{ "cells": [ { "cell_type": "markdown", "id": "ed6b2dd3-6ea4-444a-8dd2-04d0a8ff8ccc", "metadata": {}, "source": [ "# Signal LOC reçu par l'avion\n", "\n", "Franck Daout\n", "\n", "septembre 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "0ddcedf2-13f8-49e5-997d-1a9a6634febc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Using matplotlib backend: \n", "%pylab is deprecated, use %matplotlib inline and import the required libraries.\n", "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab \n", "%matplotlib inline" ] }, { "cell_type": "markdown", "id": "d43f83ee-78d3-47be-bf77-745fce3bc957", "metadata": {}, "source": [ ":::{admonition} Objectifs de cette page\n", ":class: note\n", " \n", "Dans cette partie, nous allons simuler le signal \"localizer\" reçu par l'avion (dans la suite nous l'appellerons signal LOC). Pour cela nous allons:\n", "1. \"Fabriquer\" le signal en bande de base reçu par l'avion\n", "2. Moduler ce signal (modulation d'amplitude et transposition autour de la fréquence RF)\n", "3. Simuler l'effet du canal de propagation\n", "\n", ":::" ] }, { "cell_type": "markdown", "id": "b42111f8-868e-4984-9230-e2ff8c58e73b", "metadata": {}, "source": [ "## Signal en bande de base\n", "\n", "Le signal reçu par l'avion correspond à une somme pondérée des signaux RF modulés à 90Hz ($V_{RF90}$) et 150Hz ($V_{RF150}$) :\n", "\n", "\n", "$$\n", "V_{RF} = (1 - \\alpha)V_{RF150} + \\alpha V_{RF90}\n", "$$\n", "\n", "La valeur de $\\alpha$ permet de sélectionner le décalage de l'avion par rapport à la piste. Si $\\alpha=0.5$ l'avion est aligné sur l'axe de la piste, si $\\alpha<0.5$ l'avion est à gauche de la piste, le pilote devra corriger en orientant l'avion vers la droite pour le recentrer. Dans le cas où l'avion est à droite de la piste, la valeur de $\\alpha>0.5$ \n", "\n", "Le signal $V_{RF}$ s'exprime en fonction des signaux modulant $V_{90}$ et $V_{150}$ :\n", "\n", "$$\n", "V_{RF} = (1 - \\alpha) A_{RF}(1 + m V_{150})\\cos(2 \\pi f_c t) + \\alpha A_{RF}(1 + m V_{90})\\cos(2 \\pi f_c t)\n", "$$\n", "\n", "avec $A_{RF}$ l'amplitude de la porteuse, $m$ le taux de modulation et $f_c$ la fréquence de la porteuse.\n", "\n", "L'expression de $V_{RF}$ peut se mettre sous la forme :\n", "\n", "$$\n", "V_{RF} = A_{RF}(1 + m V_{base})\\cos(2 \\pi f_c t)\n", "$$\n", "\n", "avec \n", "\n", "$$\n", "V_{base} = \\alpha V_{90} + (1 - \\alpha) V_{150}\n", "$$\n", "\n", "$V_{base}$ est le signal en bande de base (i.e. le modulant) que nous allons fabriquer. Pour cela deux générateurs d'onde CW sont créés. Le premier générateur à une fréquence de 90Hz ($f_1=90$ Hz) et une amplitude de 1V ($V_{90}(t)= 1 \\cos(2\\pi f_1t)$). Le second génère une onde de fréquence 150Hz ($f_2=150$ Hz) et d'amplitude de 1V ($V_{150}(t)= 1 \\cos(2\\pi f_2t)$). " ] }, { "cell_type": "markdown", "id": "b3beae26-1ef1-4910-a730-f492e6cb266e", "metadata": {}, "source": [ "Le programme ci-dessous permet de générer le signal LOC en bande de base ($V_{base}$) pour différentes valeurs de $\\alpha$ :\n", "* $\\alpha=0.25$, ce cas correspond à un avion à gauche de la piste\n", "* $\\alpha=0.5$, l'avion est centré (i.e. dans l'axe de la piste)\n", "* $\\alpha=0;8$, ce cas correspond à un décalage à droite " ] }, { "cell_type": "code", "execution_count": 2, "id": "29e8611d-bada-4363-8876-4000f0ac7659", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# baseband loc signal generation\n", "#--------------------------------\n", "\n", "#paramaters\n", "\n", "# Carrier frequency\n", "fc = 10e3\n", "sample_rate = fc * 10.0\n", "\n", "f150 = 150.0; A150 = 1.0\n", "f90 = 90.0; A90 = 1.0\n", "\n", "\n", "#aircraft offset\n", "alpha_range = array([0.25, 0.5, 0.8])\n", "\n", "#time\n", "t = arange(0,1.0,1/sample_rate)\n", "\n", "#sources\n", "V150 = A150 * cos(2*pi*f150*t)\n", "V90 = A90 * cos(2*pi*f90*t)\n", "\n", "figure(figsize=(6,4))\n", "for i, alpha in enumerate(alpha_range): \n", " #resistive mixer\n", " Vbase = (1.0-alpha)*V150 + alpha*V90\n", " \n", " plot(t,Vbase,label=\"alpha =\" + str(alpha))\n", " \n", "xlabel('time (s)')\n", "ylabel('Vbase (V)')\n", "legend()\n", "xlim(0,0.05)\n", "grid()\n", "title(\"Baseband LOC signal\")\n", "\n", "show()\n" ] }, { "cell_type": "markdown", "id": "addff670-f334-4a63-8ac2-4def4a2a0f4d", "metadata": {}, "source": [ "Nous allons maintenant étudier le cas où l'avion est dans l'axe de la piste. Dans ce cas $\\alpha=0.5$, le programme et la figure ci-dessous présentent le comportement temporel de $V_{base}$ " ] }, { "cell_type": "code", "execution_count": 3, "id": "1535c564-6cbb-4583-84c1-12ca009e6c9c", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#aircraft offcet\n", "alpha = 0.5\n", "\n", "#resistive mixer\n", "Vbase = (1.0-alpha)*V150 + alpha*V90\n", "\n", "figure(figsize=(6,4)) \n", "plot(t,Vbase,label=\"alpha =\" + str(alpha)) \n", "xlabel('time (s)')\n", "ylabel('Vbase (V)')\n", "legend()\n", "xlim(0,0.05)\n", "grid()\n", "title(\"Baseband LOC signal for alpha = \"+str(alpha))\n", "\n", "show()" ] }, { "cell_type": "markdown", "id": "30b82755-e542-4cd9-9f53-c66f0473fa69", "metadata": {}, "source": [ "Le spectre unilatéral d'amplitude du signal en bande de base est présenté sur la figure ci-dessous. Il est constitué de deux raies. La première raie correspond au signal \"90Hz\" et la seconde au signal \"150Hz\". Ces deux raies ont une amplitude identique, car