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Transformada de Fourier discreta en Python con SciPy
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{
"cells": [
{
"cell_type": "markdown",
"id": "74e20848",
"metadata": {},
"source": [
"# Transformada de Fourier discreta en Python con SciPy"
]
},
{
"cell_type": "markdown",
"id": "7200ee7c",
"metadata": {},
"source": [
"## Introducción"
]
},
{
"cell_type": "markdown",
"id": "e4f5e2a5",
"metadata": {},
"source": [
"En este artículo vamos a ver cómo calcular la transformada de Fourier discreta (o DFT) de una función en Python utilizando la transformada rápida de Fourier (o FFT) implementada en SciPy. El análisis de Fourier es la herramienta fundamental en procesamiento de señales y resulta útil en otras áreas como en la resolución de ecuaciones diferenciales o en el tratamiento de imágenes.\n",
"\n",
"La transformada rápida de Fourier o FFT es en realidad una familia de algoritmos muy eficientes ($O{(n \\log n)}$) para calcular la DFT de una señal discreta, de los cuales el más utilizado es el algoritmo de Cooley-Tukey. Este es el que está implementado en SciPy a través de las subrutinas FFTPACK, escritas en FORTRAN 77, y es el que vamos a utilizar. También podríamos haber utilizado la biblioteca FFTW, más moderna y escrita en C, o la implementación presente en NumPy, que es una traducción a C de FFTPACK y que funciona igual que la de SciPy, pero no lo vamos a hacer.\n",
"\n",
"Nótese que estos métodos no nos permiten calcular ni la serie de Fourier de una función periódica ni la transformada de Fourier de una función no periódica. Estas operaciones forman parte del cálculo simbólico y deben llevarse a cabo con otro tipo de programas, como SymPy o Sage. En Pybonacci puedes leer una introducción a SymPy y cómo calcular series con SymPy, así como una reseña sobre Sage.\n",
"\n",
"En este artículo nos vamos a centrar en el caso unidimensional, aunque el código es fácilmente extrapolable al caso de dos y más dimensiones, como veremos muy brevemente."
]
},
{
"cell_type": "markdown",
"id": "680eac75",
"metadata": {},
"source": [
"***En esta entrada se ha usado python 2.7.3, numpy 1.6.2, scipy 0.10.1 y matplotlib 1.1.1.***"
]
},
{
"cell_type": "markdown",
"id": "cdd3ba22",
"metadata": {},
"source": [
"## Definiciones"
]
},
{
"cell_type": "markdown",
"id": "9cb85afd",
"metadata": {},
"source": [
"Antes de empezar de lleno con las FFTs vamos a hacer una brevísima introducción matemática. He intentado que esto no se convierta en una larga introducción al procesamiento de señales digitales, pero si te interesa el tema y quieres más rigor puedes acudir a cualquiera de las referencias que doy más abajo además de la documentación de `scipy.fftpack`.\n",
"\n",
"En este artículo vamos a manejar **señales discretas reales**, bien creadas por nosotros o procedentes de *muestrear* una señal analógica a una frecuencia de muestreo $f_s$. La **transformada discreta de Fourier** o DFT de la señal de entrada, que diremos que está *en el dominio del tiempo*, será otra señal discreta, n general *compleja*, cuyos coeficientes vienen definidos en SciPy por la expresión\n",
"\n",
"$$A_k = \\sum_{m=0}^{n-1} a_m \\exp\\left(-2\\pi j{mk \\over n}\\right) \\qquad k = 0,\\ldots,n-1,$$\n",
"\n",
"siendo $a_n$ los coeficientes de la señal de entrada y $A_k$ los de la señal obtenida. Diremos que $A_k$ está *en el dominio de la frecuencia* y que es el **espectro** o **transformada** de $a_n$. La resolución en frecuencia será mayor cuanto mayor sea el número de intervalos $n$ de la señal de entrada. La DFT se calcula con el algoritmo de la **transformada rápida de Fourier** o FFT, que es más eficiente si $n$ es una potencia entera de 2.\n",
"\n",
"Cada uno de los componentes de frecuencia se puede expresar en forma compleja como $A \\exp(j \\omega t)$. El espectro complejo de una función seno, por ejemplo, se obtiene directamente de su expresión en forma compleja\n",
"\n",
"$$A \\sin(\\omega t) = A \\frac{e^{j \\omega t} - e^{-j \\omega t}}{2 j} = -j \\frac{A}{2} e^{j \\omega t} + j \\frac{A}{2} e^{-j \\omega t}$$\n",
"\n",
"y tendrá, por tanto, una raya espectral a la frecuencia $\\omega$ y otra a la frecuencia $-\\omega$, como ya comprobaremos.\n",
"\n",
"La DFT de una señal *siempre* asume que la señal de entrada es **un período de una secuencia periódica**. Esto será importante por lo que luego veremos. Sería, por tanto, el equivalente en tiempo discreto a las series de Fourier."
]
},
{
"cell_type": "markdown",
"id": "6185860d",
"metadata": {},
"source": [
"## FFT de una función senoidal sencilla"
]
},
{
"cell_type": "markdown",
"id": "aed6c57b",
"metadata": {},
"source": [
"Vamos a **calcular la FFT de una función senoidal en Python utilizando SciPy**. Para que sea verdaderamente sencilla tenemos que preparar un poco los datos, o si no acabaremos observando efectos adversos. Estos los estudiaremos más adelante. \n",
"\n",
"Para manejar números redondos, vamos a recrear una señal con un armónico de $f = 400 Hz$ y otro del doble de frecuencia:\n",
"\n",
"$$y(t) = \\sin(2 \\pi f) - \\frac{1}{2} \\sin(2 \\pi \\cdot 2 f)$$\n",
"\n",
"donde $2 \\pi f = \\omega$. Nótese que, por lo que hemos visto en el apartado anterior, veremos cuatro rayas en el espectro de esta función: dos para la frecuencia $f$ y otras dos para la $2f$. Vamos a imponer a priori el número de intervalos y la distancia entre ellos y de ahí vamos a calcular el intervalo de tiempo. Evidentemente así no se funciona cuando muestreamos un archivo de audio, pongo por caso, pero como digo así obtendremos el resultado exacto. El código y la salida serían las siguientes:"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "ede87352",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x73f9d10>"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
},
{
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Yw7fljYi3cTht71G7zkaxzpBhwdaIM9JzOMUVtrdNgPQcSbEdqZFIy/EhRzMOjS1dcHFR\nIMiGLMOA/UftOhv2BgKQnsMpsjNQhfS8Qf/AIMprWhAbaVvEGWk5PuRoxsGYft3WHri9R8M6G7am\nXzdCeg7H1uMBjJCeN6ioaUF4sD+8PN1t+r4lLePi4mSppSUoGGAciuycmjA/arenpwdfXqnBS7tf\nku3iYFFFI25NmWbz9831rGtsQV1zN/bu3SlLPXt6+1HT2I6Y8MlnGTZirufVkhr4+/lg1//8WpZ6\nGs6bst1pj7zXLxbX4zfbnpOllpYgRzMOXOyhMR5dDAC3P/g6Ft6yhAvTJEmxTm/3yZhGPa+W1WPz\nS0dleyOXVjUhJiwA7m72nYxp1PN3R06js7sPWVnp3BgoMWw9VdMc83v9+0/9FUk33caFaU4BTZ2N\ng6HxcXdksErpi/omeW7abO/qRVNbFyJDbMsyPBKV0k+2WgLG9S77HozmGPTs5Kw+qWHvHpqRqJS+\nqG+Wr54jIUczDsU2Ht88FiGBvmhokWfj0+r0UEcF2bznYyRKf290dveht3+Ak/qkBtedoJBAXzQ0\ny9hxc5AayZwQpZ+s9RwJOZoxaGrtQm/fIEKD/DirU869cHv3fIzEEA3oi0aZ9hrtDawYiUrpJ9se\n+ODgEEqrm6CO4nZE0yDjEeJIyNGMQbFOj/gY2/d8WCJE6YsGmd7MXMyBj8TQC5ernnq7AlVGEhLo\ni0aZ9sB1da0ImuoLX28PzuoMCaQRjTnkaMbAnowAY6FS+qFBpiMaLccjGuC6njK8mfv6B1FZ32rz\nng9LBE7xQUt7DwYGhzirUyrYe9SCJYJpjWYYFHVmhkajwb59+9Db24vKhg6sXPNDAKs4q18lsx64\nuZ4Xi+txy/RngVtmcFa/XPVsaetAva4Fp07O4izqztXVBcop3tC3dCI0yLYUQVLDqGdpZQOYwhWa\nRb6c6UkjmuGQo7nOyKR4APBuWwPuuHUmZ43P0AOXx4PRkp4v/M+vERbsT3ragCU9uU7aaIiKlIej\n4VtPo5aEAZo6u46lpHjVlRWcJsUzhDzKo5cjRJLBEBmFiwuip4x64XzrGRzgi6bWLgzKcCrSEuRo\nriNEUjxj4xsacv6TNoXQU04jGmH0lM+6At96uru5YoqvJ5raujmpT+qQo7mOEEnxPNxd4efjiaa2\nLs7qFCtC6BkSKJ8RjSB6yii4Qpj26SfbSL6RiNLRnDhxAomJiUhISMCLL7446vPc3FxMnToVqamp\nSE1NxfPPP2/3NYVKMBgik164EHqqlH6y2UcjjJ7y2fshhJ7BMt7OMBLRBQMMDg7isccew6lTpxAZ\nGYmFCxdi9erVmDVr1rByS5YswdGjRzm7rnlSvMLiKgQGTMHO7b/kPJeW4WbuwKzYEE7rFRvmen5+\nvhiLkmLx1JOPc6qn6vqNzBjjdL+TGDHqtmPXbnxbVocFc6YhOzubUz2DlX7Iu1TBWX1ixqjbk7/Y\njqHBAahjQjjXU86bYEciOkeTn5+P+Ph4TJ8+HQCwbt06vP/++6McDWPcr3MYk+Ld8fM3sOfJLMyN\nD+P8GqpAeYxoAIOeKQtux91P/w0f/fUxzuv39HCDl5cbWjt6EODvzXn9YiMrKwuNg6H4tqIROx67\ng/P65bYBNisrC4fPtOPB1Qvw3UXxnNcv97Q+5ojO0VRVVSE6Otr0OioqCmfPnh1WRqFQ4PTp00hJ\nSUFkZCT27NmD2bNnj6pr27Ztpr/T09ORnp4+4fV7evtRXtuMhGncbi40IqfIMwC4rK3FXDX3DtuI\nKsCQ1kcOjgYACkvqMG9mBC91G3rg8mmbjDFc0dZhjjqUl/pVSj9U1rXyUjeX5ObmIjc3l9driM7R\nWDMFMn/+fOh0Ovj4+OD48eNYs2YNvv3221HlzB2NtVwta0BcZCA83fmRRqX0RXVDGy91i5FCbR1m\n83QjAzd64TOmqXi7hpi4XFyHH62az0vdcpqKBICaxna4uLggJJC7fIbmhCh9ceFqFS91c8nITvj2\n7ds5v4boggEiIyOh0+lMr3U6HaKiooaV8ff3h4+P4XjllStXor+/H01NTZxcv1Bbx2sPPERGU2eA\nUU/+HI2sQpz7B1BS1YTE6fw4VV9vD7i6uKC9y3Lor7NRqK3FHHUob07VkHJKHm1zIkTnaBYsWICi\noiKUlZWhr68PR44cwerVq4eVqaurM63R5OfngzGGwEBu8j7x3QOX25k0Qoxo5KLnt2WNiI1QwtOD\nv4mIEKV8MmIXaut57QTRGs0NRDd15ubmhgMHDiAzMxODg4N46KGHMGvWLPz+978HAGzcuBH/+Mc/\n8Prrr8PNzQ0+Pj44fPgwZ9cv1NbiB8vmclbfSOQS3gwADc0d6OsfQKSKm8POLKFS+qFRJmf8FGpr\neXXawI0D0OI4TJkvVi5ra/H97/J3r1NizRuIztEAhumwlStXDntv48aNpr8fffRRPProo5xft39g\nEEUVeiTyGHpsDG+WA4XXF1r5nO9XKX1xpaSOt/rFBN/TkIAxUak82ucVbR2efXg5b/X7+3hicGgI\nnd19nB5BIEVEN3XmSIp1ekSopvDaKPx9PdE/OISunj7eriEWLmvrMIfH9S5AXms0Qukph164vrUL\nHd19iA6byts1FAqFKcBC7pCjMaNQW4e58fz2GOXU+AqLa/nvgctkzWtgcAjXyhowK47fjb5yWVe4\noq3DnDh+R9uAfM9MGgk5GjMKtXWYHcfvgxGAfBxNCX97FIzIJYqvpFKPsCA/+PtYztHFFcY1Gmfn\nsraW904lYMww7vx6TgQ5GjMKtbW8ZAMYiRwCAlrbe9DU2o3pEdydAmmJAH8vdPf0o7d/gNfrOBq+\no/eMGDpBzt8DF65TSYk1AXI0JoaGGL4pqcdsnqcmAHlM91wprcOs2BC4uPA7NaFQKGSRvJDv/V1G\n5BLebJgm519PuZ0COxbkaK5TVtOMgCnegqQyMaQPd+7Gd7mY/2kzIyoZPBwLeUyVYk6w0s/pO0Ht\nXb2ob+pAXCS/o21Afml9xoIczXWMi4NCIIsRjQDrM0ZUTv5wZIyhsESYqbPAKd5o6+xF/8Ag79dy\nFFdK6jBzugqurvw//kJkMNq2BnI017msrcUcARYHgesZnJ18k+FlASLOjDh7cIWuthV+3h4ImurD\n+7VcXV0QONXHqTfBCtupdO5OkLWQo7lOYbEwc+CA849ounr6UFnfivgYfjJgjyQk0Llv5svaWt73\nz5jj7McFXNbWYY4A6zOA82tpLeRocGNqQqipHmePOrta2oCE6GC4u7kKcj1nH9HwmcreEs7eCxdy\nRBMU4Ivmtm4MDg4Jcj2xQo4GQHVDG9xc+UsXPpKgAB80tXY5beMTchoSuJ5Y04kXXC8LkHrGHGeO\nPOvp7UdZTTNmTBdmtO3m6oIAfy80tXUJcj2xQo4Gwi5cA4C7myum+Hqiqa1bsGsKiZA9RsC4V8E5\nH4yMMUGSaZrjzCOaq2UNiI3g77wpSwTLZBPseJCjgSEUV6j1GSOGEGfnvJkvC7RHwYgz76Opb+rA\n0BBDeLC/YNd0Zj2vlPCfZmokctkEOx6izN4sBBqNBvv27UNvby+KK1vw8H8+AuA7gl3fmEJ8lmBX\n5Bejnj09vfjqag1KlgZi3sy7BLm2cR+NM50MadSzrrEF9S09OHYsHllZWYJcOyTQD6cvlglyLSEw\nv9cr6tpx1z0/EfT6ITSikaej0Wg02Lx5M7Rarem9P7/+IhbMiRL0ZnaWXqMlPZ95+il4ergJoqen\nuxu8vdzR0t4D5RT+N9zyjSU9N2/eDACC6OlMwRWWtPzHX/RYnpYg2L1OIxqZTp3t27dvWMMDgPKy\nUuzfv18wG5wpxNmSnlqtVlA9nSnE2dF6OlMP3JKWlbpygdum8zhuW5Glo+nttXwmek9Pj2A2OFOI\nsxj0dKZeuKP1NPbAjcelSxlHawnQUQGATB2Np6flVOteXl6C2eBMIxox6BkS6Dw5pRytp7eXOzzd\n3dDeafkhLSUcrSVAiTUBmTqaTZs2Qa1WD3tPrVYjOztbMBucKSRXHHo6z94PMehpCFaRvuMWg5bO\nHC5uLbIMBjAuAv7iN8+jubUDcxMikZ2dLdjiIOBcmwyNuj286ZcImuKJyNBAwfVUKf1Qp28X7Hp8\nkpWVhc6uPjyU/UukJKjg5+vjgPZpmNqNjxZmYyNfGDV79r93obJGj9TZMcJr6UTTurYiS0cDAKtW\nrcI+TQ3++LMM3JwcI/j1nW2vwtz5tyJ80QacfutReHoI36xUSl9cLq4V/Lp80e0ZjQef2IV9W4UJ\nER+JM03tZmVl4fCZdjy7PAl3pc8R/Pq+3h5gDOjo6oUfzyekihVZTp0BwIWr1ejvH0RaUrRDru/v\n44nBoSF0dvc55Ppc8/eTBVj73bkOcTKAsQfuHA9GxhgOf3AR962c5zAbnKkXrqttwRVtHe64daZD\nrq9QKGQfeSZbR3P4g6/xH5kpDtvgp1AonCZSqn9gEO98WIB1d6Q4zAaVE53NfvHbGvT0DeDmJOFH\n2kacaV3h7ycLsGbpHId1ggA6AE2WjqatswcnTn+L7y9LcqgdIU4S9vhRvhbTwpUOnc9XKX3R0CJ9\nLQHg0PGv8R8ZjusEAc4TXDEwOIS/f1iAdXc4bnQIOI+etiJLR3M09woWp06HSunrUDucpRd++IOv\nsS7TcaMZAJjq54We3gH09PY71A57ae/qxYkz1/CD5Q7uBDlJuPjHXxYjOnQqEgQ6G2ksVE60odgW\nZOloDn9wEesyHdvDAYwhztJufFX1rbhwtRqrbk90qB0KhQKqAF80tkg7Hfu/PrmCW5OnObwT5CzB\nKodPXHT4aAZwrg3FtmD1pGV3dzcOHTqES5cuYWBgAF1dXXBxcYG/vz/S0tJwzz33wMVFnH7LPKle\n/yDQ4jUHt817wNFmQRVoSKwpNcz1rG3qwrzb74S3l7ujzTL1GqNCpzraFKsx19LT0xPNnrOx+znh\n9niMhVRT+pjrCYUrygfisP8XjoncMydE6Ycvq3WONsNhWOVoTp06hStXriArKwsbNmwY9hljDAUF\nBXj11VexbNkypKQ4dgplJJaS6gWHFuP48VWCxtJbQqX0w/lvKh1qw2SxpGdXawM0mvki0FNavUZL\nWnr5nUfbw98FbopzoGWA0t8bnd196O0fEPTsFnuwpKcy+Bt8/O81omibUnTcnMEmoLu7mxUVFU1U\njDHG2OXLl60qNxHHjx9nM2fOZPHx8WzXrl0Wy2RnZ7P4+HiWnJzMzp8/P+pzACwjI4OlpqYyAKP+\nZWZmcmKrreTk5LAFabezsGmzWUZGBsvJyXGoPZbIyclhGRkZbMmSJSYbMzIyRKen0a6YhGSWlHqz\nKLVkbLSeYm6bGRkZbEpoAvtO+ndJTw7svHVxOguMmCnae90cK9zC5Ouc7BdqampMf3d2dnJqDGOM\nDQwMMLVazUpLS1lfXx9LSUlhV65cGVZGo9GwlStXMsYYy8vLY2lpaaPqMTYyLy8vi41vyZIlnNtu\nLTk5OUytVg+zR61Wi6oBjmVjUlKSqPSUgpaMWbaT2qbtkJ784VBHs2PHDnbs2DH2hz/8wfRefn4+\n++ijjzg16PTp08N6IC+88AJ74YUXhpXZuHEjO3z4sOn1zJkzWW1t7bAylhqcWHo5Yh4VTNQ7nBqg\nFJXtYtSSMev1FJvtpCe3iFFPSzMV5vDhaKyefF27di0+/vhjvPHGGzh69CjCwsKwaNEiVFVVYenS\npdZWMyFVVVWIjr6xWz8qKgpnz56dsExlZSVCQy0f0eri4oqhoUHTa6GT6o1EDKnLzbG4VjBGdtt+\neEEVFomG2irTe47UU2xaApPT08XVHUODN0KyqW2OZjJ6urq5Y3CA9BwLS1pevnwZ6enpSEhI4O26\nVjuaWbNmYdasWYiNjcXKlStRW1uLL7/8EvPnz+fUIGs3qbERZ2WM971581KgUqnQ09MDLy8vwZPq\njUQMqcvNsXQ41Fg3wu2LkrFpUzb2798vCj3FpiUwOT3npSRR25yAyeiZkkx6joclLaurq6HX6/H2\n228DALZv3879hSca8vT09LCGhgarhkfl5eX2jrDYmTNnhg0rd+7cOSogYOPGjezQoUOm1+NNnYlx\nPlRs87YAM4KiAAAgAElEQVRLliyxOLxXuLiJxsaxEJuWjI2jp6u7qOy0hJT0dHUjPSfLWFqar2NZ\n4RYmzYQjGk9PT3z44Ydoa2vD2rVr4e09+kz25uZmvPPOO5g1axZiYuzLz7RgwQIUFRWhrKwMERER\nOHLkCA4dOjSszOrVq3HgwAGsW7cOeXl5CAgIsDhtlpmZ6fAejSWM9uzfvx9fX9UhJiIYz/3qGdGN\nClKSkxAaGiKa3qElzLXs7u7BV9/U4JVXXhZlLzZVZKMXS5jrWV3fjOb2Pux99XlR6im20YslzPW8\nUlyNwAB/7Nj+S9Hd67yPsKz1SNXV1WzHjh1s8+bNbOPGjWzDhg3s4YcfZps3b2a7d+9mLS0tnHm/\nY8eOsRkzZjC1Ws127tzJGGPs4MGD7ODBg6Yyjz76KFOr1Sw5OZmdO3duVB2T+GkO5amXc9iRDy46\n1Aax9brsIXXdq6yxhftoyMngLHqeu1LJ7nr8L442w2n0fOkvuWzfoc8daoM1WvLx7Jx0jffffz/b\nsmULe/fdd4eFOosNqTiaXW9+zA4c/sLRZrCcnBx22+J0NjUsgWVmZkruJjaS8cgf2TeldY42g+Xk\n5LDEpEVsWkKyZPWsqGlmt63/naPNYIwZ9FTFzGXzbkqTrJ5/fv9L9uxrHzjaDJaTk8PSly5jvio1\nW75ihbiizoy89dZbuHr1KvLy8vDcc8/h3LlzuPfee7FlyxbRpqARMyGBviivaXG0GcjKysLpUlf8\nR7A/stfd5mhzbMaQEbsTidMda8cdd6zEznfK8cdnf4DZcZajIcWOMdMCY8yhmaQBYNrMmzBj6SP4\n5I2fwdVVms8ZldIP+Zcdn4YmKysL2tapuL25E//zaKYg15z0/1heXh6am5vxwAMP4Pe//z22bt2K\nNWvW4M033+TDPqdHJZKjAjq7+6D57CruWZ7saFPsQqX0RYMIUn18er4UwQE+knUyAODl6Q5PTze0\ndjgutNnI4Q8u4t6MZMk6GUA8aWgGB4fw95MFgh6sN+kRzalTp+Du7o5XX30VPj4+iImJQXBw8Jh7\nWIjxUYnk5L2cz77BwjnRCAv2d7QpdqG6fta9ozl04mvcJ4KswfZiHCEG+I8OAhKKrp4+5Hz6DY7/\nbsPEhUVMiEja5mcXShEkcCdo0o5mzZo16OrqwtatW03v/elPfxq2gZKwHrGcZHj4xEU8tu5WR5th\nNyqlL2oa2hxqQ31TB85ersBvn/qeQ+3gAmMv3JHnuWg+u4oFs6MQHjzFYTZwgUrpi/rmDodPRR4+\nIfwxKZN2NHPnzh313k9/+lNOjJEjYjib/WpZPWob27HEwRmDuUCl9EXBtzUOteGdDwuw8rZE+PlY\nDiWVEmLIiH34g4t45O6bHWoDF/h6e8DVxQUd3X3wd1DbaGjuwJlL5djzpLDh1dKd8HQSfL09wBjQ\n0WU5VYUQHD5xEfdkJMNNwvPfRgwnQzruwTg0xHDk5EWHnzjKFY4+l+ZaWQOq6luRvlDtMBu4xNFr\niP84dQkrb50peCdI+k8WiaNQKBDiwHWant5+HP3kCu7NkHYQgBFDD9xxN/Lpi+Xw9fZEyoxwh9nA\nJSqlLxpbHOe4D39wEfcsd45OEHBjzcsRDA0xHPnAMSeOSuNEIydHpTSczx4bGSjI9cxPIWzp7Eeg\n+nZEhUjnVMrxCFH6oaFJ2BvZXM+S6lb8YN16h4cDc4Uq0A9XyxoEu565lu7uHijpm47cIy8Jdn2+\nCRY48sxcz+4+hgFlClJmbBTs+kbI0YgAldIXjQL1cixlbw2vqYRG8x3Rpe+wBX9fT/QNDKK7p1+Q\n46Ut6fn+/7ZheVqCU+gpZEiuJS39lKEoOHcXop1AS0DYNS9LeoaEleDYsUzB26ZzjEcljkrAeXBL\n2Vtrqiqwf/9+Qa7PNwqFQtCb2ZKepaUlTqOnkFM9lrTsaK5zGi0B4xqi4+71+tpKh+hJjkYECPlg\nFNv5GHwg5DqNs+sp5IjG2bUE5Huvk6MRAUL2GsV2PgYfhCj90CDQAraz6xng742unj709g/wfi1n\n1xIQdtOmmPQkRyMChOw1btq0CWr18FBRR59CyDWkJ3e4uCgQHCBML9zZtQSEDW8Wk54UDCAChOzl\nGBcBd7/8Cs5fKcet89SiPMfDHoScnjDq9l/P7kBrWwdmqSOcUs/G5k7eIxNHntMUHR6Ebb/e6mRa\nCn+v7927D19cKMZt8+OxedMmh+hJjkYECL33IysrC+6BCTj8wUW8ue0ewa4rFCGBfvj6WrVg18vK\nysJnxQrMjQ/Dj7O4PdpcDAgZrJKVlYVVq1Zh4Y/24+i+BySfdmYkgVO80drRg/6BQbi7ufJ+vays\nLETGp+JXB05As99xueJo6kwEBE31QUt7DwYGhwS75mVtHeaonTMRarAD0qZc1tZhbnyYoNcUCqHT\n0NTpDU4tLEjaCV4t4erqgsCpPtC3dAl2zUJtHeaqHds2ydGIAFdXFwT4e0Mv4A7sK07saIQMIQWA\nvv5BaCv1mDlNJdg1hUTo3eyFJXWYrQ51mk2vIzEm1xSKQq1BT0dCjkYkCJ2G5rK21uG9HL4Qugde\nVNGImLAAQTaIOgKhz1EpLK7FXCftBAHCHxdQqHW8nuRoRIKQxwU0NHeip3cAkSHONf9tJDjAF02t\nXRgUaCrysrYWc5zUaQPCPxgN07rOq6cqQLjIs/6BQXxb0YhZcSGCXG8syNGIBJXSV7C9H1dKDNNm\nzjo14e7mCn8fTzS3dwtyPWeehgSED1aRh57C3OvFOj0iVVPh4+UhyPXGghyNSBAyHXuhk9/IwPUw\nUoH0vKytc/jUBJ8IGZLb3NaNts5exIQFCHI9RyBkFF+htg5z4x3fNsnRiAQhE2sWamud39EItOY1\nODiEq6X1Dp+a4BPjiIYxxvu1CrV1mBUXAhcX5xxtA8KOaAq1dYIe2TwW5GhEgpC9RtmMaATQs7S6\nCSqlL6b4Ok+alJF4erjB28sdLe3858gSw8I134QECpciqVBbK4qwe3I0IkGoyJ62jh40NHciNkKY\ns28cRUigMCGkcnDagDHEmfTkAqHu9aEhhm9K6jFbBKNtcjQiQajInisl9UiMDYGrk5xYOBZCjWgK\nnTxCyojh4ci/ns4ecQbcmDrjeyqyrKYZAVO8EeDvzet1rMG5nzYSwriJi+/GV1ji3AvXRkIE6jVe\ndvI9H0YMHSF+9ezo6kVtYzvU0UG8XsfR+Hh5wN3VBe2dltP4c4WY9iORoxEJvt4ecHVxQUd3H6/X\nKSx27j0fRoQY0TDGTLvYnR0hFrC/Ka3HjGnBcHPy0TZgiDzjW08xtU3n/x+VEEKkEC8scf45cOB6\npgWetaysa4WPpweCA3x5vY4YUAmwRlPoxPniRiJEGprCYsfnODMiKkfT1NSEFStWYMaMGcjIyEBL\nS4vFctOnT0dycjJSU1OxaNEiga3kD75zSnX39KOitgUJMcG8XUMsCJFYUy5OGxBmjaZQW4c5IgjF\nFQK+12SNo22xtE9ROZpdu3ZhxYoV+Pbbb7Fs2TLs2rXLYjmFQoHc3FxcuHAB+fn5AlvJH8E8rytc\nK2+AOioIHu78pyd3NP4+nugfHEJXD39TkYXF4rmR+UaIEc1lbR3miGBzoRDwHXlW3dAGN1cXhAT6\n8XaNySAqR3P06FGsX78eALB+/Xr885//HLOsEJvHhIbveXC5LFwDhs4I34lKL8tg46sRvrXs7RtA\naVWT02bAHgnf97rYwsRFdfBZXV0dQkMN4oSGhqKurs5iOYVCgeXLl8PV1RUbN27Eww8/bLHctm3b\nTH+np6cjPT2da5M5he/htJgWB4XAGBAwLVzJS/1iu5n5RKXk9+iFa+UNiI0MhKeHqB5JvBGi9ENR\nhZ63+idzBk1ubi5yc3N5swVwgKNZsWIFamtrR72/Y8eOYa8VCsWYSR+/+OILhIeHo6GhAStWrEBi\nYiIWL148qpy5o5ECKqUvtJU8Nr7iOtyzPJm3+sUGnyHO9U0dGBgcQoTKOTNgjyTA3ws9PQPo7Rvg\nxRkYFq7l4bQB/gN/CrV1uHtFklVlR3bCt2/fzrk9gjuaDz/8cMzPQkNDUVtbi7CwMNTU1CAkxPKO\n1vDwcACASqXC2rVrkZ+fb9HRSA0+RzT9A4Mo0jUiMVYeUxMAvyHOxoVrZ82APRKFQmEKsIgKncp5\n/WJauBYCvsObC7V1eG7jct7qnyyiWqNZvXo13nrrLQDAW2+9hTVr1owq09XVhfb2dgBAZ2cnTp48\niaQk6zy32OGjl6PRaJCZmYnbbv8O6r/8Mz7+99iO3tlQcRzibNQyPT0dP//pD+HaWcpZ3VKA6+MC\nzPX8w+4taK68zFndYoeP8Gbze/3yyf24+NXnnNZvF0xE6PV6tmzZMpaQkMBWrFjBmpubGWOMVVVV\nsVWrVjHGGNNqtSwlJYWlpKSwOXPmsJ07d1qsS2Q/zSrqmzrYTfft5ay+nJwcplarGQDTP7VazXJy\ncji7hpg5dOJr9swrGk7qsqRlWES0bLRkjLGfbv8HO/HFNU7qsqRnXFycbPQcHBxiCatfZL19A5zU\nx+W9zsezU3pPYyuRoqMZGBhk8Xe+yPr6uWl8GRkZwxqe8V9mZiYn9YudU2eL2APPHuGkLrlryRhj\nv9x/nP0t5xwndZGejKX9ZD+rqm/lpC4u9eTj2SmqqTO54+rqgsCpPtC3dHFSX2+v5VxKPT38p3sX\nA1xugJW7lgC3a16kp7zaJzkakcHl3K2np6fF9728nPfsFHO43BQndy0Baptcw+WarNj1JEcjMriM\nPNu0aRPUavWw99RqNbKzszmpX+wEBfigua0bg4NDdtcldy0Bbjdtkp7cRp6JXU957I6SEKoA7no5\nWVlZAID/2fkSSnQNmD87BtnZ2ab3nR13N1dM9fNCU1sXVEr7UnEYNdu/fz+uldbCx8cbLz3/a9lo\nCVyfOuO4be7fvx9nC0qRPCMKzzz9pMz05G6EaNTtpd2/RcG3lUhLjhXVvU6ORmRwvZcmKysLehaG\na2UN2PHYHZzVKxWMvUZ7HQ1g0DIrKwvrf3ME6++8Cd9dFM+BhdKB67QpWVlZWLY8A/PW7cWpd56A\nu5vz5+AzJyTQD9fKGjirLysrC67KePy/U5fxx2d/wFm9XEBTZyKDj6zDxRV6WWRstgQfOaWKdfLU\nM1jpi8aWTgwNcZdnsLSqCdPCA2TnZADu9yUBQFFFIxJixHdwHDkakcFHVteiikbER8vvwQgYInu4\n1LO9qxfNbd2IDOF+d7zY8XR3g6+3B1rauzmrs0inl23bVAVwf/RCcYUe8SI8oZQcjcgICfRDQwvX\nPXBx9nKEgOsRjVanhzo6EC4u8kg9MxKu0/oYeuDydDR8pJwqqmhEvAj1JEcjMrge0TS1dqG3b1A0\n51IIDdd6Fsu4Bw5wnzqluKJRlD1wITBOnTGOjjwZHBxCaXUT1FHi05McjYjQaDR46P57ce5fe5CZ\nmQmNRmN3ncU6PeJjgmST/NGIMe/TK9sfxZsvP8OJloBxGlJ8NzLfGPX89MhOZP/njznU09A+5YZG\no8Fdq7+HqtO/x/LlGZzoqatrRdBUX/h6e3BgIbdQ1JlI0Gg02Lx5M7RaLQDg5MkS09/2hCgW6xqR\nILMe+EgtAWDz5s0A7NMSMPTA/yMzxa46pMZIPStLuNGzr38QuroWxEYGcmKnVBip50cfaVFebkjQ\nate9LtJAAIBGNKJh3759wx6MAKDVarF//3676jX0GOXlaPjSEgCKdOKcA+cTvvQsr2lGZMhUeLrL\nq7/Ll55ijoYkRyMS+MpVJOZeDl/wpWVXTx/qmzoRExZgVz1Sgy89xRqKyze86akTb3QpORqRwFeu\nIjn2wPnSsqSyCbERSri5yuu24UvP4gr5TesCPOspUsctrztGxPCRq6itswftnb2ICJbHccNGLGkZ\nFT3N7rxPhsAK+T0Y+cqjVUR6mrBXz6EhhmKdHmqRBqrIa3JUxJjnfqqua0JzRz/2vvq8XYuDWp1h\n85bc9nyYa9nT04Oy2nas+/GDnAQCJIj0RuaTkXqeu1qH53fa1zYBg54/u/tmLkyUFOZ6NjS1orK+\nE3v3vmCXntWNbfD39cQUX3Fkax4JORoRYcyl9U1JHR7f8y+7b2Q5BgIYMWoJAPsPf4Hunn676yzS\nNeKu9Dl21yNFzPVc88RbSJibZld9A4NDKK1uRpzMIs6MGPXUt3Zh2X/+AatWrbKrPrFPQ9LUmQiZ\nFqFEeU2L3ent5RjabIm4yECUVjXZXU+RjHPGmRMXGYjS6ma76qiobUFooB+8vdw5skqaBE7xBgND\nc5t9aX3E3qkkRyNCfLw8EDjFGzWN7XbVI9fNhSOJjQxEaZV9D8be/gFU1bdiWriSI6ukSywHjlur\no7YJAAqFArER3Ogp1kAAgByNaImLsr/xib2XIxTTI5Qor222K+twaVUTokMD4OEuvyzDI6G2yS1c\njBDFnpyUHI1IiY0IREml3ubvd3b3Qd/aiehQ+WUZHomPlweU/t6obmizuQ7DUQvi7TEKSWxkIEoq\n7XM0xTJOpjmSWDsdN2NM9MlJydGIlNjIQJTY0cvRVuoRGxEIV5nt+RgLe6d7xJoV1xFMC1eirMa+\nEWIRTZ2ZiIu0r1NZ39QBDzdXKKd4c2gVt9BTSKTY+2CkHuNwYiMDUWKPnjrS04iv9/URYqNtI8Sh\nIQatrokczXXsXUOUwjQkORqRYu88uFyz4o6FvZFnRRV6We6hGQt72mdVfSuUU7zh52N5h7zcsHeE\naIguFXfbJEcjUiJDpqK+qQM9vbbt/xBzgj1HYM+Ipn9gEBW18ssyPB72rNNQNORw7B0hSmFalxyN\nSHFzdUF0aADKa1ps+j7toRmOPVORFTUtCA/2h5envPd8mGOPntQJGk1cVCBKbXTcxRLY30WORsTE\nRgaitHryja+ntx81je2ICZdXluHxiAo1jBB7+wYm/V0xZ8V1FLERSjscjfh74EJjz4hbCke1k6MR\nMbGRtt3MpVVNiAkLgLsb7fkw4ubqgqjQqSivmfyiK031jMbWThBwff2Q9ByGrSNEfWsXBocYggN8\nebCKO8jRiJi4qCCb5sGLdLTnwxJxkUE29RppD81oosMCUKef/AiRMYZictyjsHWEaNRS7Ee1i8rR\nvPPOO5gzZw5cXV1x/vz5McudOHECiYmJSEhIwIsvviighcIymRGN8Uz39PR0PJ39APr0RTxbJz1s\n1fPtA79EtfZrnq2TFpMdIRr1vO3276Di9B/xxacf8WyhtJjsCNGo5wM/+j7OaV6FRqPh0ToOYCLi\nm2++YdeuXWPp6ens3LlzFssMDAwwtVrNSktLWV9fH0tJSWFXrlwZVU5kP80m6pva2fx1r05YLicn\nh6nVagbA9C8sIprl5OQIYKV0OHT8Anv6lYk1saRnXFwc6TmCh7a/w058cW3Ccpb0VKvVpKcZ/QOD\nbMZdL7Ge3v4Jy/KtJx/PTlGNaBITEzFjxoxxy+Tn5yM+Ph7Tp0+Hu7s71q1bh/fff18gC4UlOMAX\nff2DaGkfP7OrpTPIa6t1dp9B7mxYuzHOkp4lJSWk5wis3ZtkSU+tVkt6mjGZEaIU9ZTceTRVVVWI\njo42vY6KisLZs2ctlt22bZvp7/T0dKSnp/NsHbcoFArTxrjUxMgxy/F1BrmzERdlXaoP0tM64iID\ncf5q1YTlSE/rMHaEZkxTjVuOaz1zc3ORm5tr03etRXBHs2LFCtTW1o56f+fOnbjzzjsn/P5kFr3M\nHY1UMUajjOdo+DqD3NkwHyEG+I+dF4r0tI7YyED8v39fnrAc6Wkd1o4QudZzZCd8+/btNtUzHoI7\nmg8//NCu70dGRkKn05le63Q6REVF2WuWaLFmumfTpk3QarXDhtNcnOnubCgUCsRGBqKsuhnzZo7t\naEhP67A2JJf0tI7YiEB8fa16wnJS1FO0U2eGNanRLFiwAEVFRSgrK0NERASOHDmCQ4cOCWydcMRG\nBuKD09+OW8b8DPLzV8oRGx2CZ3/5jN1HQTsjxo1x82ZGjFnGqNtvX9mLsxdLcNt8NTZt2kR6jkCl\n9EVv3wBa23sw1X/s3rRRt19vfwH1jS1ImhGF7Oxs0nMEcVGBePejiUeIRt0eeeI3mOLtiqjwIPHr\nyXl4gR28++67LCoqinl5ebHQ0FB2xx13MMYYq6qqYqtWrTKVO3bsGJsxYwZTq9Vs586dFusS2U+z\nmUtFNeyOR9+wqmxndy+b/f09rLO7l2erpMurb3/G9rz1iVVlj39xld3/68M8WyRt7tz0Z3bhapVV\nZZ9+JYe99a+veLZIutTp29lN9+21quzQ0BC76b69TFfXwrkdfDw7RTWiWbt2LdauXTvq/YiIiGFx\n4itXrsTKlSuFNM1hTI9Qoqy6CUNDDC4u469PnfumCrPjQuHj5SGQddLDmhGikbyCCtySPI1ni6SN\nNSNEI2cKKvDw99MEsEqaqJS+6LFihAgA35Y3wsfbHVEh0jjYUFThzcRo/Hw8McXXC7X69gnL5hVU\n4ObkGAGski6TOZ+d9JwYa9dpKuta0dM7QBkBxsGwhqi0auNmXkE5bkmSTieIHI0EsPZmPlNQTj3w\nCZgeqURZ9cRnf+hbu1Dd2Ia58WECWSZNrM22kHfJ4LTFnirF0cRFBk1KT6lAjkYCWHMzd3T14lpZ\nA+YnTjyFIWf8fTzh5+OBuqbxR4h5BRVYODsKbnQU9rhMrhMknQejo7Ami/PQEMPZyzpJdSrpLpIA\n1iSD/OpKJZISwunMFCuwJllpXkE5bpbQjewojOH3440QGWPXpyFJz4mwplN5raweAX5eCAv2F8gq\n+yFHIwGsaXxnCiqox2gl1up5cxLpORHWjBAralswMDiE2AilgJZJE2tGiGck6LTJ0UgAa3YMn5XY\nnK0jmSggoKG5Aw0tHZgdFyKgVdJlok3Fxk4Qrc9MjHFDMRtjHyEgzU4lORqRo9FosHHDfcj/526s\nyMiwmA68rbMHxTq9VSGmckej0eAPu7fgtZ2bkZmZaVHPvIIKLJoTA1danxkXY6r6M+++iJ89eN+Y\nqeppGtI6NBoN7l67GrrPD2Lpd5db1HNwcAj5hdLrVIpqHw0xHI1Gg82bN5tSTZz6sASlJSUAMGwX\n8JeFlZg3Mxye7vTfOR4j9awtv2L621xPKfYYhWakljoAmzdvBjBcS8YYzhRU4IkfL3aEmZJhpJ6f\n1BejUlcOYLieV0rqEaL0g0rp5xA7bYW6bCLG2nTg1GO0jsnoSY5mfKzVsrSqCW6uLogJCxDSPMlh\nrZ5S3cJAjkbEWJsOnBaurcMaPWsb29HS0YOZ02l9Zjwm1TZpfWZCrNUz71IF0iR4r5OjETHWpANv\nae9GeXUzkhPChTJLslij55mCcqTNjZ4w3Y/csTZVvVR74EJjjZ4Dg0P4qrBScuszAK3RiBpL6cA9\n/IIRPm0mMjMz0dvbi47uQahib4WHu6sDLZUGlvT0nqJCUkqqSc/y2jasufd+B1opDSxp6RsQAt/o\nm/Gvf+XgwIH96O3txYVrdViwezuAJMcZKwEs6enpFwxlmNrUNvsGAfcpyQia6uNAS22DHI2IMU//\n39PTAy8vL0TFzsLf/vd/0dfRaCoXXF4KjeY74k4TLgIs6QmfcPzu4BvobmswlXv3r81YnpZAeo6D\nJS0f3vgz7P2/L3D/gw+jRX/jcMPnt/0SKqUv6TkOlvRUz5yLN958C71m97pS9S00mkzpacl5PmiR\n4Kw/LSMjgwEY9S8zM9PRpkkS0pNbli1fTnpyhKPaJh/PTlqjkRh0/jq3kJ7cMtDfb/F90nPyOFPb\nJEcjMej8dW4hPbmF9OQOZ9KSHI3E2LRpE9Rq9bD3xH5euJghPbmF9OQOZ9KSggEkhqVFQ9GfFy5i\nSE9uIT25w5m0VFxf/HE6FArFuInpCIIgiNHw8eykqTOCIAiCV8jREARBELxCjoYgCILgFXI0BEEQ\nBK+QoyEIgiB4hRwNQRAEwSvkaAiCIAheIUdDEARB8Ao5GhmQm5vraBNEA2lxA9LiBqQFv4jK0bzz\nzjuYM2cOXF1dcf78+THLTZ8+HcnJyUhNTcWiRYsEtFCa0E10A9LiBqTFDUgLfhFVrrOkpCS89957\n2Lhx47jlFAoFcnNzERgYKJBlBEEQhK2IytEkJiZaXZbymBEEQUgDUSbVXLp0KV5++WXMnz/f4udx\ncXGYOnUqXF1dsXHjRjz88MOjyigUCr7NJAiCcEq4dguCj2hWrFiB2traUe/v3LkTd955p1V1fPHF\nFwgPD0dDQwNWrFiBxMRELF68eFgZEfpPgiAIWSK4o/nwww/triM8PBwAoFKpsHbtWuTn549yNARB\nEIQ4EFXUmTljjUi6urrQ3t4OAOjs7MTJkyeRlJQkpGkEQRDEJBCVo3nvvfcQHR2NvLw8ZGVlYeXK\nlQCA6upq06lytbW1WLx4MebNm4e0tDR873vfQ0ZGhiPNJgiCIMaDSYTjx4+zmTNnsvj4eLZr1y6L\nZbKzs1l8fDxLTk5m58+fn/C7er2eLV++nCUkJLAVK1aw5uZm3n8HF/ChxZYtW1hiYiJLTk5ma9eu\nZS0tLbz/DnvhQwcje/bsYQqFgun1et7s5xK+tNi3bx9LTExkc+bMYc888wyvv4Er+NDi7NmzbOHC\nhWzevHlswYIFLD8/n/ffwQX2aPHggw+ykJAQNnfu3GHlbXluSsLRDAwMMLVazUpLS1lfXx9LSUlh\nV65cGVZGo9GwlStXMsYYy8vLY2lpaRN+9+mnn2YvvvgiY4yxXbt2sa1btwr4q2yDLy1OnjzJBgcH\nGWOMbd26VfRa8KUDY4xVVFSwzMxMNn36dEk4Gr60+Oijj9jy5ctZX18fY4yx+vp6AX+VbfClxZIl\nS9iJEycYY4wdO3aMpaenC/irbMMeLRhj7NNPP2Xnz58f5WhseW6KaupsLPLz8xEfH4/p06fD3d0d\n64GsnfYAAAc7SURBVNatw/vvvz+szNGjR7F+/XoAQFpaGlpaWlBbWzvud82/s379evzzn/8U9ofZ\nAF9arFixAi4uLqbvVFZWCvvDJglfOgDAk08+iZdeeknQ32MPfGnx+uuv47/+67/g7u4OwBB8I3b4\n0iI8PBytra0AgJaWFkRGRgr7w2zAHi0AYPHixVAqlaPqteW5KQlHU1VVhejoaNPrqKgoVFVVWVWm\nurp6zO/W1dUhNDQUABAaGoq6ujo+fwYn8KWFOW+++SZWrVrFg/XcwZcO77//PqKiopCcnMzzL+AO\nvrQoKirCp59+iptvvhnp6en46quveP4l9sOXFrt27cJTTz2FmJgYPP3003jhhRd4/iX2Y48W42HL\nc1MSjsbazZfMir0zjDGL9SkUCkls8uRSC0vs2LEDHh4e+OEPf2jT94WCDx26u7uxc+dObN++3abv\nOwq+2sTAwACam5uRl5eH3bt3495777XFPEHhS4uHHnoI+/btQ0VFBV555RVs2LDBFvMExVYtJvMc\ntPa5KaoUNGMRGRkJnU5neq3T6RAVFTVumcrKSkRFRaG/v3/U+8Zhb2hoKGpraxEWFoaamhqEhITw\n/Evsh0stRn73L3/5C44dO4Z///vfPP4CbuBDB61Wi7KyMqSkpJjK33TTTcjPzxd12+CrTURFReH7\n3/8+AGDhwoVwcXGBXq9HUFAQnz/HLvjSIj8/H6dOnQIA3H333fjpT3/K58/gBFu1mGha0Kbnpq0L\nTULS39/P4uLiWGlpKevt7Z1wUevMmTOmRa3xvvv000+bIjFeeOEF0S+AM8afFsePH2ezZ89mDQ0N\nwv4gG+FLB3OkEgzAlxYHDx5kzz77LGOMsWvXrrHo6GgBf5Vt8KVFamoqy83NZYwxdurUKbZgwQIB\nf5Vt2KOFkdLSUovBAJN9bkrC0TBmiPSYMWMGU6vVbOfOnYwxw41w8OBBU5lHH32UqdVqlpyczM6d\nOzfudxkzhOktW7ZMcuHNfGgRHx/PYmJi2Lx589i8efPYI488ItwPshE+dDAnNjZWEo6GMX606Ovr\nYz/+8Y/Z3Llz2fz589nHH38s2O+xBz60+PLLL9miRYtYSkoKu/nmm4eFAYsZe7RYt24dCw8PZx4e\nHiwqKoq9+eabjDHbnpuiTKpJEARBOA+SCAYgCIIgpAs5GoIgCIJXyNEQBEEQvEKOhiAIguAVcjQE\nYYZer0dqaipSU1MRHh6OqKgopKamwt/fH4899pijzQMAXLp0adwNg3V1daLP7EDIC0ls2CQIoQgK\nCsKFCxcAANu3b4e/vz+efPJJB1s1nN27dyM7O3vMz0NDQ6FUKnH+/Pkxj0MnCCGhEQ1BjIMx+j83\nN9d01HhnZyc2bNiAtLQ0zJ8/H0ePHgVgyKywZs0aZGRkIDY2FgcOHMCePXswf/583HLLLWhubgYA\npKen4/HHH0dqaiqSkpLw5ZdfAgCampqwZs0apKSk4JZbbsGlS5dG2dPb24u8vDwsXLgQAPDJJ5+Y\nRmDz589HZ2cnAGD16tU4dOgQv+IQhJWQoyGISbJjxw4sW7YMZ8+exUcffYSnn34aXV1dAIDCwkK8\n9957+PLLL/GrX/0KU6ZMwfnz53HLLbfgr3/9KwBDfqju7m5cuHABr732mmka7LnnnsNNN92Eixcv\nYufOnbj//vtHXfvChQuYOXOm6fXLL7+M1157DRcuXMDnn38OLy8vAMCiRYvw6aef8i0FQVgFORqC\nmCQnT57Erl27kJqaiqVLl6K3txcVFRVQKBRYunQpfH19ERwcjICAANMoKCkpCWVlZaY67rvvPgCG\nVOxtbW1obW3FF198gZ/85CcAgKVLl0Kv16Ojo2PYtcvLyxEeHm56fdttt+GJJ57A/v370dzcDFdX\nVwCGtPbm1yMIR0KOhiBs4N1338WFCxdw4cIFlJWVITExEQDg6elpKuPi4mJ67eLigoGBgTHrM2bA\nnShRh0KhGFZm69ateOONN9Dd3Y3bbrsN165dM9UjhWzkhDwgR0MQkyQzMxP79u0zvTYGD4znJMw/\nY4zhyJEjAIDPP/8cAQEBmDJlChYvXoy3334bgGFNSKVSwc/Pb1g906ZNMx1MBQBarRZz5szBM888\ng4ULF5ocTU1NDaZNm2bnLyUIbqCoM4IYB+OowPzcjd/85jd4/PHHkZycjKGhIcTFxeHo0aOjzuYY\n+bd5XV5eXpg/fz4GBgbw5ptvAgC2bduGDRs2ICUlBb6+vnjrrbdG2ZOSkmJyJgCwd+9efPzxx3Bx\nccHcuXOxcuVKAIa09t/5znc4VoMgbIOSahKEwCxduhQvv/yyzaHHDzzwAB555BGkpaWNWeZHP/oR\ntmzZgtTUVFvNJAjOoKkzgpAYW7ZswcGDB8f8vL6+Hi0tLeRkCNFAIxqCIAiCV2hEQxAEQfAKORqC\nIAiCV8jREARBELxCjoYgCILgFXI0BEEQBK+QoyEIgiB45f8DW+ZilBJSVzUAAAAASUVORK5CYII=\n"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from numpy import pi\n",
"\n",
"n = 2 ** 6 # Número de intervalos\n",
"f = 400.0 # Hz\n",
