{ "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", "
\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", "
\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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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#definicion de t como variable simbolica\n", "t = sym.symbols('t', real=True) \n", "\n", "# Funcion en forma de triangulo\n", "trian = t*sym.Heaviside(t) - t*sym.Heaviside(t - 1)\n", "\n", "# Grafica de la funcion creada\n", "print('x(t) = ')\n", "sym.plot(trian,(t, -3, 3), ylabel=r'$x(t)$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Corrimiento del tiempo ( Temporal Shift)\n", "\n", "Una señal $x(t)$ o $x[n]$ que se retrasa por $\\tau$ segundos se representa como una versión desplazada hacia la derecha el eje t.\n", "\n", "Una señal desplazada en el tiempo $x(t)$ es definida como\n", "\n", "\\begin{equation}\n", "y(t) = x(t-\\tau)\n", "\\end{equation}\n", "con $\\tau \\in \\mathbb{R}$. La señal $x(t)$ es\n", "\n", "- Desplazada a La derecha (retrazada) para $\\tau>0$ \n", " - Señal continua $x(t−\\tau)$\n", " - Señal discreta $x[n − \\tau]$\n", " \n", "Ejemplo: Sonares, señales de sismos, radares, señales de varios sensores en diferentes posiciones " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x(t) = \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "x(t-1) = \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Correr la funcion 1 segundo\n", "print('x(t) = ')\n", "sym.plot(trian,(t, -3, 3), ylabel=r'$x(t)$');\n", "\n", "print('x(t-1) = ')\n", "x = trian.subs(t, t-1)\n", "sym.plot(x,(t, -3, 3), ylabel=r'$x(t-1)$', line_color='red');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Desplazada a La izquierda (adelantada) si $\\tau < 0$\n", " - Señal continua $x(t + \\tau)$\n", " - Señal discreta $x[n + \\tau]$ " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x(t) = \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "x(t+1) = \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Correr la funcion 1 segundo\n", "x = trian.subs(t, t+2)\n", "print('x(t) = ')\n", "sym.plot(trian,(t, -3, 3), ylabel=r'$x(t)$');\n", "print('x(t+1) = ')\n", "sym.plot(x,(t, -3, 3), ylabel=r'$x(t+2)$', line_color='red');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Inversion en el Tiempo (Temporal Flipping)\n", "La inversion en el