l'avion est dans l'axe de la piste (i.e. $\\alpha=0.5$). L'analyse du signal en réception consistera donc à comparer l'amplitude de ces deux raies pour en déduire la position de l'avion." ] }, { "cell_type": "code", "execution_count": 4, "id": "988d3139-6eff-4f62-b277-0a2605f73cb0", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiUAAAGJCAYAAABVW0PjAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8pXeV/AAAACXBIWXMAAA9hAAAPYQGoP6dpAABOEElEQVR4nO3deVxU9f4/8NeAMIBssgiIKIorbhAmYbmjaJZLZbiCiGYmppdvZtxKxbyX0lzKNUvUrJRWvVmhiJAbrug1TU0J1JJFUEBBmXH4/P7wx1zGYRucYY7M6/l4zOPBfM7nnPN+z+fMzJuzjUwIIUBERERkZGbGDoCIiIgIYFFCREREEsGihIiIiCSBRQkRERFJAosSIiIikgQWJURERCQJLEqIiIhIEliUEBERkSSwKCEiIiJJYFFCkieTyRAVFWXsMDR4e3tj8uTJxg6DJGTr1q3o1KkTLCws4OjoaOxwAACbN2+GTCZDVlZWvec9ceKE/gMjqgaLEhNX8cFT+dG8eXMMGDAAv/zyi7HDe+zVtaA6d+4cJk6cCE9PT8jlcrRo0QITJkzAuXPnqp0nIyMD06dPR9u2bWFlZQV7e3s8/fTT+Oijj3D37l19ptFgSktLsXDhQqSmpho7FJ1cuHABkydPho+PDz799FNs2LDB2CGZrPLycixZsgRt2rSBlZUVunfvjm3bttVp3qo+DyseOTk5Bo6cAKCJsQMgaVi0aBHatGkDIQRyc3OxefNmPPvss/jxxx/x3HPPGTu8Ru3777/HuHHj4OTkhMjISLRp0wZZWVnYuHEjvv32W2zfvh2jR4/WmOenn37CmDFjIJfLERYWhq5du0KhUODgwYOYO3cuzp0791h+MZaWliI2NhYA0L9/f+MGo4PU1FSUl5fjo48+Qrt27Ywdjkl7++238f7772PatGl48sknsXPnTowfPx4ymQxjx46t0zIqPg8rk8rer8aORQkBAIYNG4aePXuqn0dGRsLNzQ3btm1jUWJAGRkZmDRpEtq2bYv9+/fD1dVVPW327Nno06cPJk2ahDNnzqBt27YAgMzMTIwdOxatW7fGvn374OHhoZ5n5syZuHz5Mn766acGz8UYSkpK0LRpU2OHgby8PAD6/eIqLS2FjY2N3pZnCv7++28sW7YMM2fOxOrVqwEAU6dORb9+/TB37lyMGTMG5ubmtS7n4c9Dajg8fENVcnR0hLW1NZo00axbP/zwQ/Tu3RvOzs6wtrZGQEAAvv32W635k5KS8Mwzz8DR0RG2trbo2LEj/vnPf2r0KSsrw4IFC9CuXTvI5XJ4eXnhzTffRFlZWZUxffnll+jYsSOsrKwQEBCA/fv3a0y/cuUKXnvtNXTs2BHW1tZwdnbGmDFjtI6nV+yiPXToEKKjo+Hq6oqmTZti9OjRuHHjhkZfIQQWL16Mli1bwsbGBgMGDKjxkIquli5ditLSUmzYsEGjIAEAFxcXfPLJJygpKcGSJUvU7UuWLMGdO3ewceNGjYKkQrt27TB79uwa13vp0iW8+OKLcHd3h5WVFVq2bImxY8eiqKhI3afi0FNtrzvw4MtgypQpcHNzg1wuR5cuXRAfH6/V7969e1i4cCE6dOgAKysreHh44IUXXkBGRgaysrLUr0FsbKx6t/nChQsBAJMnT4atrS0yMjLw7LPPws7ODhMmTABQ/Tk+/fv319jjkpqaCplMhq+//hqxsbHw9PSEnZ0dXnrpJRQVFaGsrAxz5sxB8+bNYWtri4iIiGq3xwre3t5YsGABAMDV1VUjZgBYu3YtunTpoj4sN3PmTBQWFmrF2bVrV5w8eRJ9+/aFjY2N1vulsjNnzmDy5MnqQ3fu7u6YMmUKCgoKaoy1It7nnnsOe/bsgZ+fH6ysrODr64vvv/++yv5lZWW1vk927tyJ4cOHo0WLFpDL5fDx8cF7770HlUpVazz6tHPnTiiVSrz22mvqNplMhhkzZuCvv/5CWlpanZd1+/btBo+fuKeE/r+ioiLk5+dDCIG8vDysWrUKd+7cwcSJEzX6ffTRRxgxYgQmTJgAhUKB7du3Y8yYMdi1axeGDx8O4MH5Ec899xy6d++ORYsWQS6X4/Llyzh06JB6OeXl5RgxYgQOHjyIV155BZ07d8Zvv/2GFStW4I8//sCOHTs01vvrr78iISEBr7/+OuRyOdauXYuhQ4fi2LFj6Nq1KwDg+PHjOHz4MMaOHYuWLVsiKysL69atQ//+/fH7779r/dc5a9YsNGvWDAsWLEBWVhZWrlyJqKgoJCQkqPvMnz8fixcvxrPPPotnn30W6enpGDJkCBQKhV5e9x9//BHe3t7o06dPldP79u0Lb29vjT0fP/74I9q2bYvevXvXa50KhQIhISEoKyvDrFmz4O7ujr///hu7du1CYWEhHBwc1H3r8rrn5ubiqaeeUhcxrq6u+OWXXxAZGYni4mLMmTMHAKBSqfDcc88hOTkZY8eOxezZs3H79m0kJSXh7NmzCA4Oxrp16zBjxgyMHj0aL7zwAgCge/fu6nju37+PkJAQPPPMM/jwww/rvSchLi4O1tbWeOutt3D58mWsWrUKFhYWMDMzw61bt7Bw4UIcOXIEmzdvRps2bTB//vxql7Vy5Up8/vnn+OGHH7Bu3TrY2tqqY164cCFiY2MRHByMGTNm4OLFi1i3bh2OHz+OQ4cOwcLCQr2cgoICDBs2DGPHjsXEiRPh5uZW7TqTkpLw559/IiIiAu7u7urDdefOncORI0cgk8lqzP/SpUsIDQ3Fq6++ivDwcGzatAljxoxBYmIiBg8erNG3Lu+TzZs3w9bWFtHR0bC1tcW+ffswf/58FBcXY+nSpTXGolQqNYrhmjg5OcHMrPr/pU+dOoWmTZuic+fOGu29evVST3/mmWdqXc+AAQNw584dWFpaIiQkBMuWLUP79u3rFCM9IkEmbdOmTQKA1kMul4vNmzdr9S8tLdV4rlAoRNeuXcXAgQPVbStWrBAAxI0bN6pd79atW4WZmZk4cOCARvv69esFAHHo0CF1W0VMJ06cULdduXJFWFlZidGjR1cbmxBCpKWlCQDi888/18o5ODhYlJeXq9v/8Y9/CHNzc1FYWCiEECIvL09YWlqK4cOHa/T75z//KQCI8PDwavOrHPvMmTOrnFZYWCgAiJEjR9a4jBEjRggAori4WBQVFdVpnpqcOnVKABDffPNNjf3q+rpHRkYKDw8PkZ+frzH/2LFjhYODg3pc4uPjBQCxfPlyrXVVvL43btwQAMSCBQu0+oSHhwsA4q233tKa1rp16yrHo1+/fqJfv37q5ykpKQKA6Nq1q1AoFOr2cePGCZlMJoYNG6Yxf1BQkGjdurXWch+2YMECrW2+YvsZMmSIUKlU6vbVq1cLACI+Pl4jTgBi/fr1ta5LiKq39W3btgkAYv/+/eq2im09MzNT3da6dWsBQHz33XfqtqKiIuHh4SH8/f215q3tfVJdPNOnTxc2Njbi3r17NeZSMSZ1eVTOoyrDhw8Xbdu21WovKSmpdtupLCEhQUyePFls2bJF/PDDD+Kdd94RNjY2wsXFRVy9erXGeUk/ePiGAABr1qxBUlISkpKS8MUXX2DAgAGYOnWq1i5da2tr9d+3bt1CUVER+vTpg/T0dHV7xXH1nTt3ory8vMr1ffPNN+jcuTM6deqE/Px89WPgwIEAgJSUFI3+QUFBCAgIUD9v1aoVRo4cid27d6t3sVaOTalUoqCgAO3atYOjo6NGfBVeeeUVjf8o+/TpA5VKhStXrgAA9u7dC4VCgVmzZmn0q/jP/1Hdvn0bAGBnZ1djv4rpxcXFKC4urtM8NanYE7J7926UlpbW2Le2110Ige+++w7PP/88hBAaYxkSEoKioiL1a//dd9/BxcUFs2bN0lpPbf/ZVzZjxow6961OWFiYxl6KwMBACCEwZcoUjX6BgYG4du0a7t+/r/M6KrafOXPmaPx3P23aNNjb22ud9yOXyxEREVGnZVfe1u/du4f8/Hw89dRTAFDltv6wFi1aaJw8bW9vj7CwMJw6dUrrKpPa3icPx3P79m3k5+ejT58+KC0txYULF2qMpUePHurPntoe7u7uNS7r7t27kMvlWu1WVlbq6TV5+eWXsWnTJoSFhWHUqFF47733sHv3bhQUFOBf//pXjfOSfvDwDQF4sHuz8old48aNg7+/P6KiovDcc8/B0tISALBr1y4sXrwYp0+f1jjWXvlDKzQ0FJ999hmmTp2Kt956C4MGDcILL7yAl156Sf3hfOnSJZw/f17rPIoKFScOVqhq12mHDh1QWlqKGzduwN3dHXfv3kVcXBw2bdqEv//+G0IIdd+qdg+3atVK43mzZs0APCi2AKg/dB9et6urq7rvo6goLCqKk+pUVbzUNk9N2rRpg+joaCxfvhxffvkl+vTpgxEjRmDixIkah26A2l93MzMzFBYWYsOGDdVe7VMxlhkZGejYsaPWeUq6aNKkCVq2bFnv+Ss8PPYVeXt5eWm1l5eXo6ioCM7Ozjqto2L76dixo0a7paUl2rZtq/GlDgCenp7q91ltbt68idjYWGzfvl3rvVKXQyHt2rXTKgQ7dOgAAMjKytL48q/tfQI8OGT7zjvvYN++ferCua7xNGvWDMHBwbXGXBfW1tZVngN079499XRdPfPMMwgMDMTevXsfOT6qHYsSqpKZmRkGDBiAjz76CJcuXUKXLl1w4MABjBgxAn379sXatWvh4eEBCwsLbNq0CV999ZV6Xmtra+zfvx8pKSn46aefkJiYiISEBAwcOBB79uyBubk5ysvL0a1bNyxfvrzK9T/85VAXs2bNwqZNmzBnzhwEBQXBwcFBfRlgVXtsqjsLv3IxY0gODg7w8PDAmTNnaux35swZeHp6wt7eHsCD/3LPnj37SOtetmwZJk+ejJ07d2LPnj14/fXXERcXhyNHjuj0pV/xuk6cOBHh4eFV9ql8TsijksvlVZ5TUN2eFpVKVeU4Vzf2xtwmdPnCfPnll3H48GHMnTsXfn5+sLW1RXl5OYYOHVrt3sn6qu01KSwsRL9+/WBvb49FixbBx8cHVlZWSE9Px7x582qNR6FQ4ObNm3WKxdXVtcarZzw8PJCSkgIhhMY2kZ2dDeDBe6c+vLy8cPHixXrNS7phUULVqthlfefOHQAPdr9bWVlh9+7dGrtIN23apDWvmZkZBg0ahEGDBmH58uX497//jbfffhspKSkIDg6Gj48P/vvf/2LQoEF12nV/6dIlrbY//vgDNjY26r0t3377LcLDw7Fs2TJ1n3v37mld6VBXrVu3Vq+74nJcALhx44bGf4mP4rnnnsOnn36KgwcPVnkC3oEDB5CVlYXp06drzLNhwwakpaUhKCio3uvu1q0bunXrhnfeeQeHDx/G008/jfXr12Px4sXqPnV53e3s7KBSqWr9b9fHxwdHjx6FUqnUOHRSmS6HcSpr1qxZleN85coVjbFrSBXbz8WLFzViUCgUyMzMrPfegVu3biE5ORmxsbEaJ+BWNVbVuXz5stYX9x9//AHgwdU5ukhNTUVBQQG+//579O3bV92emZlZp/kPHz6MAQMG1KlvZmZmjfH5+fnhs88+w/nz5+Hr66tuP3r0qHp6ffz555/V7tUl/eI5JVQlpVKJPXv2wNLSUn0mu7m5OWQymcZlcllZWVpXylT1X0/Fh0HFrtWXX34Zf//9Nz799FOtvnfv3kVJSYlGW1pamsax8mvXrmHnzp0YMmSI+j8nc3Nzrf9oV61aVe/L+oKDg2FhYYFVq1ZpLHflypX1Wl5V5s6dC2tra0yfPl3rcs6bN2/i1VdfhY2NDebOnatuf/PNN9G0aVNMnToVubm5WsvMyMjARx99VO06i4uLtc6R6NatG8zMzLR2fdf2upubm+PFF1/Ed999V+Xem8qXjr744ovIz89X3z+isorXt+JqGl0LSR8fHxw5ckTjqqhdu3bh2rVrOi1Hn4KDg2FpaYmPP/5YY/vZuHEjioqK1Fer6apie394W9dlu7x+/Tp++OEH9fPi4mJ8/vnn8PPzq/W8jbrEo1AosHbt2jrNr89zSkaOHAkLCwuNdQshsH79enh6empcsZadnY0LFy5AqVSq2x6+1BkAfv75Z5w8eRJDhw6tUz70aLinhAAAv/zyi/qEtLy8PHz11Ve4dOkS3nrrLfVhg+HDh2P58uUYOnQoxo8fj7y8PKxZswbt2rXTOASxaNEi7N+/H8OHD0fr1q2Rl5eHtWvXomXLluq9AZMmTcLXX3+NV199FSkpKXj66aehUqlw4cIFfP3119i9e7fGOS5du3ZFSEiIxqWpANR3/wQe7EHYunUrHBwc4Ovri7S0NOzdu1fncwEquLq64o033kBcXByee+45PPvsszh16hR++eUXuLi41Hk5J06c0Nj7UKF///545plnsGXLFkyYMAHdunXTuqNrfn4+tm3bBh8fH/V8Pj4++OqrrxAaGorOnTtr3NH18OHD+Oabb2r8XZ59+/YhKioKY8aMQYcOHXD//n1s3bpVXWBUVpfX/f3330dKSgoCAwMxbdo0+Pr64ubNm0hPT8fevXvVRWpYWBg+//xzREdH49ixY+jTpw9KSkqwd+9evPbaaxg5ciSsra3h6+uLhIQEdOjQAU5OTujatav68uPqTJ06Fd9++y2GDh2Kl19+GRkZGfjiiy80XreG5urqipiYGMTGxmLo0KEYMWIELl68iLVr1+LJJ5/Uuty+ruzt7dG3b18sWbIESqUSnp6e2LNnT533TAAPzh+JjIzE8ePH4ebmhvj4eOTm5la517M2vXv3RrNmzRAeHo7XX38dMpkMW7durfMhL32eU9KyZUvMmTMHS5cuhVKpxJNPPokdO3bgwIED+PLLLzUO/cTExGDLli0ae1969+4Nf39/9OzZEw4ODkhPT0d8fDy8vLxqvG8M6VGDX+9DklLVJcFWVlbCz89PrFu3TuNSQCGE2Lhxo2jfvr2Qy+WiU6dOYtOmTerLISskJyeLkSNHihYtWghLS0vRokULMW7cOPHHH39oLEuhUIgPPvhAdOnSRcjlctGsWTMREBAgYmNjRVFRkbof/v9ltV988YV63f7+/iIlJUVjebdu3RIRERHCxcVF2NraipCQEHHhwgWty0Urcj5+/LjG/BWXJlZerkqlErGxscLDw0NYW1uL/v37i7Nnz1Z7CerDHn5tKz/ee+89db8zZ86IcePGCQ8PD2FhYSHc3d3FuHHjxG+//Vbtsv/44w8xbdo04e3tLSwtLYWdnZ14+umnxapVq2q8DPPPP/8UU6ZMET4+PsLKyko4OTmJAQMGiL1792rFXpfXXQghcnNzxcyZM4WXl5c6/kGDBokNGzZo9CstLRVvv/22aNOmjbrfSy+9JDIyMtR9Dh8+LAICAoSlpaXG5cHh4eGiadOm1ea1bNky4enpKeRyuXj66afFiRMnqr0k+OHLoavbJqq61LcqNfVbvXq16NSpk7CwsBBubm5ixowZ4tatWxp9+vXrJ7p06VLjOir766+/xOjRo4Wjo6NwcHAQY8aMEdevX9e6nLq6S4KHDx8udu/eLbp3765+L9f1NanqfXLo0CHx1FNPCWtra9GiRQvx5ptvit27d2v1awgqlUr8+9//Fq1btxaWlpaiS5cu4osvvtDqV3GJeeXX5u233xZ+fn7CwcFBWFhYiFatWokZM2aInJycBszAtMmEaKCz+ojosSKTyTRu102Ng7e3N7p27Ypdu3YZOxQiLTynhIiIiCSBRQkRERFJAosSIiIikgSeU0JERESSwD0lREREJAksSoiIiEgSTO7maeXl5bh+/Trs7OzqfUtrIiIiUySEwO3bt9GiRYsqf4fqUZlcUXL9+vV6/dgbERERPXDt2jW9/GL3w0yuKKn4+ffMzEw4OTkZORrDqfjtmiFDhlT742eNhankyjwbF+bZuJhKnjdv3kSbNm3U36X6ZnJFScUhGzs7O/VvujRGSqUSNjY2sLe3b9RvEMB0cmWejQvzbFxMKU+g/r/oXRue6EpERESSwKKEiIiIJIFFCREREUkCixIiIiKSBBYlREREJAksSoiIiEgSTO6SYCJ6NKpygWOZN5F3+x6a21mhVxsnmJvx7sikTVUucDTzJk7my+CceRNB7ZpzW6EaSaIoWbNmDZYuXYqcnBz06NEDq1atQq9evarsu3nzZkRERGi0yeVy3Lt3ryFCJTJpiWezEfvj78gu+t/7zcPBCgue98XQrh5GjIykRnNbMcfnl05wW6FaGf3wTUJCAqKjo7FgwQKkp6ejR48eCAkJQV5eXrXz2NvbIzs7W/24cuVKA0ZMZJoSz2ZjxhfpGgUJAOQU3cOML9KReDbbSJGR1HBbofoyelGyfPlyTJs2DREREfD19cX69ethY2OD+Pj4aueRyWRwd3dXP9zc3BowYiLToyoXiP3xd4gqplW0xf74O1TlVfUgU8JthR6FUQ/fKBQKnDx5EjExMeo2MzMzBAcHIy0trdr57ty5g9atW6O8vBxPPPEE/v3vf6NLly5V9i0rK0NZWZn6eXFxMYAHt8qtuF1uY1SRW2POsYKp5GrMPI9m3tT6r7cyASC76B7SLuchsM2j/aYUx/Px1pDbipQ01vF8mKHzM2pRkp+fD5VKpbWnw83NDRcuXKhyno4dOyI+Ph7du3dHUVERPvzwQ/Tu3Rvnzp2r8hcL4+LiEBsbq9WekpICGxsb/SQiYUlJScYOocGYSq7GyPNkvgyAea399hw4ioLz+vkPmOP5eDLGtiIljW08H1ZaWmrQ5UviRFddBAUFISgoSP28d+/e6Ny5Mz755BO89957Wv1jYmIQHR2tfl5cXAwvLy8MGDAAzs7ODRKzMSiVSiQlJWHw4MGN+sehANPJ1Zh5OmfexOeXTtTab0ifQL3sKeF4Pr4acluRksY6ng8rKCgw6PKNWpS4uLjA3Nwcubm5Gu25ublwd3ev0zIsLCzg7++Py5cvVzldLpdDLpdXOV9j3nAqmEqegOnkaow8g9o1h4eDFXKK7lV5roAMgLuDlV4v+eR4Pp6Msa1ISWMbz4cZOjejnuhqaWmJgIAAJCcnq9vKy8uRnJyssTekJiqVCr/99hs8PHiJGZGhmJvJsOB5XwAPvlQqq3i+4HnfRvklQ7rhtkKPwuhX30RHR+PTTz/Fli1bcP78ecyYMQMlJSXqe5GEhYVpnAi7aNEi7NmzB3/++SfS09MxceJEXLlyBVOnTjVWCkQmYWhXD6yb+ASa22vueXR3sMK6iU/w3hOkxm2F6svo55SEhobixo0bmD9/PnJycuDn54fExET1ya9Xr16Fmdn/aqdbt25h2rRpyMnJQbNmzRAQEIDDhw/D19fXWCkQmYyhXT3wdDsXdFu4BwCwOeJJ9Gnvyv96ScvD28pnk/wxoLMHtxWqkdGLEgCIiopCVFRUldNSU1M1nq9YsQIrVqxogKiIqCqVv1R4i3mqSeVt40nvZtxWqFZGP3xDREREBLAoISIiIolgUUJERESSwKKEiIiIJIFFCREREUkCixIiIiKSBBYlREREJAksSoiIiEgSWJQQERGRJLAoISIiIklgUUJERESSwKKEiIiIJIFFCREREUkCixIiIiKSBBYlREREJAksSoiIiEgSWJQQERGRJLAoISIiIklgUUJERESSwKKEiIiIJIFFCREREUkCixIiIiKSBBYlREREJAksSoiIiEgSWJQQERGRJLAoISIiIklgUUJERESSwKKEiIiIJIFFCREREUkCixIiIiKSBBYlREREJAksSoiIiEgSWJQQERGRJLAoISIiIklgUUJERESSwKKEiIiIJIFFCREREUkCixIiIiKSBBYlREREJAksSoiIiEgSWJQQERGRJLAoISIiIklgUUJERESSwKKEiIiIJIFFCREREUmCJIqSNWvWwNvbG1ZWVggMDMSxY8fqNN/27dshk8kwatQowwZIREREBmf0oiQhIQHR0dFYsGAB0tPT0aNHD4SEhCAvL6/G+bKysvDGG2+gT58+DRQpERERGZLRi5Lly5dj2rRpiIiIgK+vL9avXw8bGxvEx8dXO49KpcKECRMQGxuLtm3bNmC0REREZChNjLlyhUKBkydPIiYmRt1mZmaG4OBgpKWlVTvfokWL0Lx5c0RGRuLAgQM1rqOsrAxlZWXq58XFxQAApVIJpVL5iBlIV0VujTnHCqaSq1TyVCrvV/pbCaVM6Hn50sjT0EwhT81t5X4jz7Xxjydg+PyMWpTk5+dDpVLBzc1No93NzQ0XLlyocp6DBw9i48aNOH36dJ3WERcXh9jYWK32lJQU2NjY6Bzz4yYpKcnYITQYU8nV2HmWqYCKj47du/dAbm6Y9Rg7z4bSmPOsvK3s27fPYNuKlDTm8QSA0tJSgy7fqEWJrm7fvo1Jkybh008/hYuLS53miYmJQXR0tPp5cXExvLy8MGDAADg7OxsqVKNTKpVISkrC4MGDYWFhYexwDMpUcpVKnqWK+3jz2D4AQEjIENhY6vdjRCp5Gpop5Fl5Wxk4cCAcmloZOSLDMYXxBICCggKDLt+oRYmLiwvMzc2Rm5ur0Z6bmwt3d3et/hkZGcjKysLzzz+vbisvLwcANGnSBBcvXoSPj4/GPHK5HHK5XGtZFhYWjXrDqWAqeQKmk6ux87QQsodiMczHiLHzbCiNOU/NbaVJo82zssY8ngAMnptRT3S1tLREQEAAkpOT1W3l5eVITk5GUFCQVv9OnTrht99+w+nTp9WPESNGYMCAATh9+jS8vLwaMnwiIiLSI6MfvomOjkZ4eDh69uyJXr16YeXKlSgpKUFERAQAICwsDJ6enoiLi4OVlRW6du2qMb+joyMAaLUTERHR48XoRUloaChu3LiB+fPnIycnB35+fkhMTFSf/Hr16lWYmRn9ymUiIiIyMKMXJQAQFRWFqKioKqelpqbWOO/mzZv1HxARERE1OO6CICIiIklgUUJERESSwKKEiIiIJIFFCREREUkCixIiIiKSBBYlREREJAksSoiIiEgSWJQQERGRJLAoISIiIklgUUJERESSwKKEiIiIJIFFCREREUkCixIiIiKSBBYlREREJAksSoiIiEgSWJQQERGRJLAoISIiIklgUUJERESSwKKEiIiIJIFFCREREUkCixIiIiKSBBYlREREJAksSoiIiEgSWJQQERGRJLAoISIiIklgUUJERESSwKKEiIiIJIFFCREREUkCixIiIiKShCa6dC4sLMQPP/yAAwcO4MqVKygtLYWrqyv8/f0REhKC3r17GypOIiIiauTqtKfk+vXrmDp1Kjw8PLB48WLcvXsXfn5+GDRoEFq2bImUlBQMHjwYvr6+SEhIMHTMRERE1AjVaU+Jv78/wsPDcfLkSfj6+lbZ5+7du9ixYwdWrlyJa9eu4Y033tBroERERNS41ako+f333+Hs7FxjH2tra4wbNw7jxo1DQUGBXoIjIiIi01GnwzfOzs7YtWsXysvL67TQ2goYIiIioofV+eqbUaNGwcvLC2+//TYuX75syJiIiIjIBNW5KMnMzMT06dOxfft2dOzYEf369cPWrVtx9+5dQ8ZHREREJqLORYmXlxfmz5+PjIwM7N27F97e3pgxYwY8PDzw6quv4vjx44aMk4iIiBq5et08bcCAAdiyZQuys7OxdOlS/Pbbb3jqqafQo0cPfcdHREREJkKnm6c9zM7ODoMGDcKVK1dw4cIF/P777/qKi4iIiExMvfaU3L17F59//jn69++P9u3bY/v27YiOjkZWVpaewyMiIiJTodOekiNHjiA+Ph5ff/01FAoFXnjhBezduxcDBgwwVHxERERkIupclPj6+uLixYvw9/dHXFwcxo8fDwcHB0PGRkRERCakzkVJcHAwtm3bxpNZiYiIyCDqXJR8/PHHhoyDiIiITFydTnQdOnQojhw5Umu/27dv44MPPsCaNWseOTAiIiIyLXUqSsaMGYMXX3wRvr6+mDdvHr755hscOnQIJ0+exN69e/Hxxx/j5ZdfhoeHB9LT0/H888/rFMSaNWvg7e0NKysrBAYG4tixY9X2/f7779GzZ084OjqiadOm8PPzw9atW3VaHxEREUlPnQ7fREZGYuLEifjmm2+QkJCADRs2oKioCAAgk8ng6+uLkJAQHD9+HJ07d9YpgISEBERHR2P9+vUIDAzEypUrERISgosXL6J58+Za/Z2cnPD222+jU6dOsLS0xK5duxAREYHmzZsjJCREp3UTERGRdNT5nBK5XI6JEydi4sSJAICioiLcvXsXzs7OsLCwqHcAy5cvx7Rp0xAREQEAWL9+PX766SfEx8fjrbfe0urfv39/jeezZ8/Gli1bcPDgQRYlREREj7F639HVwcHhkS8JVigUOHnyJGJiYtRtZmZmCA4ORlpaWq3zCyGwb98+XLx4ER988EGVfcrKylBWVqZ+XlxcDABQKpVQKpWPFL+UVeTWmHOsYCq5SiVPpfJ+pb+VUMqEnpcvjTwNzRTy1NxW7jfyXBv/eAKGz++RbjP/qPLz86FSqeDm5qbR7ubmhgsXLlQ7X1FRETw9PVFWVgZzc3OsXbsWgwcPrrJvXFwcYmNjtdpTUlJgY2PzaAk8BpKSkowdQoMxlVyNnWeZCqj46Ni9ew/k5oZZj7HzbCiNOc/K28q+ffsMtq1ISWMeTwAoLS016PKNWpTUl52dHU6fPo07d+4gOTkZ0dHRaNu2rdahHQCIiYlBdHS0+nlxcTG8vLwwYMAAODs7N2DUDUupVCIpKQmDBw9+pMNrjwNTyVUqeZYq7uPNY/sAACEhQ2Bjqd+PEankaWimkGflbWXgwIFwaGpl5IgMxxTGEwAKCgoMunyjFiUuLi4wNzdHbm6uRntubi7c3d2rnc/MzAzt2rUDAPj5+eH8+fOIi4ursiiRy+WQy+Va7RYWFo16w6lgKnkCppOrsfO0ELKHYjHMx4ix82wojTlPzW2lSaPNs7LGPJ4ADJ5bvX6QT18sLS0REBCA5ORkdVt5eTmSk5MRFBRU5+WUl5drnDdCREREj596/YtTWFiIb7/9FhkZGZg7dy6cnJyQnp4ONzc3eHp66rSs6OhohIeHo2fPnujVqxdWrlyJkpIS9dU4YWFh8PT0RFxcHIAH54j07NkTPj4+KCsrw88//4ytW7di3bp19UmFiIiIJELnouTMmTMIDg6Gg4MDsrKyMG3aNDg5OeH777/H1atX8fnnn+u0vNDQUNy4cQPz589HTk4O/Pz8kJiYqD759erVqzAz+98OnZKSErz22mv466+/YG1tjU6dOuGLL75AaGiorqkQERGRhOhclERHR2Py5MlYsmQJ7Ozs1O3PPvssxo8fX68goqKiEBUVVeW01NRUjeeLFy/G4sWL67UeIiIiki6dzyk5fvw4pk+frtXu6emJnJwcvQRFREREpkfnokQul6tvQFbZH3/8AVdXV70ERURERKZH56JkxIgRWLRokfqubjKZDFevXsW8efPw4osv6j1AIiIiMg06FyXLli3DnTt30Lx5c9y9exf9+vVDu3btYGdnh3/961+GiJGIiIhMgM4nujo4OCApKQkHDx7EmTNncOfOHTzxxBMIDg42RHxERERkIup9K8ZnnnkGzzzzjD5jISIiIhNWp6Lk448/rvMCX3/99XoHQ0RERKarTkXJihUrNJ7fuHEDpaWlcHR0BPDgDq82NjZo3rw5ixIiIiKqlzqd6JqZmal+/Otf/1L/CN7Nmzdx8+ZNnD9/Hk888QTee+89Q8dLREREjZTOV9+8++67WLVqFTp27Khu69ixI1asWIF33nlHr8ERERGR6dC5KMnOzsb9+/e12lUqFXJzc/USFBEREZkenYuSQYMGYfr06UhPT1e3nTx5EjNmzOBlwURERFRvOhcl8fHxcHd3R8+ePSGXyyGXy9GrVy+4ubnhs88+M0SMREREZAJ0vk+Jq6srfv75Z/zxxx+4cOECAKBTp07o0KGD3oMjIiIi01Hvm6d16NCBhQgRERHpjc5FyZQpU2qcHh8fX+9giIiIyHTpXJTcunVL47lSqcTZs2dRWFiIgQMH6i0wIiIiMi06FyU//PCDVlt5eTlmzJgBHx8fvQRFREREpkfnq2+qXIiZGaKjo7VuR09ERERUV3opSgAgIyOjypuqEREREdWFzodvoqOjNZ4LIZCdnY2ffvoJ4eHheguMiIiITIvORcmpU6c0npuZmcHV1RXLli2r9cocIiIiouroXJSkpKQYIg4iIiIycTqfUzJw4EAUFhZqtRcXF/OSYCIiIqo3nYuS1NRUKBQKrfZ79+7hwIEDegmKiIiITE+dD9+cOXNG/ffvv/+OnJwc9XOVSoXExER4enrqNzoiIiIyGXUuSvz8/CCTySCTyao8TGNtbY1Vq1bpNTgiIiIyHXUuSjIzMyGEQNu2bXHs2DG4urqqp1laWqJ58+YwNzc3SJBERETU+NW5KGndujWAB7eUJyIiItK3OhUl//nPfzBs2DBYWFjgP//5T419R4wYoZfAiIiIyLTUqSgZNWoUcnJy0Lx5c4waNarafjKZDCqVSl+xERERkQmpU1FS+ZAND98QERGRIejtB/mIiIiIHoXOt5kHgOTkZCQnJyMvL09rz0l8fLxeAiMiIiLTonNREhsbi0WLFqFnz57w8PCATCYzRFxERERkYnQuStavX4/Nmzdj0qRJhoiHiIiITJTO55QoFAr07t3bELEQERGRCdO5KJk6dSq++uorQ8RCREREJkznwzf37t3Dhg0bsHfvXnTv3h0WFhYa05cvX6634IiIiMh06FyUnDlzBn5+fgCAs2fPakzjSa9ERERUXzoXJSkpKYaIg4iIiEwcb55GREREkqDznpLRo0dXeZhGJpPBysoK7dq1w/jx49GxY0e9BEhERESmQec9JQ4ODti3bx/S09Mhk8kgk8lw6tQp7Nu3D/fv30dCQgJ69OiBQ4cOGSJeIiIiaqR03lPi7u6O8ePHY/Xq1TAze1DTlJeXY/bs2bCzs8P27dvx6quvYt68eTh48KDeAyYiIqLGSec9JRs3bsScOXPUBQkAmJmZYdasWdiwYQNkMhmioqK0rsypyZo1a+Dt7Q0rKysEBgbi2LFj1fb99NNP0adPHzRr1gzNmjVDcHBwjf2JiIjo8aBzUXL//n1cuHBBq/3ChQtQqVQAACsrqzpfHpyQkIDo6GgsWLAA6enp6NGjB0JCQpCXl1dl/9TUVIwbNw4pKSlIS0uDl5cXhgwZgr///lvXVIiIiEhCdC5KJk2ahMjISKxYsQIHDx7EwYMHsWLFCkRGRiIsLAwA8Ouvv6JLly51Wt7y5csxbdo0REREwNfXF+vXr4eNjU21vzb85Zdf4rXXXoOfnx86deqEzz77DOXl5UhOTtY1FSIiIpIQnc8pWbFiBdzc3LBkyRLk5uYCANzc3PCPf/wD8+bNAwAMGTIEQ4cOrXVZCoUCJ0+eRExMjLrNzMwMwcHBSEtLq1M8paWlUCqVcHJyqnJ6WVkZysrK1M+Li4sBAEqlEkqlsk7reBxV5NaYc6xgKrlKJU+l8n6lv5VQyoSely+NPA3NFPLU3FbuN/JcG/94AobPTyaEqPcnSsUXvL29fb3mv379Ojw9PXH48GEEBQWp29988038+uuvOHr0aK3LeO2117B7926cO3cOVlZWWtMXLlyI2NhYrfavvvoKNjY29YqbyJSVqYA3jz34f2ZJr/uQmxs5IJIsbiuNT2lpKcaPH4+ioqJ6f/fXROc9JZUZIiBdvP/++9i+fTtSU1OrLEgAICYmBtHR0ernxcXF8PLywoABA+Ds