"dt = 1 / (f * 16) # Espaciado, 16 puntos por período\n",
"\n",
"t = np.linspace(0, (n - 1) * dt, n) # Intervalo de tiempo en segundos\n",
"y = np.sin(2 * pi * f * t) - 0.5 * np.sin(2 * pi * 2 * f * t) # Señal\n",
"\n",
"plt.plot(t, y)\n",
"plt.plot(t, y, 'ko')\n",
"plt.xlabel('Tiempo (s)')\n",
"plt.ylabel('$y(t)$')"
]
},
{
"cell_type": "markdown",
"id": "3728d09f",
"metadata": {},
"source": [
"Esta es la señal que vamos a transformar. Fijáos en el último punto representado. Como el intervalo va desde $0$ hasta $n - 1$, los trozos «empalman» perfectamente. Ahora vamos a hallar la DFT de la señal `y`. Para ello necesitamos dos funciones, que se importan del paquete `scipy.fftpack`:\n",
"\n",
"* La función `fft`, que devuelve la DFT de la señal de entrada. Si queremos que esté normalizada, tenemos que dividir después por el número de intervalos `N`.\n",
"* La función `fftfreq`, que devuelve las frecuencias a las que corresponde cada punto de la DFT. Se usa conjuntamente con la función anterior y acepta dos argumentos: el número de elementos `n` y el espacio entre intervalos `dt`, que ya hemos calculado antes.\n",
"\n",
"Como en este caso solo hay dos frecuencias fundamentales, vamos a representarlas utilizando la función `vlines` de matplotlib. El código y la salida quedarían así:"
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "6e1a6a2d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x5387e90>"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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GzRiLhagF+/777yGXy7F//3588cUXOHToEAYPHqzrWNTMsViIWrDVq1ejffv22LlzJxIS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\n"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.fftpack import fft, fftfreq\n",
"\n",
"Y = fft(y) / n # Normalizada\n",
"frq = fftfreq(n, dt) # Recuperamos las frecuencias\n",
"\n",
"plt.vlines(frq, 0, Y.imag) # Representamos la parte imaginaria\n",
"plt.annotate(s=u'f = 400 Hz', xy=(400.0, -0.5), xytext=(400.0 + 1000.0, -0.5 - 0.35), arrowprops=dict(arrowstyle = \"->\"))\n",
"plt.annotate(s=u'f = -400 Hz', xy=(-400.0, 0.5), xytext=(-400.0 - 2000.0, 0.5 + 0.15), arrowprops=dict(arrowstyle = \"->\"))\n",
"plt.annotate(s=u'f = 800 Hz', xy=(800.0, 0.25), xytext=(800.0 + 600.0, 0.25 + 0.35), arrowprops=dict(arrowstyle = \"->\"))\n",
"plt.annotate(s=u'f = -800 Hz', xy=(-800.0, -0.25), xytext=(-800.0 - 1000.0, -0.25 - 0.35), arrowprops=dict(arrowstyle = \"->\"))\n",
"plt.ylim(-1, 1)\n",
"plt.xlabel('Frecuencia (Hz)')\n",
"plt.ylabel('Im($Y$)')"
]
},
{
"cell_type": "markdown",
"id": "2883df5b",
"metadata": {},
"source": [
"**Nota**: Si quieres leer más sobre añadir texto y anotaciones a una gráfica en matplotlib, puedes leer la parte VIII del nuestro magnífico tutorial de matplotlib por Kiko :) http://pybonacci.wordpress.com/2012/08/24/manual-de-introduccion-a-matplotlib-pyplot-viii-texto-y-anotaciones/"
]
},
{
"cell_type": "markdown",
"id": "5def9481",
"metadata": {},
"source": [
"¡Y ya hemos hecho nuestra primera transformada discreta de Fourier con el algoritmo FFT! Pero las cosas en la realidad son bastante más complicadas. Vamos a ver algunos de los problemas que apareceran con frecuencia."
]
},
{
"cell_type": "markdown",
"id": "116a32ab",
"metadata": {},
"source": [
"## Fuga, «zero-padding» y funciones ventana"
]
},
{
"cell_type": "markdown",
"id": "bc580ab2",
"metadata": {},
"source": [
"Vamos a analizar el ejemplo anterior, pero en esta ocasión vamos a poner menos cuidado con la preparación de los datos. Veamos qué ocurre:"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "bdc70566",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7ec9710>"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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zzlo6B6Fv7kEBy3u9O0rs8zS9g2P43v6jCAr0w805iby8p5jX0rR1D6G1awg3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\nDRERyYpBQ0REsmLQEBGRrP4fH2Wk8X7MjHUAAAAASUVORK5CYII=\n"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n2 = 2 ** 5\n",
"\n",
"t2 = np.linspace(0, 0.012, n2) # Intervalo de tiempo en segundos\n",
"dt2 = t2[1] - t2[0]\n",
"y2 = np.sin(2 * pi * f * t2) - 0.5 * np.sin(2 * pi * 2 * f * t2) # Señal\n",
"\n",
"Y2 = fft(y2) / n2 # Transformada normalizada\n",
"frq2 = fftfreq(n2, dt2)\n",
"\n",
"fig = plt.figure(figsize=(6, 8))\n",
"\n",
"ax1 = fig.add_subplot(211)\n",
"ax1.plot(t2, y2)\n",
"ax1.set_xlabel('Tiempo (s)')\n",
"ax1.set_ylabel('$y_2(t)$')\n",
"\n",
"ax2 = fig.add_subplot(212)\n",
"ax2.vlines(frq2, 0, Y2.imag)\n",
"plt.xlabel('Frecuencia (Hz)')\n",
"plt.ylabel('Im($Y_2$)')"
]
},
{
"cell_type": "markdown",
"id": "f9e0807c",
"metadata": {},
"source": [
"Como se puede ver, el fenómeno no es extremadamente importante pero han aparecido otras rayas espectrales que no esperábamos. Esto se conoce como «leaking» (y yo lo voy a traducir por *fuga*) y es debido a que, en este caso, los trozos «no empalman exactamente». Recuerda que la DFT, y por extensión la FFT asume que estamos transformando un período de una señal periódica. Si utilizamos más puntos y extendemos la señal con ceros (esto se conoce como «zero-padding») la DFT da más resolución en frecuencia pero la fuga se magnifica:"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "7904b5e2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x8117c10>"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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OTZsh5yivo7fmYzDIUFWu+RAROQR88FmxYgV27tyJ4cOHY/fu3VixYgUA4MSJ\nE5g1axYAoKysDJMnT8a4ceOQlpaG6667Dtdee22j93akWisemz8d0276m0xdR0XaA+j0st1c13wY\nfIiIAmTazZfevXtj165dmucHDRqEDz74AAAwbNgw/Pe//232vWXJHmSsnqnW9cHCa4VqR4acyaMq\nQv3GVL30bFG/5mPmmg8RUeCPfNqTc9rNs6q1jzptjjRsi6K6HcPgOu2m3ecj29OzeZIpERGAoA8+\n+tWrTUYDFFXVz3ZzJhboVUWwn3CqXwmb025ERA5BHXwcU2WeRyqYTAZYrWr98dratGnHaMkzkMiy\npJvtJrlVzw7qXzkREYAgDz7OJAGPaTeTUYZV0e7/ARpGSxadCtWyJMFiVfX3+XDkQ0TkFNTBxx5I\noDlGO8RogEVRvWa72dT6gOVZekeWYFFUr2s+FquKEK75EBEFd/AxyBJU1WavVuAyijEaDbAq+ms+\nbqeceo58ZEl3zUfmyIeIyE1QBx/niaU24bHJtD412qqXPGDPkLNYtWfzyJIEq1U78pGZcEBE5Cao\ng49jpGKQ3WvGSZIEk9GAmjqrdnRjqN+AquqMcBxrPjpTdYIJB0RETkH9TWiQZXuw0BmNhNQHH02d\nNknS3RsE2LPaLDojn4Y1H4VrPkRECPLgI0sS6qyK2xHaDiaTAbV1in5h0fpsN89pN4MswWLVv0Z1\nbEzltBsRUZAHH1lCnVXVjGAA+0bTmlqrl02m9bXdPAKJfapO8XoNq1oTEdkx+FgUTco0gIY1H50K\n1VbFBiEEDLL7fh5ziBHVtRbvB9Bx5ENEBCDYg4+knxoNACFGGbU6oxhZklBbZ4U5xKg52C40xIhL\nNRbtmo9BgqLa07OZcEBEFOzBpz5BQHfazWRArUU78pFlCTV1Vt3EAXOIEdU1Ft1st7o6K0xG2etJ\nrEREwSTog0+dxUvCgWP9xmNqzR58FJhN2tMozCFGVOmsE9kTGzjlRkTkENzBx7EvRycomIwGVNfq\nrPnIEmpq7dNunkJDjKiqsehuTK2tszL4EBHVC+7gI8u6qdGAfZ9PbZ1+tltNndXryKdaZ81HliXU\nWhQGHyKiekEefBzTYXprPrJ+tpsso7rWCnOIzpqPyYBL3kY+Fm4wJSJyCOrgY5AlVNdYEGo2aV4z\nGuorHOiNYuq8TLuZTV5HPjabYKYbEVG9oP42lCQJF6stCAvVBh+T0QAhoJvtVu1t2s3LyEeuT1rg\ntBsRkV0OWjzFAAAgAElEQVRQBx9ZllBVU4ew0BDNayEm+69Gr7abzSb0U63NJi+VsBl8iIhcBXXw\nMcgSLvkY+QDakY8jGOlNu5nrA5J22s3+mGs+RER2QR18ZEmCotp8Bx+dA+MAL8Gn/jlOuxER+RbU\nwUeqDwrdmjHycQYfnTWf0Prg47kxtWHaLah/3URETkH9beiYQgvXWfMxOabQZP31G91Ua458iIia\nJOCDz9tvv41Ro0bBYDBg//79Xtvl5OQgMTERCQkJWLduXZPu7Rig6I18QupHKZ4Vqh212XxNu+kd\nJgc0BDQiomAX8MFnzJgxeO+993D11Vd7baOqKpYuXYqcnBwcOHAAW7ZswcGDBxu9tyMRwNeaj7dA\n4mvaTe94bQCaw+eIiIKV9hs0wCQmJjbaJj8/H/Hx8YiLiwMAzJs3D9u2bUNSUpKm7apVq5z/bupl\nb99NZ5Npo2s+zRj5yAZOuxFR55Gbm4vc3Nx2fY+ADz5NUVpaitjYWOfjmJgY7N27V7eta/D55ycH\ngR3bEN7Nx5qPl+Cju8/HpD/ycU67MfgQUSeQnp6O9PR05+PVq1e3+XsERPCZPn06ysrKNM+vWbMG\ns2fPbvT6lp6RI/vIdgvxMu0m+1jzCTU7st28bDI1BfwsJxGRXwRE8Nm5c2erro+OjkZxcbHzcXFx\nMWJiYhq9zhF8wnRru9UnHHgGEoMj1brpIx+Jaz5ERG461Z/iQgjd5ydMmIDCwkIUFRXBYrFg69at\nyMzMbPR+jlGMbsKBt2k3n9lujmu0IzGDLHHajYioXsAHn/feew+xsbHIy8vDrFmzkJGRAQA4ceIE\nZs2aBQAwGo3YsGEDZsyYgZEjR+LnP/+5brKBJ+fIR2/Nx2vCgffyOt6y3QD7VBzL6xAR2QXEtJsv\nc+fOxdy5czXPDxo0CB988IHzcUZGhjMwNZWvkY9jn4/nKMY58vFymJz9Gm3wkQ0c+RAROQT8yKc9\nOYJEs1KtDd4rHIT4GPnIksRNpkRE9YI6+DhGMbrBpwVrPg213bxMu3HkQ0QEIMiDjyRJCDUbdafJ\nHCMfk8E9YDjSpvUCibfaboB9fYmFRYmI7IL629BgkHTTrAF7cJGkhqQEh6YkHOgFM2a7ERE1COrg\nI0sSuulUtAbsIx9vIxhAP/gYDTJkWfI+8uGaDxERgCAPPpIkIbyb/sjHZJS9jmAA/Ww3SZJgNhl1\n9/nIssyRDxFRvaAOPt3MJvTsHqr7mslk0FQ3AFwTDvQDSajZ6CXhQGLCARFRvaAOPqPjo7Dpdzfo\nvmYyGvT36/iYdgOADSvmoF+vcJ3rOPIhInII+E2m7UmSJERGdNN9zWSUfa/56Ey7AcCVyUN0nzcw\n242IyInfhl54G/k4ptSaWyqHCQdERA0YfLzo3TMMV6cO1TxvMMgYOay/bmDyReaaDxGRE4OPFxFh\nZjx13yzN80aDjA/+tLDZ9zNwzYeIyInBx0+4yZSIqAGDj5/86oY0DIvp3dHdICIKCJLwdkJbFyRJ\nktcD6YiISF97fHdy5ENERH7H4ENERH7H4ENERH7H4ENERH7H4ENERH7H4ENERH7H4ENERH7H4ENE\nRH7H4BOAcnNzO7oLTcJ+tq3O0M/O0EeA/ewMGHwCUGf5H5L9bFudoZ+doY8A+9kZBHzwefvttzFq\n1CgYDAbs37/fa7u4uDiMHTsWKSkpuPzyy/3YQyIiaq6AP8l0zJgxeO+995CVleWznSRJyM3NRe/e\nLN5JRBToOk1h0SlTpuCZZ55Bamqq7utDhw7FF198gT59+ni9hyRJ7dU9IqIura1DRcCPfJpKkiRM\nmzYNBoMBWVlZWLx4saZNJ4mzRERdXkAEn+nTp6OsrEzz/Jo1azB79uwm3ePzzz/HwIEDcfr0aUyf\nPh2JiYmYPHlyW3eViIjaQEAEn507d7b6HgMHDgQA9OvXD3PnzkV+fj6DDxFRgAr4bDdX3qbNqqur\ncfHiRQBAVVUVduzYgTFjxviza0RE1AwBH3zee+89xMbGIi8vD7NmzUJGRgYA4MSJE5g1axYAoKys\nDJMnT8a4ceOQlpaG6667Dtdee21HdpuIiHwRndiHH34oRowYIeLj48XatWt129x1110iPj5ejB07\nVuzfv7/Ra8+ePSumTZsmEhISxPTp00VFRUVA9nPZsmUiMTFRjB07VsydO1dUVlYGZD8dnn76aSFJ\nkjh79mzA9vP5558XiYmJYtSoUWL58uUB18e9e/eKiRMninHjxokJEyaI/Pz8VvWxtf1csGCB6N+/\nvxg9erRb+0D7DHnrZ6B9hrz10yFQPkO++tmcz1CnDT6KoojLLrtMHD16VFgsFpGcnCwOHDjg1uaD\nDz4QGRkZQggh8vLyRFpaWqPXPvjgg2LdunVCCCHWrl0rHnrooYDs544dO4SqqkIIIR566KGA7acQ\nQhw/flzMmDFDxMXFtfqD01793L17t5g2bZqwWCxCCCFOnToVcH285pprRE5OjhBCiOzsbJGent7i\nPra2n0II8cknn4j9+/drvoQC6TPkq5+B9Bny1U8hAucz5Kufzf0MBfy0mzf5+fmIj49HXFwcTCYT\n5s2bh23btrm12b59O+bPnw8ASEtLQ2VlJcrKynxe63rN/Pnz8f777wdkP6dPnw5Zlp3XlJSUBGQ/\nAeD+++/Hk08+2ar+tXc/X3rpJTz88MMwmUwA7IkrgdbHgQMH4vz58wCAyspKREdHt7iPre0nAEye\nPBm9evXS3DeQPkO++hlInyFf/QQC5zPkq5/N/Qx12uBTWlqK2NhY5+OYmBiUlpY2qc2JEye8Xlte\nXo6oqCgAQFRUFMrLywOyn65eeeUVzJw5MyD7uW3bNsTExGDs2LGt6l9797OwsBCffPIJJk2ahPT0\ndHzxxRcB18e1a9figQcewODBg/Hggw/iiSeeaHEfW9tPXwLpM9RUHf0Z8iWQPkO+NPczFBCp1i3R\n1GoFogkbS4UQuveTJKnVVRHasp96Hn/8cYSEhOAXv/hFi653aI9+1tTUYM2aNW6p9C39OR3a6/ep\nKAoqKiqQl5eHffv24Wc/+xl++OGHlnSx3fq4aNEiPP/885g7dy7efvttLFy4sFXbFFraz+Z8Jjry\nM9TU6zr6M+Truurq6oD5DDV2XXM/Q5125BMdHY3i4mLn4+LiYsTExPhsU1JSgpiYGN3nHVMYUVFR\nzuHlyZMn0b9//4Dpp+e1r732GrKzs/HGG2+0qo/t1c//+7//Q1FREZKTkzF06FCUlJRg/PjxOHXq\nVED1E7D/ZffTn/4UADBx4kTIsoyzZ88GVB/z8/Mxd+5cAMCNN96I/Pz8FvWvtf1sbLovUD5DTZmW\nDITPkK9+BtJnqLHfZ7M/Qy1dtOpoVqtVDBs2TBw9elTU1dU1umj2n//8x7lo5uvaBx980Jn98cQT\nT7R6EbK9+vnhhx+KkSNHitOnT7eqf+3dT1dtsVjaXv18+eWXxe9//3shhBCHDh0SsbGxAdfHlJQU\nkZubK4QQYteuXWLChAkt7mNr++lw9OhR3YSDQPkM+epnIH2GfPXTVUd/hnz1s7mfoU4bfISwZ/wM\nHz5cXHbZZWLNmjVCCPsv4OWXX3a2ufPOO8Vll10mxo4dK7788kuf1wphTxOdOnVqm6aJtkc/4+Pj\nxeDBg8W4cePEuHHjxJIlSwKyn66GDh3aJmmi7dFPi8Uibr31VjF69GiRmpoqPvroo4Dr4759+8Tl\nl18ukpOTxaRJk9zSXzuin/PmzRMDBw4UISEhIiYmRrzyyitCiMD7DHnrZ6B9hrz101UgfIa89bO5\nn6FOU9WaiIi6jk675kNERJ0Xgw8REfkdgw8REfkdgw8REfkdgw9RI86ePYuUlBSkpKRg4MCBiImJ\nQUpKCiIiIrB06dKO7h4A4JtvvsHChQu9vl5eXt7qHfxEbanTVjgg8pc+ffqgoKAAALB69WpERETg\n/vvv7+BeuXvqqadw1113eX09KioKvXr1wv79+5GamurHnhHp48iHqJkcuxNyc3Odx7xXVVVh4cKF\nSEtLQ2pqKrZv3w7AvoN+zpw5uPbaazF06FBs2LABTz/9NFJTU3HFFVegoqICAJCeno57770XKSkp\nGDNmDPbt2wcAOHfuHObMmYPk5GRcccUV+OabbzT9qaurQ15eHiZOnAgA+Pjjj50jtdTUVFRVVQEA\nMjMzsWXLlvb95RA1EYMPURt4/PHHMXXqVOzduxe7d+/Ggw8+iOrqagDAd999h/feew/79u3Db3/7\nW/To0QP79+/HFVdcgc2bNwOw182qqalBQUEBXnzxRecU2sqVKzF+/Hh89dVXWLNmDW677TbNexcU\nFGDEiBHOx8888wxefPFFFBQU4LPPPkNoaCgA4PLLL8cnn3zS3r8KoiZh8CFqAzt27MDatWuRkpKC\nKVOmoK6uDsePH4ckSZgyZQrCw8PRt29fREZGOkdLY8aMQVFRkfMeN998MwB7yfoLFy7g/Pnz+Pzz\nz/HLX/4SADBlyhScPXsWly5dcnvvY8eOYeDAgc7HV111Fe677z786U9/QkVFBQwGAwD7kQyu70fU\nkRh8iNrIP/7xDxQUFKCgoABFRUVITEwEAJjNZmcbWZadj2VZhqIoXu/nqCLcWBESSZLc2jz00EP4\n61//ipqaGlx11VU4dOiQ8z6trTBN1FYYfIjawIwZM/D88887HzsSFHwFDtfXhBDYunUrAOCzzz5D\nZGQkevTogcmTJzsrLufm5qJfv37o3r27232GDBnirCIN2Cshjxo1CsuXL8fEiROdwefkyZMYMmRI\nK39SorbBbDeiZnKMHlzPqvnd736He++9F2PHjoXNZsOwYcOwfft2zXk2nv/ueq/Q0FCkpqZCURS8\n8sorAIBVq1Zh4cKFSE5ORnh4OF5//XVNf5KTk50BBgDWr1+Pjz76CLIsY/To0cjIyABgP5Lh6quv\nbuPfBlHLsLAoUQCYMmUKnnnmmRanQd9+++1YsmQJ0tLSvLa55ZZbsGzZMqSkpLS0m0RthtNuRF3A\nsmXL8PLLL3t9/dSpU6isrGTgoYDBkQ8REfkdRz5EROR3DD5EROR3DD5EROR3DD5EROR3DD5EROR3\nDD5EROR3DD5EROR3DD5EROR3ARd8cnJykJiYiISEBKxbt063zd13342EhAQkJyc7CzgCQGVlJW68\n8UYkJSVh5MiRyMvL81e3iYioGQIq+KiqiqVLlyInJwcHDhzAli1bcPDgQbc22dnZOHLkCAoLC7Fp\n0yYsWbLE+do999yDmTNn4uDBg/j666+RlJTk7x+BiIiaIKCCT35+PuLj4xEXFweTyYR58+Zh27Zt\nbm22b9+O+fPnAwDS0tJQWVmJ8vJynD9/Hp9++qnzBEij0YiePXv6/WcgIqLGBdSRCqWlpYiNjXU+\njomJwd69exttU1JSAoPBgH79+mHBggX46quvMH78eKxfvx5hYWHOtjxIi4ioZdq6DGhAjXyaGhw8\nfwmSJEFRFOzfvx+/+c1vsH//foSHh2Pt2rW613bVf1auXNnhfeDPx58v2H62YPj52kNABZ/o6GgU\nFxc7HxcXFyMmJsZnm5KSEkRHRyMmJgYxMTGYOHEiAODGG2/E/v37/dNxIiJqloAKPhMmTEBhYSGK\niopgsViwdetWZGZmurXJzMzE5s2bAQB5eXmIjIxEVFQUBgwYgNjYWBw+fBgAsGvXLowaNcrvPwMR\nETUuoNZ8jEYjNmzYgBkzZkBVVSxatAhJSUnYuHEjACArKwszZ85EdnY24uPjER4ejldffdV5/Z/+\n9CfccsstsFgsuOyyy9xeCwbp6ekd3YV2xZ+v8+rKPxvQ9X++9hBUh8lJktRu85dERF1Ve3x3BtS0\nGxERBQcGHyIi8jsGHyIi8jsGHyIi8jsGHyIi8jsGHyIi8jsGHyIi8jsGHyIi8jsGHyIi8jsGHyIi\n8jsGHyIi8jsGHyIi8jsGH+qSBg0ahO+//76ju0FEXrCqNXVJvXr1Qk1NDWprazu6K0SdHqtaExFR\nl8DgQ0REfsfgQ0REfsfgQ0REfsfgQ0REfsfgQ0REfsfgQ0REfsfgQ0REfsfgQ13O1KlTYbPZOrob\nROQDgw91OWVlZaxkQRTgGHyoyxJC4Mknn+zobhCRjoALPjk5OUhMTERCQgLWrVun2+buu+9GQkIC\nkpOTUVBQ4PaaqqpISUnB7Nmz/dFdCnAvvfRSR3eBiHQEVPBRVRVLly5FTk4ODhw4gC1btuDgwYNu\nbbKzs3HkyBEUFhZi06ZNWLJkidvr69evx8iRIyFJkj+7TkREzRBQwSc/Px/x8fGIi4uDyWTCvHnz\nsG3bNrc227dvx/z58wEAaWlpqKysRHl5OQCgpKQE2dnZuOOOOzjnT0QUwIwd3QFXpaWliI2NdT6O\niYnB3r17G21TWlqKqKgo3HfffXjqqadw4cIFr++xatUq57+np6cjPT29zfpPRNQV5ObmIjc3t13f\nI6CCT1OnyjxHNUII/POf/0T//v2RkpLi85fmGnyIiEjL8w/z1atXt/l7BNS0W3R0NIqLi52Pi4uL\nERMT47NNSUkJoqOjsWfPHmzfvh1Dhw7FzTffjN27d+O2227zW9+JiKjpAir4TJgwAYWFhSgqKoLF\nYsHWrVuRmZnp1iYzMxObN28GAOTl5SEyMhIDBgzAmjVrUFxcjKNHj+LNN9/Ej3/8Y2c7IiIKLAE1\n7WY0GrFhwwbMmDEDqqpi0aJFSEpKwsaNGwEAWVlZmDlzJrKzsxEfH4/w8HC8+uqruvdithsRUeCS\nRBClhbXHOeQUeEaNGoXi4mLU1dVh0KBBOHr0aEd3iahTa4/vzoCadiMiouDA4ENERH7H4ENERH7H\n4ENERH7H4ENERH7H4ENERH7H4ENdSklJCdPpiToBBh/qUm6//XZUV1d3dDeIqBEMPkRE5HcMPkRE\n5HcMPtSl1dbWYvLkyR3dDSLywOBDXZ6qqh3dBSLywOBDRER+x+BDRER+x+BDRER+x+BDRER+x+BD\nRER+x+BDRER+x+BDRER+x+BDREEjJycHR48e7ehuEBh8iCiIvPTSS/j66687uhsEBh8iChKffvop\nLl682NHdoHoMPkQUFN544w2cPXu2o7tB9Rh8iCioPP300/jmm286uhtBj8GHiIJKeXk5ampqOrob\nQS/ggk9OTg4SExORkJCAdevW6ba5++67kZCQgOTkZBQUFAAAiouLMWXKFIwaNQqjR4/G888/789u\nExFRMwRU8FFVFUuXLkVOTg4OHDiALVu24ODBg25tsrOzceTIERQWFmLTpk1YsmQJAMBkMuHZZ5/F\nd999h7y8PLzwwguaa4mIKDAEVPDJz89HfHw84uLiYDKZMG/ePGzbts2tzfbt2zF//nwAQFpaGior\nK1FeXo4BAwZg3LhxAIDu3bsjKSkJJ06c8PvPQEREjTN2dAdclZaWIjY21vk4JiYGe/fubbRNSUkJ\noqKinM8VFRWhoKAAaWlpmvdYtWqV89/T09ORnp7edj8AEQWkmpoaKIrS0d3oNHJzc5Gbm9uu7xFQ\nwUeSpCa1E0J4ve7SpUu48cYbsX79enTv3l1zrWvwIaLg8NRTTznXh6lxnn+Yr169us3fI6Cm3aKj\no1FcXOx8XFxcjJiYGJ9tSkpKEB0dDQCwWq244YYbcOutt2LOnDn+6TQFjEWLFqGsrKyju0FETRBQ\nwWfChAkoLCxEUVERLBYLtm7diszMTLc2mZmZ2Lx5MwAgLy8PkZGRiIqKghACixYtwsiRI3Hvvfd2\nRPepg1mtVs2omEjPH/7wB5w5c6ajuxHUAmrazWg0YsOGDZgxYwZUVcWiRYuQlJSEjRs3AgCysrIw\nc+ZMZGdnIz4+HuHh4Xj11VcBAJ9//jn+/ve/Y+zYsUhJSQEAPPHEE/jJT37SYT8PEQWmvXv3ora2\ntqO7EdQCKvgAQEZGBjIyMtyey8rKcnu8YcMGzXU/+tGPYLPZ2rVv1DlVVFTgzjvvxAsvvNDRXSGi\negE17UbUHmw2G8rLyzu6G0TkgsGHiIj8jsGHiIj8jsGHiIj8jsGHiIj8jsGHiIj8jsGHiLq0119/\nHdnZ2R3dDfLA4ENEXZrFYoHVau3obpAHBh8iCkpxcXFQVbWjuxG0GHyIqM1lZ2dj9+7dHd0Nn1gH\nsGMx+BCRV6qq4ptvvmnWNSUlJdi2bRvy8/PbqVfUFTD4EJFXNTU1SEtLw3XXXdfka9599118+eWX\n7dgr6goYfIioUYcOHeroLlAXw+BDRER+1+zgU1tbi7q6uvboCxF1IRaLhd8V5FWjwcdms+Ef//gH\nbrrpJkRHR2Po0KEYMmQIoqOjceONN+K9995j1ggRaWzbtg1vvvlmR3eDAlSjwSc9PR1ffvklli1b\nhh9++AEnT55EWVkZfvjhByxbtgz79u3DNddc44++UgB65ZVXcPz4cb+818aNG3HkyBG/vBfZvfTS\nSx3dBeqiGj3JdOfOnTCbzZrnzWYzJk2ahEmTJnFoHcT++te/YsSIERg8eHC7v9fWrVuhKAoGDhyI\n8PDwNrvvhQsXcPToUSQnJ7fZPbuKRx99tKO7QF1UoyMfvcDTkjbUda1ZswZlZWV+ea8nn3xSd6RV\nUFCAysrKZt/v7NmzuOuuuzRHtVPXcPToUXz11Ve6rwkhcO7cOT/3iBxane12+PBhjnyC1LPPPouL\nFy+ioKAANTU17fpen332GWpra72+/uabb6KkpKTZ97106RL+9a9/taZrQUFRlDZfv9m0aRP+/ve/\nt/o+Fy5cwMWLF3Vf++677/DJJ594vXbUqFGtfn9qmRYFn0ceeQR33HEHNm7ciD//+c/4wx/+0Nb9\nog5gtVqb9YfE559/DovF0mi7S5cuQVEUn23eeustFBcXe339pZdewvnz55vcN0+KorRoZNSVWa1W\nbNu2rcltX3zxxUbbff311/jiiy8abffPf/4T//jHP1q9XlhVVYXHH38cf/zjH1t1H/K/RoOP3l8N\n1157LVavXo1rrrkGq1atwowZM9qlc+Q/Qghs3rwZS5YsafN7Z2Rk4LXXXvM5OnrxxRfx2GOP4fTp\n023+/gBQVFSE3/3ud15fr6iowE033dQu7x2oampqcMstt2DOnDltds9Dhw41qRxPUVERTp8+jePH\nj+OHH37QbXPp0iX8/ve/x9NPP+31Pn//+9+xa9euFveXOk6jwWfFihWav2779u2Lffv2ITExES+8\n8AJkmXtVO7ucnBw899xzbX5fR9XgVatWobS0VLfNp59+itraWmRnZ6OioqLN+9AUQgivo7Oqqio8\n/fTTuOOOO/zcK/84ePBgh733vn378PHHH+u+tnnzZmRnZzdpSveTTz7Bu+++29bdo3bUaNRYtmwZ\n3njjDbe/TkaPHu38a2n58uW46qqr2q+H5FdfffUVfv/73zf7urvuukt3Cu7mm2/GmTNnfF774osv\n4sKFC01+r927d7fJ+SyKouChhx5qtF1FRQWefPJJfP31117bCCFw+vRpFBQUtLpfbeHChQsYP348\nnnzySa9t4uLi/NehVvjnP/+J119/3Web8+fP4+zZs37qEbWFRoPPT3/6UyxYsABHjx5FTk6OP/pE\nfqYoituCrc1ma/Y9du7c2aLrWmLFihWorq5u9X2EEHjnnXea3P7ChQv4zW9+o/vayZMnMXLkSJ+j\no4sXL+KBBx7A6tWrvbapqqrCqlWr8Oqrr3ptU1FRgeTkZPz617/22qawsBCHDx/Ga6+95rWNI4FD\nVVXk5eV5bdcaTz31FHbu3On2XFlZmc/1PU+Kouj+sVFUVITvvvuu1X305u2338alS5fa7f7BrtHg\n45g2mTp1Krp164Y777wTn332Gaqrq/HBBx+0eYdycnKQmJiIhIQErFu3TrfN3XffjYSEBCQnJ7v9\npdmUa0nr22+/xYoVK9r9faZMmdJo0Jg9e7bmA79v375WJRu0hs1mw9133w3A/lnQmzoUQjj/6q6q\nqsJjjz2me6+qqiq89tprePfdd3Hs2DHdNufOncP69evx7LPPeu3T//7v/6KoqAifffaZ1zaO2QhF\nUbB3716v7QCgrq4ODz/8sOb566+/vl2ql3z++eeNZhh++umnjSZDfP31116n7Frrm2++wQMPPIC+\nffvyFNR20mjwWbJkCVauXInk5GQsXrwYZrMZf/vb33DNNddg4cKFbdoZVVWxdOlS5OTk4MCBA9iy\nZYtmPjo7OxtHjhxBYWEhNm3a5Fwgb8q1wWrv3r3IzMzEggULmvUXpy81NTXNHunoTb+Vlpa6ZdiV\nlpZqvvDeeustnDhxomUdbYaKigpkZ2e7PSeEwPvvv9/otWPHjgVgzwrz9mWfmJgIwB6EvCV2OKbC\nLl686DUR4L777gNgX5CfOXOmz37V1dXhkUceabT/er7//nu/lM7asWOHJknh7Nmzfts7pmfx4sWw\nWq1QFMVnJt23336L06dPs8RYCzRa4WD37t2444478OabbyIpKcnttfXr17dpZ/Lz8xEfH+/8AM6b\nNw/btm1ze9/t27dj/vz5AIC0tDRUVlairKwMR48ebfRawL7w7ZCeno709PQ2/RmaymazwWazQZZl\nrwkb586dw9dff43IyEgkJiYiNDTU7fWqqip88MEHyM7ORmRkJG655RZMnDjRrc3333+PFStW4MyZ\nMygtLcWf//znNtm1vnz5cq9ZSg5//OMfG02lfeaZZ1BUVNTq/rSFiooKfPDBBz6/0CsrK5Gdne2z\njc1mQ11dnWbz9fnz59G7d+8m98fXviYHvb/Km3KWzrRp0wLmC/Pbb79FaWkpxowZ47XNxo0bMWTI\nEEyfPt1rm3feeQcjR47Ej370oya/txACFy9eREREhNc2Tz31lO7a4P3334+33noLp06dwrPPPos7\n77xT0+bgwYPYuXMnhBD4xS9+gX79+um+x4kTJ6AoCmJiYgIigSs3Nxe5ubnt+h6SaOT/wF27dmHa\ntCX6DOEAAB/oSURBVGm6r+l9wFrjnXfewb/+9S/8+c9/BmBPo9y7dy/+9Kc/OdvMnj0bDz/8MK68\n8koA9g/RunXrUFRUhJycHJ/XSpLUrh84q9WKAwcO4MyZMzAYDBg0aBAiIiJw/PhxlJeXQ5ZlDBs2\nDBEREfjmm29w/vx59OzZE6NGjUJZWRm++OILVFRUYOTIkbjmmmuwa9cuqKoKSZIwcuRIFBUV4V//\n+hcqKirQu3dvPPzww/j4448hSRJkWUZ8fDx27tyJwsJC1NXVobq6Gs8++yz27Nnj/PlHjBiBnTt3\n4tChQ7BYLKiqqsL69evx6aefOv+nr6urw3fffYezZ8/CYrHg4sWL6NatG0JDQ2E0GmE0GhEbG4th\nw4ZBCAGbzYbq6mr8+9//RmhoKEwmEwwGAwYPHuxsI4RAdXU1duzYgW7duiEkJAQGgwGxsbG47LLL\nANi/tGtqapCTk+NsYzQaERMTg/j4eOd96urq8MEHHyAsLMztPgkJCbDZbBBCQFVVWK1WZ8CWZRlH\njx7F8ePHna/V1tZiypQpCA8Pd/7sx44dQ1FREWw2GxRFQU1NDdLT051tZFlGUVERjh07BlVVoSgK\nunXrhrFjxzrbSJKE48eP4+jRoxBCwGq1YtasWTh//jxCQkIgyzL69OmD8vJy/Oc//3G+18MPP4y8\nvDwIIWAwGNC7d2+cPn0ae/bscd4nIyMDVVVVkCQJRqMRqqqiuLgYxcXFsNlsUFUVEyZMQGhoKCRJ\ngslkwpkzZ3DgwAFIkuTWxmw2O9ucPXvW2cbx+0tNTXW7z7lz5/Dtt99ClmW333FVVRVUVUV4eDj6\n9u2LtLQ0532EEPj0009x7tw51NbWIiIiAr1798YVV1zh/H/SZrPh888/x5kzZ1BTU4OIiAj06dMH\nkyZNgiRJzjZ79uzB2bNnUVVVhe7du6NPnz644oorNG0qKipw/vx59OjRA7169dIEI8f/I7W1tTCZ\nTLh06RIKCgpgMBggSRJmzpzp/J3U1dUhIiICQ4YMwV/+8hfnf9+f/OQnMJvNzp+re/fuzjYGgwHh\n4eHIyMiAzWbDmTNnUFdXh/DwcEycOBHvvvsuTp48idjYWMycORNnzpzB8ePHUVtbi6ioKFx++eX4\n73//i7KyMnTv3h1JSUkIDQ3FDz/8gDNnzqBPnz4YMWIEFEXBsWPHYLFYEBkZieHDh6NHjx7t8t3W\nLt+dohGqqjbWRNhstkbbNMU777wj7rjjDufjv/3tb2Lp0qVuba677jrx2WefOR9PnTpVfPHFF026\ntgk/bsA7e/asOHDggLBarbqvnzp1SixatEiMGjVKrFu3Tve/TWZmpkhISBD9+/cXsiwLRVE0bebO\nnSsSEhLEgAEDhNFoFD179hRDhgwRo0aNEqmpqWLFihVu7WtqasTy5cvF4MGDxciRI0VKSopYvny5\nW5uqqioxb948ERMTI5KSkkRKSop44IEH3NpcuHBBhIWFiejoaJGYmCjGjRsn7rvvPs19zGazGDRo\nkBgxYoRITk4W99xzT6O/uxUrVojU1FQxevRoERcXJyIjI8Xp06fd2vz2t791thk2bJjIysoSFy5c\ncGvzu9/9TqSmpooxY8aIYcOGiS+//FLzXqtWrRKpqali7NixIj4+XuTn52vaPProo2L8+PFi7Nix\nIiEhQeTl5WnaPPbYY2L8+PEiOTlZDB8+XOzZs0fT5oknnhDjx48X48aNEyNGjBCffvqp2+sVFRXi\n4YcfdrZJTEwUH3/8sVubN954Q6SkpIjx48eLlJQUkZSUJHbv3u3WZsuWLWLcuHHONiNHjhSDBw8W\n3bt3FyEhIWLgwIHiqquu0vRv1KhRokePHsJkMokBAwaISZMmadqMGTNGREZGClmWRVRUlLj++us1\nbcaNGyd69eolAIioqCjx17/+VdMmNTVV9O3bVwAQffv2Fb/61a80bTxlZ2eL0aNHi9TUVDF+/Hix\nYcMGTZvdu3eLiRMnipSUFPGzn/1M979nbW2t+Oyzz8TGjRtFQUFBo+/bmbTHd2ej47spU6bgqaee\nwuHDhzWvHTp0COvWrWuzqtbR0dFuaxLFxcWIiYnx2aakpAQxMTFNurYr6N27N5KSkmA06s+Y9uvX\nD3/5y1/w7bffYvny5ZAkSdNm/fr1zmmGPn36tEm/QkNDcdttt/lsExYWhpUrV/ps061bN5+L7f72\n61//WjMl4/jr15eRI0eiV69ePtuMHj3a+fsfPnw4evbsqWnTq1cv5+gtNTXV67SNw+DBgzX9jYyM\nRGRkpM/rMjIyGl0/8peQkJBG19kMBkOja85GoxEbN25skz5NmTIFzzzzDGbOnIn7779fM70N2Gtc\nXnXVVfjVr36FcePGtcn7dmWNBp8dO3agT58+uPPOOzFw4EAMHz4cCQkJGDhwIJYuXYqoqKg222E8\nYcIEFBYWoqioCBaLBVu3bkVmZqZbm8zMTGzevBkAkJeXh8jISERFRTXpWrKLi4vDtGnTIMsyvvzy\nSxgMhg7pR//+/TF79my354xGo9s6nCRJ7da/22+/Hd26dXN7rinz7atWrUJKSgoAICoqSrMWBwA3\n3XSTczrx0UcfdbZ3NXfuXGebO+64w5mQ4Oo3v/mN84vsxhtvRHx8vKbNzJkznfdZvHhxo9W5b7jh\nBs1aaK9evRoNlm0hJCREN9Pt1ltvbTSg33DDDe2+HhIZGYkBAwbovjZ58mQ89thjSEtLa9c+BItG\nEw7MZjMWLlyIhQsXQlVVZ8ZS37592/xLwWg0YsOGDZgxYwZUVcWiRYuQlJTk/OslKysLM2fORHZ2\nNuLj4xEeHu7cD+HtWtK3bt06PPzww+02Rzx8+HD8z//8j882ffr0aXTUPGLECDz11FNuzxkMBvz4\nxz/2Wq24qRYuXKg5muHRRx9FSUkJ9u3b16R7PPLIIxg5cqTua7fccgsGDx6MsWPHeh2prly5EmVl\nZT43fP7qV7/C3Llzvf41PXbsWAwdOtS5ZqDn8ssvx549e3Ds2DGMHj260RFUe5EkSff/ueXLl/vc\nEAsA//M//4Pnn3++vboGAJg0aRJuuOGGdn0Psms0+LgyGAxe/+duKxkZGcjIyHB7zrPc/YYNG5p8\nLXnX2FRMa5hMJt0Moh49euDKK69sUv0vb8xmM55//vl2P8Rw/PjxXn9Hy5cvd/4R5M3VV1+Nq6++\n2ud7REVFNfqZcqRx+7J27Vqfr6enp2Pbtm1e9xd5uummmzB69OgmtW3MV1991ebBburUqbrPr1q1\nCosXL27WvaKiohAfH++3QxHJrslj2H379mHu3LlISUnBmDFjMGbMmCZ9KCh49OvXD9dff73PNoMG\nDUJWVhZMJhOGDh3qp561zIIFC7yOSBISEnDPPffoTpUFqtmzZ+O5557D3LlzG207YsSINgsYzZ0h\nOXDggNfXevfuDUmSnFPvnmbPnt3sqbnU1FRcd9116NGjR6f679nZNXnkc8stt+Dpp5/G6NGjAyIP\nnQJP//79kZmZiU8++QTDhg3z2m7gwIG45ZZbsHz5ct3X4+Pj8corr+Cee+5pr676dP311+PQoUMd\n8t7t6cc//rHP14cPH45+/fqhvLxc9/VevXqhT58+7XY0xfvvv4/09HR0797da5sDBw54HfW0xqBB\ngzBr1izceuutbX5v0tfk4NOvXz8u4FOjHNNqvuqXJSUl+VyPk2UZZrMZERERTZpCiY2Nxb333tui\n/uq5/vrrcd111zW6AN7VzJ49G7m5uV6Dz4wZM3DgwAG88cYb7fL+V111lW5WrStZlvHRRx+1+Xtz\nyt7/mhx8Vq5ciUWLFmHatGkICQkBYF88/OlPf9punaOOk5SU1KK//i+//HJcfvnlrX7/YcOGYdmy\nZY3+tQ7Y07ObUqF52bJlKCoqwrffftto247KAOzqfP3uJUnyOWJurqYcfkcdp8nB5/XXX8ehQ4eg\nKIrbtBuDT9f0+OOP49///rfuGfcjRozwOmXWVmJjYxEbG9um9+zTp0+bVuToisLCwjBjxowWlZ0y\nm83YsWOH7mvdu3d3ViZob+vWrcNtt93WpLUt6jhNDj5ffPEFvv/++6CbiiCtkJAQv+wJIf/7wx/+\n0OJrJUlCWFiY7muFhYXtltbv6Ze//GWjG56p4zU5c+DKK6/0mYVC1Jk8+uijGD58eEd3I2iYTKZ2\nWavxJlAO9SPvmjzy+c9//oNx48Zh6NChzqkLSZJ8nu5I1F5CQ0ORlJSEkpKSFl3fv39/TsH5kSzL\nzmLA/sDyNoGvycGnscOfiPwpJiYGK1eubPaGQiIKDI0Gn+7du3td55EkCf+/vXsPiqr8/wD+Xm7e\nb1guyDKSLAgK7CKI05TJhKs1FpCOiJqR1xkdrUYztSbDPzDQqBkv00ylI1HjvcRKUdLQMgXTsryM\ngO7mym1U8IKpK+vz/cMf58e6u8ginL34fs04w57z7NnPx93lze455zk3btxo96KIiMizPTJ8eA1z\nIiJqbw7N7Ubkary8vOweYWVLcnIyrly5YnMmaiKSD8OH3Frfvn2xcePGVo8fN24cz00jcgGcpI3c\nVkxMDNatW+fsMoioDRg+ZNfIkSNdehLZXr16cWZ1Ijflur9ZyOlycnLsXgSNiOhxMHzIIV26dMHz\nzz/v7DKIyM0xfMghffr0wcyZM51dBhG5OYYPERHJjuFDRESyY/gQEZHsGD5ERCQ7hg8REcmO4UNE\nrTZ06NB2v7w5PZlcJnzq6uqg0+kQHh6O0aNH49q1azbHFRYWIiIiAmFhYcjJyZGWL1q0CJGRkdBo\nNBg3bhyuX78uV+lET4yRI0ciLCzM2WWQB3CZ8MnOzoZOp0NZWRmSkpKQnZ1tNcZsNmPevHkoLCzE\nmTNnsGnTJpw9exYAMHr0aJw+fRonT55EeHg4Pv74Y7lb8EjNA56IqL24TPjs2rULGRkZAICMjAzs\n3LnTakxpaSnUajVCQkLg6+uL9PR0FBQUAAB0Op00D9nw4cPbfHllspSenu7sEsgNKBQKjB071tll\nkBtxmYm7amtroVQqAQBKpRK1tbVWYyorKy2+b1apVCgpKbEat2HDBkyaNMnm42RmZko/JyYmIjEx\n8fEKf4J4e3sjOjra2WWQC1IoFFizZo2zy6B2UlxcjOLi4g59DFnDR6fToaamxmp5VlaWxW2FQmHz\n0t32Luf98Lb8/PwwefJkm+ubhw85pmvXrsjNzXV2GUTUwR7+w3z58uXt/hiyhk9RUZHddUqlEjU1\nNQgICEB1dTX69etnNSYoKAhGo1G6bTQaoVKppNsbN27E7t27sX///vYtnIiI2pXL7PNJTk5GXl4e\nACAvLw+pqalWY+Lj41FeXg6DwQCTyYQtW7YgOTkZwIOj4FatWoWCggJeIpmIyMW5TPgsWbIERUVF\nCA8Px4EDB7BkyRIAQFVVlbQj08fHB2vXrsWYMWMwePBgTJw4EZGRkQCA+fPno6GhATqdDrGxsZg7\nd67TeiEiopYphBDC2UXIRaFQ4Alqt934+vqiW7duCA4Oxj///OPscsjJ3nvvPfz888+4e/cuGhoa\nUFdXh8bGRty+fdvZpVEH6YjfnS7zyYdc19tvv+3sEojIwzB86JGavgIlImovDB9qFW9v7w4/7p+I\nnhwMH2oVhUKBvn37OrsMIvIQDB96JH9/f5w6dcrZZRCRB2H40CN5eXkhICDA2WUQkQdh+BARkewY\nPkREJDuGDxERyY7hQ0REsmP4EBGR7Bg+REQkO4YPERHJjuFDRA6Jjo5Gjx49nF0GuTmGDxE5ZOrU\nqQgODnZ2GeTmGD5ERCQ7hg8RPbawsDBnl0BuhuFDRI9FoVDg0KFDzi6D3AzDh4iIZMfwISIi2TF8\niIhIdgwfIiKSHcOHiIhkx/AhIiLZMXyIiEh2LhM+dXV10Ol0CA8Px+jRo3Ht2jWb4woLCxEREYGw\nsDDk5ORYrc/NzYWXlxfq6uo6umQiImojlwmf7Oxs6HQ6lJWVISkpCdnZ2VZjzGYz5s2bh8LCQpw5\ncwabNm3C2bNnpfVGoxFFRUUYMGCAnKUTEZGDXCZ8du3ahYyMDABARkYGdu7caTWmtLQUarUaISEh\n8PX1RXp6OgoKCqT1CxYswMqVK2WrmYiI2sbH2QU0qa2thVKpBAAolUrU1tZajamsrLSYTVelUqGk\npAQAUFBQAJVKhZiYmBYfJzMzU/o5MTERiYmJj188EZEHKS4uRnFxcYc+hqzho9PpUFNTY7U8KyvL\n4rZCoYBCobAaZ2sZANy+fRsrVqxAUVGRtEwIYXNs8/AhIiJrD/9hvnz58nZ/DFnDp3k4PEypVKKm\npgYBAQGorq5Gv379rMYEBQXBaDRKt41GI1QqFc6fPw+DwQCNRgMAuHTpEuLi4lBaWmpzO0RE5Fwu\ns88nOTkZeXl5AIC8vDykpqZajYmPj0d5eTkMBgNMJhO2bNmC5ORkREVFoba2Fnq9Hnq9HiqVCidO\nnGDwEBG5KJcJnyVLlqCoqAjh4eE4cOAAlixZAgCoqqrC2LFjAQA+Pj5Yu3YtxowZg8GDB2PixImI\njIy02pa9r+eIiMg1KIS9nSMeSKFQ2N0XREStV1FRgenTp+Pff/9FfX09Ll68iN69ezu7LOogHfG7\n02U++RCR+1Cr1fD19XV2GeTGGD5E9FjS0tLg5+fn7DLIzTB8iOixLFiwAF27dnV2GeRmGD5ERCQ7\nhg8REcmO4UNERLJj+BARkewYPkREJDuGDxERyY7hQ0REsmP4EFGbREZGwtvb29llkJti+BBRm6xd\nuxbjx49Hz549nV0KuSFOLEpERC3ixKJEROQRGD5ERCQ7hg8REcmO4UNERLJj+BARkewYPkREJDuG\nDxERyY7hQ0REsmP4EBGR7Bg+REQkO4YPERHJjuHjQYqLi51dQodif+7Lk3sDPL+/juAy4VNXVwed\nTofw8HCMHj0a165dszmusLAQERERCAsLQ05OjsW6NWvWIDIyElFRUVi8eLEcZbsUT38DsD/35cm9\nAZ7fX0dwmfDJzs6GTqdDWVkZkpKSkJ2dbTXGbDZj3rx5KCwsxJkzZ7Bp0yacPXsWAPDLL79g165d\n+Pvvv3Hq1Cm8++67crdARESt5DLhs2vXLmRkZAAAMjIysHPnTqsxpaWlUKvVCAkJga+vL9LT01FQ\nUAAA+Pzzz7F06VL4+voCAJ5++mn5iiciIoe4zPV8+vTpg/r6egCAEAL+/v7S7Sbbt2/H3r178eWX\nXwIAvvnmG5SUlGDNmjWIjY1FSkoKCgsL0blzZ3zyySeIj4+3uL9CoZCnGSIiD9PeUeHTrlt7BJ1O\nh5qaGqvlWVlZFrcVCoXNoGgpPBobG1FfX4+jR4/i2LFjSEtLw4ULFyzGuEjOEhE98WQNn6KiIrvr\nlEolampqEBAQgOrqavTr189qTFBQEIxGo3TbaDRCpVIBAFQqFcaNGwcAGDZsGLy8vHD16lX07du3\nnbsgIqLH5TL7fJKTk5GXlwcAyMvLQ2pqqtWY+Ph4lJeXw2AwwGQyYcuWLUhOTgYApKam4sCBAwCA\nsrIymEwmBg8RkYtymX0+dXV1SEtLw8WLFxESEoKtW7eid+/eqKqqwqxZs/DTTz8BAPbs2YN33nkH\nZrMZM2bMwNKlSwEA9+7dw/Tp0/HXX3/Bz88Pubm5SExMdGJHRERkl/AgW7duFYMHDxZeXl7i+PHj\n0nK9Xi86d+4stFqt0Gq1Ys6cOdK6P/74Q0RFRQm1Wi3eeustafmdO3dEWlqaUKvVYvjw4cJgMMja\niy32+hNCiBUrVgi1Wi0GDRok9u7dKy13p/6afPTRRyIoKEh6vnbv3i2tc7RPd7Fnzx4xaNAgoVar\nRXZ2trPLaZMBAwaI6OhoodVqxbBhw4QQQly9elWMGjVKhIWFCZ1OJ+rr66Xx9p5LVzFt2jTRr18/\nERUVJS1rSz+u+tq01Z+c7z2PCp+zZ8+Kc+fOicTERKvwaf4f3NywYcNESUmJEEKIl19+WezZs0cI\nIcS6deukkNq8ebOYOHFiB1f/aPb6O336tNBoNMJkMgm9Xi9CQ0PF/fv3hRDu1V+TzMxMkZuba7W8\nLX26g8bGRhEaGir0er0wmUxCo9GIM2fOOLssh4WEhIirV69aLFu0aJHIyckRQgiRnZ0tFi9eLISw\n/VyazWbZa27JoUOHxIkTJyx+dzjSj6u/Nm31J+d7z2X2+bSHiIgIhIeHt3p8dXU1bt68iYSEBADA\nG2+8IZ1f1Py8o/Hjx2P//v3tX7CD7PVXUFCASZMmwdfXFyEhIVCr1SgpKXG7/poTNr4Nbkuf7qCl\n89fczcPPm73z92w9l6WlpbLX25IRI0agT58+Fssc6cfVX5u2+gPke+95VPi0RK/XIzY2FomJifjt\nt98AAJWVldLRcsCDo+kqKyuldcHBwQAAHx8f9OrVC3V1dfIX3gpVVVUWfahUKlRWVlotd6f+1qxZ\nA41GgxkzZkhTLbWlT3fQ/LkA/r8vd6NQKDBq1CjEx8dL5+LV1tZCqVQCeHBEa21tLQD7z6Wrc7Qf\nd3xtyvXek/VQ6/Zg71yhFStW4NVXX7V5n/79+8NoNKJPnz44ceIEUlNTcfr06Y4utU3a0p87aumc\nrzlz5mDZsmUAgA8//BALFy7E+vXr5S5RNp5y8vPhw4cRGBiIy5cvQ6fTISIiwmK9vfP3mq93J4/q\nxx3J+d5zu/Bp6Vwhe/z8/ODn5wcAGDp0KEJDQ1FeXo6goCBcunRJGnfp0iUpxYOCgnDx4kX0798f\njY2NuH79Ovz9/duniRa0pb+Hz39q6sMV+2vS2j5nzpwpha4jfQYFBbVvwR2opfPX3ElgYCCAB1Nb\nvfbaaygtLbV7/p6t59IdnjNH+nHH12bz8ys7+r3nsV+7Nf/e8sqVKzCbzQCACxcuoLy8HAMHDkRg\nYCB69uyJkpISCCGQn5+PlJQUAJbnHW3fvh1JSUnyN9GC5v0lJydj8+bNMJlM0Ov1KC8vR0JCAgIC\nAtyyv+rqaunn77//HtHR0QAc69PWeWKuqqXz19zFf//9h5s3bwIAbt26hX379iE6Otru+Xv2nktX\n52g/7vbalPW91+ZDJVzQd999J1QqlejcubNQKpXipZdeEkIIsX37djFkyBCh1WrF0KFDxY8//ijd\np+kwwdDQUDF//nxp+Z07d8SECROkQ5H1er3c7Vix158QQmRlZYnQ0FAxaNAgUVhYKC13p/6aTJ06\nVURHR4uYmBiRkpIiampqpHWO9ukudu/eLcLDw0VoaKhYsWKFs8tx2IULF4RGoxEajUYMGTJE6uHq\n1asiKSnJ5qHJ9p5LV5Geni4CAwOFr6+vUKlUYsOGDW3qx1Vfmw/3t379elnfey5zkikRET05PPZr\nNyIicl0MHyIikh3Dh4iIZMfwISIi2TF86Ink7e2N2NhY6d/FixedXVKLqqqqMGHCBIfuc/fuXYwc\nORJCCBgMBumw2SaZmZnIzc21e//Vq1cjPz+/TfUSPYrbnWRK1B66du2KP//80+a6pgNAXens9f79\n+2Pbtm0O3efbb7/FK6+8YrePR/U3bdo0JCUlYerUqQ49LlFr8JMPEQCDwYBBgwYhIyMD0dHRMBqN\nWLVqFRISEqDRaJCZmSmN/frrr6HRaKDVaqVJJt98803s2LFDGtO9e3fpZ1vbMRgMiIyMxOzZsxEV\nFYUxY8bgzp07AICKigqMGjUKWq0WcXFx0Ov1Fp9cDAYDXnjhBcTFxSEuLg5Hjhyx2dOmTZukk4pt\naQrZ6upqi0+BPj4+MBqN6NGjB/r27euyU1GRe+MnH3oi3b59G7GxsQCAgQMH4tNPP0VFRQXy8/OR\nkJCAffv2oaKiAqWlpbh//z5SUlLw66+/wt/fH1lZWThy5Aj8/f2liRcf/hTRdNvedoKDg1FRUYEt\nW7bgiy++wMSJE7Fjxw5MmTIFU6ZMwfvvv4+UlBSYTCaYzWZpAkvgwRQvRUVF6NSpE8rLyzF58mQc\nO3bM4vHNZjNOnTplMQv6+fPnpZ4BoKamBosWLUJgYKD0KXDdunVSfQCQkJCAQ4cOYciQIe31X08E\ngOFDT6guXbpYfO1mMBgwYMAAaYqXffv2Yd++fdIv61u3bqGiogK3bt1CWlqaNA9e7969W3wce9sJ\nDg7GM888g5iYGABAXFwcDAYDGhoaUFVVJX1iaZqTsDmTyYR58+bh5MmT8Pb2RllZmdWYK1euoEeP\nHhbLQkNDLXpevny5xTRNhw8fxldffYXDhw9Ly/r3748LFy602CNRWzB8iP5Pt27dLG4vXboUs2fP\ntli2du1am9c78fHxwf379wEA9+/fh8lkanE7BoMBnTp1km57e3tLX7s9ymeffYbAwEDk5+fDbDaj\nc+fONsc5MnlJdXU1Zs6ciR9++AFdu3a12IYr7fsiz8F9PkQ2jBkzBhs2bMCtW7cAPLjmzuXLl/Hi\niy9i27Zt0rWP6uvrAQAhISE4fvw4gAcXHLt3716L27FFCIHu3btDpVJJF5O7e/cubt++bTHuxo0b\nCAgIAPBg/1PTpLnNPfXUU2hoaGhVr42NjZgwYQJWrlwJtVptsa66uhohISGt2g6RIxg+9ESy9dd8\n82U6nQ6TJ0/Gs88+i5iYGKSlpaGhoQGDBw/GBx98gJEjR0Kr1WLhwoUAgFmzZuHgwYPQarU4evSo\ndMCBve3YqqHpdn5+PlavXg2NRoPnnntO2t/TtH7u3LnIy8uDVqvFuXPnLA5uaOLt7Y2oqCicO3fu\nkT3//vvvOH78OJYtWyYddNB0raXS0lKMGDGilf+rRK3HiUWJPNTGjRtRW1uLxYsXt+n+N27cQFJS\nktXBDETtgeFD5KFMJhNGjRqFgwcPtmm/zerVq+Hv74/XX3+9A6qjJx3Dh4iIZMd9PkREJDuGDxER\nyY7hQ0REsmP4EBGR7Bg+REQkO4YPERHJ7n+i/Ax9ziIEZwAAAABJRU5ErkJggg==\n"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t3 = np.linspace(0, 0.012 + 9 * dt2, 10 * n2) # Intervalo de tiempo en segundos\n",
"y3 = np.append(y2, np.zeros(9 * n2)) # Señal\n",
"\n",
"Y3 = fft(y3) / (10 * n2) # Transformada normalizada\n",
"frq3 = fftfreq(10 * n2, dt2)\n",
"\n",
"fig = plt.figure(figsize=(6, 8))\n",
"\n",
"ax1 = fig.add_subplot(211)\n",
"ax1.plot(t3, y3)\n",
"ax1.set_xlabel('Tiempo (s)')\n",
"ax1.set_ylabel('$y_3(t)$')\n",
"\n",
"ax2 = fig.add_subplot(212)\n",
"ax2.vlines(frq3, 0, Y3.imag)\n",
"plt.xlabel('Frecuencia (Hz)')\n",
"plt.ylabel('Im($Y_3$)')"
]
},
{
"cell_type": "markdown",
"id": "099edf38",
"metadata": {},
"source": [
"Existe una manera de reducir la fuga y es mediante el uso de **funciones ventana**. Las funciones ventana no son más que funciones que valen cero fuera de un cierto intervalo, y que en procesamiento de señales digitales se utilizan para «suavizar» o filtrar una determinada señal. NumPy trae unas cuantas funciones ventana por defecto; por ejemplo, la ventana de Blackman tiene este aspecto:\n",
"\n",
"http://docs.scipy.org/doc/numpy/reference/routines.window.html"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "92bd237e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x886d5d0>]"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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DTtwS6QYndnWPpa9jnLgl0i1O7OoWS1/HOHFLpFuc2NUtlr4OceKWqH5wYld3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\nxENl7wAAAABJRU5ErkJggg==\n"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(np.arange(20), np.blackman(20))"
]
},
{
"cell_type": "markdown",
"id": "e540c916",
"metadata": {},
"source": [
"Como se puede ver, en los extremos del intervalo es nula. Las funciones ventana reciben un único argumento que es el número de puntos. Si multiplicamos la ventana por la señal, obtenemos una nueva señal que vale cero en los extremos. Comprobemos el resultado, representando ahora el **espectro de amplitud** y comparando cómo es el resultado si aplicamos o no la ventana de Blackman:"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "cbc2cb46",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x8b3f510>"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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yLIj+ohDR77ohgU+/abbKEf2+DhQFEQRB6JEe9XTiq734CXx/28IY2jOH08ae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\n"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n4 = 2 ** 8\n",
"\n",
"t4 = np.linspace(0, 0.05, n4)\n",
"dt4 = t4[1] - t4[0]\n",
"y4 = np.sin(2 * pi * f * t4) - 0.5 * np.sin(2 * pi * 2 * f * t4)\n",
"y5 = y4 * np.blackman(n4)\n",
"\n",
"t4 = np.linspace(0, 0.12 + 4 * dt4, 5 * n4)\n",
"y4 = np.append(y4, np.zeros(4 * n4))\n",
"y5 = np.append(y5, np.zeros(4 * n4))\n",
"\n",
"Y4 = fft(y4) / (5 * n4)\n",
"Y5 = fft(y5) / (5 * n4)\n",
"frq4 = fftfreq(5 * n4, dt4)\n",
"\n",
"fig = plt.figure(figsize=(6, 8))\n",
"\n",
"ax1 = fig.add_subplot(411)\n",
"ax1.plot(t4, y4)\n",
"plt.xlabel('Frecuencia (Hz)')\n",
"plt.ylabel('$y_4(t)$')\n",
"\n",
"ax2 = fig.add_subplot(412)\n",
"ax2.vlines(frq4, 0, abs(Y4)) # Espectro de amplitud\n",
"plt.xlabel('Frecuencia (Hz)')\n",
"plt.ylabel('Abs($Y_4$)')\n",
"\n",
"ax3 = fig.add_subplot(413)\n",
"ax3.plot(t4, y5)\n",
"plt.xlabel('Frecuencia (Hz)')\n",
"plt.ylabel('$y_5(t)$')\n",
"\n",
"ax4 = fig.add_subplot(414)\n",
"ax4.vlines(frq4, 0, abs(Y5)) # Espectro de amplitud\n",
"plt.xlabel('Frecuencia (Hz)')\n",
"plt.ylabel('Abs($Y_5$)')"
]
},
{
"cell_type": "markdown",
"id": "cccd1c5a",
"metadata": {},
"source": [
"Esto ya ha sido más interesante, ¿no? :)"
]
},
{
"cell_type": "markdown",
"id": "82e4b768",
"metadata": {},
"source": [
"## Otros ejemplos"
]
},
{
"cell_type": "markdown",
"id": "5fcd5013",
"metadata": {},
"source": [
"Para acabar de manera triunfal, vamos a ver **cómo representar el espectrograma de un fragmento de audio**, utilizando la función `specgram` de matplotlib. El espectrograma se obtiene de aplicar la transformada corta de Fourier (STFT) a una señal, que es como aplicar una DFT a pequeños fragmentos de la misma, para ver la evolución de las frecuencias a lo largo del tiempo. Para ello, vamos a usar este fragmento de una melodía tocada con un violín, disponible libremente en Wikimedia Commons y que está muestreado a 44,1 Hz:\n",
"\n",
"http://commons.wikimedia.org/wiki/File:Violin_for_spectrogram.ogg\n",
"\n",
"Al tratarse de un archivo OGG, vamos a utilizar el SciKit audiolab.\n",
"\n",