tiempo de una señal $x(t)$ esta definida como\n", "\\begin{equation}\n", "y(t) = x(- t)\n", "\\end{equation}\n", "Se interpreta geometricamente como el reflejo de la señal respecto al eje vertical" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x(t) = \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "x(-t) = \n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# invertir la funcion en el tiempo\n", "\n", "#Grafica Original\n", "print('x(t) = ')\n", "sym.plot(trian,(t, -3, 3), ylabel=r'$x(t)$');\n", "\n", "# Inversion\n", "x = trian.subs(t, -t)\n", "# Grafica de la funcion modificada\n", "print('x(-t) = ')\n", "sym.plot(x,(t, -3, 3), ylabel=r'$x(-t)$', line_color='red');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Escalamiento en el tiempo (Temporal Scaling)\n", "La compresión o expansión de la señal en el tiempo es conocida como escalamiento en el tiempo.\n", "\n", "El escalamiento temporal de la señal $x(t)$ se define como\n", "\n", "\\begin{equation}\n", "y(t) = x(a \\cdot t)\n", "\\end{equation}\n", "\n", "con $a \\in \\mathbb{R}$. La señal $x(t)$ es\n", "\n", "* Estirada o expandida para $0 < a < 1$\n", "* Comprimida para $a > 1$\n", "* Invertida en el tiempo y escalda para $a < 0$\n", "\n", "Una aplicacaion del escalamiento temporal en procesamiento de señales en la adaptacion de la escala de tiempo para el modelamiento del efecto [Doppler](https://es.wikipedia.org/wiki/Efecto_Doppler)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x(t) = \n" ] }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Escalamiento temporal por un numero menor que 1\n", "\n", "#Grafica Original\n", "print('x(t) = ')\n", "sym.plot(trian,(t, -3, 3), ylabel=r'$x(t)$');\n", "\n", "# Escalamiento por 0.5\n", "a = .5\n", "x = trian.subs(t, a*t)\n", "display(Latex(r'$\\large x \\left (\\frac{1}{2} t \\right)$'))\n", "# Grafica de la funcion modificada\n", "sym.plot(x,(t, -3, 3), ylabel=r'$x(1/2*t)$', line_color='red');" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x(t) = \n" ] }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Escalamiento temporal por un numero mayor que 1\n", "\n", "#Grafica Original\n", "print('x(t) = ')\n", "sym.plot(trian,(t, -3, 3), ylabel=r'$x(t)$', title = 'x(t)');\n", "\n", "# Escalamiento por 0.5\n", "a = 2\n", "x = trian.subs(t, a*t)\n", "# Grafica de la funcion