7NxQoTY4pVKJpKQkDB48WOv3iRobU8lVKnmWKu7jzWP7AAAhIUNgY/lIHyNapJKnoZlCnpW3lYEDB8KhadWf042BKYwnABQUFBh0+fX6NPn222/x9ddf4+rVq1AoFBrT0tPT67wcFxcXmJubqw8DVcjNzYW7u3uN83744Yd4//331T8MWB25XA65XK7VbmFh0ag3nAqmkidgOrkaO08L8b+T2B/Eot+iRHPZHM/Hmea20qTR5llZYx5PAAbPTecTXT/++GNERETAzc0Np06dQq9eveDs7Iw///wTw4YN02lZlpaWCAgI0DhJteKk1cqHcx62ZMkSvPfee0hMTETPnj11TYGIiIgkSOeiZO3atdiwYQNWrVoFS0tLvPnmm0hKSsLrr7+OoqIinQOIjo7Gp59+ii1btuD8+fOYMWMGSkpKEBERAQAICwvTOBH2gw8+wLvvvov4+Hh4e3sjJycHOTk5uHPnjs7rJiIiIunQeb/r1atX0bt3bwCAtbU1bt++DeDBpcJPPfUUVq9erdPyQkNDcePGDcyfPx85OTnw8/NDYmIi3Nzc1OurfKO2devWQaFQ4KWXXtJYzoIFC7Bw4UJd0yEiIiKJqNdt5m/evInWrVujVatWOHLkCHr06IHMzEzU90KeqKgoREVFVTktNTVV43lWVla91kFERETSpvPhm4EDB+I///kPACAiIgL/+Mc/MHjwYISGhmL06NF6D5CIiIhMg857SjZs2IDy8nIAwMyZM+Hs7IzDhw9jxIgRmD59ut4DJCIiItOgc1FiZmamcY7H2LFjMXbsWL0GRURERKanXjcYuHfvHs6cOYO8vDz1XpMKI0aM0EtgREREZFp0LkoSExMRFhaG/Px8rWkymUz9S8FEREREutD5RNdZs2ZhzJgxyM7ORnl5ucaDBQkRERHVl85FSW5uLqKjo9X3ESEiIiLSB52Lkpdeeknr3iFEREREj0rnc0pWr16NMWPG4MCBA+jWrZvWj/O8/vrreguOiIiITIfORcm2bduwZ88eWFlZITU1FTLZ/34FUiaTsSghIiKietG5KHn77bcRGxuLt956S+N+JURERESPQueqQqFQIDQ0lAUJERER6ZXOlUV4eDgSEhIMEQsRERGZMJ0P36hUKixZsgS7d+9G9+7dtU50Xb58ud6CIyIiItOhc1Hy22+/wd/fHwBw9uxZjWmVT3olIiIi0oXORUlKSooh4iAiIiITx7NViYiISBJYlBAREZEksCghIiIiSWBRQkRERJLAooSIiIgkgUUJERERSQKLEiIiIpIEFiVEREQkCSxKiIiISBJYlBAREZEksCghIiIiSWBRQkRERJLAooSIiIgkgUUJERERSQKLEiIiIpIEFiVEREQkCSxKiIiISBJYlBAREZEksCghIiIiSWBRQkRERJLAooSIiIgkgUUJERERSQKLEiIiIpIEFiVEREQkCSxKiIiISBJYlBAREZEksCghIiIiSWBRQkRERJLAooSIiIgkwehFyZo1a+Dt7Q0rKysEBgbi2LFj1fY9d+4cXnzxRXh7e0Mmk2HlypUNFygREREZlFGLkoSEBERHR2PBggVIT09Hjx49EBISgry8vCr7l5aWom3btnj//ffh7u7ewNESERGRIRm1KFm+fDmmTZuGiIgI+Pr6Yv369bCxsUF8fHyV/Z988kksXboUY8eOhVwub+BoiYiIyJCaGGvFCoUCJ0+eRExMjLrNzMwMwcHBSEtL09t6ysrKUFZWpn5eXFwMAFAqlVAqlXpbj9RU5NaYc6xgKrlKJU+l8n6lv5VQyoSely+NPA3NFPLU3FbuN/JcG/94AobPz2hFSX5+PlQqFdzc3DTa3dzccOHCBb2tJy4uDrGxsVrtKSkpsLGx0dt6pCopKcnYITQYU8nV2HmWqYCKj47du/dAbm6Y9Rg7z4bSmPOsvK3s27fPYNuKlDTm8QQenEZhSEYrShpKTEwMoqOj1c+Li4vh5eWFAQMGwNnZ2YiRGZZSqURSUhIGDx4MCwsLY4djUKaSq1TyLFXcx5vH9gEAQkKGwMZSvx8jUsnT0Ewhz8rbysCBA+HQ1MrIERmOKYwnABQUFBh0+UYrSlxcXGBubo7c3FyN9tzcXL2exCqXy6s8/8TCwqJRbzgVTCVPwHRyNXaeFkL2UCyG+Rgxdp4NpTHnqbmtNGm0eVbWmMcTgMFzM9qJrpaWlggICEBycrK6rby8HMnJyQgKCjJWWERERGQkRj18Ex0djfDwcPTs2RO9evXCypUrUVJSgoiICABAWFgYPD09ERcXB+DBybG///67+u+///4bp0+fhq2tLdq1a2e0PIiIiOjRGbUoCQ0NxY0bNzB//nzk5OTAz88PiYmJ6pNfr169CjOz/+3MuX79Ovz9/dXPP/zwQ3z44Yfo168fUlNTGzp8IiIi0iOjn+gaFRWFqKioKqc9XGh4e3tDCP1efkhERETSYPTbzBMREREBLEqIiIhIIliUEBERkSSwKCEiIiJJYFFCREREksCihIiIiCSBRQkRERFJAosSIiIikgQWJURERCQJLEqIiIhIEliUEBERkSSwKCEiIiJJYFFCREREksCihIiIiCSBRQkRERFJAosSIiIikgQWJURERCQJLEqIiIhIEliUEBERkSSwKCEiIiJJYFFCREREksCihIiIiCSBRQkRERFJAosSIiIikgQWJURERCQJLEqIiIhIEliUEBERkSSwKCEiIiJJYFFCREREksCihIiIiCSBRQkRERFJAosSIiIikgQWJURERCQJLEqIiIhIEliUEBERkSSwKCEiIiJJYFFCREREksCihIiIiCSBRQkRERFJAosSIiIikgQWJURERCQJLEqIiIhIEliUEBERkSSwKCEiIiJJaGLsAIzlWOZN2N8SyCu+h5slCjjaWKKwVAEnWzma28oBGRpkmqGWXXDnLq7dkKFZRgHMmzQxep6GnHZfdR/Hb8iQezgLzrbWRnvNpZanoaY1s7HQeB/dKlHgZon+XnOp5GnoaTdu38WVvAd5utrbPDafLbpMu154V72tHM+6hRLlTbg0leZ46OMz15DjKZVpf+XeMOh3s0wIIQy6hjpYs2YNli5dipycHPTo0QOrVq1Cr169qu3/zTff4N1330VWVhbat2+PDz74AM8++2yd1lVcXAwHBwd4zfkaZnIbfaVARETU6JWXleLaypdRVFQEe3t7vS/f6IdvEhISEB0djQULFiA9PR09evRASEgI8vLyqux/+PBhjBs3DpGRkTh16hRGjRqFUaNG4ezZsw0cOREREemT0feUBAYG4sknn8Tq1asBAOXl5fDy8sKsWbPw1ltvafUPDQ1FSUkJdu3apW576qmn4Ofnh/Xr19e6voo9JT5RW2HOPSVERER1piorRcbqSQbbU2LUc0oUCgVOnjyJmJgYdZuZmRmCg4ORlpZW5TxpaWmIjo7WaAsJCcGOHTuq7F9WVoaysjL18+LiYgDAtsRFsDU3f8QMiIiITMcdlQrVn1zx6Ix6+CY/Px8qlQpubm4a7W5ubsjJyalynpycHJ36x8XFwcHBQf3w8vLST/BERESkV43+6puYmBiNPSvFxcXw8vLCuKHzefiGiIhIB6qyUmD1JIMt36hFiYuLC8zNzZGbm6vRnpubC3d39yrncXd316m/XC6HXC7Xalc0kcOsiXY7ERERVa1cpTLo8o16+MbS0hIBAQFITk5Wt5WXlyM5ORlBQUFVzhMUFKTRHwCSkpKq7U9ERMZm9DtP0GPC6IdvoqOjER4ejp49e6JXr15YuXIlSkpKEBERAQAICwuDp6cn4uLiAACzZ89Gv379sGzZMgwfPhzbt2/HiRMnsGHDBmOmQWRSHP//DdQKS5VGjoQeBzKwLKG6MXpREhoaihs3bmD+/PnIycmBn58fEhMT1SezXr16FWZm/9uh07t3b3z11Vd455138M9//hPt27fHjh070LVrV53W+8kEP9g7NjP6XfMMekfXS+cx+JleJnFH16SDx9CqfedGf0dXXfI01DR3eyv0auME4MEdXXOK7ur9jq5SyLNB7uj6x3m07tC50d7RNf9OGZxtmiD33BG4dXkKBaX3G/cdXQ04nlKZ9lfuDcxZqbcSQIvRixIAiIqKQlRUVJXTUlNTtdrGjBmDMWPGPNI6e7VxgrOz8yMtQ8qUSiV+LvwdQT7OsLCwqH2Gx5hSqUThRYFne3s36lylmGeQj/7fQ1LM0xAq3qMmked5ILCNU+PP0wTGs6DAGnMMuHyj39GViIiICGBRQkRERBLBooSIiIgkgUUJERERSQKLEiIiIpIEFiVEREQkCZK4JLghCfHgFj63b99u1JdtKZVKlJaWori4uFHnCZhOrsyzcWGejYup5Hn79m0A//su1TeTK0oKCgoAAG3atDFyJERERI+ngoICODg46H25JleUODk9uBPl1atXDfKCSkXFryFfu3YN9vb2xg7HoEwlV+bZuDDPxsVU8iwqKkKrVq3U36X6ZnJFScUt6x0cHBr1hlPB3t7eJPIETCdX5tm4MM/GxVTyrPzzL3pdrkGWSkRERKQjFiVEREQkCSZXlMjlcixYsAByudzYoRiUqeQJmE6uzLNxYZ6NC/PUD5kw1HU9RERERDowuT0lREREJE0sSoiIiEgSWJQQERGRJLAoISIiIkkwuaJkzZo18Pb2hpWVFQIDA3Hs2DFjh/RI4uLi8OSTT8LOzg7NmzfHqFGjcPHiRY0+/fv3h0wm03i8+uqrRoq4fhYuXKiVQ6dOndTT7927h5kzZ8LZ2Rm2trZ48cUXkZuba8SI68fb21srT5lMhpkzZwJ4fMdy//79eP7559GiRQvIZDLs2LFDY7oQAvPnz4eHhwesra0RHByMS5cuafS5efMmJkyYAHt7ezg6OiIyMhJ37txpwCxqV1OeSqUS8+bNQ7du3dC0aVO0aNECYWFhuH79usYyqtoG3n///QbOpGa1jefkyZO1chg6dKhGn8dhPIHac63q/SqTybB06VJ1H6mPaV2+R+ryGXv16lUMHz4cNjY2aN68OebOnYv79+/rFItJFSUJCQmIjo7GggULkJ6ejh49eiAkJAR5eXnGDq3efv31V8ycORNHjhxBUlISlEolhgwZgpKSEo1+06ZNQ3Z2tvqxZMkSI0Vcf126dNHI4eDBg+pp//jHP/Djjz/im2++wa+//orr16/jhRdeMGK09XP8+HGNHJOSkgAAY8aMUfd5HMeypKQEPXr0wJo1a6qcvmTJEnz88cdYv349jh49iqZNmyIkJAT37t1T95kwYQLOnTuHpKQk7Nq1C/v378crr7zSUCnUSU15lpaWIj09He+++y7S09Px/fff4+LFixgxYoRW30