{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# TRANSFORMACION DE LA VARIABLE INDEPENDIENTE\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": "markdown",
"metadata": {
"toc": true
},
"source": [
"Contenido
\n",
""
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
""
],
"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",
"''')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Modificacion basicas de la variable independiente, generalemente el tiempo. Permiten introducir varias propiedades basicas de los sistemas y señales"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# importar librerias de python\n",
"\n",
"import sympy as sym # Libreria de operaciones matematicass simbolicas\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use('bmh') # estilo de las graficas\n",
"%matplotlib inline\n",
"\n",
"from IPython.display import Latex # para visualizar ecuaciones en jupyter\n",
"\n",
"#sym.init_printing()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Definicion de la funcion a graficar que se usara como ejemplo"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x(t) = \n"
]
},
{
"data": {
"image/png": 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\n",
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