modificada\n", "\n", "display(Latex(r'$\\large x \\left ( 2 t \\right)$'))\n", "\n", "sym.plot(x,(t, -3, 3), ylabel=r'$x(2*t)$', line_color='red');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Transformacion General\n", "\n", "El efecto de transformar la variable independiente de una señal $x(t)$ para obtener la señal modificada es de la forma:\n", "\n", "\\begin{equation}\n", "y(t) = x(a \\cdot t +b)\n", "\\end{equation}\n", "\n", "Con la transformación, la variable independiente conserva la forma de x(t). La señal puede ser:\n", "\n", "- Alargada linealmente cuando $|a| < 1$ ,\n", "- Comprimida si $|a| > 1$,\n", "- Invertida en el tiempo si $a < 0$, y\n", "- Desplazada en el tiempo si $b$ es diferente de cero.\n", " - siendo desplazada a la derecha si se resta el valor de $|b|$\n", " - siendo desplazada a la izquierda si se suma el valor de $|b|$\n", " \n", "**Nota: Primero se hace el desplazamiento y luego se escala** " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x(t) = \n" ] }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Transformaciones Generales\n", "\n", "#Grafica Original\n", "print('x(t) = ')\n", "sym.plot(trian,(t, -3, 3), ylabel=r'$x(t)$');\n", "\n", "# Escalamiento por 0.5\n", "a = .5\n", "# Desplazamiento de -1\n", "x = trian.subs(t, a*t+1)\n", "# Grafica de la funcion modificada\n", "display(Latex(r'$\\large x \\left (\\frac{1}{2} t +1\\right)$'))\n", "sym.plot(x,(t, -3, 3), ylabel=r'$x(1/2*t+1)$', line_color='red');" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Otro Ejemplo = \n", "x(t) = \n" ] }, { "data": { "image/png": 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\n", 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OnTuxe/duPProowCAl156Cfv27cOGDRvi79myZQuklFi7di327t2L22+/HXv27EFGxtC/BH700Ue48MILJ3T9E4lyfQK083k8HqUvmdZhDcrjSpSzDZGTA5mdDdHdDfQfLkiX4uJinDhxIv7rxsbGYYctnn/+eZSXlwMAFixYgJ6eHrS2tk7oOs2Aen1Sz6dCqzmHQiGj1mE6lLOdySxXCc6bNw91dXWor69HJBLB9u3bUVZWNuQ906ZNw5///GcAwKeffoqenh4UJnhyOPUvN/X6pJ5PBT/gNQnK2c5klqsEMzMzsXHjRqxatQoLFy5EeXk5Zs+ejcrKyviJwZ/85Cd49tlncfnll2PNmjV47LHHEp7Zpz7nTL0+qedToXVCsKmpCdOnTzdqLaZCOduZzHSVYGlpKUpLS4f83r333hv/5/PPPx+vv/76qNuhfuMj6vVJPZ8KrT1nynsnlLOdieJVgtTnZKnXJ/V8KrSas9vtNmodpkM525nMdpWgEajflY56fVLPp0KrObe0tBi1DtOhnO1MZjkhaCTql29Tr0/q+VTwnnMSlLOdieJhDd5ztjbq+VRoNedIJGLUOkyHcrYzxZ+GQqg5U38GHfX6pJ5PhVZzDofDRq3DdChnO5OZbn5klFgslu4lpBT1+qSeTwXPOSdBOduZZP/DNIXfDxC5eIP62X7q9Uk9nwqt5tzU1GTUOkyHcrZh7HbECgogYjEIIidivghzzpRRz6dCqzk7HA6j1mE6lLMlYparBI1y5o2QqKFen9TzqdCq4NzcXKPWYTqUsyVipqsEjUC9OVOvT+r5VGhVMOW7gVHOlgi1cTrqc87U65N6PhVazZnq/VYB2tmQYMyM2jgd9SehkK5P0M+ngkfpkqCcLW7Q/SfM9LgqI/AonbVRz6dCqzl3d3cbtQ7ToZwtEWqHNag3Z+r1ST2fCp5zToJytkSoHdbgOWdro55PBc85J0E5WyLUrhLkOWdro55PhVZzzsrKMmodpkM5WyIDtw3NIPKloD5KR70+qedToVXBTqfTqHWYDuVsici8PEi7HaKzE+jqSvdytFFvztTrk3o+FVoV3N7ebtQ6TIdytoSE+OdVgn5/mhejj/qcM/X6pJ5PhVZzLigoMGodpkM5WzIDExsUrhKkPudMvT6p51Oh1Zw7OzuNWofpUM6WDKWTgtRH6ajXJ/V8Kvhm+0lQzpYMpXE66s2Zen1Sz6eC55yToJwtGUrPEuQ5Z2ujnk8FzzknQTlbMrH+LwSFwxo852xt1POp4FG6JChnS4bSYQ0epbM26vlU8M32k6CcLRlKhzXEoJs6UUS9PqnnU6HVnAOBgFHrMB3K2ZIZuEqQwp5zlMizEJOhXp/U86nQGgYtLCw0ah2mQzlbMjGvF31z50JmZ5++57OF9z6pzzlTr0/q+VTwnnMSlLMlNXkybHV1sO/ZA3HqVLpXo4X3nK2Nej4VWs2Z8hlxytlGQuUqQZngaS+UUK9P6vlU8JxzEpSzjSTdVwlWV1djwYIFKCkpwebNmxO+Z8eOHVi4cCEWLVqENWvWJHwPzzlbG/V8KnjOOQnK2UaSznG6aDSK9evXY9u2baipqUFVVRUOHTo05D1Hjx7F5s2b8frrr6OmpgaVlZUJt0V9z4t6fVLPp0KrOWdnZxu1DtOhnG0k6Rynq62txcyZMzFjxgw4HA6sWLECu3btGvKeZ599Ft/97neRl5cHAPB6vQm3ZbPZUr7edKJen9TzqdBqzpS/AJSzjUSm8VmCPp8PU6dOjf+6uLgYPp9vyHuOHj2Ko0ePoqysDKWlpaiurp7oZZoC9fqknk+F1rzRyZMn0dHRgcLCQgQCAfT29qKoqAhNTU3Izs6GzWZDR0cHvF4v2traIKWE1+tFc3MzcnJyAADBYBBTpkyB3++HEAL5+fnw+/1wuVyIRqMIhULxbdrtdrjdbrS0tMDtdiMSiSAcDsdfdzgcyM3NRWtrKzweD8LhMLq7u+OvZ2Vlwel0or29HQUFBejs7EQkEom/7nQ64XA4EAgE4tumlGngc8rp60MGgOPHj2OS3T4kU9DhwJcAxHw+1NfXT2im3t5eBINBNDc3w+l0oqWlBX19ffD5fPFMnZ2dOHjwIJ577jl89tlnuPXWW7F9+3Y4nc4hn5Pf78dll10Gu92Ovr4+rFy5EhUVFZb6nEaqvePHjyMYDFqu9lS/Tw0NDfGbV1HJNPA5eTwepf4qdM5qnzhxQk6ePHncP29mXV1doJrNfcEFyGhqwqmPP4Y8++whr2VWVyP3X/8VvVdeieD27RO6rr1792LDhg2oqqoCAGzatAkAcMcdd8Tfc+edd2L+/PlYvXo1AKC8vBz3338/5s2bN2Rbn3zyCS644IIJWvnEo1yfAO18Ho9H6QICrcMabW1tOj9uapSzjSSdVwnOmzcPdXV1qK+vRyQSwfbt21FWVjbkPddeey3effddAEBrayuOHDmCGTNmDNsW9SehUK9P6vlUaB3WoDxLSjnbSNI5SpeZmYmNGzdi1apViEajuOmmmzB79mxUVlbi4osvxrJly3D11VfjrbfewsKFC2Gz2fDjH/8Y+fn5E77WdKNen9TzqdA6rOHz+STVp+R2d3eTfQLwSIc1EI0ib8oUiFgM7c3NgEXnhakf1qBcnwDtfBNyWKPZ4leRjYRyNoz0H2SbDbL/vgbCwg96pT7nTLo+QT+fCq3mPHCGmCLK2eKS3Ngo3VcJGoH6KBb1+qSeTwXtO5KzcaF0033GrEqrOQeDQaPWYTqUs41m4OZHVr7pPvW70lGvT+r5VGg15yn9X2KKKGcbjSRwWIP6jY+o1yf1fCq0mrPfwieMRkM522hiBA5rUJ9zpl6f1POp0GrOlJ/TRjnbaCg9S5Aq6vVJPZ8KreZMefifcrbRyP576Vp5z5n6Y6qo1yf1fCr4sEYSlLONhsIoHfU5Z+r1ST2fCq3m7HK5jFqH6VDONppYGm8bahTqc87U65N6PhVazZnyuBLlbKPKzYXMyoIIBgEeaTIl6vVJPZ8KreYcCoWMWofpUM42KiEsf2iD+peben1Sz6eCH/CaBOVsKqx+lSD1OWfq9Uk9nwp+wGsSlLOpsPpVgtRPCFKvT+r5VGg1Z8p7J5SzqbD6VYLU52Sp1yf1fCq0mrPb7TZqHaZDOZsKq18lSH1ag3p9Us+nQqs5t7S0GLUO06GcTYXVD2tQv3yben1Sz6eC95yToJxNhdVPCPKes7VRz6dCqzlHIhGj1mE6lLOpsPqFKNSfQUe9PqnnU6HVnMPhsFHrMB3K2VRY/bBGLBZL9xJSinp9Us+ngueck6CcTYX0egH0P0fQgo2O+tl+6vVJPZ8KnnNOgnI2JZMmIZaXB9HXB9Henu7VjBnPOVsb9XwqtJqzw+Ewah2mQzmbqvhJQQse2sjIoP14TOr1ST2fCq0Kzs3NNWodpkM5myorH3em3pyp1yf1fCq0Kri1tdWodZgO5WyqrHyVIPU5Z+r1ST2fCq3m7PF4jFqH6VDOpipm4cMa1J+EQr0+qedTwaN0SVDOpsrKs848Smdt1POp0GrO3d3dRq3DdChnU2XlqwSpN2fq9Uk9nwqec06CcjYoXj1n5Rvu85yztVHPp4LnnJOgnC1ulNtqSgtPa/Ccs7VRz6dCqzlnZWUZtQ7ToZxN1cAxZyse1qA+Ske9PqnnU6FVwU6n06h1mA7lbKpkfj6kzYaM9nagp2dC/szq6mosWLAAJSUl2Lx5c9L3vfzyy8jPz8cHH3yQ8HXqzZl6fVLPp0KrgtsteFmvKsrZlGVk/POkoN+f8j8uGo1i/fr12LZtG2pqalBVVYVDhw4Ne19nZyd+85vfoKSkJOm2qM85U69P6vlUaDXngoICo9ZhOpSzjcVEnhSsra3FzJkzMWPGDDgcDqxYsQK7du0a9r7KykrcfvvtI/7Vl/qcM/X6pJ5PhVYFnzx5Eq2trSgsLEQgEEBvby+KiorQ1NSE7Oxs2Gw2dHR0wOv1oq2tDVJKeL1eNDc3IycnBwAQDAYxZcoU+P1+CCGQn58Pv98Pl8uFaDSKUCgU36bdbofb7UZLSwvcbjcikQjC4XD8dYfDgdzcXLS2tsLj8SAcDqO7uzv+elZWFpxOJ9rb21FQUIDOzk5EIpH4606nEw6HA4FAAFJKdHR0kMo08DnlRKPIAHD8+HFMstlGzHRuXh4yAbR89BGcF1yQ0kwNDQ1wu91obm6Or/vIkSPw+XzxTG+//Tbq6upw99134+GHH0Y4HEZjY+Owz8nv9+Oyyy6D3W5HX18fVq5ciYqKCkt9TiPVXkNDA3JycixXe6rfp/r6+vjEBpVMA5+T6gU2Quem5Pv375fTp08f98+bWX19Pahmc59/PjJOnsSpgwfjExnJTP7BDzDphRcQeuQRRP7931O6rp07d2L37t149NFHAQAvvfQS9u3bhw0bNgA4Pbt8/fXXY8uWLTjnnHOwfPlyPPTQQ7j44ouHbevAgQOYO3duStebTpTrE6Cdz+PxKD19mOeck6CcbSwm8irB4uJinDhxIv7rxsbGIZ9DMBjEwYMHsXz5csydOxfvv/8+brrppoQnBXnO2dqo51PBc85JUM42FhN5leC8efNQV1eH+vp6RCIRbN++HWVlZfHXXS4Xjhw5ggMHDuDAgQOYP38+XnjhhYR7zjznbG3U86ngUbokKGcbi4k8IZiZmYmNGzdi1apVWLhwIcrLyzF79mxUVlYmPDE4Eh6lszbq+VRonRCkfENsytnGYqKvEiwtLUVpaemQ37v33nsTvvePf/xj0u2IUa5+tDrq9Uk9nwqt3YtAIGDUOkyHcraxiJ11FqTNNmEXoRglGo2mewkpRb0+qedTodWcCwsLjVqH6VDONhaxs86CiEZh++wz5RsmmQH1OWfq9Uk9nwrec06CcrYxyc2FzM6GCIeBzs50r0YZ7zlbG/V8KrSaM+Uz4pSzjZUVbx2qM79vBdTrk3o+FTznnATlbGNlxWcJ8pyztVHPp4LnnJOgnG2srPgsQep7XtTrk3o+FVrNOTs726h1mA7lbGNlxWcJ2my2dC8hpajXJ/V8KrSaM+UvAOVsYyUtuOdMHfX6pJ5PhVZz7ujoMGodpkM521jFTwhaqDlTn9agXp/U86nQas5er9eodZgO5WxjJS14WIP6CUHq9Uk9nwqt5tzW1mbUOkyHcraxik3gzY+MQv1JKNTrk3o+FVrNmfIsKeVsY2XFOWfqqNcn9Xwq+LBGEpSzjZXs/3ch/H7AIsdyqV++Tb0+qedTodWcmy10gmisKGcbM4cDsfx8iFgMorU13atRQn3OmXp9Us+nQqs5Dzy3jCLK2cbDalcJUh/Fol6f1POpoH1HcmaYgQtReNaZsYmh1ZyDwaBR6zAdytnGc+