WLFmmM8axZsxoi/DqrbTwBYOjQoRo5bNu2TWP64zCeQO25Vs4xOzsb8fHxkMlkePHFFzX6SXlM6/I9UttnrEqlwvDhw6FQKHD48GFs2bIFmzdvxvz583ULRpiQXr16iZkzZ6qfq1Qq0aJFCxEXF2fEqPQrLy9PABC//vqruq1fv35i9uzZxgtKDxYsWCB69OhR5bTCwkJhYWEhvvnmG3Xb+fPnBQCRlpbWQBEaxuzZs4WPj48oLy8XQjSOsQQgfvjhB/Xz8vJy4e7uLpYuXapuKywsFHK5XGzbtk0IIcTvv/8uAIjjx4+r+/zyyy9CJpOJv//+u8Fi18XDeVbl2LFjAoC4cuWKuq1169ZixYoVhg1Oj6rKMzw8XIwcObLaeR7H8RSibmM6cuRIMXDgQI22x21MH/4eqctn7M8//yzMzMxETk6Ous+6deuEvb29KCsrq/O6TWZPiUKhwMmTJxEcHKxuMzMzQ3BwMNLS0owYmX4VFRUBgNaPJX355ZdwcXFB165dERMTg9LSUmOE90guXbqEFi1aoG3btpgwYQKuXr0KADh58iSUSqXG2Hbq1AmtWrV6rMdWoVDgiy++wJQpUyCTydTtjWEsK8vMzEROTo7G+Dk4OCAwMFA9fmlpaXB0dETPnj3VfYKDg2FmZoajR482eMz6UlRUBJlMBkdHR432999/H87OzvD398fSpUt13gUuBampqWjevDk6duyIGTNmqH+hHWi845mbm4uffvoJkZGRWtMepzF9+HukLp+xaWlp6NatG9zc3NR9QkJCUFxcjHPnztV53Sbzg3z5+flQqVQaLxgAuLm54cKFC0aKSr/Ky8sxZ84cPP300+jatau6ffz48WjdujVatGiBM2fOYN68ebh48SK+//57I0arm8DAQGzevBkdO3ZEdnY2YmNj0adPH5w9exY5OTmwtLTU+mB3c3NDTk6OcQLWgx07dqCwsBCTJ09WtzWGsXxYxRhV9d6smJaTk4PmzZtrTG/SpAmcnJwe2zG+d+8e5s2bh3Hjxmn8gNvrr7+OJ554Ak5OTjh8+DBiYmKQnZ2N5cuXGzFa3QwdOhQvvPAC2rRpg4yMDPzzn//EsGHDkJaWBnNz80Y5ngCwZcsW2NnZaR06fpzGtKrvkbp8xubk5FT5Hq6YVlcmU5SYgpkzZ+Ls2bMa51oA0DhO261bN3h4eGDQoEHIyMiAj49PQ4dZL8OGDVP/3b17dwQGBqJ169b4+uuvYW1tbcTIDGfjxo0YNmwYWrRooW5rDGNJD056ffnllyGEwLp16zSmRUdHq//u3r07LC0tMX36dMTFxT02tzAfO3as+u9u3bqhe/fu8PHxQWpqKgYNGmTEyAwrPj4eEyZMgJWVlUb74zSm1X2PNBSTOXzj4uICc3NzrbOFc3Nz4e7ubqSo9CcqKgq7du1CSkoKWrZsWWPfwMBAAMDly5cbIjSDcHR0RIcOHXD58mW4u7tDoVCgsLBQo8/jPLZXrlzB3r17MXXq1Br7NYaxrBijmt6b7u7uWiek379/Hzdv3nzsxriiILly5QqSkpJq/Zn7wMBA3L9/H1lZWQ0ToAG0bdsWLi4u6u20MY1nhQMHDuDixYu1vmcB6Y5pdd8jdfmMdXd3r/I9XDGtrkymKLG0tERAQACSk5PVbeXl5UhOTkZQUJARI3s0QghERUXhhx9+wL59+9CmTZta5zl9+jQAwMPDw8DRGc6dO3eQkZEBDw8PBAQEwMLCQmNsL168iKtXrz62Y7tp0yY0b94cw4cPr7FfYxjLNm3awN3dXWP8iouLcfToUfX4BQUFobCwECdPnlT32bdvH8rLy9WF2eOgoiC5dOkS9u7dC2dn51rnOX36NMzMzLQOdzxO/vrrLxQUFKi308YynpVt3LgRAQEB6NGjR619pTamtX2P1OUzNigoCL/99ptGsVlRdPv6+uoUjMnYvn27kMvlYvPmzeL3338Xr7zyinB0dNQ4W/hxM2PGDOHg4CBSU1NFdna2+lFaWiqEEOLy5cti0aJF4sSJEyIzM1Ps3LlTtG3bVvTt29fIkevm//7v/0RqaqrIzMwUhw4dEsHBwcLFxUXk5eUJIYR49dVXRatWrcS+ffvEiRMnRFBQkAgKCjJy1PWjUqlEq1atxLx58zTaH+exvH37tjh16pQ4deqUACCWL18uTp06pb7q5P333xeOjo5i586d4syZM2LkyJGiTZs24u7du+plDB06VPj7+4ujR4+KgwcPivbt24tx48YZK6Uq1ZSnQqEQI0aMEC1bthSnT5/WeL9WXJ1w+PBhsWLFCnH69GmRkZEhvvjiC+Hq6irCwsKMnJmmmvK8ffu2eOONN0RaWprIzMwUe/fuFU888YRo3769uHfvnnoZj8N4ClH7tiuEEEVFRcLGxkasW7dOa/7HYUxr+x4RovbP2Pv374uuXbuKIUOGiNOnT4vExETh6uoqYmJidIrFpIoSIYRYtWqVaNWqlbC0tBS9evUSR44cMXZIjwRAlY9NmzYJIYS4evWq6Nu3r3BychJyuVy0a9dOzJ07VxQVFRk3cB2FhoYKDw8PYWlpKTw9PUVoaKi4fPmyevrdu3fFa6+9Jpo1ayZsbGzE6NGjRXZ2thEjrr/du3cLAOLixYsa7Y/zWKakpFS5nYaHhwshHlwW/O677wo3Nzchl8vFoEGDtPIvKCgQ48aNE7a2tsLe3l5ERESI27dvGyGb6tWUZ2ZmZrXv15SUFCGEECdPnhSBgYHCwcFBWFlZic6dO4t///vfGl/mUlBTnqWlpWLIkCHC1dVVWFhYiNatW4tp06Zp/fP3OIynELVvu0II8cknnwhra2tRWFioNf/jMKa1fY8IUbfP2KysLDFs2DBhbW0tXFxcxP/93/8JpVKpUyyy/x8QERERkVGZzDklREREJG0sSoiIiEgSWJQQERGRJLAoISIiIklgUUJERESSwKKEiIiIJIFFCREREUkCixIiIiKSBBYlRI2EEAKvvPIKnJycIJPJ1L+LQ9oUCgXatWuHw4cP63W5iYmJ8PPzQ3l5uV6XS2QqWJQQNRKJiYnYvHkzdu3ahezsbHTt2tXYIUnW+vXr0aZNG/Tu3VvdJpPJsGPHDq2+kydPxqhRo+q03KFDh8LCwgJffvmlniIlMi0sSogaiYpfTe7duzfc3d3RpEkTrT4KhcIIkUmLEAKrV69GZGSkQZY/efJkfPzxxwZZNlFjx6KEqBGYPHkyZs2ahatXr0Imk8Hb2xsA0L9/f0RFRWHOnDlwcXFBSEgIAODs2bMYNmwYbG1t4ebmhkmTJiE/P1+9vJKSEoSFhcHW1hYeHh5YtmwZ+vfvjzlz5qj7VLVnwdHREZs3b1Y/v3btGl5++WU4OjrCyckJI0eORFZWlkbco0aNwocffggPDw84Oztj5syZUCqV6j5lZWWYN28evLy8IJfL0a5dO2zcuBFCCLRr1w4ffvihRgynT5+GTCbD5cuXq3ytTp48iYyMDAwfPlyHV/iBrKwsyGQyrUf//v3VfZ5//nmcOHECGRkZOi+fyNSxKCFqBD766CMsWrQILVu2RHZ2No4fP66etmXLFlhaWuLQoUNYv349CgsLMXDgQPj7++PEiRNITExEbm4uXn75ZfU8c+fOxa+//oqdO3diz549SE1NRXp6uk4xKZVKhISEwM7ODgcOHMChQ4dga2uLoUOHauyxSUlJQUZGBlJSUrBlyxZs3rxZo7AJCwvDtm3b8PHHH+P8+fP45JNPYGtrC5lMhilTpmDTpk0a6920aRP69u2Ldu3aVRnXgQMH0KFDB9jZ2emUDwB4eXkhOztb/Th16hScnZ3Rt29fdZ9WrVrBzc0NBw4c0Hn5RCbvEX/xmIgkYsWKFaJ169Yabf369RP+/v4abe+9954YMmSIRtu1a9cEAHHx4kVx+/ZtYWlpKb7++mv19IKCAmFtbS1mz56tbgMgfvjhB43lODg4qH/ufOvWraJjx46ivLxcPb2srExYW1uL3bt3CyGECA8PF61btxb3799X9xkzZowIDQ0VQghx8eJFAUAkJSVVmfPff/8tzM3NxdGjR4UQQigUCuHi4iI2b95czaskxOzZs8XAgQO12gEIKysr0bRpU41HkyZNxMiRI7X63717VwQGBornnntOqFQqjWn+/v5i4cKF1cZARFXTPuhMRI1KQECAxvP//ve/SElJga2trVbfjIwM3L17FwqFAoGBgep2JycndOzYUaf1/ve//8Xly5e19kjcu3dP49BGly5dYG5urn7u4eGB3377DcCDQzHm5ubo169fleto0aIFhg8fjvj4ePTq1Qs//vgjysrKMGbMmGrjunv3LqysrKqctmLFCgQHB2u0zZs3DyqVSqvvlClTcPv2bSQlJcHMTHOns7W1NUpLS6uNgYiqxqKEqJFr2rSpxvM7d+7g+eefxwcffKDV18PDo9pzMR4mk8kghNBoq3wuyJ07dxAQEFDllSiurq7qvy0sLLSWW3FJrbW1da1xTJ06FZMmTcKKFSuwadMmhIaGwsbGptr+Li4u6qLnYe7u7lqHfezs7FBYWKjRtnjxYuzevRvHjh2r8jDQzZs3NXIkorphUUJkYp544gl899138Pb2rvIKHR8fH1hYWODo0aNo1aoVAODWrVv4448/NPZYuLq6Ijs7W/380qVLGnsHnnjiCSQkJKB58+awt7evV6zdunVDeXk5fv31V609GBWeffZZNG3aFOvWrUNiYiL2799f4zL9/f2xbt06CCEgk8l0jum7777DokWL8Msvv8DHx0dresWeIH9/f52XTWTqeKIrkYmZOXMmbt68iXHjxuH48ePIyMjA7t27ERERAZVKBVtbW0RGRmLu3LnYt28fzp49i8mTJ2sdohg4cCBWr16NU6dO4cSJE3j11Vc19npMmDABLi4uGDlyJA4cOIDMzEykpqbi9ddfx19//VWnWL29vREeHo4pU6Zgx44d6mV8/fXX6j7m5uaYPHkyYmJi0L59ewQFBdW4zAEDBuDOnTs4d+6cDq/aA2fPnkVYWBjmzZuHLl26ICcnBzk5Obh586a6z5EjRyCXy2uNg4i0sSghMjEtWrTAoUOHoFKpMGTIEHTr1g1z5syBo6OjuvBYunQp+vTpg+effx7BwcF45plntM5NWbZsGby8vNCnTx+MHz8eb7zxhsZhExsbG+zfvx+tWrXCCy+8gM6dOyMyMhL37t3Tac/JunXr8NJLL+G1115Dp06dMG3aNJSUlGj0iYyMhEKhQERERK3Lc3Z2xujRo+t1g7MTJ06gtLQUixcvhoeHh/rxwgsvqPts27YNEyZMqPEQEhFVTSYePihMRFSF/v37w8/PDytXrjR2KFoOHDiAQYMG4dq1a3Bzc6u1/5kzZzB48GBkZGRUecJvfeXn56Njx444ceIE2rRpo7flEpkK7ikhosdWWVkZ/vrrLyxcuBBjxoypU0ECAN27d8cHH3yAzMxMvcaTlZWFtWvXsiAhqiee6EpEj61t27YhMjISfn5++Pzzz3Wad/LkyXqPp2fPnujZs6fel0tkKnj4hoiIiCSBh2+IiIhIEliUEBERkSSwKCEiIiJJYFFCREREksCihIiIiCSBRQkRERFJAosSIiIikgQWJURERCQJ/w/sTZerOuAzDQAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#spectral