{ "cells": [ { "cell_type": "markdown", "metadata": { "nbsphinx": "hidden" }, "source": [ "# Design of Digital Filters\n", "\n", "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Design of Non-Recursive Filters using the Frequency Sampling Method\n", "\n", "For some applications, the desired frequency response is not given at all frequencies but rather at a number of discrete frequencies. For this case, the frequency sampling method provides a solution for the design of non-recursive filters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Frequency Sampling Method\n", "\n", "Let's assume that the desired transfer function $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ is specified at a set of $N$ equally spaced frequencies $\\Omega_\\mu = \\frac{2 \\pi}{N} \\mu$\n", "\n", "\\begin{equation}\n", "H_\\text{d}[\\mu] = H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\frac{2 \\pi}{N} \\mu})\n", "\\end{equation}\n", "\n", "for $\\mu = 0, 1, \\dots, N-1$. The coefficients of a non-recursive filter with finite impulse response (FIR) can then be computed by inverse discrete Fourier transformation (DFT) of $H_\\text{d}[\\mu]$\n", "\n", "\\begin{equation}\n", "h[k] = \\text{DFT}_N^{-1} \\{ H_\\text{d}[\\mu] \\} = \\frac{1}{N} \\sum_{\\mu = 0}^{N-1} H_\\text{d}[\\mu] \\; \\mathrm{e}^{\\,\\mathrm{j}\\,\\frac{2 \\pi}{N} \\mu\\,k}\n", "\\end{equation}\n", "\n", "for $k = 0,1, \\dots, N-1$. \n", "\n", "In order to investigate the properties of the designed filter, its transfer function $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ is computed. It is given by discrete-time Fourier transformation (DTFT) of its impulse response $h[k]$\n", "\n", "\\begin{equation}\n", "H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\sum_{k = 0}^{N-1} h[k] \\; \\mathrm{e}^{\\,-\\mathrm{j}\\,\\Omega\\,k} = \n", "\\sum_{\\mu = 0}^{N-1} H_\\text{d}[\\mu] \\cdot \\frac{1}{N} \\sum_{k = 0}^{N-1} \\mathrm{e}^{\\,-\\mathrm{j}\\,k\\,(\\Omega - \\frac{2 \\pi}{N}\\,\\mu)}\n", "\\end{equation}\n", "\n", "When comparing this result with the [interpolation of a DFT](../spectral_analysis_deterministic_signals/zero_padding.ipynb#Interpolation-of-the-Discrete-Fourier-Transformation), it