tPq10lSH3OmXR9gn4+FVrNecooT262MsrZ4sbwtJCJfJagEajPOVOvT+r5VGg1Z7/fb9Q6TIdytvGw2lWC1Oecqdcn9XwqtJoz5ee0Uc42Hla8SpAy6vVJPZ8Kreacn59v1DpMh3K28bDabUOpzzlTr0/q+VTwYY0kKGcbD6tdJUh9zpl6fVLPp0KrObtcLqPWYTqUs42HtNgoHfU5Z+r1ST2fCq3mTHlciXK28ZB5eZB2OzI6OoBwON3L+cKjXp/U86nQas6hUMiodZgO5WzjkpERv8dGhgX+ykn9y029PqnnU8EPeE2CcrbxstJVgtTnnKnXJ/V8KvgBr0lQzjZeVjopSP2EIPX6pJ5PhVZzprx3QjnbeMVPClqgOVOfk6Ven9TzqdBqzm6326h1mA7lbONlpasEqU9rUK9P6vlUaDXnlpYWo9ZhOpSzjZeVrhKkfvk29fqknk8F7zknQTnbeE3EswSrq6uxYMEClJSUYPPmzcNe37JlCxYuXIglS5agvLwcDQ0NCbfDe87WRj2fCq3mHIlEjFqH6VDONl6pPqwRjUaxfv16bNu2DTU1NaiqqsKhQ4eGvOeiiy7C7t278e677+K6667DAw88kHBb1J9BR70+qedTodWcw4QvRqCcbbxSfZVgbW0tZs6ciRkzZsDhcGDFihXYtWvXkPdcfvnlmDx5MgBg/vz5aGxsTLitWCyWkjWaBfX6pJ5PBc85J8IfJWcAAAySSURBVEE523jFBi5COXlyXDfsH43P58PUqVPjvy4uLobP50v6/ueffx5Lly5N+Br1s/3U65N6PhVat+76/PPPkZWVhcLCQgQCAfT29qKoqAhNTU3Izs6GzWZDR0cHvF4v2traIKWE1+tFc3Nz/BlhwWAQU6ZMgd/vhxAC+fn58Pv9cLlciEajCIVC8W3a7Xa43W60tLTA7XYjEokgHA7HX3c4HMjNzUVrays8Hg/C4TC6u7vjr2dlZcHpdKK9vR0FBQXo7OxEJBKJv+50OuFwOBAIBBCJRJCdnU0q08DnlBONIgPA8ePHMSkjY0yZotnZsIVCCPt8ONnba2im3t5eBINBNDc3w+l0oqWlBX19ffD5fMMyvfbaa/jrX/+KHTt2oLGxcdjn1NzcjDVr1sBut6Ovrw8rV65ERUWFpT6nkWrv6NGjyMvLs1ztqX6fDh8+HP8PNZVMA5+Tx+NR6q9C59jcJ598Is8+++xx/7yZ+Xw+UM3mPu88ZPj9OHXoUPwJJ6pcl1wC29GjCNTUIHbeeYaua+/evdiwYQOqqqoAAJs2bQIA3HHHHUPe9/bbb+Puu+/Gq6++Cm//3vyZ/v73v+MrX/mKoeszE8r1CdDO5/F4lIbwtQ5r5Obm6vy4qVHOpiOVVwnOmzcPdXV1qK+vRyQSwfbt21FWVjbkPR9++CHuvPNO/O53v0vamAEgI4P2s4up1yf1fCq0Kri1tdWodZgO5Ww6UvkswczMTGzcuBGrVq3CwoULUV5ejtmzZ6OysjJ+YvCBBx5AKBTCLbfcgiuuuAKrV69OuC3qc87U65N6PhVax5xVj51YEeVsOuJP4U7RxEZpaSlKS0uH/N69994b/+cdO3YobYf6k1Co1yf1fCp4lC4Jytl0SIvc/IhH6ayNej4VWs25u7vbqHWYDuVsOmIWufkR9eZMvT6p51PBc85JUM6mwyo3P+I5Z2ujnk8F3885CcrZdFjltqF8P2dro55PhVZzzsrKMmodpkM5mw6r3HCf+igd9fqknk+FVgU7nU6j1mE6lLPpkIWFkEJAtLQAJh5Xo96cqdcn9XwqtCq4vb3dqHWYDuVsWvfFyMyELCyEkBLCxA96pT7nTLo+QT+fCq3mXFBQYNQ6TIdytrhxPsrJCoc2qM85U69P6vlUaDXnzs5Oo9ZhOpSz6UrlVYJGoT5KR70+qedTwTfbT4JyNl2pvkrQCNSbM/X6pJ5PBc85J0E5my4rXCXIc87WRj2fCp5zToJyNl0T8SxBXTznbG3U86ngUbokKGfTZYXDGjxKZ23U86nQqmCHw2HUOkyHcjZdVrhKUIxzEsUqqNcn9XwqtJpzIBAwah2mQzmbLiuM0kWj0XQvIaWo1yf1fCq0mnNhYaFR6zAdytl0SQsc1qA+50y9PqnnU8F7zklQzqZLulyQkyZBBINAKJTu5STEe87WRj2fCq3mTPmMOOVs2oT456ENk17CrfPgYiugXp/U86ngOeckKGczQvwqQZOOPPGcs7VRz6eC55yToJzNCPFxOpOeFKS+50W9PqnnU6F11iQ7O9uodZgO5WxGiJ53HqJHjkCY9CnJNpst3UtIKer1ST2fCq09Z8pfAMrZDGG3w3b4MDIaG9O9