analysis\n", "\n", "Sbase = rfft(Vbase)\n", "Sbase /= len(Sbase)\n", "freq = rfftfreq(len(Vbase),d=1/sample_rate)\n", "\n", "figure(figsize=(6,4))\n", "stem(freq,abs(Sbase))\n", "grid()\n", "xlim(0,200)\n", "xlabel('frequency (Hz)')\n", "ylabel('magnitude (V)')\n", "title('Baseband LOC spectrum for alpha = '+str(alpha))\n", " \n", "show()" ] }, { "cell_type": "markdown", "id": "7592a741-02f8-4b29-8889-35f2f7e3420f", "metadata": {}, "source": [ "\n", "## Modulation d'amplitude \n", "\n", "Le signal en bande de base est ensuite modulé en amplitude autour de la fréquence de la porteuse $f_c$. Le taux de modulation est de 40% :\n", "\n", "$$\n", "V_{RF} = A_{RF}(1 + 0.4 V_{base})\\cos(2 \\pi f_c t)\n", "$$\n", "\n", "ou $A_{RF}$ est l'amplitude de la porteuse, dans notre cas 1V.\n", "\n", "Pour des raisons de simulation, dans ce travail le signal est échantillonné à 100KHz avec $f_c$= 10KHz. \n", "\n", ":::{warning}\n", "Notons que la fréquence de la porteuse ne correspond pas à la valeur utilisée dans le domaine aéronautique (i.e. entre 108.1 et 111.95 MHz). Il s'agit d'une simplification permettant d'économiser nos ressources de calcul.\n", ":::\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "1df833e6-7fef-41c8-b7c5-3f4025bbc98d", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# RF signal\n", "\n", "#parameters\n", "\n", "#modulation depth\n", "m = 0.4\n", "\n", "Arf = 1.0\n", "\n", "#set the RF signal (Amplitude Modulation)\n", "Vrf = Arf*(1.0 + m*Vbase)*cos(2*pi*fc*t)\n", "\n", "figure(figsize=(6,4))\n", "plot(t,Vrf,'b')\n", "grid()\n", "xlabel('time (s)')\n", "ylabel('magnitude (V)')\n", "title('RF signal for alpha = '+str(alpha))\n", "xlim(0,0.05)\n", "\n", "show()" ] }, { "cell_type": "markdown", "id": "ad8cb132-6891-4859-b609-62cf0cff7fc0", "metadata": {}, "source": [ "Le spectre d'amplitude unilatéral est présenté sur la figure suivante." ] }, { "cell_type": "code", "execution_count": 6, "id": "3efc962c-ec66-46a6-bd52-b582309be3b9", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#spectral analysis\n", "\n", "Srf = rfft(Vrf)\n", "Srf /= len(Srf) \n", "Vfreq = rfftfreq(len(Vrf),d=1/sample_rate)\n", "mar150 = (1-alpha)*m/2\n", "mar90 = alpha*m/2\n", "\n", "figure(figsize=(6,4))\n", "stem(freq/1e3,abs(Srf))\n", "plot(freq/1e3,mar90*ones_like(abs(Srf)),'--r',label=\"V = {0:3.2f}V\".format(mar90))\n", "plot(freq/1e3,mar150*ones_like(abs(Srf)),'--m',label=\"V = {0:3.2f}V\".format(mar150))\n", "legend()\n", "grid()\n", "xlim(10-0.2,10+0.2)\n", "xlabel(' frequency (KHz)')\n", "ylabel('magnitude (V)')\n", "title('RF LOC spectrum for alpha = '+str(alpha))\n", " \n", "show()" ] }, { "cell_type": "markdown", "id": "f4924955-de17-43af-93f1-bd65bf0cff59", "metadata": {}, "source": [ "Le spectre du signal RF présente une raie principale à la fréquence de la porteuse (dans notre cas $f_c$=10 KHz) et de part et d'autre de cette fréquence, le spectre du signal en bande de base constitué de deux raies dont l'amplitude est liée à la position de l'avion (i.e. $\\alpha$) mais aussi au taux de modulation.\n", "\n", "Pour cet exemple, comme l'avion est centré ($\\alpha=0.5$), l'amplitude des raies \"90Hz\" et \"150Hz\" est identique." ] }, { "cell_type": "markdown", "id": "d0803c69-ae81-4f22-87ae-20c143e1fecb", "metadata": {}, "source": [ "Il convient de s’arrêter sur la nécessité de moduler puisque l'information de la position de l'avion est déjà \"portée\" par le signal en bande de base. \n", "\n", ":::{tip} Pourquoi moduler ! 💬\n", ":class: dropdown\n", "\n", "La modulation RF permet de transposer le signal en bande de base autour de la fréquence de la porteuse. Il s'agit donc de \"déplacer\", le signal informatif vers une fréquence plus élevée. On peut s'interroger sur la nécessité de réaliser cette transposition fréquentielle ?\n", "\n", "IL existe plusieurs réponses à cette question :\n", "\n", "* La dimension des antennes est liée à la fréquence transmise (plus exactement à la longueur d'onde $\\lambda$ qui est définie par $\\lambda = c/f$ avec $c=3e8$m/s et $f$ la fréquence du signal en Hz). Dans notre cas la fréquence du signal en bande de base est voisin de 120Hz, ce qui entraîne une longueur d'onde de 2500Km !, il faudrait donc avoir des antennes dont les dimensions sont proches de cette valeur !. Le fait de transposer le signal de 90Hz où 150Hz autour de 110MHz entraine des dimensions d'antenne dans le domaine métrique. Ainsi le fait d'augmenter la fréquence permet de réduire la taille des antennes mais aussi leurs encombrements et leurs poids. Toutefois le fait d'augmenter la fréquence présente aussi des inconvénients notamment sur les conditions de propagation: les pertes de propagations sont inversement proportionnelles au carré de la fréquence. De plus les ondes ont plus de difficultés à se propager à travers des interfaces telle que des murs lorsque la fréquence augmente.\n", "* Le bruit de fond notamment celui provenant des activités humaines est plus important en basse fréquence. De ce fait pour pouvoir détecter le signal, il faudra l'émettre avec plus de puissance en basse fréquence.