"
]
},
{
"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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