{
"cells": [
{
"cell_type": "markdown",
"id": "c9df0f50-7e21-4f44-afcd-0411b083ddbd",
"metadata": {},
"source": [
" Vamos a hacer algunos ejemplos de convolución y sistemas LTI. Empezamos cargando algunas librerías: "
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "0c00c2ac-8fa5-43cc-8598-0af1e3b291d1",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy import fft, signal\n",
"import sys\n",
"sys.path.insert(1, 'Some functions/')\n",
"from generate_signals import *"
]
},
{
"cell_type": "markdown",
"id": "db4510a0-d2de-4980-bfcf-2fc51e8a8e40",
"metadata": {},
"source": [
"Empecemos con un ejemplo ya visto en la clase. Sea $h(t)=u(t)$ y $x(t)=e^{-\\alpha t}u(t)$ con $0<\\alpha$. Queremos calcular $y(t)=h(t)*x(t)$. Empecemos tomando algunas definiciones para \"simular\" señales de tiempo continuo en la computadora. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "faaa8caa-26ad-4fa5-aa87-d3e4da73c981",
"metadata": {},
"outputs": [],
"source": [
"# Signal duration in seconds\n",
"D = 15\n",
"# Sampling rate in Hz\n",
"fs = 1000\n",
"#Sampling period\n",
"T = 1/fs\n"
]
},
{
"cell_type": "markdown",
"id": "0fe505df-ee07-42bc-a322-f10e21e2c943",
"metadata": {},
"source": [
"Vamos a generar las señales $h(t)$ y $x(t)$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "f44ca6b8-bf68-4c20-babc-8fffa0000fc7",
"metadata": {},
"outputs": [],
"source": [
"amplitude = 1\n",
"alpha = -1\n",
"sample_rate = fs\n",
"duration = D\n",
"position = 0.5 #Position of impulse. Value between 0 a 1. The start of exponential will be positioned in the index closer \n",
" #to duration*position \n",
"tx,x=generate_right_exponential(amplitude,alpha, sample_rate, duration, position) "
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "f9c1b7c7-813d-4faa-bc7c-59adfacd480c",
"metadata": {},
"outputs": [],
"source": [
"amplitude = 1\n",
"alpha = 0\n",
"sample_rate = fs\n",
"duration = D\n",
"position = 0.5 #Position of impulse. Value between 0 a 1. The start of exponential will be positioned in the index closer \n",
" #to duration*position \n",
"th,h=generate_right_exponential(amplitude,alpha, sample_rate, duration, position) "
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "1ce08dd3-1381-4607-990e-b80831cec999",
"metadata": {},
"outputs": [
{
"data": {
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jjjtum/c0NjamsbFxi+fr6+u3+Afc0dGRUqmUmpqa1NRsPLi0XE7at2wkOzs7k/Z1KbXXPndtb6sf2rXOeAdWrlyZm266KTfeeGNe/vKXJ0n23nvvLWagrVy5Mh//+Mfz3//932ltbc3RRx+diy++OIcddliS5LOf/WyuuOKKfOxjH8u5556bFStW5NWvfnUuvfTSjBgxIklyzTXX5P/7//6/PPDAA6mtrc1xxx2Xb37zm9l3332TpPufxWb/DLdi/fr1efe7351f/vKXGTNmTD7zmc9sVuD94he/yBlnnNH9Hp/97Gfzb//2b0nSvSTzhhtuyIknnpgXvvCFmTp1av77v/8773rXu7b4rJqampRKpa3+nhehv+Rg4DBmqJQxQ0+MHFKfrO363pihEsYLlTJmqJQxQ6V2dcz09N5CS7Q1a9bkiSee6H48Z86c3HPPPRk7dmz23HPPnHPOOZk/f353efLe97433/nOd/JP//RPeec735nf//73+cUvfpErr7yy70K2r0u+NHWLp2uSjO67T+3yqWeThmE7vGz48OEZPnx4rrjiirz4xS/eammYJH/1V3+VIUOG5Oqrr86oUaPy/e9/P6985Svz2GOPdc/gmj17dq644or85je/yYoVK/LXf/3X+fKXv5wvfvGLSbqWac6aNSuHHnpo1qxZk/POOy9/8Rd/kXvuuaeiMvHrX/96vvCFL+RTn/pU/vM//zPve9/78vKXvzwHHnhgkuTmm2/OW9/61u7rP/7xj+fhhx9Oc3Nz/vVf/zVJNpt1dswxx+Smm27aaokGAGxpRNNzf1ns6CzHf6oAAGxfH02h6pk77rgjRxxxRI444ogkyaxZs3LEEUfkvPPOS5IsWLAg8+bN675+7733zpVXXpnrrrsuhx12WL7+9a/nsssuy2mnnVZI/v6irq4uP/zhD/OjH/0oo0ePzktf+tJ86lOfyn333dd9zc0335zbb789v/zlL3P00Udn//33z4UXXpjRo0fnP//zP7uv6+zszA9/+MPMnDkzJ5xwQt761rfm+uuv7379DW94Q/7yL/8y++23Xw4//PBcfvnluf/++/PQQw9VlPn000/P+9///uy33375xCc+kfHjx+eGG25I0jVjbtWqVZk69bnycvjw4RkyZEgaGxszefLkTJ48OQ0NDd2vT506NU89ZVdkAOip4Y3PHbazdE3rdq4EACApeCbaiSee2H3K5db88Ic/3Oo9d999dx+m+jP1Q7tmhP2Zzs7ONK9enZEjRvTtcs4eesMb3pDXvOY1uemmm/KnP/0pV199db761a/msssuyzve8Y7ce++9WbNmTcaNG7fZfevXr8/s2bO7H8+YMaN76WaSTJkyJYsXL+5+/Pjjj+e8887LbbfdlqVLl3afTDpv3rzMnDmzx3kPPfTQ7u9LpVImT57c/Tnr169Pkor2LxsyZEiPNwIEAJJSntsyYvHq1uwxbsR2rgYAYEDtiVaIUmnrSyo7O5P6jq7X+qpEq1BTU1NOOeWUnHLKKTn33HPz7ne/O+eff37e8Y53ZM2aNZkyZUpuvPHGLe4bPXp09/d/vg64VCp1F2VJcsYZZ2SvvfbKpZdemqlTp6azszMzZ87s8WmmPfmccePGpVQqZcWKFT1+v+XLl2fChAkVZQAAuixqNhMNAGBHlGiD2CGHHJIrrrgiSXLkkUdm4cKFqaury4wZM3bq/ZYtW5ZHH300l156aU444YQkXctEe1tDQ0MOOeSQPPTQQ5udztnQ0JCOjo6t3vPAAw/kxBNP7PUsAFANFq1WogEA7Ej/mELFLlm2bFlOOumk/PjHP859992XOXPm5Je//GW++tWv5vWvf32S5OSTT85xxx2XM888M9dee23mzp2bW265JZ/+9Kdzxx139OhzxowZk3HjxuVf/uVf8sQTT+T3v/99Zs2a1Sc/02mnnbZFQTdjxozcd999efTRR7N06dK0t7cnSdatW5c777xzs8INAOi5Rc0tRUcAAOj3zEQbBIYPH55jjz02F198cWbPnp329vZMnz49Z599dj71qU8l6VouedVVV+XTn/50zjrrrCxZsiSTJ0/Oy172skyaNKlHn1NTU5Of/exn+fCHP5yZM2fmwAMPzLe+9a0+mQH2rne9K0cffXRWrVqVUaNGJUnOPvvs3HjjjTn66KOzZs2a3HDDDTnxxBPz3//939lzzz27Z8cBAJVZbCYaAMAOKdEGgcbGxlxwwQW54IILtnvdiBEj8q1vfSvf+ta3tvr6Zz/72Xz2s5/d7Ll/+Id/yD/8wz90Pz755JO3OInz+YdDzJgxY7uHRSTJ3Llzt3junnvu2ezxIYcckte85jX553/+55xzzjlJkgkTJuTaa6/d4t5vfvOb3Se6AgCVsycaAMCOWc5Jv/W1r30tw4cP3+41S5cuzV/+5V/mzW9+825KBQCDj+WcAAA7ZiYa/daMGTPyoQ99aLvXjB8/Pv/0T/+0mxIBwOBkOScAwI6ZiQYAUOVWrd+Qlvatn4ANAEAXJRoAAJZ0AgDsgBJtK3a0MT4Di99PANixhauUaAAA26NEe576+vokybp16wpOQm/a9Pu56fcXANjSIvuiAQBsl4MFnqe2tjajR4/O4sWLkyRDhw5NqVTa6rWdnZ1pa2tLS0tLamp0kf1RuVzOunXrsnjx4owePTq1tbVFRwKAfmuRmWgAANulRPszkydPTpLuIm1byuVy1q9fnyFDhmyzaKN/GD16dPfvKwDQpZTNtzuwJxoAwPYp0f5MqVTKlClTMnHixLS3t2/zuvb29vzxj3/My172MssE+7H6+noz0ACgBxYq0QAAtkuJtg21tbXbLV9qa2uzYcOGNDU1KdEAgAGrttQ1I21xsz3RAAC2x2ZeAABVrK6ma1sKM9EAALZPiQYAUMXqN/5tcFFzS8rl8vYvBgCoYko0AIAqtqlEa93QmVXrt70fLABAtVOiAQBUsVKSMUO79nddZF80AIBtUqIBAFS5SSMak9gXDQBge5RoAABVbuLIrhJt0SolGgDAtijRAACq3KSRTUm6DhcAAGDrlGgAAFVuouWcAAA7pEQDAKhykzYt53SwAADANinRAACq3KaZaJZzAgBsmxINAKDKTbYnGgDADinRAACq3KaZaEvXtGZDR2fBaQAA+iclGgBAlRs3rCG1NaV0lpOla9qKjgMA0C8p0QAAqlxNTckJnQAAO6BEAwAgk+yLBgCwXUo0AAAcLgAAsANKNACAqlTe7NGkkV3LOZVoAABbp0QDACCTRnXNRFu4qrXgJAAA/ZMSDQCgipU2ft20nHNh8/riwgAA9GNKNACAKrZpUefk7plolnMCAGyNEg0AgEwZNSRJsmBVS8rl8g6uBgCoPko0AAC6l3Oua+vI6tYNBacBAOh/lGgAAGRIQ21GD61PYkknAMDWKNEAAEjy3Gy0BUo0AIAtKNEAAEiSTNl4uMCClU7oBAD4c0o0AACSJJOfd7gAAACbU6IBAJDkuZlo9kQDANiSEg0AgCTJ5E3LOZuVaAAAf06JBgBAkmTqxuWcC1fZEw0A4M8p0QAASPK8mWiWcwIAbEGJBgBAkudKtNUtG7KmdUPBaQAA+hclGgAASZLhjXUZ0VSXxOECAAB/TokGAEA3J3QCAGydEg0AgG6TNx4usMDhAgAAm1GiAQDQbcpIM9EAALZGiQYAUJXKW3120+ECzyrRAAA2o0QDAKDbc3uiWc4JAPB8SjQAALptmom2wEw0AIDNKNEAAOg2ZePBAgublWgAAM+nRAMAqGLllDZ7vGkm2sp17Vnf1lFEJACAfkmJBgBAt5FNdRnWUJvEbDQAgOdTogEA0K1UKj1vXzSHCwAAbKJEAwBgM937ojlcAACgmxINAIDNOKETAGBLSjQAADYzZWOJZiYaAMBzlGgAAGzGnmgAAFtSogEAsJkplnMCAGxBiQYAwGYmj3SwAADAn1OiAQCwmU0z0ZatbUtLe0fBaQAA+gclGgAAmxk9tD6NdV1/TVzc3FpwGgCA/kGJBgDAZkql0vP2RXO4AABAokQDAGArNp3QubDZvmgAAIkSDQCArZg6qutwASd0AgB0UaIBALCF7ploSjQAgCRKNACA6lQub/flTXuiPbvSnmgAAIkSDQCArZhiOScAwGaUaAAAbGHq6K4SzUw0AIAuSjQAgGpW2vrTU0d3LedctrYtLe0duzEQAED/pEQDAKhqW2/RRg2pz9CG2iSWdAIAJEo0AAC2olQqWdIJAPA8SjQAALZqU4k2X4kGAKBEAwBg66aO6toXbcFKyzkBAJRoAABsleWcAADPUaIBALBV3SXaKiUaAIASDQCArZo6ums5pz3RAACUaAAAbMPUUV0z0RasbEm5XC44DQBAsZRoAABs1eSNBwusb+/IynXtBacBACiWEg0AgK1qqq/N+OGNSSzpBABQogEAsE3TNu6L5oROAKDaKdEAANimKZv2RVvVUnASAIBiKdEAANimqaO7SjQz0QCAaqdEAwBgm6ZuXM5pTzQAoNop0QAA