ6gaAEAcVA0AIA6qtiXeRQIAhkPVAADioGoAAHFQNQCAOKgaAEAcVA0AIA6qBgAQB1UDAIiDqgEAxEHVAADioGoAAHFQNQCAOKgaAEAcVA0AIA6qBgAQB1UDAIiDqgEAxEHV/gf/p1AAMDSqBgAQhymqtvjUBa2XAADGZpRLWaaoGgBgW0bpVnl6r1o0GpVLHD16tHSaSCTa29vr6uo6OjrGxsa0WiQAQCf0XjVJkurr69M/uX37tnp8cnIyFAr19fVNTU11dnYGg8FUKqXhOgHAcMR4fVbKAFXbSiwW8/l8iqLY7fZAIFBTUxOPx7VeFAAYXuEPbVovYfcMULWFhYWGhobGxsbe3t7FxcXiwUKhkEwmvV6verempqa5uTmN1ggA0AW9V62ysjIcDk9MTIyMjBw6dKi7u/vu3buSJOXz+bW1NYfDod7T4XAsLy9rt1IAMCqRrkPqvWpdXV1PP/203W5/7LHHBgcHDx48ODw8rPWiAAA6pfeqlaqoqHC5XJlMRpIkm81mtVqz2aw6zWazTqdTu9UBALRnpKqtr69nMpmqqipJkiwWi9vtnpmZUafT09Mej2evvpahf1gKAOUJfIrTe9WCweDs7Gw+n19aWjpz5szKykpXV1dx1NPTMz4+nkgkcrnc0NDQ/Py83+/XdLEAAI0d0HoB2zh16lQ0Gk0mk1artb6+/urVq4cPHy6OWlpawuFwNBo9e/asy+WKRCK1tbXarhYAoC29V83j8cRisa2miqIoirKf6wEA6Jner0ACALBzVA0AIA6qBgAQh6mrJvB7WwFgd4x+YjR11QAAgjF71Yz+XyUAsG8Wn7qg9RK2Z/aqAQBEYtKq8RINAHbCcGdLk1YNACBtiJbhGrYRVQMAiIOqAQDEQdUAAOKgaiJcRwYAFFE1AIA4qBoAQBxmrBqXHAFgWwY9VZqxalsx6LcQAKCiav+DsAEwG8HOe2ap2n192wT7HgPARvd7ojPKidEsVQMAmAFVAwCIw1xV28kraKO8ygaAB7TD052xzoqmqNrj138jGe0bAwD6YaDzpymqBgB4cMVXCDpn7KolEon29va6urqOjo6xsTGtlwMA0JiBqzY5ORkKhfr6+qampjo7O4PBYCqV2vazNn0dbaAX19qSZVnrJQiCndxDbOaeKPyhbeNLMSOeGw1ctVgs5vP5FEWx2+2BQKCmpiYej2u9KACAloxatUKhkEwmvV6veqSpqWlubu4+HkG4/685AOzOxhOgcU+JRq1aPp9fW1tzOBzqEYfDsby8rOGSAACaO6D1AvbJbq68P3XB8urNh7AWI2NP9go7uYfYzPu31SlRgB9SGrVqNpvNarVms1n1SDabdTqdm945nU7v17oAwAj+IOxZ0ahXIC0Wi9vtnpmZUY9MT097PB4NlwQA0JxRqyZJUk9Pz/j4eCKRyOVyQ0ND8/Pzfr9f60UBALRkKRQKWq9h9xKJRDQa/eqrr1wu1+nTp0+cOKH1igAAWjJ21QAAKGXgK5AAANyDqgEAxEHVAADiELxq/FH/nYtGo3KJo0ePqqMy28gOF62urg4PDyuKIsvy6OjoPdNdbKBpN7bMTpZ5ikrs5AapVKq/v7+5udnr9QYCgXv++LvIz8mCuP72t7/V1NRcu3btu+++i8ViNTU1d+7c0XpR+vXHP/7x2Wef3Xi8zDayw6orV66EQqE7d+48/vjjH3/8celoFxto5o0ts5NbPUUL7ORment7b9y48e9///s///nPm2++eezYsX/961/FkdjPSZGr9uKLL/72t79VP3zmmWd+97vfabgendvqlFFmG9nhjTaei3exgWxsYbOdLFM1drK8H374oaamZmRkpPih2M9JYa9AFh74j/qb0MLCQkNDQ2NjY29v7+LiolR2G9nhndjFBrKxZWx8ikrs5A6srKz8+OOPdrtdMsFzUtiq8Uf971dlZWU4HJ6YmBgZGTl06FB3d/fdu3fLbCM7vBO72EA2diubPkUldnIH3n777erq6uPHj0smeE4KWzXcr66urqefftputz/22GODg4MHDx4cHh7WelHA/+Epujvnz5+fmJh45513rFar1mvZD8JW7b7+qD/uUVFR4XK5MplMmW1kh3diFxvIxu6E+hSV2MmyIpHIlStXLl68WF9fXzwi/HNS2KrxR/0fxPr6eiaTqaqqKrON7PBO7GID2didUJ+iEju5tUgkcunSpYsXLx47dkw9KP5zUqN3qeyH0reiXrp0Sc9vRdWDl156aWZmZmVl5Z///Ocrr7zys5/97B//+Eeh7DaywxuVf2f/DjeQjS1stpNbPUUL7ORmotGo2+2enZ3dOBL7OSly1QqFwrVr137xi1/U1tb+8pe//Otf/6r1cnTt9u3bgUDA4/H8/Oc//81vfrO4uKiOymwjO1z097///fH/FQqF1OkuNtC0G1tmJ8s8RQvs5Aa1tbX37OS7776rTgV+TvI3+wEA4hD252oAABOiagAAcVA1AIA4qBoAQBxUDQAgDqoGABAHVQMAiIOqAQDEQdUAAOKgagAAcVA1AIA4qBoAQBxUDQAgDqoGABAHVQMAiIOqAQDEQdUAAOKgagAAcVA1AIA4qBoAQBxUDQAgDqoGABAHVQMAiIOqAQDEQdUAAOKgagAAcVA1AIA4qBoAQBz/Hyf//gfBTqFAAAAAAElFTkSuQmCC"
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sJESqvfnmmzt27MjPz8/Ly3v55Zdv3rx56dKlJb/K7/e7XC5N02w2W3Nzc3FxcXd3d/qbBQCIS4hUSzYzM3P79m2bzaaPXLt2bePGjRUVFa2trdevX08MxuPxYDBYXl6uX62ysnJ8fDzT7QIARLLO6AYWOnz4cGFh4ZYtWxL/zc/P93g8NTU10Wj02LFju3btevfddwsLC2Ox2NzcnN1u17/QbrdPT08vdrOqqiYuhMPhtPYPADLRF0+zECvVjh07Njg4ePr0aavVmhhpbGxMXLDZbEeOHKmtre3p6Wlvb1/pLRNmALAKyYunKRJOoB1Ir9d75syZkydPlpWV3fUKOTk5RUVFk5OTiqLk5uZardZIJKJXI5FIXl5ehnoFAAhJlFTzer2nTp06efLk5s2bF7vO/Pz85ORkQUGBoigWi8XhcIyOjurVkZERp9OZiV4BAKISItVef/31xSLN7XaPjY3FYrGpqakDBw7MzMzoe5ItLS0DAwOBQCAajXZ1dU1MTDQ1NWW6dQCASIR4Xu3111+fn59/6qmn9JFnn33W7XYrirJnzx6fzxcMBq1Wa1lZ2dmzZ9evX5+4TnV1tcfj8fl8Bw8eLCoq8nq9JSUlxkwAACAGIVLt6tWri5WcTqff71+sqmmapmnpaQqpWPZfjB+tNboLAFhIiB1IAMvHQwogBVINYuEzMAHcC1INACAPUg0AIA9SDQAgD1INACAPUg0AIA9SDavEmYoABESqAQDkQaoBAORBqgEA5EGqAQDkQaoBAORBqgEA5EGqwRi88TyAdCDVAADyINWwYhxmARAWqQYAkAepBgCQB6kGAJAHqQYAkAepBgCQB6mGVYofreXDaACIhlQDAMhDiFQLhULt7e1VVVXl5eXNzc2hUCi5GggE6urqSktL6+vr+/v7l1kCAGQhIVLt+PHjO3bseOeddy5cuFBYWNjU1PTFF18kSkNDQx0dHW1tbcPDww0NDW63W8+8FCUAQHYSItXefPPNHTt25Ofn5+Xlvfzyyzdv3rx06VKi5Pf7XS6Xpmk2m625ubm4uLi7u3vJEgAgOwmRaslmZmZu375ts9kURYnH48FgsLy8XK9WVlaOj4+nLgEAstY6oxtY6PDhw4WFhVu2bFEUJRaLzc3N2e12vWq326enp1OX7kpV1cSFcDicrtYBQDr64mkWYqXasWPHBgcHT58+bbVa1/aWCTMTSbxmgDdQBkSQvHiaIuEE2oH0er1nzpw5efJkWVlZYiQ3N9dqtUYiEf06kUgkLy8vdQkAkLVESTWv13vq1KmTJ09u3rxZH7RYLA6HY3R0VB8ZGRlxOp2pSwCArCVEqr3++ut3RlpCS0vLwMBAIBCIRqNdXV0TExNNTU1LlgAA2UmUVJudnX3qqafUr3m93kSpurra4/H4fL6qqqre3l6v11tSUrJkCQCQnYQ4W+Tq1aspqpqmaZq20hIAIAsJcawGAMCaINUAAPIg1bB6fBgNANGQagAAeZBqAAB5kGoAAHmQagAAeZBqAAB5kGoAAHmQagAAeZBqAAB5kGqAmfB5qkBqpBoAQB6kGgBAHqQaVoYdMAAiI9UAAPIg1QAA8iDVcE/4MBoAQiHVAADyINWQ1TjQBCRDqgEA5EGqAQDkQaoBAORBqkFE5j210pC2zfvjAtacEKk2Ozvb09OjaZqqqn19fckln8+nJtm0aVNyNRAI1NXVlZaW1tfX9/f3Z7ZrSII8AGQiRKqdO3fuypUrnZ2dd62WlZWFv3b58mV9fGhoqKOjo62tbXh4uKGhwe12h0KhTLUMABDROqMbUBRFefrpp1fxVX6/3+VyaZqmKEpzc/Pvfve77u7uV199da27AwCYhhDHaqldu3Zt48aNFRUVra2t169fTwzG4/FgMFheXq5frbKycnx83KAeAQBCEOJYLYX8/HyPx1NTUxONRo8dO7Zr16533323sLAwFovNzc3Z7Xb9mna7fXp6erHbUVU1cSEcDqe9aQCQhb54moXoqdbY2Ji4YLPZjhw5Ultb29PT097evtLbIcwAYBWSF09TJJwJdiB1OTk5RUVFk5OTiqLk5uZardZIJKJXI5FIXl6ecd1hBeT+kDZOqgQMZKZUm5+fn5ycLCgoUBTFYrE4HI7R0VG9OjIy4nQ6jesOAGA80VPN7XaPjY3FYrGpqakDBw7MzMzoe5ItLS0DAwOBQCAajXZ1dU1MTDQ1NRnaLADAYEKk2vDwcOJF1oqiPP/886qqvvTSS4nSnj173njjjZqaml27dt26devs2bPr169PlKqrqz0ej8/nq6qq6u3t9Xq9JSUlhs0BJpTYCOWNOQCZCHG2SFVV1WJnczidTr/fv9gXapqWeL0aAACKIMdqAACsCVIN94odPJ3c53YCpkCqAQDkQaqJyLL/Ikc/ALAKpJpYEnnGLhYArI4Q50AigTwDgHvEsRoAQB6k2orxjJd8OI0TkAapBqwxMhIwEKkGAJAHqQYAkAepBgCQB6mGFeC1BwAER6oJijMOAGAVSDV8A1EKwNRItZVJbMGlY+lncw8A7h2phv8R6kAtw3uwbPkCciDVMiGbl8tsnjuAzCPVAADyINWQRhyoAcgwUi1DDF/fl2yA01UASIBUQ7oQk4Yz/LEUkHmkGr6BUwHXBC//AIxCqsnGsv/iKtbT9C2XxCSATBIi1WZnZ3t6ejRNU1W1r69vQTUQCNTV1ZWWltbX1/f39y+zlIUSeSbIY3lxOslyKR5S3LXEQxCYnRCpdu7cuStXrnR2dt5ZGhoa6ujoaGtrGx4ebmhocLvdoVBoyZKAMnPIYlSQmPGAbM1zlyAHRCBEqj399NOdnZ0lJSV3lvx+v8vl0jTNZrM1NzcXFxd3d3cvWRJKFi52WThl0zHdoxBgmYRItcXE4/FgMFheXq6PVFZWjo+Ppy4BALLWOqMbSCUWi83Nzdntdn3EbrdPT0+nLt2VqqqJC+FwOG39mhWHVgAWoy+eZiH0sdoaCn9tTW7NdE8jpe+jBmBGqR/H8HuCZOEkRveyLEKnWm5urtVqjUQi+kgkEsnLy0tdSh+OaWA6K3o0w284JCB0qlksFofDMTo6qo+MjIw4nc7UJWGt9GiJoyukgx5d/IJBSkKnmqIoLS0tAwMDgUAgGo12dXVNTEw0NTUtWQJWgVUekIAQqTY8PKyqauI5yeeff15V1ZdeeilRqq6u9ng8Pp+vqqqqt7fX6/XqLwBIUcpC4uwdZawTEijZnZF81ztCnN8TIE2EOAeyqqoqxfOQmqZpmrbSUjZLLHDLXLwysMytqB8AuBdCHKuBRV8+Au5n8muGbECqYSEBl2Pci8QdSqQhS5BqEBf5CmClSDUgKyz/QI0HEzA1Ug2QH3uPyB6kWlZb0XMtPDEjN+5fyIFUyyj2dtYK72wJ4K5INQCAPEg1AIA8SLXlWvCswzK3v7LtuYpsmy8A0ZBq8iNpsBiem4R8SLUssmAJy2TasXoCyAxSDZnGsaP4eBQC8yLVAADyINWwNrL80f1dD0Az/DPJ8rsASCDVhLbYOsXihbXFtjCkQarJYM2XJHEe9aepExZxQFakmvmsySrPsg5ASqQaAEAepJrx0vHG+eJsIZoLPzfA7Ei1TJN73UyRuHJPXDTsMCNrkWowH5ZsAIsh1cx0ljyr+QIc/wFYgFRbFhFeYyvItwYAkYmeaj6fT02yadOm5GogEKirqystLa2vr+/v71/1dxE8IRLtcaCGdFjsERKPnGBSoqeaoihlZWXhr12+fFkfHxoa6ujoaGtrGx4ebmhocLvdoVBopTcuflTEj9au+foi/qyR4UTh9wHSMEGqLcbv97tcLk3TbDZbc3NzcXFxd3e30U19wxqGRyLbjO1hSayMa4tDJWAVTJBq165d27hxY0VFRWtr6/Xr1xOD8Xg8GAyWl5frV6usrBwfHzeoRyyLrJtaKR46yDplQFiip1p+fr7H4xkcHOzt7X3wwQd37dr12WefKYoSi8Xm5ubsdrt+TbvdPj09vdjt6M/M3bWaPUvP8mdq4EeM3jvL/osZu0PT8ZNJ3Gb2/FpCZMlnNhjdy7KsM7qBJTQ2NiYu2Gy2I0eO1NbW9vT0tLe3r/R2wuHwWrcGESViIGN5IFrYJyYuVEswu+TF0xTBJvqxWrKcnJyioqLJyUlFUXJzc61WayQS0auRSCQvL29FN8jfvymsNKIydp9m4PeHwzVgpcyUavPz85OTkwUFBYqiWCwWh8MxOjqqV0dGRpxOp3HdAWbFYzvIRPRUc7vdY2NjsVhsamrqwIEDMzMz+p5kS0vLwMBAIBCIRqNdXV0TExNNTU2r/kZr9aCYR9YGyuTBd/q+F1sIwL0Q/Xm1PXv2+Hy+YDBotVrLysrOnj27fv36RKm6utrj8fh8voMHDxYVFXm93pKSEmO7TdCf2lnmle9xCVvFLbBomhFpByyH6KnmdDr9fv9iVU3TNE1b3S2nb41I3GyKg7Zsfko/Y08UZfMPGchmou9AimB1r0Za9eumkZohR7fpuIVlXpMTRoAVIdUgCdMdmd01q0w3C0A0pNr/3PuD4gy/PdXqumXRFETiHuQ4DFhbpBoWlaa9r1XEauqd3gwHwxpuYPIGIsCay9JUy4Z9HsmWS8mmk0ziqQGZl6WpBsmY/WGKvhsp1CyIW5gRqQbTMOkia9K2AZMi1YyUmTcSTOvtZ1gGpmNUCK3h1EQ75gMyiVT7hlWsaDwSzzBj1+u0BgYf0gbcu2xMNR7Jyueud6iYYcCvH5BW2ZhqacJqZQrS301yzw5YEqkGAJAHqbYE6R/apybmJt4C2XwHAViAVDOGKdICa4W7G8iYrEu1JY+9WICQDmK+zhqQT9alWlZZqwWUtRiAWZBqRrr3qCBv0mrBUfs9/rSN+logq4j+WdhGWdEmpIHvRsFmaZqk6QdLOAHpRqrdxeqWHhYsmej3phmPhk3XMLCGsmsH0owrFO7F6g5n+SUBzCu7Ug1ZbhUPa9jmBcyFVDMMBwRYEUN+YQh1mE52pVrm321dAhJPDYB8OFsEWIJ+vELAA+Izd6oFAgGfz/f5558XFRXt27dv27ZtRncEEbGHBmQPE+9ADg0NdXR0tLW1DQ8PNzQ0uN3uUChkdFNppKrqnYNmPHq460TSJ360Nvnfqm/kzsEMTyR9mIhopJmIIUycan6/3+VyaZpms9mam5uLi4u7u7uNbgoAYCSzplo8Hg8Gg+Xl5fpIZWXl+Pi4gS1JzIxHhGuOHwJgCmZNtVgsNjc3Z7fb9RG73T49PW1gSwAAw5n7bJHlk2OfWo5ZKExEPKkm8vgJ05xuY6JWUxN1It81uoHlMGuq5ebmWq3WSCSij0Qikby8vLteORwOZ6ovAJDXUROspWbdgbRYLA6HY3R0VB8ZGRlxOp0GtgQAMJxZU01RlJaWloGBgUAgEI1Gu7q6JiYmmpqajG4KAGAkSzweN7qH1eNV2ACAZOZONQAAkpl4BxIAgAVINQCAPEg1AIA8JE+1QCBQV1dXWlpaX1/f399vdDvLFQqF2tvbq6qqysvLm5ubF7xrsxkndfr0aVVV9+7dmzxorol88cUXL7zwwve///2KiorOzs7Z2Vm9ZKKJzM3NdXZ21tTUlJaWbtu27fjx47dv39argk9kdna2p6dH0zRVVfv6+pJLKToXcFKLTUS+P3xjxOX15z//ubi4+Pz581999ZXf7y8uLr569arRTS1La2vrhQsX/vWvf/373/9+6aWXNm/e/M9//jNRMuOkQqHQ1q1bE5+roA+aayI3btzYunXrT3/606mpqZs3b/7mN795//33EyVzTeTw4cNbtmy5evXqrVu3/va3v23cuPGNN95IlMSfyJkzZzo6Oq5evfrd7373nXfe0cdTdC7mpBabiGR/+EaROdV27979s5/9TP/vzp07n3vuOQP7WZ1bt24VFxf39vYm/mu6Sd28eXP79u1/+tOfWltbk1PNXBN55ZVXqqqqZmdn7yyZayI//vGPOzo69P8+88wzzz6/yj+/AAADjElEQVT7bOKyiSayIAxSdC74pBZMJJnZ//ANJO0OZFyWN/WfmZm5ffu2zWZTzDmpQ4cOVVVV1dTUJA+abiLvv//+o48+arVaF4ybbiKPPfbY0NBQKBT6z3/+MzY2duXKlccff1wx4UR0KTo376QU8//hG8is7wO5JGne1P/w4cOFhYVbtmxRTDipvr6+jz766Ny5cwvGTTeRTz