"http://scikits.appspot.com/audiolab"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "8311375f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x8876c50>"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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2MQjypzHisUJAJq8R5paX/ffnykCuDDAippW44b+vY8+44c/Z9Odk4O3APDQXpmABUr8m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+/Dj33HMPm5ubgzn7W9/61itauL/rXe/iT//0T3nve9870G0EXhHs9HLjVQPK17/+9UE/Q9M0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P0xBDVgH6y/d56l3U3ZGEqBP11nYekxJvHdPRznV4oITYXKPg6jNRGS/T5U67C9Jdb3AOgY\nh9pNjZX7Ri5X8OC6AswdRQT2IURg+dDdl6d0YcB4wYOOR+hl9Eye4njAaN4j1zOkNbHOlXKEZRue\n+jaSKzoHZke8tk5HwnilMoxH0O5IOK9vHHr28DlJqgfvRXjFekxaDkxYDbSqWpXmGJZPbkqxqnJ9\n7UB9HmqKZhvgaNzrTAoKjeYY3oQo+DmLHnszkktQRuYIUQwa7lG4rMFRsqgyTYCnwDuOWMDnoLXu\nFEQUyhx1By76MjRy/3lPnldqYGQEMTXryS0deTciKFV4lmB4J3hjn625Oo3eLvEzRu5tGfpHPQpN\nA23YO1ygdqHP+rE6S2tN/PxYlKKyNfiQixMGYYHIS9h4b5WxH7DYaxKHA9q1PPWNgVTJq+GgIUU1\nCNTgmMo/egFwBoq1BJ6Dua0mP/eO72EueETnx3h/YuBpMAP5/mAkFDrdDuRzAgIILBggX7bPvQi0\nYbwDoyEUlTLJx9X8qIG4aNflZaQGZteuo3P2c+9EDJ9ZiLyEcl/d5atwvM42/FN+tBGBsoFYNt9D\nYuZNxIKZA/MNa4lXEbqMAkLPHUPwHxACxTkmSDBf3Wyl3LA9LCaxeS3U0rDFfuAOmN/dlIV8Acf7\npWGPaWSNhkMyHHQ4jyg+zdH0RUhhJDlMKCExzwM/hcSDnCcCKgXKHrStQomBUhXZeB4ivN8J5KC0\nIXU3IVa6xVAcSJvBXEtOFmzbuewjRJqVgFapzNK9e4JCyiQkFRgJ26VWyYZ5qYsJI/BGNlqXwagH\nwRkIdF5VaSjUGJwnpMp8DEGWioC7A7L7wH8ZvCdtOE6/oywD0yzOGiK7Sd7v3h1ROpWIF7WCWLwN\nxJq94K43eU2n/taiuxawBuN/7RE+Iu5RyVLI+IGEP6OCfT5DG4Iz1gFSDjfPRRdroYTnGCJ5jQok\npZDo1jFp0WfsR7TCCuV8l+h9I7yOPJt2VCUf7Nli/gBSmN9qwgDKZ2S+PDVYRhAODaV6jyzxuDA7\nQ2XQJdg0BGnK3o0lvEsDV2+1iyjYdRwpqBo7GiK198UPwDsH5gfgdwz+342l9uk8IugTCRuHeWsP\nhJDPQ1QWb5IAInX180woWsKeMEBMQm+7uJqsPOINr+BySQUcaGEW2QB1GP3PPowDSqMuha5Fx1yN\n4/WQ10/5oTDT54ANhMH3NHjfFGy9l0J/V9BTJmcX8wwSRrkRESrPgPlvwHSQ/iTncaguDWeMcfxe\nttbA7AeTF0itl0DwrD3vSVwC3586D7hchf6MBN3kWxJGAiQU8y9EOOFb1E0MFY2PD2BJrXON4S8g\nCqlizzEH/PeIQJ6Dcc4j3DRyv7vIhkxwXFR5XPgJGRddoCbth4d3JsKrlAN+lgnVfWwT1cRAGaot\nuX5F8zQduX+j3uOLOIGlkFhwNRUXcYp3iHgYAfhqlR6Sa6dFn2BXkuNEkDU8/G3jQnX7kZzZJpRM\nMoELmzeA96I97xn7o3T9MS4HorBkm9xlF3gDhI8auB84JmGxqrIpDIADEPehuoWDCKdAAxrKeqCW\n/oK9/wpwP5gGfOfON/PzTzxBMcvo35MQ5UZU14Y09+epbw2gCwuv7E3W5ly/Ay0ILFhDwRwTQWs9\nDm8ePAwzxSblUwPJzQVCasoLdo2E9lntIHkJDXcaQeMp4CE5C6N18M/CeBe6LVi+y54D+3qrzG/Y\nB+rWmCtBpGAZSzszmfMOklvbljXiKShBvaUb7fPaAI5D9iaP9nKOXDcj//TIgWx8O8cXIP5Bxsl7\nlzmydQn/KqVPgNdDXj/1h6JnQhHumc2p+F3BvXsRZDHSI0Q78e3H9fuIgIuQ+R5ZxUgcWTejNtRa\nsH+rd2GFoFmBtAbe2CN8ypD+JTSfF9hmaus7gsiGykIwoQ2X2dNkXXkdjKBUEF6w+aPI5vhZriQ8\nrOK4yXa5ouhv0gPDhncmxXVPIIn4cxA2jeQ9WsgmVVZhtfCK9rwVHK2KFg72YSbqyVhmEI9uGYeC\n08QtuJzWdMIXhH5lAzgBOxsS/sl2rdK3FfUZMGoKfBdPQibRGai8DJUUCVmlQAeS6wKCUTah2UkX\nfPyd1HVSXIXsryW8xLrMQWcTwi9CewOCBRifEZiyskFjocteKqg7P5T8l5+HSgFKHQRB9HYkFKeM\nyorO0mLMIaL8FMnVsGPaQyxsRVbdZZ/TZVkXP//UE5IvmYECGdGsgdNQ6w4kXKusCOrVKjw5sr+f\nm1ozmrMoyf/8DhQ6Q4InIH1cnnP1GyOGlyHZgySQORi2JE+V9SW0ZVIJIWaW7qbfF7ulASxEFvwx\nnc9RZ+B6xEPU+e8irACKrlT02pN23A27vmtIvdMZJrx1XLbXWJU11Hl7jsvFeWY2e+Qr247Z+DSi\nzL4l6+7gbZcE/KFs3VfjeI1gw/8cjmtDoewxYdb1SpaKJAO+40JG5Tkk5OMDJTDzNvkcIgJvGYK/\nMw4eq7BOxforUkot7hBJtl8CPwKqBvag/Q14bneCJJ3UQKpOyLgCSDX5SYDyAOab8AsHZDwsIMJ8\nz56kAOl1nvBp1SCbB38Vlz/QqvVbEMv3zxBP6S24vhhrsLMNuR6MQ6vYIglLpSGEXehVwbfMv0Eq\n1dGVwxAct/d9N8KFpclRrJe2iWz6kh1HHxEQSr5YBV6F7kl4YceljjS/rFROSsOG/X9hDw6+Cm/R\n4tJVeRb5pxMRQpZHK3reQnibTPqeXP4rmJ+H8EZofx1OXxZn48LU9RSQpc9HU2Y6rsj+3DAHR9+E\nhKc8+xrae9T5z9sPa/fIgR2PCt1VROmP5BklB0OiE2N41gI3GvZ5nwYuw8HNdZgF76zM3STRr95z\nwz5rZI7HF6GdSJ5NyUf9CKohRA2ITxq4CHvflq/U52F1FTqZTNkIcVD6OL5GtRWMfbQrds4WZ2B+\nEcIaQgbpI57EmElDtvRXwYx8wrVMCjV/QdZtBpgCRKuIh5QhRcFKnXIDUs0PzkvcsxfvQC8uMjPe\npTYeuOLPdXuOPpNePvEaziO/WsfrIa+f8uMIIqzeCWyBuQ68C8gi3UTCLHOINWhb+3rablctpVWk\nIdUmjl5DXdsUt5F9SDrC6DvsQK7ChIackoTLqohcUUNRa8P+MZI0mzptai9bVUt3DhdG0vcSSBZ8\nAlKHClNYsCLBtOBvjCTP+8Dz8t3Ry7DbgRO9KxtIGly6J8K1RFeBugAc/AfY/wATCPak1kOLOjem\n5kvhwypkq8hmzwFNScbWcMI6sactyL+p4WjCNHQfYZ/ReRlg2hXr2V/GQXYTud64A72W1LVc7sBs\nCcItGLds80UfZjOXGlsIRQBHHvSsgpxGUOdt/qM6RnIEx3DJ+gUZ9JljBzh84YJ8aQFXoV2YWkva\nTC2xN5qA/7KBv0DCPRHS7KuMY8u+aNfWJmQvSA4mGUKvK3mrag1aLfHySjGsdWBj7J6h1vMeC2H5\nNjuunq18twuyEApybZy5FFLZflc96aL9fT4PC7fAuARzBTtuNRZ6TAQ+J+R5e5UpUEsZ0gOwWZ/B\nC1ISP2JffxtvBQljnrTraA5aK0WqxZ7M1RKihPeA+2CvWMSPUyqtAdFgLNfXNaALt2Hn+SKiTC5w\n9Y7XFcpP+ZFHlEURxgs+YcdKi3uRRfomxOI5iWzqS8hiuxuRMFWECuQZJkgiuvbcibVezRQyxVZS\npyOhKfGLyCY6BuW3wc1zwEVb1GgRPWQS7qInHsG0GWzszvVDpNvfMcRC1Wr8IhMm23A2E4tuDvxT\nuPDSHg45tiOfT8YQJchmWpJEOZJ7nwhpVWoarVL9pMII+7sZIKGE5+QcXMCBERLwXsJVgLcQIbqI\nKIBZO79zSMHjO+DGsVTCe5aexIsEsjqu2bm0RZVmBOYg+OpNnpNzZD0L61VmYIvMMm1hHxh1xeua\nmYH4FmADqndCaU7mealn4dYlyG1AFkicP7MCyYNJUaofiwcW9BHI9QFcf5WuvC6WtuRLG4gA27LP\nZNH+rXU7GaJcbb1K0EvpfQuKP4drATCLq4TX+pg1CcOZvtz/WNenrXXyDOQiGNuxaz5bcSAzRXve\nS0AZCm8H3grmPCx0IfNhaSzPOWva+zM25OVbxF8AURGC/xan7K6z83ECpziLyJ57E/hb4KcZW79S\noXFLG78LfmPMerCE8Tz257bh/dA6nqP67aF8vwa9OE/13/QENt+G9BdhWAop9scUS0PC8YDcupFa\nHWWBuISEIot2nbYQr24PQXtereMazqFcEy2Azb9EFvB0DYcmxD1kI88irvEOYvH1cfxcv4ws3G8i\nQrOICC6lTVfJaiuRsfh+MwKviFjiiih7AyJod9znJgVYFtI68SKURNEqC4qIaahwSU1aNpFNq8jH\nQ4jAOmk/r+SVCgSw7219FRpvQjbUIfmf2YFsCRFcK4gQ27DnK8n1jBbNae6jAP458O5BBMcD9jtn\nkdCX1p+ct/M9g/SeOWPH/j6kaPSAvaaSSSpMV8EIGVe2HtZq7Vn73RHwkH1uWmiy4saJYdJywOi5\nl8F7By5MedjO+TQ78gUcQmxa2WsOSIs2bbU4dwD/wT7rp3He2BLiAbdxrW/fYM+vEHIQAfgD+50A\nmv8O6nfigCK2Tol5ZB0u4opKh3IukwJHbO7H9srxjkL2kkWTdcFTxJUHQcvOFfb+loH/CVkbmo9T\nEMEqsn4Vmu0zSc5TRuD4dcTouUHOP2yE5P54LOfuAB/G1ej4YEoeHgbKkO3z6FUCenGBhVNtyCCZ\n84g2zIRZYbzfI+wZ16iribQ/1mLLuj3/JTu+NftTtPP+PfuZhp27l8G7xNVpAcyPe47XWwD/szzM\nBdj4moQrFP3o4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K//+q/zla985XWF8hMfMzDXFTqtfB6its11IO76OIU4D7N1YRzOGaHQ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\nTkSuQmCC\n"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"import scikits.audiolab as audiolab\n",
"\n",
"sound = audiolab.sndfile('Violin_for_spectrogram.ogg', 'read')\n",
"y = sound.read_frames(sound.get_nframes())\n",
"\n",
"Pxx, freqs, bins, im = plt.specgram(y, NFFT=512, Fs=44100)\n",
"plt.xlim(0, len(y) / 44100.0)\n",
"plt.ylim(0, 22050.0)\n",
"plt.colorbar(im).set_label(u'Intensidad (dB)')\n",
"plt.xlabel(u'Tiempo (s)')\n",
"plt.ylabel(u'Frecuencia (Hz)')"
]
},
{
"cell_type": "markdown",
"id": "c64f1f32",
"metadata": {},
"source": [
"Se puede apreciar cómo va cambiando la frecuencia fundamental (barras horizontales inferiores) y los armónicos (todas las que están encima, cada vez más débiles) a medida que el intérprete toca una nota distinta. En definitiva, una preciosidad :P"
]
},
{
"cell_type": "markdown",
"id": "d70e2f7a",
"metadata": {},
"source": [
"Espero que te haya gustado el artículo. Más abajo tienes las referencias en las que me he basado y unos cuantos enlaces que me han sido muy útiles para aprender procesamiento de señales digitales, porque cuando empecé a escribir el artículo no sabía nada sobre el tema. Sobre todo he aprendido la teoría con [II] y los ejemplos están inspirados en el capítulo «Example Applications of the DFT» de [I]. Si ves algún error o quieres apuntar alguna sugerencia, no dudes en decirlo en los comentarios.\n",
"\n",
"¡Un saludo desde Milano! :)"
]
},
{
"cell_type": "markdown",
"id": "379cd3a5",
"metadata": {},
"source": [
"## Referencias"
]
},
{
"cell_type": "markdown",
"id": "bdefe178",
"metadata": {},
"source": [
"1. SMITH, Julius O. *Mathematics of the discrete Fourier transform (DFT) with audio applications* [en línea]. Segunda edición. Disponible en Web: <https://ccrma.stanford.edu/~jos/mdft/mdft.html>. [Consulta: 28 de septiembre de 2012]\n",
"2. LOPEZ-LEZCANO, Fernando; CACERES, Juan-Pablo. *Introducción al Procesamiento Digital de Señales y a la Música por Computador* [en línea]. Disponible en Web: <https://ccrma.stanford.edu/workshops/cm2007/index.shtml>. [Consulta: 28 de septiembre de 2012]"
]
},
{
"cell_type": "markdown",
"id": "83d6fdf9",
"metadata": {},
"source": [
"## Enlaces"
]
},
{
"cell_type": "markdown",
"id": "b08eb94f",
"metadata": {},
"source": [
"* Documentación http://docs.scipy.org/doc/numpy/reference/routines.fft.html\n",
"* Análisis espectral de una sinusoide https://ccrma.stanford.edu/~jos/mdft/Spectrum_Analysis_Sinusoid_Windowing.html\n",
"* Teoría general http://paulbourke.net/miscellaneous/dft/\n",
"* NumPy no es adecuado para *series de Fourier* http://stackoverflow.com/questions/4258106/how-to-calculate-a-fourier-series-in-numpy\n",
"* Reconstrucción de la señal a partir de algunos términos calculados con fft http://stackoverflow.com/questions/5843085/fourier-series-in-numpy-question-about-previous-answer\n",
"* Uso de fftfreq http://stackoverflow.com/questions/9456037/scipy-numpy-fft-frequency-analysis\n",
"* Unidades de fftfreq http://stackoverflow.com/questions/8573702/units-of-frequency-when-using-fft-in-numpy\n",
"* Frecuencias de fftfreq http://stackoverflow.com/questions/3694918/how-to-extract-frequency-associated-with-fft-values-in-python\n",
"* Artículo de The Glowing Python http://glowingpython.blogspot.com.es/2011/08/how-to-plot-frequency-spectrum-with.html\n",
"* Demo de MathWorks http://www.mathworks.es/products/matlab/examples.html?file=/products/demos/shipping/matlab/fftdemo.html\n",
"* Documentación de MATLAB http://www.mathworks.es/help/matlab/ref/fft.html\n",
"* Diferencias entre NumPy y SciPy http://stackoverflow.com/questions/6363154/what-is-the-difference-between-numpy-fft-and-scipy-fftpack\n",
"* Zero-padding of a signal http://dsp.stackexchange.com/questions/741/why-should-i-zero-pad-a-signal-before-taking-the-fourier-transform\n",
"* Uso de funciones ventana https://docs.google.com/open?id=1FliaqX0ModFkrPEvCtconY4vNlzU0r3luLkSl9Zk3WB48YyyAd12oD-Pw9IQ\n",
"* Para ampliar: DSP con SciPy http://docs.scipy.org/doc/scipy/reference/signal.html\n",
"* Python para procesamiento de audio http://lac.linuxaudio.org/2011/papers/40.pdf\n",
"* Definición de intervalos de frecuencia http://www.maximintegrated.com/glossary/definitions.mvp/term/frequency_bin/gpk/136"
]
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