2KZpZqIBACRRogEAsB1TRtsTDQAgUaIBALAdm5ZzLmpuSXtHZ8FpAACKo0QDAGCbxg9rTENtTTrLXUUaAEC1UqIBALBNNTWlTNk4G82STgCgminRAACqWLkH10wZ1VWiOVwAAKhmSjQAALZr6sbDBeYr0QCAKqZEAwBgu6ZtLNHMRAMAqpkSDQCA7do0E23BSnuiAQDVS4kGAMB2bdoTzXJOAKCaKdEAANguyzkBAJRoAADswJSNJVpzy4asad1QcBoAgGIo0QAA2K7hjXUZNaQ+SbLAbDQAoEop0QAA2KFNhwvYFw0AqFZKNAAAdmjqxsMFnnVCJwBQpZRoAADs0FSHCwAAVU6JBgDADnWXaKuUaABAdVKiAQCwQ1NHdy3nnL9CiQYAVCclGgAAO7THGAcLAADVTYkGAMAOTRs9NEmyYFVLNnR0FpwGAGD3U6IBAFShUrlc0fUTRzSmvraUjs5yFq1u7aNUAAD9lxINAIAdqqkpdR8u8MzydQWnAQDY/ZRoAAD0iH3RAIBqpkQDAKhC5VS2nDNJpm2aieaETgCgCinRAADokT3GdB0uMF+JBgBUISUaAEBVK/X4yu6ZaCvtiQYAVB8lGgAAPdK9J5qZaABAFVKiAQDQI9M2lmjPrmxJZ2fle6oBAAxkSjQAAHpk8sim1NaU0tbRmSVrWouOAwCwWynRAADokbramkwe2ZQkeWaFfdEAgOqiRAMAoMc27Yv2jH3RAIAqo0QDAKDHpinRAIAqpUQDAKDH9hgzNEkyf6USDQCoLko0AAB6bI/RZqIBANVJiQYAQI9tWs4538ECAECVUaIBANBjmw4WmL9yfcrlcsFpAAB2HyUaAAA9NmXUkJRKSUt7Z5atbSs6DgDAbqNEAwCgxxrqajJpRFOSZL590QCAKqJEAwCoQqXs/FLMTfuiOVwAAKgmSjQAACry3L5oDhcAAKqHEg0AgIpMG20mGgBQfZRoAABUZI8xQ5PYEw0AqC6Fl2jf/e53M2PGjDQ1NeXYY4/N7bffvt3rv/GNb+TAAw/MkCFDMn369Hz0ox9NS0vLbkoLAIA90QCAalRoifbzn/88s2bNyvnnn5+77rorhx12WE477bQsXrx4q9f/9Kc/zSc/+cmcf/75efjhh/ODH/wgP//5z/OpT31qNycHAKhez+2Jtj7l8s4fUAAAMJAUWqJddNFFOfvss3PWWWflkEMOySWXXJKhQ4fm8ssv3+r1t9xyS1760pfmb//2bzNjxoyceuqpefOb37zD2WsAAGxdOaWK79m0J9qa1g1Ztb69tyMBAPRLhZVobW1tufPOO3PyySc/F6amJieffHJuvfXWrd7zkpe8JHfeeWd3afbkk0/mqquuyumnn75bMgMAkDTV12b88MYklnQCANWjrqgPXrp0aTo6OjJp0qTNnp80aVIeeeSRrd7zt3/7t1m6dGmOP/74lMvlbNiwIe9973u3u5yztbU1ra2t3Y+bm5uTJO3t7Wlv3/n/53TTvbvyHlQXY4ZKGTNUypihEp3PW4a5M2Nm6ujGLF3TmqeWrs6BE4f2ZjT6KX/GUCljhkoZM1Sqt8ZMT+8vrETbGTfeeGO+9KUv5Z//+Z9z7LHH5oknnshHPvKRfOELX8i555671XsuuOCCfO5zn9vi+WuvvTZDh+76X/iuu+66XX4PqosxQ6WMGSplzNATrUuWdH+/M2Omdn1Nkpr87ta7smGufdGqiT9jqJQxQ6WMGSq1q2Nm3bp1PbqusBJt/Pjxqa2tzaJFizZ7ftGiRZk8efJW7zn33HPz1re+Ne9+97uTJC984Quzdu3avOc978mnP/3p1NRsuTr1nHPOyaxZs7ofNzc3Z/r06Tn11FMzcuTInc7f3t6e6667Lqecckrq6+t3+n2oHsYMlTJmqJQxQyVuXnFXsrbr+50ZM/fXPpa7b56bkVP2zumnH9QHCelv/BlDpYwZKmXMUKneGjObVi3uSGElWkNDQ4466qhcf/31OfPMM5MknZ2duf766/PBD35wq/esW7dui6KstrY2SbZ5MlRjY2MaGxu3eL6+vr5X/qXsrfehehgzVMqYoVLGDD1RU3ruQIGdGTN7jRuWJHl2VavxVmX8GUOljBkqZcxQqV0dMz29t9DlnLNmzcrb3/72HH300TnmmGPyjW98I2vXrs1ZZ52VJHnb296WadOm5YILLkiSnHHGGbnoootyxBFHdC/nPPfcc3PGGWd0l2kAAPS9PcZ0bYvhYAEAoFoUWqK96U1vypIlS3Leeedl4cKFOfzww3PNNdd0HzYwb968zWaefeYzn0mpVMpnPvOZzJ8/PxMmTMgZZ5yRL37xi0X9CAAAVWn62CFJkmeWr0u5XE7peTPbAAAGo8IPFvjgBz+4zeWbN95442aP6+rqcv755+f888/fDckAANiWTTPRVrduyMp17RkzrKHgRAAAfWvLnfgBAGAHmuprM3FE176zT6/o2YlWAAADmRINAICdMn1s12y0p5fbFw0AGPyUaAAA7JTpY7r2RZu33Ew0AGDwU6IBALBT9tw0E81yTgCgCijRAADYKXt0L+dUogEAg58SDQCAnbKnEg0AqCJKNAAAdsqmgwXmr1yfjs5ywWkAAPqWEg0AgJ0yeWRT6mtLae8oZ1FzS9FxAAD6lBINAICdUltTyrTRTugEAKqDEg0AoAqVe2n15XT7ogEAVUKJBgDATttjzMYSbcX6gpMAAPQtJRoAQBXb1QlpTugEAKqFEg0AgJ02fWzXnmhKNABgsFOiAQCw06Z3L+dUogEAg5sSDQCAnbZpOeei5ta0tHcUnAYAoO8o0QAA2Gmjh9ZneGNdkuQZhwsAAIOYEg0AgJ1WKpWyx5iN+6JZ0gkADGJKNAAAdokTOgGAaqBEAwBgl0xXogEAVUCJBgDALpm+aTnncnuiAQCDlxINAIBdsue4rplo88xEAwAGMSUaAAC7ZPqY55ZzlsvlgtMAAPQNJRoAALtkj40l2urWDVm1vr3gNAAAfUOJBgBQhUrpvRljQxpqM2FEYxL7ogEAg5cSDQCAXdZ9uMAK+6IBAIOTEg0AgF2251iHCwAAg5sSDQCAXTZ97HOHCwAADEZKNAAAdtmmEzrNRAMABislGgAAu2zPcWaiAQCDmxINAIBdttfGEu2ZFeuzoaOz4DQAAL1PiQYAUNVKvfIuk0Y0paGuJhs6y3l2ZUuvvCcAQH+iRAMAYJfV1JS6T+h8avnagtMAAPQ+JRoAAL1ixsYlnU8tsy8aADD4KNEAAOgVe44dliR5apmZaADA4KNEAwCgV+xlJhoAMIgp0QAA6BWbSrR5y5VoAMDgo0QDAKBX7DVu03LOdSmXywWnAQDoXUo0AAB6xbTRQ1JTSta3d2TJ6tai4wAA9ColGgAAvaKhriZTRw9JkjxlSScAMMgo0QAA6DUznrekEwBgMFGiAQDQa/bsPqFzbcFJAAB6lxINAIBes9fYTSWamWgAwOCiRAMAqEp9c3rmXptmotkTDQAYZJRoAAD0mr027ok2z3JOAGCQUaIBANBr9ty4nHPFuvasWt9ecBoAgN6jRAMAoNcMa6zL+OGNSZJ59kUDAAYRJRoAAL1qRve+aJZ0AgCDhxINAIBetec4J3QCAIOPEg0AgF6119iuwwWecrgAADCIKNEAAKpYOaVef8+9zEQDAAYhJRoAAL1KiQYADEZKNAAAetVe47qWcy5sbklLe0fBaQAAeocSDQCAXjVmaH1GNNYlSZ5ebjYaADA4KNEAAOhVpVLJCZ0AwKCjRAMAoNfN2Likc64TOgGAQUKJBgBAr9s0E22e5ZwAwCChRAMAoNftNbarRJtrOScAMEgo0QAA6HWbTuh8ynJOAGCQUKIBANDr9pnQVaI9s2J92jZ0FpwGAGDXKdEAAOh1E0c0ZmhDbTo6y3l6hSWdAMDAp0QDAKDXlUql7iWdc5da0gkADHxKNACAqlTu80/YZ3xXiTZHiQYADAJKNAAA+sSM8V0ndCrRAIDBQIkGAECfmLFpOacTOgGAQUCJBgBAn9h0QufcpQ4WAAAGPiUaAAB9YtNMtPkr16elvaPgNAAAu0aJBgBAnxg7rCEjmuqSJE8tMxsNABjYlGgAAPSJUqn0vBM61xScBgBg1yjRAADoMzO6SzQz0QCAgU2JBgBAn+k+oXOpEzoBgIFNiQYAQJ/ZdELnHCUaADDAKdEAAOgzm2aizVmmRAMABjYlGgAAfWbTnmhLVrdmTeuGgtMAAOw8JRoAAH1m1JD6jBvWkMS+aADAwKZEAwCgTz13QqcSDQAYuJRoAAD0KSd0AgCDgRINAIA+5YROAGAwUKIBANCnnNAJAAwGSjQAAPrUjPFDk1jOCQAMbEo0AAD61KaZaCvWtWfluraC0wAA7BwlGgBAFSqVd99nDWusy6SRjUnsiwYADFxKNAAA+lz3vmhKNABggFKiAQDQ5zad0GlfNABgoFKiAQDQ5547oXNdwUkAAHaOEg0AgD639/hNyznXFJwEAGDnKNEAAOhz+0wYniR5csnalMu78VQDAIBeokQDAKhKu7fI2nPs0NTWlLKurSMLm1t262cDAPQGJRoAAH2uoa4me40dmiSZvdjhAgDAwKNEAwCoaqXd9kndSzrtiwYADEBKNAAAdot9J3QdLjB7sRINABh4lGgAAOwW+3bPRLOcEwAYeJRoAADsFvuYiQYADGBKNAAAdotNM9GeXdWSdW0bCk4DAFAZJRoAALvFmGENGTO0Pkny5BJLOgGAgUWJBgDAbmNfNABgoFKiAQCw29gXDQAYqJRoAADsNptmos1eokQDAAYWJRoAALtN93JOe6IBAAOMEg0AgN1m03LOJ5euSWdnueA0AAA9p0QDAKhKxRRY08cOTX1tKS3tnVnQ3FJIBgCAnaFEAwBgt6mvrcmeY4cmcbgAADCwKNEAANitntsXTYkGAAwcSjQAAHarfbpP6HS4AAAwcCjRAADYrfZ93uECAAADhRINAIDdat+JG2eiLTYTDQAYOJRoAADsVvuO7yrRFja3ZE3rhoLTAAD0jBINAIDdatTQ+owf3pAkmWNfNABggFCiAQCw2+0zftPhAvZFAwAGBiUaAEAVKxf0uftO3Hi4gBINABgglGgAAOx2z81Es5wTABgYlGgAAOx2m2aiWc4JAAwUSjQAAHa7/SeOSJI8uXRtNnR0FpwGAGDHlGgAAOx200YPSVN9Tdo2dObpFeuLjgMAsENKNAAAdruamlL2ndC1L9rji1YXnAYAYMeUaAAAFGL/iRtLtMX2RQMA+j8lGgAAhdh/Ute+aE8o0QCAAUCJBgBAIfbrnolmOScA0P8p0QAAKMSm5ZyzF69NZ2e54DQAANunRAMAqEKlcvGl1Z5jh6ahtibr2zsyf6UTOgGA/k2JBgBAIepqa7L3+GFJ7IsGAPR/SjQAAAqz3yT7ogEAA4MSDQCAwmzaF+3xRWaiAQD9mxINAIDC7D9xRJLkccs5AYB+TokGAEBh9t+4nPOJxWtS7geHHQAAbIsSDQCAwswYNyy1NaWsad2QRc2tRccBANgmJRoAQBXqL3O+Gupqste4oUkcLgAA9G9KNACAalYqOoDDBQCAgUGJBgBQxcr9oEVzuAAAMBAo0QAAKNRzhwtYzgkA9F+Fl2jf/e53M2PGjDQ1NeXYY4/N7bffvt3rV65cmQ984AOZMmVKGhsbc8ABB+Sqq67aTWkBAOht+21azumETgCgH6sr8sN//vOfZ9asWbnkkkty7LHH5hvf+EZOO+20PProo5k4ceIW17e1teWUU07JxIkT85//+Z+ZNm1annrqqYwePXr3hwcAoFfsO2F4SqVk5br2LFvblvHDG4uOBACwhUJLtIsuuihnn312zjrrrCTJJZdckiuvvDKXX355PvnJT25x/eWXX57ly5fnlltuSX19fZJkxowZuzMyAAC9rKm+NtPHDM285evy+KI1SjQAoF8qbDlnW1tb7rzzzpx88snPhampycknn5xbb711q/f8+te/znHHHZcPfOADmTRpUmbOnJkvfelL6ejo2F2xAQDoA5tO6LQvGgDQXxU2E23p0qXp6OjIpEmTNnt+0qRJeeSRR7Z6z5NPPpnf//73ectb3pKrrroqTzzxRN7//venvb09559//lbvaW1tTWtra/fj5ubmJEl7e3va29t3Ov+me3flPaguxgyVMmaolDFDJTqft/dYfxgz+4wfmuuTPLqwuV/kYUv+jKFSxgyVMmaoVG+NmZ7eX+hyzkp1dnZm4sSJ+Zd/+ZfU1tbmqKOOyvz58/O1r31tmyXaBRdckM997nNbPH/ttddm6NChu5zpuuuu2+X3oLoYM1TKmKFSxgw9sWHZsu7v+8OYWbe4lKQ2f3r4qVxVM6foOGxHfxgvDCzGDJUyZqjUro6ZdevW9ei6wkq08ePHp7a2NosWLdrs+UWLFmXy5MlbvWfKlCmpr69PbW1t93MHH3xwFi5cmLa2tjQ0NGxxzznnnJNZs2Z1P25ubs706dNz6qmnZuTIkTudv729Pdddd11OOeWU7v3ZYHuMGSplzFApY4ZK/O/SPyUb/77YH8bM9Pmr8pPZt2VFR1NOP/3EQrOwdf6MoVLGDJUyZqhUb42ZTasWd6SwEq2hoSFHHXVUrr/++px55plJumaaXX/99fngBz+41Xte+tKX5qc//Wk6OztTU9O1ndtjjz2WKVOmbLVAS5LGxsY0Nm65OW19fX2v/EvZW+9D9TBmqJQxQ6WMGXqiplTq/r4/jJmDpo5OqZQsW9uWVa2dDhfox/rDeGFgMWaolDFDpXZ1zPT03sIOFkiSWbNm5dJLL82PfvSjPPzww3nf+96XtWvXdp/W+ba3vS3nnHNO9/Xve9/