/99Dvf+U5ra+vIyMhDDz20ffv2vXv33n///aabyNNPP/2Pf/xj586diqJYLJb9+/dv375dMeE9okvRuXknpZj8D99Y0qaaHI4dOzY4OHj69Ok7jxLENzU11dnZeerUKTM2v0A8Hv/Vr3716quvHj9+/O9//7vb7Z6Zmens7DS6rxV75ZVX3n///d/+9reqql65cmXv3r333Xff7t27je4L32DqP3zDSbsDuaI39ReT1+s9c+bMyZMny8rKEiPmmtTHH39848aNnTt3qqqqqurg4OAf/vAHVVU//fRTc01EUZSHHnqourr6hz/84f33319WVrZ79+7f//73itnukf/+97+//vWvm5qaHA6H1WqtqKh48sknT58+rZhtIslSdG7SSZn9D99w0qaa2d/U3+v1njp16uTJk5s3b9YHzTWpurq6cJKamprt27eHw+GHH37YXBNRFGXTpk0LRr71rW8pZrtHLBbLt7/97eSReDxuxokkS9G5GSclwR++8Yw6TSUDks+FPXXqlInOhfX5fA6HY2xs7M6SeSe14BxIc03kypUrpaWl77333uzs7JUrV37wgx8cOnQoUTLXRJ577rmtW7d++OGHs7Ozf/3rX7/3ve+98soriZKJJpLizP4FnQs+qQUTkfIPP/NkTrV4PH7+/PlHH320pKTkscce++Mf/2h0O8tVUlLy3W967bXX9KpJJ7Ug1eJmm8jFixd/9KMflZSUuFyuX/ziF7du3dJLJprIzMzM4cOHt27dmngV9i9/+UsTTeQvf/nLgr8L/VUKKToXcFKLTUTKP/zM4z37AQDykPZ5NQBAFiLVAADyINUAAPIg1QAA8iDVAADyINUAAPIg1QAA8iDVAADyINUAAPIg1QAA8iDVAADyINUAAPIg1QAA8iDVAADyINUAAPIg1QAA8iDVAADyINUAAPIg1QAA8iDVAADyINUAAPIg1QAA8iDVAADyINUAAPIg1QAA8iDVAADyINUAAPIg1QAA8vg/xngHNVXJrJ4AAAAASUVORK5CYII="
     },
     "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": 35,
   "id": "2fb11406-756c-4257-8115-d7cfe186d0c0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time_bp = abs(fftshift(ifft(psd_ausgang)));\n",
    "%time_tp = abs(fftshift(ifft(psd_ausgang_tp)));\n",
    "%xc = xcorr(ifft(psd_ausgang), ifft(psd_ausgang_tp));\n",
    "%plot(time_bp)\n",
    "%figure(2)\n",
    "%plot(time_tp)\n",
    "%figure(3)\n",
    "%plot(abs(xc))\n",
    "%axis([0 length(xc) 0 1.2*max(xc)]);\n",
    "plot(abs(fftshift(ifft(psd_ausgang.*psd_ausgang_tp))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "47899a4d-6101-446e-94cd-726795eb0557",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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
}