{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ " # SEÑALES PARES E IMPARES\n", " ## SISTEMAS Y SEÑALES \n", " ### Ingenieria de Telecomunicaciones \n", " ### Universidad Pontificia Bolivariana \n", " ### Por: Jose R. Zapata - [https://joserzapata.github.io/](https://joserzapata.github.io/) \n", " **joser.zapata@upb.edu.co**" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Script para ver y ocultar el codigo del jupyter \n", "from IPython.display import HTML\n", "\n", "HTML('''\n", "
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''')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Contenido

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " # Señales Pares\n", " Una señal $x(t)$ ó $x[n]$ es par si se «refleja» en el eje vertical u ordenadas.\n", "\n", " $x(t) = x(-t)$\n", "\n", " $x[n] = x[-n]$\n", "\n", " La señal tiene los mismos valores para el lado positivo o negativo de $|t|$.\n", "\n", " Es como si se aplicara el valor absoluto de t antes de hacerlo en la ecuación." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "plt.style.use('bmh') # estilo de las graficas\n", "%matplotlib inline\n", "\n", "\n", "\n", "# parámetros\n", "T = 2*np.pi\n", "m = 1 #periodos para la gráfica\n", "t0 = -m*T #usa lado negativo de abscisas\n", "n = 100\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " ## Ejemplo función par\n", " Una señal par conocida es $\\large cos(\\omega t)$\n", "\n", " Para observar mejor, se marcará el área que genera la función dentro de un periodo centrado en el origen.\n", "\n", " Se marcara el periodo comprendido en: $[-T/2,T/2]$, sombreando alrededor de $t=0$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# PROCEDIMIENTO\n", "# vector de tiempo\n", "tn = -t0 # completa el reflejo positivo\n", "dt = (tn-t0)/n\n", "t = np.arange(t0,tn,dt)\n", "\n", "# Señal\n", "f = 1/T\n", "w = 2*np.pi*f\n", "senalpar = np.cos(w*t)\n", "\n", "# marcar un periodo en [desde, hasta)\n", "desde = -T/2\n", "hasta = desde + T + dt\n", "tperiodo = np.arange(desde,hasta,dt)\n", "periodopar = np.cos(w*tperiodo)\n", "\n", "# Gráficas\n", "plt.plot(t,senalpar)\n", "plt.xlabel('t')\n", "plt.ylabel('señal $x(t) = cos(\\omega t)$')\n", "plt.grid(True)\n", "\n", "# marcar un periodo\n", "plt.title('Señal par')\n", "plt.fill_between(tperiodo,0, periodopar,color='lightgreen')\n", "plt.axvline(x=0, color='red')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " # Señales Impares\n", " Una señal $x(t)$ ó $x[n]$ es impar si se cumple que:\n", "\n", " $x(t) = -x(-t)$\n", "\n", " $x[n] = -x[-n]$\n", "\n", " Una señal impar debe ser necesariamente 0 en $t=0$ o $n=0$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " ## Ejemplo función impar\n", " Una señal impar conocida es $\\large sin(\\omega t)$\n", "\n", " Para observar mejor, se marcará el area que genera la función dentro de un periodo centrado en el origen.\n", "\n", " Como el eje t ya fué generado en el ejercicio anterior, se continúa con la generación de la gráfica." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# señal\n", "senalimpar = np.sin(w*t)\n", "\n", "# marcar un periodo\n", "periodoimpar = np.sin(w*tperiodo)\n", "\n", "# SALIDA\n", "# Gráficas\n", "plt.plot(t,senalimpar)\n", "plt.xlabel('t')\n", "plt.ylabel('señal $x(t) = sin(\\omega t)$')\n", "plt.grid(True)\n", "\n", "# marcar un periodo\n", "plt.title('Señal impar')\n", "plt.fill_between(tperiodo,0, periodoimpar,color='lightblue')\n", "plt.axvline(x=0, color='red')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Cualquier señal se puede separar en la suma de 2 señales, una de las cuales es par y la otra impar\n", "\n", " \\begin{equation}\n", " \\large Par|x(t)|= \\frac{1}{2}[x(t)+x(-t)]\n", " \\end{equation}\n", "\n", " \\begin{equation}\n", " \\large Impar|x(t)|= \\frac{1}{2}[x(t)-x(-t)]\n", " \\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " # Ejercicios\n", " probar Si las siguientes funciones son pares o impares\n", "\n", " - $\\large t$\n", " - $\\large |t|$\n", " - $\\large t^2$\n", " - $\\large t^3$\n", " - $\\large |-e^t|$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " # REFERENCIAS\n", " Oppenheim Seccion 1.2.3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **Phd. Jose R. Zapata**\n", " - [https://joserzapata.github.io/](https://joserzapata.github.io/)\n", " - https://twitter.com/joserzapata\n", " " ] } ], "metadata": { "file_extension": ".py", "hide_input": false, "kernelspec": { "display_name": "Python 3", "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": "3.7.3" }, "mimetype": "text/x-python", "name": "python", "npconvert_exporter": "python", "pygments_lexer": "ipython3", "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false }, "version": 3 }, "nbformat": 4, "nbformat_minor": 2 }