7snz58nzkIx/JY489liuvvDJf+tKX8oEPfKCoHwEAYEAq7fiS3WpoQ132HNu11cZjCx0uAAD0P4XuifamN70pS5YsyXnnnZeFCxfm8MMPzzXXXNN92MC8efO6Z5wlyfTp0/Pb3/42H/3oR3PooYdm2rRp+chHPpJPfOITRf0IAAD0kgMmjchTy9bl0UWr85L9xhcdBwBgM4UfLPDBD35wm8s3b7zxxi2eO+644/KnP/2pj1MBALC7HTR5RK57aFEeNRMNAOiHCl3OCQAAmxwwaUSS5NFFSjQAoP9RogEA0C8cOLmrRHts4eqUy+WC0wAAbE6JBgBAv7D3+GGpry1lbVtHnlmxvug4AACbUaIBANAv1NfWZN8Jw5Mkj1nSCQD0M0o0AAD6jU1LOu2LBgD0N0o0AAD6je7DBZzQCQD0M0o0AICqVio6wGYOVKIBAP2UEg0AgH5j03LOJ5esTXtHZ8FpAACeo0QDAKDfmDZ6SIY11KatozNzl64tOg4AQDclGgAA/UZNTSn7T3K4AADQ/yjRAADoVw7auKTzMfuiAQD9iBINAIB+ZdMJnY8o0QCAfkSJBgBAv7LpcIHHLOcEAPoRJRoAAP3KphLtqeXrsr6to+A0AABdlGgAAPQr44c3ZtywhpTLyeOLzUYDAPoHJRoAQFUqFx1guzbti/aofdEAgH5CiQYAQL9jXzQAoL9RogEA0O9sKtGc0AkA9BdKNAAA+p1NJZrlnABAf6FEAwCg3zlw0oiUSsni1a1Ztqa16DgAAEo0AAD6n2GNddlr7NAkycMLzEYDAIqnRAMAoF86eMrIJMnDC5oLTgIAoEQDAKCfUqIBAP2JEg0AgH5pU4n2kBINAOgHlGgAAFWoXHSAHjh4StcJnbOXrEnbhs6C0wAA1U6JBgBAvzRt9JCMbKpLe0c5TyxeU3QcAKDKKdEAAKpYf56RViqVcpB90QCAfkKJBgBAv3WIEg0A6CeUaAAA9Fub9kV7eKESDQAolhINAIB+66DJm2airU653J8XnwIAg50SDQCAfuvAySNSU0qWr23L4tWtRccBAKrYTpVoK1euzGWXXZZzzjkny5cvT5LcddddmT9/fq+GAwCgujXV12bv8cOS2BcNAChWxSXafffdlwMOOCBf+cpXcuGFF2blypVJkl/96lc555xzejsfAABV7uApzy3pBAAoSsUl2qxZs/KOd7wjjz/+eJqamrqfP/300/PHP/6xV8MBAMDBTugEAPqBiku0//u//8vf//3fb/H8tGnTsnDhwl4JBQBA3yoNoE36D1GiAQD9QMUlWmNjY5qbt/wLzGOPPZYJEyb0SigAANhk00y0J5euTUt7R8FpAIBqVXGJ9rrXvS6f//zn097eniQplUqZN29ePvGJT+QNb3hDrwcEAKC6TRrZmDFD69PRWc7ji9YUHQcAqFIVl2hf//rXs2bNmkycODHr16/Py1/+8uy3334ZMWJEvvjFL/ZFRgAAqlipVLIvGgBQuLpKbxg1alSuu+663HzzzbnvvvuyZs2aHHnkkTn55JP7Ih8AAOTgKSNzy+xleUiJBgAUpOISbZPjjz8+xx9/fG9mAQCArTITDQAoWo9KtG9961s9fsMPf/jDOx0GAAC25uApI5IkDy1oTrlcTqlUKjgRAFBtelSiXXzxxZs9XrJkSdatW5fRo0cnSVauXJmhQ4dm4sSJSjQAAHrd/hNHpKG2JqtbNuTp5euz57ihRUcCAKpMjw4WmDNnTvevL37xizn88MPz8MMPZ/ny5Vm+fHkefvjhHHnkkfnCF77Q13kBAKhCDXU1OXBy12y0B59dVXAaAKAaVXw657nnnptvf/vbOfDAA7ufO/DAA3PxxRfnM5/5TK+GAwCATV4wtWtftAeUaABAASou0RYsWJANGzZs8XxHR0cWLVrUK6EAAODPvWDaqCTJA/MdLgAA7H4Vl2ivfOUr8/d///e56667up+788478773vS8nn3xyr4YDAKCvDZwN+mdunIn24LOrUi6XC04DAFSbiku0yy+/PJMnT87RRx+dxsbGNDY25phjjsmkSZNy2WWX9UVGAADIQZNHpqaULF3TlsWrW4uOAwBUmR6dzvl8EyZMyFVXXZXHHnssjzzySJLkoIMOygEHHNDr4QAAYJMhDbXZb+LwPLZoTR6YvyqTRjYVHQkAqCIVl2ibHHDAAYozAAB2q5lTR+WxRWvy4LPNeeXBk4qOAwBUkYpLtHe+853bff3yyy/f6TAAALA9h0wdmV/dPT8PzHdCJwCwe1Vcoq1YsWKzx+3t7XnggQeycuXKnHTSSb0WDAAA/tzMjSd0PvisEzoBgN2r4hLtv/7rv7Z4rrOzM+973/uy77779kooAADYmkM2ntA5f+X6rFjbljHDGgpOBABUi4pP59zqm9TUZNasWbn44ot74+0AAGCrRjbVZ69xQ5OYjQYA7F69UqIlyezZs7Nhw4beejsAAPpUuegAO23m1E1LOu2LBgDsPhUv55w1a9Zmj8vlchYsWJArr7wyb3/723stGAAAbM0Lpo3MlfcvyANmogEAu1HFJdrdd9+92eOamppMmDAhX//613d4cicAAOyqF2yaieaETgBgN6q4RLvhhhv6IgcAAPTICzYeLjBn2dqsad2Q4Y0V/5UWAKBiFe+JdtJJJ2XlypVbPN/c3JyTTjqpNzIBAMA2jR/emMkjm1IuJw8vsKQTANg9Ki7RbrzxxrS1tW3xfEtLS2666aZeCQUAANszc1rXbLQHLOkEAHaTHs99v++++7q/f+ihh7Jw4cLuxx0dHbnmmmsybdq03k0HAABb8YKpo/K7hxfnQYcLAAC7SY9LtMMPPzylUimlUmmryzaHDBmSb3/7270aDgAAtmbTvmhmogEAu0uPS7Q5c+akXC5nn332ye23354JEyZ0v9bQ0JCJEyemtra2T0ICAMDzvXCPrhM6H1+8JuvbOjKkwd9DAYC+1eMSba+99kqSdHZ29lkYAADoickjmzJhRGOWrG7NQwtW5ai9xhYdCQAY5HpUov3617/Oq1/96tTX1+fXv/71dq993ete1yvBAABgW0qlUg6dNirXP7I49z2jRAMA+l6PSrQzzzwzCxcuzMSJE3PmmWdu87pSqZSOjo7eygYAANt06B6ju0s0AIC+1qMS7flLOC3nBAAYPMopFR1hpx06vWtftHufWVlsEACgKtQUHQAAAHbGodO6SrQnl6zN6pb2gtMAAINdj2aifetb3+rxG374wx/e6TAAANBT44Y3ZtroIZm/cn3un78qL9l3fNGRAIBBrEcl2sUXX9yjNyuVSko0AAB2m0P3GNVVoj2jRAMA+laPSrQ5c+b0dQ4AAKjYoXuMztUPLHS4AADQ53ZpT7RyuZxyudxbWQAAoCKH7eFwAQBg99ipEu0HP/hBZs6cmaampjQ1NWXmzJm57LLLejsbAABs1ws2Hi7wzIr1Wb62reA0AMBg1qPlnM933nnn5aKLLsqHPvShHHfccUmSW2+9NR/96Eczb968fP7zn+/1kAAA9LbBsZpg1JD67DN+WJ5cujb3PbMyJx44sehIAMAgVXGJ9r3vfS+XXnpp3vzmN3c/97rXvS6HHnpoPvShDynRAADYrV64x6iNJdoqJRoA0GcqXs7Z3t6eo48+eovnjzrqqGzYsKFXQgEAQE8dusfoJHG4AADQpyou0d761rfme9/73hbP/8u//Eve8pa39EooAADoqU2HC9zncAEAoA9VvJwz6TpY4Nprr82LX/ziJMltt92WefPm5W1ve1tmzZrVfd1FF13UOykBAGAbDpk6MjWlZPHq1ixqbsmkkU1FRwIABqGKS7QHHnggRx55ZJJk9uzZSZLx48dn/PjxeeCBB7qvK5VKvRQRAAC2bWhDXQ6YNCKPLFyde59emVNfMLnoSADAIFRxiXbDDTf0RQ4AANhpL5w2Ko8sXJ37nlmlRAMA+kTFe6IBAEB/c+j00UmS++Y7XAAA6BsVz0RraWnJt7/97dxwww1ZvHhxOjs7N3v9rrvu6rVwAADQE88/XKBcLttaBADodRWXaO9617ty7bXX5o1vfGOOOeYYf0EBAKBwB00emYa6mqxc1565y9Zl7/HDio4EAAwyFZdov/nNb3LVVVflpS99aV/kAQCAijXU1eSF00blzqdW5O55K5RoAECvq3hPtGnTpmXEiBF9kQUAAHba4Rv3Rbt73spCcwAAg1PFJdrXv/71fOITn8hTTz3VF3kAANiNykUH6EVH7Dk6SXLP0ysLzQEADE4VL+c8+uij09LSkn322SdDhw5NfX39Zq8vX76818IBAEBPHbHnmCTJwwuas76tI0MaagtOBAAMJhWXaG9+85szf/78fOlLX8qkSZMcLAAAQL8wdVRTJoxozJLVrXng2VV50YyxRUcCAAaRiku0W265JbfeemsOO+ywvsgDAAA7pVQq5Yjpo3PtQ4tyz7yVSjQAoFdVvCfaQQcdlPXr1/dFFgAA2CWblnTe/fSKgpMAAINNxSXal7/85XzsYx/LjTfemGXLlqW5uXmzXwAAUJRNhws4oRMA6G0VL+d81atelSR55Stfudnz5XI5pVIpHR0dvZMMAAAq9MJpo1JTShasasnCVS2ZPKqp6EgAwCBRcYl2ww03bPO1+++/f5fCAACwe5RSLjpCnxjWWJcDJ4/Mwwuac8/TK/KqUVOKjgQADBIVl2gvf/nLN3u8evXq/Md//Ecuu+yy3HnnnfngBz/Ya+EAAKBSR+w5Og8vaM7dT6/Mq2Yq0QCA3lHxnmib/PGPf8zb3/72TJkyJRdeeGFOOumk/OlPf+rNbAAAULHDp49OYl80AKB3VTQTbeHChfnhD3+YH/zgB2lubs5f//Vfp7W1NVdccUUOOeSQvsoIAAA9duTGwwXuf2ZVNnR0pq52p/9/YwCAbj3+G8UZZ5yRAw88MPfdd1++8Y1v5Nlnn823v/3tvswGAAAV22f88Ixoqsv69o48umh10XEAgEGixyXa1VdfnXe961353Oc+l9e85jWpra3ty1wAALBTampKlnQCAL2uxyXazTffnNWrV+eoo47Ksccem+985ztZunRpX2YDAICdcoQSDQDoZT0u0V784hfn0ksvzYIFC/L3f//3+dnPfpapU6ems7Mz1113XVavNlUeAID+4Yg9xyRJ7n56RcFJAIDBouJdVocNG5Z3vvOdufnmm3P//ffnYx/7WL785S9n4sSJed3rXtcXGQEAoCKblnM+uWRtVqxtKzYMADAo7NJRRQceeGC++tWv5plnnsl//Md/9FYmAADYJWOGNWTfCcOSJHc+ZTYaALDreuW879ra2px55pn59a9/3RtvBwAAu+zovcYmSe5QogEAvaBXSjQAAAaWcrnoBH3vqBld+6Ld+dTygpMAAIOBEg0AoIqVig7Qh47eq6tEu/eZVWnd0FFwGgBgoFOiAQBUsfIgrtH2Hj8s44Y1pG1DZx6Y31x0HABggFOiAQAwKJVKpRy5lyWdAEDvUKIBADBobVrSecdchwsAALtGiQYAwKB1dPfhAitSrobTFACAPqNEAwBg0Jo5bVQa6mqybG1b5i5bV3QcAGAAU6IBADBoNdbV5tBpo5Ikd8y1LxoAsPOUaAAAVaiU6lnaeNTzlnQCAOwsJRoAAIPa0XuNTZLcoUQDAHaBEg0AgEHtqI0ndD6xeE1WrmsrOA0AMFAp0QAAGNTGDmvIPhOGJbGkEwDYeUo0AAAGvaP27JqNZkknALCzlGgAAAx6R286XGCuEg0A2DlKNAAABr2jZ3QdLnDPMyvTuqGj4DQAwECkRAMAYNDbZ/ywjB/ekLYNnbnvmVVFxwEABiAlGgAAg16pVMoxe3fNRrvtyWUFpwEABiIlGgAAVeHYvcclSW6bs7zgJADAQKREAwCgKmyaiXbnUyuyoaOz4DQAwECjRAMAoCocOGlERg2pz7q2jjzwbHPRcQCAAUaJBgBAVaipKeVFG0/pvH2OfdEAgMoo0QAAqlqp6AC71bF7byrR7IsGAFRGiQYAQNU4dp/nSrSOznLBaQCAgUSJBgBA1ThkysgMa6hNc8uGPLpwddFxAIABRIkGAEDVqKutyVEb90W7zb5oAEAFlGgAAFQV+6IBADtDiQYAQFV5folWLtsXDQDomX5Ron33u9/NjBkz0tTUlGOPPTa33357j+772c9+llKplDPPPLNvAwIAMGgcusfoNNbVZNnatsxesqboOADAAFF4ifbzn/88s2bNyvnnn5+77rorhx12WE477bQsXrx4u/fNnTs3H//4x3PCCSfspqQAAAwGDXU1OXLPMUmS2yzpBAB6qPAS7aKLLsrZZ5+ds846K4ccckguueSSDB06NJdffvk27+no6Mhb3vKWfO5zn8s+++yzG9MCADAYHGNfNACgQoWWaG1tbbnzzjtz8skndz9XU1OTk08+Obfeeus27/v85z+fiRMn5l3vetfuiAkAwCBz7D4bT+h80r5oAEDP1BX54UuXLk1HR0cmTZq02fOTJk3KI488stV7br755vzgBz/IPffc06PPaG1tTWtra/fj5ubmJEl7e3va29t3LvjG+5//FXbEmKFSxgyVMmaoxPOLo2ocMy+cMjz1taUsbG7J4wtXZe/xw4qO1O/5M4ZKGTNUypihUr01Znp6f6ElWqVWr16dt771rbn00kszfvz4Ht1zwQUX5HOf+9wWz1977bUZOnToLme67rrrdvk9qC7GDJUyZqiUMUOPLH9uGWO1jpm9htXkieaaXPrrP+b4yWaj9VS1jhd2njFDpYwZKrWrY2bdunU9uq7QEm38+PGpra3NokWLNnt+0aJFmTx58hbXz549O3Pnzs0ZZ5zR/VxnZ2eSpK6uLo8++mj23Xffze4555xzMmvWrO7Hzc3NmT59ek499dSMHDlyp7O3t7fnuuuuyymnnJL6+vqdfh+qhzFDpYwZKmXMUIk/Lf5jMr/r+2odM08OmZ1v/n521gydmtNPP6zoOP2eP2OolDFDpYwZKtVbY2bTqsUdKbREa2hoyFFHHZXrr78+Z555ZpKuUuz666/PBz/4wS2uP+igg3L//fdv9txnPvOZrF69Ot/85jczffr0Le5pbGxMY2PjFs/X19f3yr+UvfU+VA9jhkoZM1TKmKEnSqVS9/fVOmZOOGBivvn72blt7orU1talpqa045uo2vHCzjNmqJQxQ6V2dcz09N7Cl3POmjUrb3/723P00UfnmGOOyTe+8Y2sXbs2Z511VpLkbW97W6ZNm5YLLrggTU1NmTlz5mb3jx49Okm2eB4AALbn0D1GZ2hDbZavbcuji1bn4Ck7v0oBABj8Ci/R3vSmN2XJkiU577zzsnDhwhx++OG55pprug8bmDdvXmpqCj1EFACAQaihriYvmjE2f3hsSW6ZvUyJBgBsV+ElWpJ88IMf3OryzSS58cYbt3vvD3/4w94PBABAVXjJvuPyh8eW5NbZS/Ou4/cuOg4A0I+Z4gUAQNV6yb5dJ77f9uTybOjoLDgNANCfKdEAAKhah0wdmVFD6rO6dUMeeLZnJ3MBANVJiQYAUMXKVX4gZW1NKS/eZ2yS5JbZSwtOAwD0Z0o0AACq2qYlnbfOXlZwEgCgP1OiAQBQ1V6y77gkyf/NXZ7WDR0FpwEA+islGgAAVW2/icMzfnhjWto7c8+8lUXHAQD6KSUaAABVrVQqdc9Gu8WSTgBgG5RoAABUvU0lmn3RAIBtUaIBAFSjcrnoBP3KpsMF7n56Rda2big4DQDQHynRAACoenuOG5o9xw5Ne0c5t80xGw0A2JISDQAAkpywf9dstD8+trTgJABAf6REAwCAJCfsPyFJctPjSwpOAgD0R0o0AABIcty+41JbU8rsJWszf+X6ouMAAP2MEg0AAJKMGlKfw6ePTpLcbDYaAPBnlGgAALBR975oj9sXDQDYnBINAAA22rQv2v8+sTQdneWC0wAA/YkSDQAANjpsj1EZ0VSXleva88D8VUXHAQD6ESUaAABsVFdbk5fu27Wk0ymdAMDzKdEAAOB5TjjAvmgAwJaUaAAA8Dwv27gv2l1Prcia1g0FpwEA+gslGgAAPM/0sUMzY9zQbOgs50+zlxUdBwDoJ5RoAADwZzad0mlfNABgEyUaAEAVK6dUdIR+6YT97YsGAGxOiQYAAH/muH3Hpa6mlDlL12besnVFxwEA+gElGgAA/JkRTfU5aq8xSZIbH1tccBoAoD9QogEAwFa84qCJSZIbHlGiAQBKNAAA2KpXHNhVot0ye1la2jsKTgMAFE2JBgBQhUopFx2h3ztg0vBMHdWU1g2dufXJZUXHAQAKpkQDAICtKJVKOdGSTgBgIyUaAABsw0kbl3T+/pHFKZfN3gOAaqZEAwCAbXjJfuPSUFuTZ1asz+wla4uOAwAUSIkGAADbMLShLsfuMzZJcuOjlnQCQDVTogEAwHZsOqXzBiUaAFQ1JRoAAGzHKzYeLnD7nOVZ07qh4DQAQFGUaAAAsB17jx+WvccPS3tHOTc/vrToOABAQZRoAACwAyceOCGJfdEAoJop0QAAYAeevy9auVwuOA0AUAQlGgAA7MAxe4/NkPraLGpuzYPPNhcdBwAogBINAAB2oKm+NifsPz5J8ruHFxWcBgAoghINAKAKWZBYuZMPmZQkue4hJRoAVCMlGgAA9MArD5qYmlLy4LPNeXbl+qLjAAC7mRINAKCqlYoOMGCMG96Yo/Yak8SSTgCoRko0AADooZMPtqQTAKqVEg0AAHrolI37ov3pyWVpbmkvOA0AsDsp0QAAoIf2mTA8+04YlvaOcv7w6JKi4wAAu5ESDQCgCpWcz7nTnNIJANVJiQYAABU4dWOJdsOji9Pe0VlwGgBgd1GiAQBABQ6fPibjhzdkdcuG3D5nedFxAIDdRIkGAAAVqK0p5aSDJiaxpBMAqokSDQAAKnTKIZOTdJVo5bL95QCgGijRAACgQsfvNz5N9TWZv3J9Hl6wuug4AMBuoEQDAIAKDWmozQn7T0iSXPPgwoLTAAC7gxINAAB2wukv7FrSefX9CwpOAgDsDko0AADYCScdNCn1taU8vnhNnlhsSScADHZKNAAA2AmjhtTnpfuNT5Jcfb8lnQAw2CnRAABgJ50+c0qS5OoHlGgAMNgp0QAAYCedcsik1NaU8tCC5jy1bG3RcQCAPqREAwCAnTRmWENevM/YJGajAcBgp0QDAIBd8GpLOgGgKijRAABgF5z6gkkplZJ7n16Z+SvXFx0HAOgjSjQAANgFE0c05UV7dS3pvMZsNAAYtJRoAACwi179wslJkmseWFBwEgCgryjRAABgF71qZleJdsdTK7K4uaXgNABAX1CiAQDALpoyakgOnz465bIDBgBgsFKiAQBUo3K56ASDzmsP7Tql83/ufbbgJABAX1CiAQBAL3jtoVNTKnUt6XRKJwAMPko0AADoBZNHNeWYGV2ndF55n9loADDYKNEAAKCXnHHY1CTJry3pBIBBR4kGAAC95NUzJ6e2ppQH5jfnySVrio4DAPQiJRoAAPSSccMbc/x+45Mkv7lvQcFpAIDepEQDAIBe9PwlnWWnoALAoKFEAwCAXnTqCyaloa4mTyxek0cWri46DgDQS5RoAADQi0Y21ecVB05IkvyPAwYAYNBQogEAQC/btKTzf+6zpBMABgslGgAA9LJXHjQpQxtq8/Ty9bnn6ZVFxwEAeoESDQAAetmQhtqccsikJMkVd88vOA0A0BuUaAAA0AfOPGJakuR/7luQ9o7OgtMAALtKiQYAAH3ghP3GZ/zwxixf25Y/PLqk6DgAwC5SogEAQB+oq63J6w/vOmDgV3c/U3AaAGBXKdEAAKCP/OWRXUs6f/fw4qxa115wGgBgVyjRAACqWDmloiMMaodMGZmDJo9I24bOXHn/gqLjAAC7QIkGAAB9pFQq5S82HjDwq7ss6QSAgUyJBgAAfejMI6alppTc8dSKPLVsbdFxAICdpEQDAKhK5aIDVI1JI5vy0v3GJ0n+6+75BacBAHaWEg0AAPrYpgMG/uvu+SmXFZgAMBAp0QAAoI+d9oLJGdpQm6eWrctd81YUHQcA2AlKNAAA6GNDG+ryqpmTkyT/eacDBgBgIFKiAQDAbvBXR01PkvzPvQuyrm1DwWkAgEop0QAAYDd48T5js9e4oVnTuiFX3reg6DgAQIWUaAAAsBuUSqX89dFds9F+ccfTBacBACqlRAMAgN3kjUftkZpS8n9zV+SJxWuKjgMAVECJBgAAu8mkkU15xYETkyS/NBsNAAYUJRoAAOxGf/2iriWd/++uZ9Le0VlwGgCgp5RoAACwG5100MSMH96YpWva8vtHFhcdBwDoISUaAADsRvW1NXnDkdOSJD//P0s6AWCgUKIBAMButmlJ542PLs7CVS0FpwEAekKJBgAAu9m+E4bnRTPGpLOc/OedZqMBwECgRAMAgAK86UV7Jkl+9n9Pp6OzXHAaAGBHlGgAAFCA17xwSkY21eWZFevzh8ccMAAA/Z0SDQCgipn/VJwhDbX5q6O79kb78Z/mFZwGANgRJRoAABTkLcd2Lem84dHFeXr5uoLTAADbo0QDAICC7DNheF6637iUy8l/3G42GgD0Z0o0AICqZCFnf/HWF++VJPn5/z2d1g0dBacBALZFiQYAAAU6+eBJmTSyMcvWtuWaBxYWHQcA2AYlGgAAFKiutiZvPqZrb7SfOGAAAPotJRoAABTsb160Z2prSrl97vI8unB10XEAgK1QogEAQMEmj2rKKQdPSpL8+E9PFZwGANgaJRoAAPQDbz2u64CBX931TJpb2gtOAwD8OSUaAAD0Ay/Zd1z2nzg8a9s68ov/e7roOADAn1GiAQBAP1AqlXLWS/dOkvzo1rnp6CwXnAgAeD4lGgAA9BN/ccS0jB5an6eXr8/vHl5UdBwA4HmUaAAA0E8MaajNm4/ZM0ly+c1zCk4DADyfEg0AAPqRtx23V2prSrltzvI8+OyqouMAABsp0QAAoB+ZMmpITn/hlCTJv/7v3GLDAADdlGgAANDPnPXSGUmSX9/zbJasbi02DACQRIkGAAD9zpF7jsnh00enraMzP7ntqaLjAABRogEAQL+0aTbaj/80Ly3tHcWGAQCUaAAAValcdAB25PQXTsmUUU1ZuqY1/3X3/KLjAEDVU6IBAEA/VF9bk3cdv3eS5NI/PpmOTs0nABRJiQYAUNVKRQdgO/7mmD0zsqkuTy5dm+seWlh0HACoako0AADop4Y31uVtx81IknzvD0+mXDYbDQCKokQDAKhC5p8NHG9/yYw01NXk3qdX5vY5y4uOAwBVS4kGAAD92IQRjXnjUXskSS75w+yC0wBA9VKiAQBAP/eeE/ZJqZTc8OiSPLKwueg4AFCVlGgAANDPzRg/LK+eOTlJ8i9/fLLgNABQnZRoAAAwAPz9y/ZNkvz6nmfzzIp1BacBgOqjRAMAgAHgsOmj89L9xmVDZ9neaABQACUaAAAMEB86af8kyS/+75ksXNVScBoAqC5KNAAAGCBevM+4HLP32LR1dJqNBgC7Wb8o0b773e9mxowZaWpqyrHHHpvbb799m9deeumlOeGEEzJmzJiMGTMmJ5988navBwCAweQjr+yajfYft8/L4maz0QBgdym8RPv5z3+eWbNm5fzzz89dd92Vww47LKeddloWL1681etvvPHGvPnNb84NN9yQW2+9NdOnT8+pp56a+fPn7+bkAACw+71k33E5cs/Rad3Q6aROANiNCi/RLrroopx99tk566yzcsghh+SSSy7J0KFDc/nll2/1+p/85Cd5//vfn8MPPzwHHXRQLrvssnR2dub666/fzckBAGD3K5VK+fDG2Wg/vu2pLF3TWnAiAKgOhZZobW1tufPOO3PyySd3P1dTU5OTTz45t956a4/eY926dWlvb8/YsWP7KiYAAPQrLz9gQg7bY1Ra2jtz2U1zio4DAFWhrsgPX7p0aTo6OjJp0qTNnp80aVIeeeSRHr3HJz7xiUydOnWzIu75Wltb09r63P8719zcnCRpb29Pe3v7TiZP97278h5UF2OGShkzVMqYoRLlcrn7e2NmYHr/ifvk7398d/7t1rk567jpGTusoU8/z58xVMqYoVLGDJXqrTHT0/sLLdF21Ze//OX87Gc/y4033pimpqatXnPBBRfkc5/73BbPX3vttRk6dOguZ7juuut2+T2oLsYMlTJmqJQxQ0/UrlzR/b0xMzCVy8kew2rzzNqOfOrffp/X7dW5Wz7XeKFSxgyVMmao1K6OmXXr1vXoukJLtPHjx6e2tjaLFi3a7PlFixZl8uTJ2733wgsvzJe//OX87ne/y6GHHrrN684555zMmjWr+3Fzc3P3YQQjR47c6ezt7e257rrrcsopp6S+vn6n34fqYcxQKWOGShkzVOL2Bb9LFnZ9b8wMXE37Ls57f3JP/ndJXb7wdydkwojGPvssf8ZQKWOGShkzVKq3xsymVYs7UmiJ1tDQkKOOOirXX399zjzzzCTpPiTggx/84Dbv++pXv5ovfvGL+e1vf5ujjz56u5/R2NiYxsYt/zJRX1/fK/9S9tb7UD2MGSplzFApY4aeKJVK3d8bMwPXaTOn5vDpc3PP0yvz/Zvm5nOvn9nnn2m8UCljhkoZM1RqV8dMT+8t/HTOWbNm5dJLL82PfvSjPPzww3nf+96XtWvX5qyzzkqSvO1tb8s555zTff1XvvKVnHvuubn88sszY8aMLFy4MAsXLsyaNWuK+hEAAKAQpVIp/3TagUmSn94+L8+s6NlyFACgcoWXaG9605ty4YUX5rzzzsvhhx+ee+65J9dcc033YQPz5s3LggULuq//3ve+l7a2trzxjW/MlClTun9deOGFRf0IAAADVjmlHV9Ev/aS/cbnJfuOS3tHOd/83eNFxwGAQatfHCzwwQ9+cJvLN2+88cbNHs+dO7fvAwEAwADy8dMOzF/+8y35f3c9k/eeuG/2nTC86EgAMOgUPhMNAIAilIsOQC86cs8xOfngieksJxdd91jRcQBgUFKiAQDAIPCxU7v2RrvyvgV58NlVBacBgMFHiQYAAIPAwVNG5ozDpiZJvnrNowWnAYDBR4kGAACDxMdOOSD1taX84bEluenxJUXHAYBBRYkGAACDxIzxw/J3L94rSfLFKx9OR6e97wCgtyjRAABgEPnwSftnRFNdHlm4Or+665mi4wDAoKFEAwCAQWTMsIZ88BX7JUm+fu1jWd/WUXAiABgclGgAADDIvP0lMzJt9JAsbG7JD25+sug4ADAoKNEAAGCQaaqvzT+96sAkyfdunJ0lq1sLTgQAA58SDQAABqEzDp2aw/YYlbVtHbn4d48VHQcABjwlGgAADEI1NaV86vSDkyQ/u31eHnq2ueBEADCwKdEAAGCQOnafcXnNoVPSWU4+++sHUy6Xi44EAAOWEg0AAAaxT59+cJrqa3L73OX59b3PFh0HAAYsJRoAAAxiU0cPyQdO3C9JcsFVj2Rt64aCEwHAwKREAwCAQe7sl+2T6WOHZGFzS757wxNFxwGAAUmJBgAAg1xTfW3Ofc0hSZLLbpqTuUvXFpwIAAYeJRoAAFSBUw6ZlJcdMCFtHZ35wm8eKjoOAAw4SjQAAKgCpVIp5732kNTVlHL9I4tz7YMLi44EAAOKEg0AAKrEfhOH5+yX7ZMkOf/XD2aNQwYAoMeUaAAAValcdAAK8uGT9s/0sUOyYFVLLr7usaLjAMCAoUQDAIAqMqShNl94/cwkyb/+75w8MH9VwYkAYGBQogEAQJU58cCJOeOwqeksJ+f86v50dJqZCAA7okQDAIAqdO5rD86IprrcP39V/u3WuUXHAYB+T4kGAABVaOKIpnzy1QclSS787aNZsGp9wYkAoH9TogEAQJV684v2zFF7jcnato586lf3p1y2rBMAtkWJBgAAVaqmppQv/+UL01BbkxseXZL/d9f8oiMBQL+lRAMAgCq2/6QR+egpByRJPvc/D2bhqpaCEwFA/6REAwCAKnf2CXvnsD1GZXXLhnzqvyzrBICtUaIBAECVq6utydf+6rA01Nbk948szn/dbVknAPw5JRoAAJADJo3IR07eP0ny2V8/mMXNlnUCwPMp0QAAgCTJ379sn7xw2qg0t2zIJ53WCQCbUaIBAABJupZ1Xvi8ZZ0/uW1e0ZEAoN9QogEAAN0OnDwi//SqA5Mk/9+VD+WJxWsKTgQA/YMSDQAA2Mw7X7p3jt9vfFraO/MPP787bRs6i44EAIVTogEAAJupqSnl6399WEYPrc8D85tz0XWPFR0JAAqnRAMAALYwaWRTvvyXL0ySfP+Ps3PbnOUFJwKAYinRAACArXrVzCn566P3SLmc/OP/eyBr24tOBADFUaIBAFS1UtEB6OfOP+MFmTFuaBasaslPZ9ekXC4XHQkACqFEAwCoQqUoQuiZYY11+c7fHpn62lIeWFGTy295quhIAFAIJRoAALBdM6eNyqdPPyhJcuG1j+fOp1YUnAgAdj8lGgAAsEN/+6I9csS4zmzoLOdDP70rK9a2FR0JAHYrJRoAALBDpVIpf7NPZ2aMG5pnV7XkY7+8N52dlgUDUD2UaAAAQI801SXffNOhaairye8fWZxL/ji76EgAsNso0QAAgB47ZMrIfO51L0iSfO23j+YPjy0pOBEA7B5KNAAAoCJ/86Lp+ZsXTU+5nHzop3dl7tK1RUcCgD6nRAMAACpSKpXyude/IEfsOTrNLRvynn+/I2tbNxQdCwD6lBINAACoWGNdbS75u6MyYURjHlu0Jh//5b0plx00AMDgpUQDAAB2yqSRTbnk745MfW0pVz+wMP98o4MGABi8lGgAAMBOO2qvsfnc62YmSS689tFc88DCghMBQN9QogEAALvkb4/dM2998V4pl5N/+Pndue+ZlUVHAoBep0QDAAB22flnHJKXHzAhLe2dedeP7sj8leuLjgQAvUqJBgAA7LK62pp852+PyEGTR2TJ6ta864f/l9Ut7UXHAoBeo0QDAAB6xYim+vzgHS/KhBGNeWTh6nzwp3dnQ0dn0bEAoFco0QAAgF4zbfSQ/ODtR6epviZ/eGxJzv3vB1Mul4uOBQC7TIkGAAD0qkP3GJ1vvOmIlErJf9w+Lxf/7vGiIwHALlOiAQBUIROD6Guvmjk5n3/9zCTJt65/PD+6ZW6xgQBgFynRAACqWanoAAxmb33xXvnoyQckST77Pw/m1/c+W3AiANh5SjQAgCpUStdUtLIWjT724Vful7cdt1fK5eRjv7gnf3xsSdGRAGCnKNEAAIA+UyqVcv4ZL8hrDp2S9o5y3vvjO3PnUyuKjgUAFVOiAQAAfaq2ppSL/vqwHL/f+Kxr68g7Lr899z2zsuhYAFARJRoAANDnGutq8y9vOyrHzBib1a0b8neX3ZYH5q8qOhYA9JgSDQAA2C2GNtTl8rNelCP3HJ3mlg156w9uyyMLm4uOBQA9okQDAAB2m+GNdfnhO4/JYXuMyop17XnLpbfl8UWri44FADukRAMAAHarkU31+bd3HpsXTB2ZZWvb8uZLb8tjijQA+jklGgAAsNuNGlqfH7/r2Bw0eUSWrmnNm75/qz3SAOjXlGgAAEAhxgxryM/e8+IcunFp55sv/VPufGpF0bEAYKuUaAAAQGFGD23Ij999bF40Y0xWbzxs4NbZy4qOBQBbUKIBAACFGtlUnx+985gcv9/4rGvryDv+9fbc8OjiomMBwGaUaAAAQOGGNtTlsrcfnVceNDGtGzpz9o/uyK/ueqboWADQTYkGAAD0C031tbnkrUfl9YdPzYbOcmb94t5878bZKZfLRUcDACUaAADQf9TX1uTivz4873nZPkmSr1zzSD776wfT0alIA6BYSjQAAKBfqakp5VOnH5xzX3tISqXkR7c+lQ/9x11pae8oOhoAVUyJBgAA9EvvOn7vfPvNR6ShtiZX3b8wf3fZbVm6prXoWABUKSUaAADQb7320Kn50TuPycimutzx1Iq8/jv/m0cWNhcdC4AqpEQDAAD6teP2HZf/+sBLs/f4YZm/cn3e8M+35HcPLSo6FgBVRokGAAD0e/tOGJ7/ev9L8pJ9x2VtW0fO/vc7cskfnNwJwO6jRAMAqErl5/0vDAyjhzbkR+88Jm85ds+Uy8mXr34kH/35PVnXtqHoaABUASUaAAAwYNTX1uT/O3NmPve6F6S2ppQr7nk2f/HdWzJn6dqiowEwyCnRAACAAaVUKuXtL5mRn7z72Iwf3phHF63O6759c3774MKiowEwiCnRAACAAenF+4zLlR8+PkfvNSarWzfk7//9znz56keyoaOz6GgADEJKNAAAYMCaNLIp//GeF+edL907SXLJH2bnby+7Lc+uXF9wMgAGGyUaAAAwoNXX1uS8Mw7Jd/72iAxrqM3tc5bn1d+8Kdc8sKDoaAAMIko0AABgUHjtoVNz5YdPyGF7jMqq9e1574/vyjm/uj/r2zqKjgbAIKBEAwAABo0Z44fll+99Sd778n1TKiX/cfu8nPGdm/PQs81FRwNggFOiAQAAg0pDXU0++eqD8uN3HZuJIxrzxOI1ef13b863r3887Q4dAGAnKdEAAIBB6aX7jc81//CynHrIpLR3lPP16x7LX/7zLXl04eqiowEwACnRAACAQWvssIZ8/61H5RtvOjyjhtTn/vmrcsa3b853b3giG8xKA6ACSjQAAGBQK5VKOfOIabnuoy/LKw+amLaOznztt4/mDd+7JQ8+u6roeAAMEEo0AACgKkwc2ZTL3n50vv5Xh2VEU13ufWZVXved/83/95uHsrZ1Q9HxAOjnlGgAAEDVKJVKecNRe+R3s16e17xwSjo6y7ns5jk55aI/5NoHFxYdD4B+TIkGAABUnUkjm/LdtxyZf33Hi7LHmCF5dlVL3vPvd+bsf7sjz6xYV3Q8APohJRoAAFC1XnHQxFz30ZfnfSfum7qaUq57aFFe+fU/5KJrH826Nks8AXiOEg0AAKhqQxpq84lXHZQrP3xCjt17bFo3dOZbv38iJ134h/zX3c+ks7NcdEQA+gElGgBANdIJwBYOnDwiP3vPi/O9txyZPcYMycLmlnz05/fmL793S+6et6LoeAAUTIkGAFCVtGiwNaVSKa9+4ZT8btbL84+nHZihDbW55+mV+Yt/viXv+/GdeWLxmqIjAlAQJRoAQFUrFR0A+qWm+tp84BX75YaPn5g3HrVHSqXk6gcW5tSL/5BP/Od9eXbl+qIjArCbKdEAAAC2YdLIplz4V4flmo+8LCcfPCmd5eTndzydEy+8MV+88qEsX9tWdEQAdhMlGgAAwA4cOHlELnv70fl/73tJjtl7bNo2dObSm+bkhK/8Phdc/XCWrmktOiIAfUyJBgAA0ENH7TUmP3/Pi/PDs16UF0wdmbVtHfn+H57M8V/5fT7/Pw9lUXNL0REB6CNKNAAAgAqUSqWceODE/OZDx+eytx2dw/YYlZb2zlz+v3NywldvyLlXPJBnVqwrOiYAvayu6AAAAAADUalUysmHTMorD56YPz6+NN++/vHc8dSK/PufnspPb5+X0184Je8+fu8cNn100VEB6AVKNAAAgF1QKpXy8gMm5GX7j8+tTy7Ld37/RG6ZvSz/c++z+Z97n80xM8bm3SfsnVcePCm1NU7EBRiolGgAAAC9oFQq5SX7js9L9h2fB+avyg9unpP/uffZ3D53eW6fuzwzxg3NO4/fO39xxLSMaKovOi4AFbInGgAAQC+bOW1ULn7T4bn5EyflvS/fNyOb6jJ32bqc998P5tgvXZ9zfnV/Hnx2VdExAaiAmWgAAAB9ZPKopnzy1QflQyftl1/e8XT+/U9PZfaStfmP2+flP26flyP2HJ2/O3avvObQKWmqry06LgDboUQDAADoY8Ma6/KOl+6dt79kRv705PL8+Lan8tsHFubueStz97yV+cKVD+XMw6flDUfukZnTRqZUsncaQH+jRAMAANhNSqVSjtt3XI7bd1wWr27JL+94Jj+9bV7mr1yfH94yNz+8ZW4OnDQibzhqWs48fFomjmwqOjIAGynRAAAACjBxRFM+8Ir98t6X75s/Pr4k/+/OZ3LtQ4vy6KLV+dJVj+TLVz+Slx8wIX955B555cETM7TBf74BFMmfwgAAAAWqrSnlFQdOzCsOnJhV69vzm/uezf+785ncNW9lbnh0SW54dEmG1NfmlQdPzGsPnZoTD5xg/zSAAijRAAAA+olRQ+rzlmP3yluO3Suzl6zJr+56Jv99z7N5ZsX6/Oa+BfnNfQsyrKE2pxwyKa89dGpOOGB8GusUagC7gxINAACgH9p3wvD842kH5eOnHph7n1mVK+97NlfetyDPrmrJFfc8myvueTYjGuvy8gMn5JRDJuXEAydm1JD6omMDDFpKNAAAgH6sVCrl8Omjc/j00Tnn1Qfn7qdX5jf3PZur7l+QRc2t3TPU6mpKOWbvsTnlkEk5+eBJmT52aNHRAQYVJRoAAMAAUVNTylF7jclRe43Jua85JPc8szK/e2hRrntoUR5fvCa3zF6WW2Yvy+f+56EcNHlEXn7ghLxs/wk5esYYyz4BdpESDQCgCpWKDgDsspqaUo7cc0yO3HNM/ulVB2Xu0rX53cNdhdr/zV2eRxauziMLV+f7f3gyTfU1efE+43LC/hPy8gPGZ98Jw1Mq+ZMAoBJKNAAAgEFgxvhhefcJ++TdJ+yTFWvb8sfHl+SPjy3NHx9fkiWrW3Pjo0ty46NL8oUkU0c15aX7jc+x+4zLsXuPtfQToAeUaAAAVc1MFBiMxgxryOsPn5bXHz4t5XI5jyxcnZs2lmq3z12eZ1e15Jd3PpNf3vlMkmTa6CE5dp+xefHe43LsPmOz59ihZqoB/BklGgAAwCBWKpVy8JSROXjKyLznZftmfVtHbpuzLLc+uSy3Pbk8989flfkr1+dXd83Pr+6anySZPLIpx+w9NkfuOTpH7DkmB08ZmYa6moJ/EoBiKdEAAACqyJCG2px44MSceODEJMna1g2586kVuW1OV6l27zMrs7C5Jb++99n8+t5nkyQNdTV54bRROWJ6V6l2xJ6jM3X0kCJ/DIDdTokGAABQxYY11uVlB0zIyw6YkCRZ39aRu+etyJ1PrcjdT6/M3fNWZMW69tz5VNdzyZwkyaSRjXnhtFF5wdRRmTltVF4wdWSmjGqyDBQYtJRoAAAAdBvSUJuX7Dc+L9lvfJKkXC5n7rJ1uXveitw9b2XufnpFHl6wOouaW7OoeXF+9/Di7nvHDmvIC6aOzAumjspBk4Zlyfqko7Oc+qJ+GIBepEQDAABgm0qlUvYePyx7jx+WvzxyjyRds9UeeHZVHpi/Kg8+25wH5q/K44vXZPnattz0+NLc9PjSjXfX5esPXp/9Jg7PAZNG5IBJI3LgpBHZf9LwTBs9xKw1YEBRogEAAFCRIQ21edGMsXnRjLHdz7W0d+SxRavzwPzmjQXbyjw8f1Va2ju7npvfvNl7DGuozf6TRuSAScOz/8QRXUXdhGGZPmaoQwyAfkmJBgAAwC5rqq/NoXuMzqF7jE6StLe35zdXXpUXHPvyPLmsJY8vWp1HF63O44vW5Mmla7K2rSP3PL0y9zy9crP3qa0pZfqYIRtnvw3P3hOGZZ/xwzJj/LBMGdmUmhqz14BiKNEAAADoEzWlZO/xw3LAlNF51czJ3c+3d3Rm7tK1eWzRmjy6aHVmL1mTOUvWZs7StVnf3pG5y9Zl7rJ1ueHRJZu9X2NdTaaNGZLpY4ZmjzFDMn3sxq8bH48d1mCJKNBnlGgAAADsVvW1Ndl/0ojsP2lEXpMp3c+Xy+UsXt2aJzcWanOWrtn4dW3mLV+X1g2deXLJ2jy5ZO1W33doQ232GDMke2ws1SaPasqUUU2ZPLLr+8kjmzKkoXZ3/ZjAIKNEAwAAoF8olUqZNLIpk0Y25bh9x2322oaOzjy7siXPrFiXp1esyzMr1ufp5Ru/rliXRc2tWdfWkccWrclji9Zs8zNGD63P5JFN3QXbpJHPfR0/vDETRjRm7LCG1Nfalw3YnBINAACAfq+utiZ7jhuaPccN3errLe0deXbl+u5Sbf6K9VnY3JKFq1qysLklC1a2ZH17R1aua8/Kde15ZOHq7X7emKH1mTCiMeOHP+/XiIbuom3C8MaMG96QMUMb0lRvdhtUAyUaAAAAA15TfW32mTA8+0wYvtXXy+Vymls2ZFFzSxasasmiVV1fFzav31i0tWbpmtYsX9uWjs5yVqxrz4p17dud1fbcZ9dkzNCGjB7akDFD6zd+v/nXMcPqN77edc2IpvrUOiQBBhQlGgAAAINeqVTKqCH1GTWkPgdMGrHN6zo7y1mxri1L17Rl6ZquYm3J6tYsWdOapas3f2752rZs6Cynpb0zCzaWcpUY3liXEU11GdlU3/V1SP0OH49sqsuIpvoMa6zL0Ppap5XCbtQvSrTvfve7+drXvpaFCxfmsMMOy7e//e0cc8wx27z+l7/8Zc4999zMnTs3+++/f77yla/k9NNP342JAQAAGIxqakoZN7wx44Y35sBsu2xLuma3rWndkJXr2rNiXVuWr23r/n7Fuvas3OxrW1