\n", "\n", "Voici donc les deux principaux arguments pour utiliser une fréquence RF pour transmettre une information.\n", ":::" ] }, { "cell_type": "markdown", "id": "db043f59-190a-4a51-aa89-9084f2ec74e0", "metadata": {}, "source": [ "## Signal reçu par l'avion\n", "\n", "Dans une première approximation, on considère que le signal reçu par l'avion $Vr_{RF}$ correspond au signal transmis $V_{RF}$ retardé et atténué :\n", "\n", "$$\n", "Vr_{RF}(t) = \\beta V_{RF}(t-t_d)\n", "$$\n", "\n", "avec $\\beta$ l'atténuation du signal ($0<\\beta < 1$) et $t_d$ le temps de propagation du signal." ] }, { "cell_type": "markdown", "id": "f915d764-cdb0-43fe-8fef-e257a91f6ec1", "metadata": {}, "source": [ "La figure ci_dessous présente le signal reçu lorsque l'avion est à une distance de $R=$3000m de l'émetteur du \"localiser\". Pour des raisons de simplification, on suppose que le signal n'est pas atténué ($\\beta=1$). Le temps de propagation $t_d$ s'exprime simplement à partir de :\n", "\n", "$$\n", "t_d = \\frac{R}{c}\n", "$$\n", "\n", "avec $c=$ 3e8m/s." ] }, { "cell_type": "code", "execution_count": 7, "id": "d34d7deb-9103-4cca-a425-5788a2e7c1ab", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "temps de propagation : 10.00us\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# LOC signal received by aircraft\n", "\n", "def Vrf(t,alpha):\n", " \"\"\"\n", " LOC signal calculation\n", " \"\"\"\n", " A90 =1.0\n", " A150 = 1.0\n", " f90 = 90.0\n", " f150 = 150.0\n", " Arf =1.0\n", " m = 0.2\n", " fc = 10e3\n", " \n", " V150 = A150 * cos(2*pi*f150*t)\n", " V90 = A90 * cos(2*pi*f90*t)\n", " Vbase = (1.0-alpha)*V150 + alpha*V90\n", " Vrf = Arf*(1.0 + m*Vbase)*cos(2*pi*fc*t)\n", " return Vrf\n", " \n", "distance = 3000.0\n", "tp = distance / 3e8\n", "beta = 1\n", "\n", "print(f\"temps de propagation : {tp/1e-6:3.2f}us\")\n", "\n", "Vr_rf = beta*Vrf(t-tp,alpha)\n", "\n", "figure(figsize=(6,4))\n", "plot(t,Vr_rf,'b')\n", "grid()\n", "xlabel('time (s)')\n", "ylabel('magnitude (V)')\n", "title('RF signal after propagation for alpha = '+str(alpha))\n", "xlim(0,0.05)\n", "show()" ] }, { "cell_type": "markdown", "id": "d380c20b-3420-4b4a-860d-e4e852af89b9", "metadata": {}, "source": [ "### Ajout d'un bruit gaussien avec un SNR fixé\n", "\n", "L'avion reçoit le signal atténué et retardé additionné d'un bruit ($b(t)$) qui provient de l'environnement :\n", "\n", "$$\n", "Vr_{RF}(t) = \\beta V_{RF}(t-t_d) + b(t)\n", "$$\n", "\n", "Classiquement la puissance du bruit s'exprime en fonction de la puissance du signal en utilisant la définition du [rapport signal sur bruit](https://fr.wikipedia.org/wiki/Rapport_signal_sur_bruit) (SNR: Signal Noise Ratio) :\n", "\n", "$$\n", "SNR_{dB}=10\\log(\\frac{P_{signal}}{P_{bruit}})\n", "$$\n", "\n", "Dans cette équation, le SNR est exprimé en dB. $P_{signal}$ est la puissance du signal exprimée en W et $P_{bruit}$, la puissance du bruit en W." ] }, { "cell_type": "markdown", "id": "cbb787b9-8648-4afd-ba11-b02d14676b97", "metadata": {}, "source": [ "Dans notre exemple, nous considérons un SNR de 20dB." ] }, { "cell_type": "code", "execution_count": 10, "id": "0b345739-2b5c-4792-9596-4654f1a1ccf7", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# add noise \n", "\n", "def add_noise(s, SNR):\n", " \"\"\" \n", " Compute d = s + n such that SNR = Ps/Pn\n", " s: Input signal\n", " SNR: Desired signal-to-noise ratio\n", " d: Output signal\n", " \"\"\"\n", " n = random.randn(len(s))\n", " Es = sum(s**2)\n", " En = sum(n**2)\n", " alpha = sqrt(Es/(SNR*En))\n", " d = s+alpha*n\n", " return d\n", "\n", "#SNR in dB\n", "SNR = 20\n", "snr = 10**(SNR/10)\n", "Vr_rfb = add_noise(Vr_rf,snr) \n", "\n", "figure(figsize=(6,4))\n", "plot(t,Vr_rfb,'b')\n", "grid()\n", "xlabel('time (s)')\n", "ylabel('magnitude (V)')\n", "title('RF signal after propagation with noise for alpha = '+str(alpha))\n", "xlim(0,0.05)\n", "show()" ] }, { "cell_type": "markdown", "id": "145a582c-61d1-4801-9998-77aa2bb6e515", "metadata": {}, "source": [ "Finalement nous sauvegardons le signal reçu par l'avion dans un fichier texte pour pouvoir le réutiliser lors de la prochaine leçon." ] }, { "cell_type": "code", "execution_count": 17, "id": "30943243-ae29-40a5-a924-0065cd59ac64", "metadata": {}, "outputs": [], "source": [ "#save the LOC data\n", "\n", "#parameter\n", "file_name = '../_static/data/loc_data.txt'\n", "\n", "with open(file_name, 'w') as f:\n", " for i in range(len(t)):\n", " line = str(t[i])+','+str(Vr_rfb[i])+'\\n'\n", " f.write(line)" ] }, { "cell_type": "markdown", "id": "01cbc915-4ebe-4386-941a-d3f06c2f96b1", "metadata": {}, "source": [ ":::{admonition} Synthèse\n", ":class: tip\n", "\n", "Dans cette page nous avons vu comment simuler le signal reçu par l'avion en fonction de sa position par rapport à l'axe de la piste. Pour cela nous avons \"fabriqué\" le signal en bande de base, puis nous l'avons transposé autour de la fréquence de la porteuse en utilisant une modulation d'amplitude. Le canal de propagation a été ensuite simulé et enfin un bruit gaussien à été ajouté.\n", "\n", "Dans la suite nous allons chercher à traiter le signal reçu par l'avion pour en déduire une information de position.\n", "\n", ":::" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.4" } }, "nbformat": 4, "nbformat_minor": 5 }