ki8k6vVJPZ8Krebc0dFh1DpMh3I2I5j9sAb1aQ3q9Uk9nwqt5uz1eo1ah+lQzmYEs982lPoJQer1ST2fCq3m3NbWZtQ6TIdyNiOY/SpB6k9CoV6f1POp0GrOlGdJKWczguwfdTLzVYKUUa9P6vlU8GGNJChnM0Ks/9+P8PsBE97Ynvrl29Trk3o+FVrNuZnwXhPlbIbIykLM7Ybo7YU4dSrdqxmG+pwz9fqknk+FVnPOyckxah2mQzmbUcx8lSD1USzq9Uk9nwradyRnKWX2cTrGrEyrOQeDQaPWYTqUsxml76KL0Lt4sSkPa1Cfc6Zen9TzqdBqzm+++aZR6zAdytmMImIx2PfsQUZDg2HbrK6uxoIFC1BSUoLNmzcPe72npwff+c53UFJSgqVLl+LYsWMJt0P9Igbq9Uk5nxDiv6u8T6s5P/PMMzo/bmqUsxnF6MMa0WgU69evx7Zt21BTU4OqqiocOnRoyHuef/555OXloba2FhUVFXjwwQcTbqvVpPf8MAr1+iSeT6k5C615QiF4GNHCTn36KaTGyJK9qgqTnnwS9r17DVyVMfZu2YIF3/9+upfB2DACqJVSzh/1fTrN+YP//E/Z63KN++dZ+pwqLMQkrxcZ/fPA0WgUdrs9fmVdZmYment741MPiV7vC4eR2dMDe319ekKMoGvaNEw+fjzdy2BsmE9zcz+++eabLxztfVrNef/+/XL69Onj/nkzq6+vB9VsgDnz7dy5E7t378ajjz4KAHjppZewb98+bNiwIf6eRYsW4Q9/+AOmTp0KAJg3bx6qq6uRn58/ZFtmzGckzmddHo9H6dHwWsecXYT3milnA8yZr7i4GCdOnIj/urGxcdgTMQa/p6+vDx0dHfB4PMO2ZcZ8RuJ89Gk1Z8rjSpSzAebMN2/ePNTV1aG+vh6RSATbt29HWVnZkPcsW7YMW7duBQC8/PLLuPzyyyHE8B0RM+YzEuejT6s5b9y4EUuWLMEVV1yBFStWwOfzGbWutAuFQrj//vtx6aWXYsmSJbj55ptJPRE4FAph586dWLRoEQoKCvDBBx+ke0nIzMzExo0bsWrVKixcuBDl5eWYPXs2KisrsWvXLgDAt771LbS1taGkpAS/+tWv8MADDwzZxsAo3tVXX51wFM/q1q5di1mzZmHZsmXpXorhjh8/juuuuw6XXnopysrK8Otf/zrdSzJUd3c3li5dCiHEASHEx0KIH4/0fq1jzp999pksLCwEADzxxBP49NNP8cgjj4x7e2bS09OD9957D1dccQUyMzPjI1vJRrespqenB59//jkyMjJw55134qGHHsLFF1+c7mVpiUajuOSSS7B9+3YUFBTg2muvxZNPPonzzz8/3UszzJ49e5CdnY3vfe97qKmpSfdyDNXU1ITm5mbMnTsXra2tKCsrw3PPPUfm85NSIhQK4Utf+pIQQtgBvAvgh1LKvyR6v9aecygUiv9zV1dXwr9eWlVTUxOuuuqq+N3N5s+fj0ZCj2RqamrCeeedh3PPPTfdSzFMbW0tZs6ciRkzZqCtrQ0rVqyI73FTsXjxYng8HpL3qy4qKsLcuXMBnL5CcNasWaT+Ni6EGHzPEHv//5LuHWvdV9Fut+OnP/0ptm7dCpfLhVdeeUVnc6Zy5pM0XnjhBdxwww1pWo3xKD4pxOfzxac47HY7iouLUVtbm+ZVpQalHaFETp48iQ8//BAlJSXpXoqhotEohBD7AfxXAFuklH9N9t5Rm7MQohpAUYKX/mdDQwPuu+8+3Hfffdi0aROefPJJ/OhHPxr/ytPghhtuSHh7wnXr1mHFihUAgF/84hfIzMzEN77xjYlenjaVfFQMPkTndrsB0G1iGRl071kWDAaxbt06VFZWkpvasNlskFL+ixAiD8AOIcSFUsqPEr131OYspVya7LX9+/fHH2G+atUqfPOb37Rcc96xY0fC36/vv7DixRdfxBtvvIGdO3da8os+Wj5KBo/ZtbS0JBzFo4LqNENvby++/e1vo7S0FMuXL0/3clJGSnlKCPE2gDIACZuz1glBIcS5UsrP+v/5BwC+KqVcNe4NmowQogzAIzidy5/u9aRKf5Gsk1K+n+616BBCZAI4DOBqACcA/A3Aainlx2ldmMGEEDMAvCqlHPUqMysRp/d+fgugTUr5P9K9HqMJIbwAevsbsxPA/wGwQUr5asL3azbnKgDnAYgBqAfwPSnliZF/yjqEEEcATAIwcBedv0gpv5fGJRlKCHEDgF8C8AI4BWC/lPKa9K5KjxDiWgCbAdgA/C8p5c/SvCRDCSFeBHAlgEIAzQAekFI+ndZFGUQIsQTA/wPwd5zuKQBwr5TytfStyjhCiItw+j8+NpwextgmpXwo6fv5QYqMMWY+dM8qMMaYhXFzZowxE+LmzBhjJsTNmTHGTIibM2OMmRA3Z8YYMyFuzowxNkGEEJ8LIZJedT0YN2fGGDMhbs6MMTYBhBDPATgHwB+FEEEhxPoR389XCDLG2MQQQnwO4FYpZfVo7+U9Z8YYMyFuzowxZkLcnBljbOIoH0fm5swYYxOnGcB/UXkjN2fGGJs4/wHgPiHEKSHEupHeyNMajDFmQrznzBhjJsTNmTHGTIibM2OMmRA3Z8YYMyFuzowxZkLcnBljzIS4OTPGmAlxc2aMMRPi5swYYyb0/wEzcmpHNEUXowAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Transformaciones Generales\n", "\n", "#Grafica Original\n", "print('Otro Ejemplo = ')\n", "print('x(t) = ')\n", "sym.plot(trian,(t, -3, 3), ylabel=r'$x(t)$');\n", "\n", "# Escalamiento por -3\n", "a = -3\n", "# Desplazamiento de 2\n", "x = trian.subs(t, a*t-2)\n", "# Grafica de la funcion modificada\n", "display(Latex(r'$\\large x \\left ( -3 t -2 \\right)$'))\n", "sym.plot(x,(t, -3, 3), ylabel=r'$x(-3*t-2)$', line_color='red');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Cambio de Amplitud de la señal\n", "\n", "Estos cambios no se realizan en la variable independiente, si no que afectan la amplitud de la señal" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x(t) = \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "2 x(t) = \n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Grafica Original\n", "print('x(t) = ')\n", "sym.plot(trian,(t, -3, 3), ylabel=r'$x(t)$')\n", "\n", "# Multiplicar por dos la amplitud\n", "print('2 x(t) = ')\n", "sym.plot(2*trian,(t, -3, 3), ylabel=r'$2*x(t)$');" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x(t) = \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-2 x(t) = \n" ] }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Grafica Original\n", "print('x(t) = ')\n", "sym.plot(trian,(t, -3, 3), ylabel=r'$x(t)$')\n", "\n", "# Multiplicar por dos la amplitud\n", "print('-2 x(t) = ')\n", "sym.plot(-2*trian,(t, -3, 3), ylabel=r'$-2*x(t)$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# REFERENCIAS\n", "- https://github.com/spatialaudio/signals-and-systems-lecture\n", "- http://blog.espol.edu.ec/telg1001/senales-operaciones-en-tiempo/" ] }, { "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": { "celltoolbar": "Slideshow", "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" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Contenido", "title_sidebar": "Contenido", "toc_cell": true, "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 } }, "nbformat": 4, "nbformat_minor": 2 }