as7fp+bVtHkmRN64asad1Qcfn2fEPqazOssTZDG+oytKG2q1xrqM3wxroMbajrfm1YQ22GNj73dXhjbYbU16WpviZN9bVpqq/NkPra7seNdTVOOoU/U3iJ9vOf/zyzZs3KJZdckmOPPTbf+MY3ctppp+XRRx/NxIkTt7j+lltuyZvf/OZccMEFee1rX5uf/vSnOfPMM3PXXXdl5syZBfwEAAAAVKNSqZQRTV1LM6eP3fpebVvTtqEzq1va09yyoevr+q6vq1s2pHnj883rn3v8/NdWt2zI6pYN6egsJ0nWt3dkfXtHkrZe//m6C7a62gxp6CrWmjYWbUM2Fm9Nzyvemupr01Bbk4a6mue+VvB9qdyRte3J2tYNGVZTm7qakiKPfqXwEu2iiy7K2WefnbPOOitJcskll+TKK6/M5Zdfnk9+8pNbXP/Nb34zr3rVq/KP//iPSZIvfOELue666/Kd73wnl1xyyW7NDgAAAJVqqKvpnu22M8rlclo3dGZdW0fWtm7I2rYNWdvakXXP/7rxtXWtXd8//7U1rRuyrq0j69o60tK+6VdnWto7smFjOZdk43OdSdp76Sfvibp86o7fJ0lKpaS+tiaNG8u2+tqa1NWWUldTSl1tTepqSqmvrUltTSn1taXU1Wz+en1tKbU1NamvKaVu0/dbu66mlNraUur/7PnamlJqS1331pRKqa157mttTZ77vlRKTc2fvV4qpaYmm7++6T2e//qfPff896gpRYnYzxRaorW1teXOO+/MOeec0/1cTU1NTj755Nx6661bvefWW2/NrFmzNnvutNNOyxVXXNGXUfu1e67/WcobWouOwQ50dHSm9eknc+91y1PruGx6wJihUsYMlWhaPbfoCADspFKp1D3za+ywhl597/aOzs1Kte7vN3R9v76tIy0bul5r3TgL7rlrO9PW0ZG2DZ1dvzo607ahvPFrR/dz7d3PdaZ1w8bXOjrT3lHunmGXJOVyut8rVfqfvDWldBdrXb+6yrtSqWvpcU2plFK6xsSm1zaVb6XnPa553uPnvm5+T7byHjWlpJSuwu/599TV1OSytx9d9D+e3a7QEm3p0qXp6OjIpEmTNnt+0qRJeeSRR7Z6z8KFC7d6/cKFC7d6fWtra1pbn/u3rbm5OUnS3t6e9vadb9M33bsr79Fb9rrp4xmT7R/PTP9wdJIsLToFA4kxQ6WMGSrVWarpF3+fof/rT3//ZWAwZgauptqkqbYmaar5/9u796Co6/+L42cXETHATAQ1CcwsZ7wAopKXikwxR51oHHTKDMmxLDSJPwpvkOUl8xKFhZfKLHW0ctSakiK8xtSAYpaVMmpODt7QVBD66rK7vz/ULX6oHzaBzyLPxwzD8t7bWecFLofPRZJ3vT2vzWbTN9/m6MGHB8hp8dKlSodsdoercLPZnbLZHbI7nKp0OK+Ubg5V2p2yOZyqvHLd5cuXr7t6udLuUOWV+1Xanap0OP51+crX9urX2Z1OORyXP9sdTjmcuvL5yteu6/TP2nVu+89jyXU/p/PG/yYOp+SwOyUZ3LCeeXtZPOJ7u7Z+ztT0/qbvzlnX5s6dq5kzZ1Zb//bbb9W8ec33Wb+enJycm36Mm9XWerd8nX+bHQMAADQw/7M004XgPh7xfgYNB/MCdzEzcIfVIn2/bct/u++VD7dqP68rHyZxOiXH1c9XLjuc/6z/+7LTeblKc33+f/fXDdYcrvtaqtz3mp9rsCZJX3/9dV3/89TYzf6cqaioqNHtTC3RAgMD5eXlpZMnT1ZZP3nypNq0aXPN+7Rp08at20+ZMqXK7p+lpaUKCQlRbGysAgIC/nN2m82mnJwcDRo0SN7e9dfMXxNnJm0QPGpm0CAwM3AXMwN32Ww2HWNmUEP8jIG7mBm4i5mBu2prZq7utWjE1BKtadOmioqKUm5uruLi4iRJDodDubm5mjhx4jXv06dPH+Xm5io5Odm1lpOToz59+lzz9j4+PvLxqX6wRm9v71r5pqytx0HjwczAXcwM3MXMwF3MDNzBvMBdzAzcxczAXTc7MzW9r+m7c6akpCghIUE9e/ZU7969lZGRofLyctfZOp9++mndeeedmjt3riRp8uTJeuihh7Rw4UINHTpUa9eu1a5du7Rs2TIzXwYAAAAAAABuYaaXaKNGjVJJSYnS0tJ04sQJRUREKDs723XygD///FNW6z9nGOvbt6/WrFmj6dOna+rUqerUqZM2btyorl27mvUSAAAAAAAAcIszvUSTpIkTJ153981t27ZVW4uPj1d8fHwdpwIAAAAAAAAusxrfBAAAAAAAAGjcKNEAAAAAAAAAA5RoAAAAAAAAgAFKNAAAAAAAAMAAJRoAAAAAAABggBINAAAAAAAAMECJBgAAAAAAABigRAMAAAAAAAAMUKIBAAAAAAAABijRAAAAAAAAAAOUaAAAAAAAAIABSjQAAAAAAADAACUaAAAAAAAAYIASDQAAAAAAADBAiQYAAAAAAAAYoEQDAAAAAAAADFCiAQAAAAAAAAYo0QAAAAAAAAADlGgAAAAAAACAAUo0AAAAAAAAwAAlGgAAAAAAAGCAEg0AAAAAAAAwQIkGAAAAAAAAGKBEAwAAAAAAAAxQogEAAAAAAAAGKNEAAAAAAAAAA5RoAAAAAAAAgAFKNAAAAAAAAMBAE7MD1Den0ylJKi0tvanHsdlsqqioUGlpqby9vWsjGm5xzAzcxczAXcwM3MXMwB3MC9zFzMBdzAzcVVszc7UjutoZXU+jK9HKysokSSEhISYnAQAAAAAAgKcoKytTixYtrnu9xWlUs91iHA6Hjh07Jn9/f1kslv/8OKWlpQoJCdHRo0cVEBBQiwlxq2Jm4C5mBu5iZuAuZgbuYF7gLmYG7mJm4K7amhmn06mysjK1a9dOVuv1j3zW6LZEs1qtat++fa09XkBAAN/ccAszA3cxM3AXMwN3MTNwB/MCdzEzcBczA3fVxszcaAu0qzixAAAAAAAAAGCAEg0AAAAAAAAwQIn2H/n4+Cg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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15, 10))\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Amplitude')\n",
"plt.plot(tx-position*duration, x, label='Señal x(t)') # Notar que desplazamos el eje del tiempo para que veamos la señal como que empieza en t=0. Esto es una cuestión simplemente\n",
" # de visualización, ya que el cero de tiempo lo ponemos en el indice del array que contiene la señal x(t) \n",
" # en donde más nos convenga.\n",
"plt.plot(tx-position*duration, h, label='Señal h(t)') #Como las señales se generan con los mismos parámetros de duration y sample_rate tx=th asi que puedo usar cualquiera.\n",
"plt.grid()\n",
"plt.legend(loc='best')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "f9622c62-4e25-450a-a826-b9ead7c216a2",
"metadata": {},
"source": [
"Para realizar la convolución vamos a usar el método [convolve](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.convolve.html#scipy.signal.convolve) de [scipy.signal](https://docs.scipy.org/doc/scipy/reference/signal.html). Miren un poco la documentación para entender como usarlo. Hay cosas que todavía no van a entender pero\n",
"a medida que avancemos con la materia muchas cosas quedarán más claras!\n",
"\n",
"La sintaxis general del comando es \n",
"\n",
"output=signal.convolve(in1, in2, mode='full', method='auto')\n",
"\n",
"donde in1 y in2 son los arrays de las señales a convolucionar (tienen que ser el mismo número de dimensiones pero no necesariamente del mismo tamaño). \n",
"\n",
"El argumento mode específica particularidades de el array de salida. El que usaremos el modo por defecto que es 'full'. \n",
"\n",
"El argumento method especifica como se computará la convolución. El default que es 'auto' permite que el programa selecciona el método más eficiente en término de recursos y tiempo. También están 'direct' y 'fft'. El segunda hace la convolución vía transformadas de Fourier (lo veremos más adelante). El 'direct' es método estandar que implementa la convolucion con productos y sumas (o integrales) tal como vimos en clase."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "0fb17100-42ab-4e99-a720-76141ba9e4fb",
"metadata": {},
"outputs": [],
"source": [
"y=signal.convolve(x, h, mode='full', method='direct')"
]
},
{
"cell_type": "markdown",
"id": "f747b793-77fb-490c-97a1-02a26e4e1b5b",
"metadata": {},
"source": [
"Veamos el tamaño de las entradas y la salida"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "a7cd6e25-c05c-48ee-bbc4-8d304cfc9598",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(15000,)\n",
"(15000,)\n",
"(29999,)\n"
]
}
],
"source": [
"print(h.shape)\n",
"print(x.shape)\n",
"print(y.shape)"
]
},
{
"cell_type": "markdown",
"id": "4300de8f-8805-4a54-b697-55040a312fe3",
"metadata": {},
"source": [
"Vemos que el tamaño de la salida es igual a igual al doble de la entradas menos 1. En general, para entradas de distinto tamaño va a ser $N_y=N_x+N_h-1$."
]
},
{
"cell_type": "markdown",
"id": "07f08814-0f49-468f-a45e-0f6eafed296f",
"metadata": {},
"source": [
"Para graficar con el eje temporal tal como teniamos arriba tenemos que tener en cuenta esto. Sino podemos graficar directamente la salida sin referencia al eje temporal"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "c9a10234-1c14-4a87-83ea-d5896b5ba011",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15, 10))\n",
"plt.ylabel('Amplitude')\n",
"plt.plot(y, label='Señal y(t)') \n",
"plt.legend(loc='best')\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "31f3fc34-b9c6-48c3-82f1-e0a79eae7b21",
"metadata": {},
"source": [
" Qué pasó??? Es correcto el resultado?? "
]
},
{
"cell_type": "markdown",
"id": "37d61c58-182a-49b0-a0ea-59a48fcb0f6f",
"metadata": {},
"source": [
"Corrijamos esto: vamos usar mode='same'. Esto fuerza a que la salida tenga la misma dimension que el array in1 y que al hacer la convolución, la función no nos\n",
"haga un zero padding de $x(t)$ y $h(t)$ para llevarlas dimensión $N_y=N_x+N_h-1$ para luego hacer la convolución!"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "39eb76dc-7b1f-4e43-b05e-9b013bd48c4a",
"metadata": {},
"outputs": [],
"source": [
"y=signal.convolve(x, h, mode='same', method='direct')"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "305c6b50-9a7c-44a8-a71c-7b37ba2dc2bc",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(15000,)\n",
"(15000,)\n",
"(15000,)\n"
]
}
],
"source": [
"print(h.shape)\n",
"print(x.shape)\n",
"print(y.shape)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "d35d726a-077a-4fb4-9d5f-108a4774231d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15, 10))\n",
"plt.ylabel('Amplitude')\n",
"plt.plot(tx-position*duration, y, label='Señal y(t)') \n",
"plt.legend(loc='best')\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "30d887c7-e9c5-4a4f-b18c-662a74195161",
"metadata": {},
"source": [
"Conclusión: usar este comando para realizar la convolución es muy útil. Pero como ven, para usarlo hay que saber un poco de la teoría (lo que hacemos en esta materia)\n",
"y tener claro como se implementan estas funciones. Como regla general para hacer una convolución entre dos señales lo que se puede hacer es hacer que la primera de ellas tenga una duración que capture la parte importante de dicha señal. La otra la hacemos \"lo suficientemente larga\" para que al momento de \"deslizarse\" sobre la primera capture todos los detalles de la misma. Con el mode='same' fijamos que la salida tenga la longitud de la primer señal y deberiamos apreciar prácticamente todos los detalles importantes de la señal de salida. Esto igual depende de la situación y de que queramos ver en la salida. Las otras opciones del argumento mode existen porque tienen su utilidad. Es importante que jueguen un poco con ejemplos conocidos para ver como esos parámetros influyen en los resultados, ya que no hay forma \"canónica\" de usar este comando. Lo más importante al final del dia es siempre\n",
"\n",
" ANALIZAR LOS RESULTADOS OBTENIDOS Y PENSAR Y RAZONAR SI TIENEN SENTIDO. MUCHAS VECES NO SABEMOS EXACTAMENTE QUE ES LO QUE TIENE QUE ENTREGARNOS UN COMANDO O EL RESULTADO FINAL CORRECTO DE UN EJERCICIO. PERO CASI SIEMPRE PODEMOS RAZONAR SI ALGÚN RESULTADO TIENE SENTIDO O NO! \n",
"\n",
"Lo mismo pasa para los comandos equivalentes en Matlab, Octave, etc. "
]
},
{
"cell_type": "markdown",
"id": "4bee105f-959f-43ec-8cb0-8c0bd3f6d74a",
"metadata": {},
"source": [
"Repitamos este ejemplo para el caso equivalente de tiempo discreto que también consideramos en clase: Sea $x[n]=\\alpha^nu[n]$ con $0<\\alpha< 1$y $h[n]=u[n]$. En realidad esto lo podemos implementar con las mismas herramientas que usamos arriba (no nos olvidemos que la computadora en realidad trabaja con señales de tiempo discreto!). Por completitud y porque las funciones que usamos lo requieren vamos a definir los parámetros que usamos arriba para \"simular\" señales de tiempo continuo: "
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "daaa97ec-3480-49ad-9c9e-abcaac58fb37",
"metadata": {},
"outputs": [],
"source": [
"# Signal duration in samples\n",
"D = 50\n",
"# Sampling rate in Hz\n",
"fs = 1 \n",
"#Sampling period\n",
"T = 1/fs"
]
},
{
"cell_type": "markdown",
"id": "08df0fff-243e-42ff-8ada-6bb4447b543c",
"metadata": {},
"source": [
"Generemos $h[n]$ y $x[n]$:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "e591e326-3577-44f7-990a-e61459b9cbac",
"metadata": {},
"outputs": [],
"source": [
"amplitude = 1\n",
"alpha = 0\n",
"sample_rate = fs\n",
"duration = D\n",
"position = 0.5 #Position of impulse. Value between 0 a 1. The start of exponential will be positioned in the index closer \n",
" #to duration*position \n",
"nh,h=generate_right_exponential(amplitude,alpha, sample_rate, duration, position) "
]
},
{
"cell_type": "markdown",
"id": "2d06b67f-f4a8-41a6-b3c9-d51ef805ae27",
"metadata": {},
"source": [
"Para generar $\\alpha^nu[n]$ usando la misma función que usamos arriba para generar exponenciales continuas tengamos en cuenta lo siguiente. El valor de $\\alpha$ que requerimos\n",
"ahora se puede escribir como $\\alpha=e^{\\alpha_{c}}$ donde $\\alpha_c$ es el usado anteriormente. Supongamos que deseo que $\\alpha=\\frac{1}{2}$ entonces $\\alpha_c=\\ln \\left(\\frac{1}{2}\\right)$ y este es el valor a usar en la función."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "0fb7e9a2-1f94-4c31-a179-6f64fb3bfd6a",
"metadata": {},
"outputs": [],
"source": [
"amplitude = 1\n",
"alpha_c = np.log(0.5)\n",
"sample_rate = fs\n",
"duration = D\n",
"position = 0.5 #Position of impulse. Value between 0 a 1. The start of exponential will be positioned in the index closer \n",
" #to duration*position \n",
"nx,x=generate_right_exponential(amplitude,alpha_c, sample_rate, duration, position) "
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "f203f0a4-4990-4d13-805b-bb2bcb75cc09",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15, 10))\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Amplitude')\n",
"markerline1, stemlines1, baseline1 = plt.stem(nx-position*duration, x, label='Señal x[n]') \n",
"markerline1.set_markerfacecolor('red')\n",
"markerline2, stemlines2, baseline2 = plt.stem(nx-position*duration, h, label='Señal h[n]') \n",
"markerline2.set_markerfacecolor('blue') \n",
"plt.grid()\n",
"plt.legend(loc='best')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "8fe8e27f-1109-4707-b042-c87c116301a3",
"metadata": {},
"outputs": [],
"source": [
"y=signal.convolve(x, h, mode='same', method='direct')"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "5742feaa-a524-4d8e-b8ce-c4553291de76",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15, 10))\n",
"plt.ylabel('Amplitude')\n",
"plt.stem(nx-round(position*duration+1), y, label='Señal y[n]') \n",
"plt.legend(loc='best')\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "7e287a9e-c6e3-42ef-b303-7b819c7d8998",
"metadata": {},
"source": [
" Veamos algunos sistemas LTI descriptos por ecuaciones en diferencias: "
]
},
{
"cell_type": "markdown",
"id": "01633881-aca7-4410-8825-d6c1ff71d3f8",
"metadata": {},
"source": [
"Consideremos este tipo de ecuaciones\n",
"\n",
"$$ \\sum_{k=0}^N a_ky[n-k]=\\sum_{k=0}^M b_k x[n-k] $$"
]
},
{
"cell_type": "markdown",
"id": "c44dcdbb-9aa7-4ad9-9b92-7acd2bea1c9f",
"metadata": {},
"source": [
"Para realizar la convolución vamos a usar el método [lfilter](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.lfilter.html) de [scipy.signal](https://docs.scipy.org/doc/scipy/reference/signal.html). \n",
"Miren un poco la documentación para entender como usarlo. Hay cosas que todavía no van a entender pero a medida que avancemos con la materia muchas cosas quedarán más claras!"
]
},
{
"cell_type": "markdown",
"id": "2519ed26-f838-43d4-9b41-107a4cf929bc",
"metadata": {},
"source": [
"Implementemos la siguiente ecuación en diferencias $y[n]= 0.9 y[n-1]+x[n]$. Para ello vamos a definir los coeficientes $a[k]$ y los coeficientes $b[k]$ de esta ecuación."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "acbeb4b2-b4bd-4f60-8ba9-8405fe2a6725",
"metadata": {},
"outputs": [],
"source": [
"a=[1, -0.9]\n",
"b= [1]"
]
},
{
"cell_type": "markdown",
"id": "69a03f89-a3f7-49b6-a792-eae717e2aafa",
"metadata": {},
"source": [
"Notar que para la definición de los coeficientes $a[k]$ se considera la siguiente forma de la ecuación:\n",
" $$a[0]*y[n] = b[0]*x[n] + b[1]*x[n-1] + ... + b[M]*x[n-M]\n",
" - a[1]*y[n-1] - ... - a[N]*y[n-N] $$\n",
"\n",
"Vamos a usar como señal de entrada un impulso, o sea $x[n]=\\delta[n]$."
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "32e624c4-6622-4870-8e62-e43e54bdfa25",
"metadata": {},
"outputs": [],
"source": [
"# Signal duration in samples\n",
"D = 50\n",
"# Sampling rate in Hz\n",
"fs = 1 \n",
"#Sampling period\n",
"T = 1/fs\n"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "52d65643-40a0-485a-9ec1-44cd1e2782bd",
"metadata": {},
"outputs": [],
"source": [
"amplitude = 1\n",
"sample_rate = fs\n",
"duration = D\n",
"position = 0 #Position of impulse. Value between 0 a 1. The start of exponential will be positioned in the index closer \n",
" #to duration*position \n",
"n,x = generate_impulse(amplitude, sample_rate, duration, position)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "95b6a1ce-81a7-4251-aced-0d885657357b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15, 10))\n",
"plt.ylabel('Amplitude')\n",
"plt.stem(x, label='Entrada x[n]') \n",
"plt.legend(loc='best')\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "8b0bdd93-3ffe-48a7-b20b-7d239432afad",
"metadata": {},
"source": [
"Implementemos la ecuación para obtener su salida"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "a6a52c05-510e-4289-b139-2c0dea63b3b8",
"metadata": {},
"outputs": [],
"source": [
"y = signal.lfilter(b, a, x, axis=-1, zi=None)"
]
},
{
"cell_type": "markdown",
"id": "aa91cc5c-477c-43e7-a0e5-8b1bbd3ed009",
"metadata": {},
"source": [
"La opción axis=-1 es default y se puede obviar si se quiere cuando se trabajan con array 1D como es nuestro caso. zi=None también es default y lo que indica es que se usará la condición de reposo inicial. \n",
"En general zi es un array cuyas componentes se relacionan con la condiciones iniciales que deseemos para la ecuación en diferencias. Si dichas condiciones son los valores $y[-N], \\dots, y[-1]$ es necesario usar la función \n",
"[lfiltic](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.lfiltic.html#scipy.signal.lfiltic) para construir el zi adecuado. Esto es porque zi en realidad representa un estado interno de la maáquina de estados que implementa la ecuación en diferencias. \n"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "198bdff2-740d-4ac7-9c88-ceffb95cd706",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15, 10))\n",
"plt.ylabel('Amplitude')\n",
"plt.stem(y, label='Salida y[n]') \n",
"plt.legend(loc='best')\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "8bd782de-e48a-44ae-b4f7-e400fabb72ba",
"metadata": {},
"source": [
"Consideremos ahora el caso de un sistema no lineal. Sea un caso sencillo en el cual la salida del sistema se encuentra dada por:\n",
"\n",
"$$y[n]= 0.9 y[n] + |x[n]|^2 $$\n",
"\n",
"Usando la condición de reposo inicial $y[-1]=0$ podemos calcular la respuesta al impulso ( Ojo! no podemos usar el comando lfilter! <\\b>). Por su sencillez podemos hacer como hicimos en clase para $y[n]= 0.9 y[n] + x[n]$:\n",
"\n",
"$$y[0]=|x[0]|^2=|\\delta[0]|^2 = 1$$\n",
"$$y[1]=0.9 y[0]= 0.9$$\n",
"$$y[2]= 0.9 y[1]=0.9^2$$\n",
"$$y[3]= 0.9 y[2]=0.9^3$$\n",
"$$ \\vdots $$\n",
"\n",
"O sea la solución es $h[n]=0.9^n u[n]$."
]
},
{
"cell_type": "markdown",
"id": "637585fd-04d1-495e-9323-3a6435f4d098",
"metadata": {},
"source": [
"Vamos a usar esta respuesta al impulso para calcular la respuesta a una exponencial compleja que comienza en tiempo $n=0$, o sea cuando $x[n]= Ae^{j2\\pi f_0 n}u[n]$. Para ello usamos la función convolve. Generemos\n",
"primero el escalón:"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "6ae768ab-2f3f-4ce6-9523-e67681014357",
"metadata": {},
"outputs": [],
"source": [
"# Signal duration in samples\n",
"D = 120\n",
"# Sampling rate in Hz\n",
"fs = 1 \n",
"#Sampling period\n",
"T = 1/fs\n",
"\n",
"amplitude = 1\n",
"freq = 0.1\n",
"sample_rate = fs\n",
"duration = D\n",
"phase = 0 \n",
"nx,x=generate_complex_exponential(amplitude,freq, sample_rate, duration, phase)\n",
"\n",
"#Generemos también h[n]\n",
"\n",
"alpha_c = np.log(0.9)\n",
"position = 0.5 #Position of impulse. Value between 0 a 1. The start of exponential will be positioned in the index closer \n",
" #to duration*position \n",
"nh,h=generate_right_exponential(amplitude,alpha_c, sample_rate, duration, position) "
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "5547d833-fdee-4056-ba24-8ffe39afa1fb",
"metadata": {},
"outputs": [],
"source": [
"y=signal.convolve(h, x, mode='same', method='direct')"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "83df1eb5-ca0f-42e2-b1a0-67b9ee3c71c6",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig,axs = plt.subplots(2, figsize=(15, 10))\n",
"markerline1, stemlines1, baseline1 = axs[0].stem(np.real(y[1:,]), label='Parte real de y[n]') \n",
"markerline1.set_markerfacecolor('red')\n",
"markerline2, stemlines2, baseline2 = axs[1].stem(np.imag(y[1:,]), label='Parte imaginaria de y[n]') \n",
"markerline2.set_markerfacecolor('green')\n",
"for ax in axs:\n",
" ax.set(xlabel='Time', ylabel='Amplitude')\n",
" ax.grid()\n",
" ax.legend(loc='upper right')"
]
},
{
"cell_type": "markdown",
"id": "bd8aa6cd-8c1f-4520-9bfd-79829946f3f5",
"metadata": {},
"source": [
" Estamos claros que esto que hicimos está mal no?? La respuesta al impulso de un sistema que no es LTI no nos sirve en general para calcular la respuesta \n",
"del mismo a cualquier otra entrada!!\n",
"\n",
"Para calcular entonces la respuesta otra entrada necesitamos lidiar con el sistema y hacer el cálculo para cada entrada que se me ocurra. No tenemos en general un método general para realizar dicho cálculo y que se universal para cualquier sistema y cualquier entrada! Esto está en claro contraste con el resultado para un sistema LTI!\n",
"\n",
"Afortunadamente el sistema que planteamos es lo suficientemente simple y podemos calcular su salida para la entrada considerada.\n",
"\n",
"Dado que $|x[n]|^2=1 \\ \\forall \\neq>0$ para $x[n]=e^{j2\\pi f_0 n}u[n]$ y igual a cero para $n<0$, entonces es claro que para esta señal $x[n]$ en particular:\n",
"\n",
"$|x[n]|^2=u[n]\\ \\forall n\\in\\mathbb{Z}$\n",
"\n",
"Entonces la salida del sistema planteado cuando $x[n]=e^{j2\\pi f_0 n}u[n]$ obedece a:\n",
"\n",
"$$y[n]= 0.9 y[n] + u[n] $$\n",
"\n",
"Y esto ya sabemos resolverlo con lfilter!!"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "ae5e2ad9-32af-4dd3-8393-8fc2f3489482",
"metadata": {},
"outputs": [],
"source": [
"amplitude = 1\n",
"alpha = 0\n",
"sample_rate = fs\n",
"duration = D\n",
"position = 0 #Position of impulse. Value between 0 a 1. The start of exponential will be positioned in the index closer \n",
" #to duration*position \n",
"nu,u=generate_right_exponential(amplitude,alpha, sample_rate, duration, position) "
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "64638956-f01e-4c52-aee8-6344c0dc3e52",
"metadata": {},
"outputs": [],
"source": [
"y=signal.convolve(h, u, mode='same', method='direct')"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "082bc68a-bebc-4778-8ac8-a3819903a110",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig,axs = plt.subplots(2, figsize=(15, 10))\n",
"markerline1, stemlines1, baseline1 = axs[0].stem(np.real(y[1:,]), label='Parte real de y[n]') \n",
"markerline1.set_markerfacecolor('red')\n",
"markerline2, stemlines2, baseline2 = axs[1].stem(np.imag(y[1:,]), label='Parte imaginaria de y[n]') \n",
"markerline2.set_markerfacecolor('green')\n",
"for ax in axs:\n",
" ax.set(xlabel='Time', ylabel='Amplitude')\n",
" ax.grid()\n",
" ax.legend(loc='upper right')"
]
},
{
"cell_type": "markdown",
"id": "60ddb484-cf6f-45ef-b527-e8d746daa3e8",
"metadata": {},
"source": [
" Claramente esta salida (que es la correcta!) para el sistema no lineal considerado no tiene nada que ver con la calculada usando la respuesta al impulso del sistema real!!!"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3b67e624-a6d4-469f-b799-44abdaeb09d2",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "signal_proc_env",
"language": "python",
"name": "signal_proc_env"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.12"
}
},
"nbformat": 4,
"nbformat_minor": 5
}