can be concluded that $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ is yielded by interpolation of the desired transfer function $H_\\text{d}[\\mu]$\n", "\n", "\\begin{equation}\n", "H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\sum_{\\mu=0}^{N-1} H_\\text{d}[\\mu] \\cdot \\mathrm{e}^{-\\,\\mathrm{j}\\, \\frac{( \\Omega - \\frac{2 \\pi}{N} \\mu ) (N-1)}{2}} \\cdot \\text{psinc}_N ( \\Omega - \\frac{2 \\pi}{N} \\mu)\n", "\\end{equation}\n", "\n", "where $\\text{psinc}_N(\\cdot)$ denotes the $N$-th order periodic sinc function.\n", "\n", "Both the transfer function of the filter $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ and the desired transfer function $H_\\text{d}[\\mu]$ are equal at the specified frequencies $\\Omega_\\mu = \\frac{2 \\pi}{N} \\mu$. Values in between adjacent $\\Omega_\\mu$ are interpolated by the periodic sinc function. This is illustrated in the following." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example: Approximation of an ideal low-pass\n", "\n", "The design of an ideal low-pass filter using the frequency sampling method is considered. For $|\\Omega| < \\pi$ the transfer function of the ideal low-pass is given as\n", "\n", "\\begin{equation}\n", "H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\begin{cases}\n", "1 & \\text{for } |\\Omega| \\leq \\Omega_\\text{c} \\\\\n", "0 & \\text{otherwise}\n", "\\end{cases}\n", "\\end{equation}\n", "\n", "where $\\Omega_\\text{c}$ denotes its corner frequency. The desired transfer function $H_\\text{d}[\\mu]$ for the frequency sampling method is derived by sampling $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$. Note that for sampling on the unit circle with $0 \\leq \\Omega < 2 \\pi$, the periodicity $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}(\\Omega + n 2 \\pi)})$ for $n \\in \\mathbb{Z}$ has to be considered." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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sf24fK5cvqSmi3rVu0xBvvu4uTrr6i7z5urtYt2mo7pB6ksehftZLmoyTBDTrjQ64vfKO+9mz/wADhzFbytlW0+eg6DJ4HNpnOvVCO+olzW4maOoJK5YOcOvdjwFw22XntPReG7T2mGhQtOXYPR6H9mhHvTCdekmzn12c0iScbdUeDooug8ehPawX1GkmaNIkbNDaw0HRZfA4tIf1gjrNBE2ahA1ae7RjULSD2xumUw4OTm8P6wV1mgmaNAkbtPZYsXSAj73r9czra1Q7A/P7+di7Xj/l8TqjY36GhkdIDo756bUkbbrlMN3joAbrBXWakwSkSTjb6qDpzmadzqBoB7c3tKMc2jE4vddnNlsvqNNM0FS8EhoCZ1vVP5vVMT8NJZRD3edCKUqoF0qoH9UZdnGqaHZrlaPuWWuO+WkooRzqPhfUYP04u5mgqWg2BOWo+8qNY34aSiiHus8FNVg/zm5dTdAi4ryI2BoR2yLi6jFePyIibqte/1ZELO5mfCqPDUE56r5y4+D2hhLKoe5zQQ3Wj7Nb1xK0iOgDbgDOB04DLoqI0w5Z7TeAZzPzFOB64I+7FZ/KZENQjhKu3KxYOsDSE+dz9knH8LWrz+255GxU3eVQwrkg68fZrptX0M4CtmXmw5m5B1gDXHDIOhcAn60e3wH8fEREF2NUYWwIylHClRuVwXOhDNaPs1tkZnd2FPFu4LzM/M3q+a8BZ2fm5U3rPFCt83j1/LvVOk+Nt91ly5blxo0bOxb3TRf9J165azunverow97GQ088B3DY25ju+x95+gUAFh975GG9vx3bmM77n3p+N9/d9QKZyRFz+jjhmH4WHHVEy9up+zhAveXYjvdD/eXocWgooRzrrptKqNvqPg7tqB89Dge38f2FJ/D+W//8sLcxFRFxT2Yum2y9GXmbjYi4FLgU4MQTT+zovo458ghe9i99k684gZfNq+/9Tz2/myef201m8uwLew87ufnhnv2Tr9Sh9y846gie370PmF4FUOdxGFVnObbj/VB/OXocGkoox+luo4RynO426j4O7agf6z4O7Win2nU+H3Nk6+1jp3TzCto5wIczc3n1fBVAZn6saZ3Bap1vRMQc4PvAwpwgyE5fQZvJDr1XETQufx9OV8Qvf+obwOHf62e6758N1m0amvZNLT0O7VF3OXocGuoux3Z8J2eDOo9DO9upmWKqV9C6OQZtA3BqRJwUEfOAC4H1h6yzHrikevxu4K6JkjNNzCnY5RithPbsPwB4v6I6rds0xKbHhvnW956p5fc8696/GvxOlsF2anxdS9Aycx9wOTAIbAFuz8wHI+LaiHhntdqngWMjYhtwBfCvbsWhqXMKdjmshMpQd6Nc9/51kN/JMthOja+r90HLzDsz8zWZeXJmfrRadk1mrq8e/ygz35OZp2TmWZn5cDfjm22cgl0OK6Ey1N0o171/HeR3sgy2U+PzlwRmMadgl6OESsiutfob5br3X5K6z8cSvpOynZqICdosNnqvooH5/QTeq6hOdVdCdq011N0o173/UpRwPtb9nVSD7dT4ZuRtNjR1K5YOeKIXYPQYrB7cyo7hERZ1ecbYRF1rvXR+rFy+ZMwZY91qlOvefylKOB/r/k7qINupsZmgSV1SZyVk11pDOxrl0a65PfsP8Obr7mrp/SYFDaWcjyYGKpkJmtQDFs3vZ2iMxq/XutZgeo3yeF1zo9vt9P5nC89HaXKOQZNmiOkMqna8TXs4C7M92nE+1j3JQOo0r6BJM8B0r9zYtdYepXTNzXTTPR/bcSVTKp0JmjQDtGNQtV1r02fXXPtM53wsYZKB1Gl2cUozgFduymBXcRn8PqgXmKBJM4D3zyqD92wqg98H9QITNHWcg3mnzys35VixdICvXX0u37vuHXzt6nNNzmrg96F9rJ/L5Rg0dZSDedvDQf7SQX4f2sP6uWwmaOooB/O2j4P8pYP8Pkyf9XPZ7OJURzmYV5LKZP1cNhM0dZSDeSWpTNbPZTNBU0c5mFeSymT9XDbHoKmjHMwrSWWyfi6bCZo6zsG8klQm6+dy2cWpSXmfHEnSWGwfOscETRMa7z45fgklqbfZPnSWCZomNNF9ciRJvcv2obNM0DQh75MjSRqL7UNnmaBpQt4nR5I0FtuHzjJB04S8T44kaSy2D53lbTY0Ie+TI0kai+1DZ0Vm1h3DtCxbtiw3btxYdxiSJEmTioh7MnPZZOvZxSlJklQYEzRJkqTCmKBJkiQVZsaPQYuIXcCjHd7NAuCpDu+jF1iO7WE5tofl2B6W4/RZhu0xU8rx1Zm5cLKVZnyC1g0RsXEqA/o0McuxPSzH9rAc28NynD7LsD1mWznaxSlJklQYEzRJkqTCmKBNzY11BzBLWI7tYTm2h+XYHpbj9FmG7TGrytExaJIkSYXxCpokSVJhTNAmERHnRcTWiNgWEVfXHc9MFRGPRMTmiLgvIvxtrimKiM9ExM6IeKBp2TER8eWI+E7170/WGWPpxinDD0fEUHU+3hcRb68zxpkgIk6IiK9ExEMR8WBEfLBa7vnYggnK0XOyBRHx4xFxd0T8c1WOf1AtPykivlW12bdFxLy6Yz1cdnFOICL6gG8DvwA8DmwALsrMh2oNbAaKiEeAZZk5E+5RU4yIeCvwPPC5zPypatnHgWcy87rqPw0/mZlX1RlnycYpww8Dz2fmn9QZ20wSEa8CXpWZ90bETwD3ACuA9+H5OGUTlON78ZycsogI4MjMfD4i5gJfBT4IXAGszcw1EfFJ4J8z8y/rjPVweQVtYmcB2zLz4czcA6wBLqg5JvWQzPxH4JlDFl8AfLZ6/FkalbvGMU4ZqkWZ+URm3ls9/gGwBRjA87ElE5SjWpANz1dP51Z/CZwL3FEtn9HnownaxAaA7U3PH8cv0uFK4EsRcU9EXFp3MDPccZn5RPX4+8BxdQYzg10eEfdXXaB2y7UgIhYDS4Fv4fl42A4pR/CcbElE9EXEfcBO4MvAd4HhzNxXrTKj22wTNHXLWzLzp4HzgQ9U3U6apmyMUXCcQuv+EjgZOBN4AvjTesOZOSLiKOBvgQ9l5nPNr3k+Tt0Y5eg52aLM3J+ZZwLH0+jxem3NIbWVCdrEhoATmp4fXy1TizJzqPp3J/B3NL5MOjxPVuNYRsez7Kw5nhknM5+sKvcDwF/h+Tgl1VifvwX+OjPXVos9H1s0Vjl6Th6+zBwGvgKcA8yPiDnVSzO6zTZBm9gG4NRqVsg84EJgfc0xzTgRcWQ1GJaIOBL4ReCBid+lCawHLqkeXwL8jxpjmZFGE4rKv8fzcVLVoOxPA1sy8xNNL3k+tmC8cvScbE1ELIyI+dXjfhqT+bbQSNTeXa02o89HZ3FOoprq/F+BPuAzmfnRmkOacSLi39C4agYwB7jFcpyaiLgV+DlgAfAk8PvAOuB24ETgUeC9mekg+HGMU4Y/R6MrKYFHgMuaxlFpDBHxFuCfgM3AgWrx79AYP+X5OEUTlONFeE5OWUS8gcYkgD4aF5tuz8xrq/ZmDXAMsAm4ODN31xfp4TNBkyRJKoxdnJIkSYUxQZMkSSqMCZokSVJhTNAkSZIKY4ImSZJUGBM0SZKkwpigSZIkFcYETZKaRMTPR8Tn645DUm8zQZOklzqDxh3IJak2JmiS9FJnAJsi4oiIuDki/qj6/URJ6po5k68iST3lDcBOYBD475n5hZrjkdSD/C1OSapExFzgKRo/+n1ZZn6j5pAk9Si7OCXpoNcBG4B9wP6aY5HUw0zQJOmgM4CvAxcCN0XEcTXHI6lHmaBJ0kFnAA9k5reBq4Dbq25PSeoqx6BJkiQVxitokiRJhTFBkyRJKowJmiRJUmFM0CRJkgpjgiZJklQYEzRJkqTCmKBJkiQVxgRNkiSpMP8flAKhgrmFqmQAAAAASUVORK5CYII=\n", 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lCEJxs3bt2uI24RLJyclo3br1pf/Pnz+PjIwMNG7cGB9//DGGDBmC0NBQv8fYuHEj2rZti4yMDLR05WWUKVMGVapUQZkyZdCrVy/MnTvX0dcB6Gu38CWAdQBiiegAEd1HROOIaJzj1glCKeC337h/Vbt2+rbv3JlDgW43ToIgCIZ49dVX0bhxY3Tp0gU7d+689PysWbPQvn17JCQkYOzYscjLy8O5c+dw8803o2XLloiLi7skLipWrHhpv5dffhmxsbHo0qULhg8fjilTpiAjIwNNmzbFAw88gObNm6N3797Izs72O5Y/2/yRlJRUSFglJyejcePGCA0NxezZszFw4MBL6/bu3YuBAweibdu2aN++/aUxNGHVq1cvfPXVVwCA48ePQymFkJAQDBo0CLNnzzZ6qg2jpypwuFKqtlIqTClVVyn1kVJqhlJqhpdtRyul5jtjqiCUTLZuBWJjgQoV9G3foQNw7hyg8/dGEAShEJs3b8acOXOQmJiIJUuWYOPGjQCAtLQ0zJ07F2vWrEFiYuIlUbJ06VLUqVMH27ZtQ0pKCvr2LdxBaePGjfj666+xbds2/PDDD9i0adOldbt27cLDDz+M1NRUREZG4uuvv/Y7li/bApGamoohQ4YgOjoa0dHR6NevH1q0aIGLFy9iz549iI6OBsCd7++//37861//wqZNmzBp0iRMnjwZAAuumJgYZGZm4qWXXsLKlSvRq1cvnDx5EqdPn0ZcXJxue6wg/Z8FwSJbtugLA2poN2VbtwLNmztjkyAIzvPoo0Bior3HTEgApk71v82qVaswePBglC9fHgAwYMAAAMCKFSuwefNmtHO5z7Ozs1GzZk3ceeedmDBhAp566inccsst6Orxg7VmzRoMHDgQ4eHhCA8PR//+/S+ti4mJQUJCAgCgTZs2l3KSfI114sQJr7b5IzMzEzVq1MCOHTsuPTd+/HjExMTg+PHjiIyMvPT8woULkZqailtvvRUAkJubi65du2LatGm49tprAQAPP/wwHn74YQDAtm3bCo1VtmxZnDlzBpUqVQpol1lEWAmCBY4fBzIzgVat9O8TGwtERLAgGzHCOdsEQbiyUEph1KhReP3114us27JlC5YsWYLnn38evXr1wsSJE3Uds1y5cpf+Dg0NvRQK9DXW1ECq0AvJyclo7nGXuX37dgwcOBARERGFuqBv27YNr776Ku677z7D4wDAhQsXEB4ebmpfvdhRFSgIVyxbt/LSiLAqU4YT2LdsccYmQRCCw9SpwM8/2/vQo0u6deuGhQsXIjs7G2fOnMGiRYsAAL169cL8+fNx9Cj36j5x4gT27duHQ4cOoXz58hgxYgSefPJJbPH48encuTMWLVqE8+fP4+zZs1i8eHFAG3yN5cs2fyQlJaFZs2aFnktNTUV8fDyqVq2KvLy8S+Kqdu3aWLZsGfLzucNTcnIylFIBxwCArKwsVK9e3fTkynoRj5UgWMCMsAI4HDh7Nve0CpHbG0EQDNC6dWsMGzYMLVu2RM2aNS+F45o1a4ZXXnkFvXv3Rn5+PsLCwjBt2jScPn0aTz75JEJCQhAWFobp0wv3827Xrh0GDBiAFi1a4Oqrr0Z8fDyqVKni1wZfY3Xs2NGrbf5ITk7GLbfccun/EydOQCmFWrVqAQB69+6N1atX44YbbsC9996LlStXomnTpoiIiEBcXBxmzZql67ytXLkSN/ubd8wulFLF8mjTpo0ShNLOsGFKNWhgfL8PPlAKUCo93XaTBEFwkO3btxe3CY5w5swZpZRS586dU23atFGbN292dLzu3burvXv36tp28+bNasSIEZbHHDx4sNq5c6cuG7y9zwA2KR36RjxWgmCB5GQO6xnFlQuKbduAhg3ttUkQBMEoY8aMwfbt23H+/HmMGjWqUOuD4qZ169a4/vrrkZeXF7CXlS8uXryIQYMGoXHjxjZbVxQRVoJgkpwcYNcuQEfRSxGaNuVlaiowZIi9dgmCIBjliy++COp4o0ePLlTtF4h7773X0nhly5bF3XffbckGvYiwEgST7N7N4koTSUaoUAGIjga2b7fdLEEQhBLP6NGji9sEx2yQtFlBMElaGi89ill007w5e6wEQRCEywcRVoJgEs3b1KSJuf2bNePu6zK1jSAIwuWDCCtBMElaGlC/PuA23ZYhmjcHLl7kkKIgCIJweSDCShBMsn27ufwqDS2EKHlWgiAIlw8BhRURfUxER4koxcf6u4goiYiSiWgtEbW030xBKFnk5wM7dpjPrwIKVwYKgiAIlwd6PFYzAfT1s34vgO5KqXgALwN43wa7BKFEs28fkJ1tzWNVsSLQoIEIK0EQhMuJgO0WlFK/ElG0n/Vr3f5dD6CudbMEoWSzcycvzSaua8TGAr//bt0eQRAEoWRgdx+r+wD84GslEY0BMAYA6tevb/PQghA80tN52aiRteM0agSsWwcoBRBZt0sQhJLFwq0H8eaynTh0Kht1IiPwZJ9YDGoVVdxmCQ5iW/I6EV0PFlZP+dpGKfW+UqqtUqptjRo17BpaEIJOejo3+bz6amvHadQIOHMGcE0QLwjCZcTCrQfxzIJkHDyVDQXg4KlsPLMgGQu3HrR1nEmTJmHKlCmG9+vUqZNj4/bo0QMZGRkAgPfeew8PPvhgofVxcXFI05oBupGRkYGIiAgkaPN++SE7OxsJCQkoW7Ysjh8/XmTc4sIWYUVELQB8CGCgUirLjmMKQiCOHQOWLwdOnQr+2Lt38xx/Vr1M2rRVu3ZZt0kQhJLFm8t2IjsnDyfC3seJME4/zs7Jw5vLdhazZczatWuLPKeUQn5+vq3jJCcnF5p78Pz588jIyPA5b1/Dhg2RmJgY8LgRERFITExEnTp1bLPVDiwLKyKqD2ABgJFKKckWEYLC8uUsbG68Ebj2WuC334I7fno6j2sVLZQowkoQLj8OncoGAFykPbhIe4o8b4VXX30VjRs3RpcuXbBzZ4FQmzVrFtq3b4+EhASMHTsWeXl5OHfuHG6++Wa0bNkScXFxmDt3LgCgoqsJX0ZGBmJjY3H33XcjLi4OmZmZXo/jb1x/JCUlFRJWycnJaNy4se4JlXv06IEdO3YAALKyshAXF6drv+IiYI4VEX0JoAeA6kR0AMA/AIQBgFJqBoCJAKoBeJf49j1XKdXWKYMF4eBB4LbbuKLu5ZeBxx8HBg3i9geVKzs/fl4esGcP0L+/9WNFRwNlyoiwEoTLkTqRETjoRUTViYywdNzNmzdjzpw5SExMRG5uLlq3bo02bdogLS0Nc+fOxZo1axAWFoaHHnoIs2fPRoUKFVCnTh18//33AIDTp08XOeauXbvw6aefomPHjj6P07x5c6/jBiI1NRVDhgyBSyPg7NmzuOWWW3S/3vT09EveraSkJMTHx+vetzjQUxU4PMD6+wHcb5tFghCAiROBv/4CvvmGvUZ16wLt2wOvvQZMnuz8+AcPcsd0OzxWZcoAMTEirAThcuTJPrF4ZkFyoeciwkLxZJ9YS8ddtWoVBg8ejPLlywMABgwYAABYsWIFNm/ejHbt2gHgHKSaNWvizjvvxIQJE/DUU0/hlltuQdeuXYscs0GDBujYsaPf45w4ccLruP7IzMxEjRo1LnmcAGD8+PGIiYkpsu2yZcvwm0f4Yd++fYiKikJICAfYkpKS0KJFi4DjFid2VwUKgqMcOgR8+inw8MMFwqZtW+D224EZM4DnngMqVXLWBq0i0A5hBXA4UISVIFx+aNV/oxaF4kJuHqIcrgpUSmHUqFF4/fXXi6zbsmULlixZgueffx69evXCxIkTC62vUKFCwONMnTrVsE3Jyclo3rx5oee2b9+OgQMHAgAuXryIxx9/HJUrV8aGDRswbdq0S6FKANi2bVshIbV582YMGzbMsB3BRISVUKr45BMOxT3ySOHnH38cmDcPmDMHeOABZ23Q5vZr2NCe4zVqBPzyi7RcEITSxpHXXsOFtB1+t2kF4LMj+QAICbVmAqnAPj/bl2vaBLWefdbvMbt164bRo0fjmWeeQW5uLhYtWoSxY8eiV69eGDhwIB577LFLHqYzZ84gLCwMV111FUaMGIHIyEh8+OGHfo/v6zi+xvVHUlISmnlMUZGamnopnDd9+nSMGjUK7dq1Q5cuXVCuXLlC2yYmJuL8+fMAOFz57bff4pVXXvE7ZnEjwkooNSgFfPQR0LNnUW9R+/ZcYffll84Lq/R0oGxZDkHaQaNGwLlzwOHDQAkrbhEEwQYqljU5U7sPWrdujWHDhqFly5aoWbPmpZBds2bN8Morr6B3797Iz89HWFgYpk2bhtOnT+PJJ59ESEgIwsLCMH36dL/H93Wcjh07eh3XH8nJyYXyqU6cOAGlFGrVqgUA2Lp1K8aOHYszZ86gevXql/KwNLZt24bw8HC0bNkSLVq0QLNmzfDpp5/ihRdeMHragoYIK6HUkJQE7N3L4T5PiIDhw4GXXmKBUru2c3akp3NelM6CloC4VwaKsBKE0kMgz5JGAwfGfu655/Cclx/DYcOGeQ2V9enTp8hzZ8+eBQBER0cjJaXwdMC+juNrXF/Mnj270P9XXXUVjro17uvTpw/GjRuH8uXLe22/kJSUhC1btqCS0zkeNmJbg1BBcJpFi1hA+SomGTKEvVpLlzprx+7d9uVXAQXH0kKMgiAIVwrDhw/HzJkz8e677+Kf//wnQkNDcfr0aSQkJODMmTMgIp+iSmsQmpOTcym5vSQgHiuh1PDddxzy89XtPD6ePVU//gjcc48zNijFAqh7d/uOWa8eEBLC3jhBEITLgdGjRyMyMtLwfvXq1UNmZual/3/3M5mq1iDUjnHtpORIPKFEc/w4sGoV4PIcF8v4Gzf69lYB7M3q3Rv43/8AmxsHX+LUKT4Hdk51GRbG+VoirARBuFwoLoEjwkooFXz3HecUdevGlXAbNwbfhtWreXn99f63690byMoCtm51xo4DB3hZr569x42JAYp5eitBEATBBkRYCX7ZsQMYOhRo2pTbGVSowF6jrCDPCPnrr0B4OPes8ke3brxcs8YZOzQPtRPCSjxWgiAIpR8RVoJfxo8HIiI4cfz227nbeVYWdz8PJr/+CnTsCHi0OClC3bosetatc8YOJ4XVoUOAq12LIAglGKVUcZsgOIjV91eEleCTjRuBFSuAF14oSBhv2RK4917uJ/XHH8Gx488/ObSneaMCcd11gJdJ220hM5PbLNjdzkGb3WGfv86BgiAUO+Hh4cjKyhJxdZmilEJWVhbCw8NNH0OqAksgWVkcdouMBG69lZtRFgdTp/Kkxvd7zAT5xBPAhx8C770XHM/Vhg2cjN6li77tO3Xi83fwIBBl88wRmZnca8quHlYamrDauxeItTaNmCAIDlK3bl0cOHAAx44dK25TBIcIDw9HXQsdoCmQ6iaijwHcAuCoUirOy3oC8DaAmwD8BWC0UmpLoIHL1W6k2v7fe47OmxSIhVsP4s1lO3HoVDbqODyHkxFb8s9G4PhPsfgrLQqdO3Nfpor2Nu4NaMsbP+zEodPZKK8i8PrwouelZ09O5N6509lpWBZuPYjn5+3Emfxs1KkSgaf6BX6PfvsN6NABmD+fhamdtjzx2U7kls1GVFV7Py8HD3IY8913gQcftOWQgiAIgo0Q0WalVIBMX32hwJkA+vpZ3w9AI9djDAD/vfLdOHgqG88sSMbCrQf17mIbC7cexDMLknHwVDZUCbOFKmYjanAyJvznINauBR59NPi2HP4zG0RAdoj38zJiBHcKd7JCULPlrGJbDv+p7z1q0YI9SnZWBmq25JbLBsj+z0vt2uyZlMpAQRCE0k3AUKBS6lciivazyUAAnyl2fa0nokgiqq2UOuzvuDEn9mLmF08DAMrODgXqR3L52UMPAX/9Bdx0U9GdRo/mx/HjwG23FV3/4IPAsGEcrxk5suj6CROA/v2BnTtR/9Zh+CQ3DznEZoap2vhPpzvw6qKyGETHvKuZ117jONPatYC3qQymTgUSEoDlywFvk0S+9x7HeRYtAt5669LT9fefwie5ebhnUG0crBKBu5OaYMTWJShbJhQP1o1E5kfA2USg4tL5QPXqwMyZ/PBkyRKgfHl2e8ybV3T9zz/zcsoUYPHiwut4yYWJAAAgAElEQVQiIoAffsCby3bi/p9nof3+pZfOCwCc/6YqkPIrb/vMM7h71To0BFD9dgAxYHfLrFm8/tFHAY+mbWjcGHj/ff57zBjAs+lbQgKfP4BV24EDl85LDh3Gb3Wr4j9dpyI7Jw+RI4cD1T3uCXr14mQwAOGD+2FduWyUmw7A1aYBt9zCMUwA6NGj6LkJ8NlLrdEe2Q27Azn/wefzN106L5c+u74+e3feya83ACEhQIMGUhkoCIJQ2rEjeT0KQKbb/wdczxWBiMYQ0SYi2gQUhCAv5ubZYIYxtDEVZUNR9qXnj57LDlpStqctObQPF2lPoecb1AfKhAbPk3HoFJ8Lz/OSnVP4PSpTBqhcBTjhYNsF9/coH6d82uKNipXsbWZ68q8cAPweuZ8Xv5/dxETgiy90jyEtFwRBEEo/AXOsAMDlsVrsI8dqMYDJSqnVrv9XAHhKKbXJ3zFD6kSo+nfPBwDUrhyBdc/2NGy8FTpP/gkHT2XjSFn2mtW6OBkAkPdnBDoc7Yn584vflqjICKx5uieefRZ44w1g/377k7GN2uLOG28ATz/NuVZO2GXEFk/+/W/g8ce5crFmzWKyRfOMaZ7CAIwbx3lhx49bNFYQBEGwHTtzrAJxEIB7V5+6rud0kZ8Tinong18GNbRJLPJzCpd2RYSFome1WHz9ddFIlpM82ScWlFfUlif78Hm57z6uivvkk+DYEqp82+JOv368/PFH52wpA322eJKQwEu73scn+8QiLMSgLRMm8EMnMTFcEXrmjFkrBUEQhOLGDmH1HYC7iekI4HSg/CqNqMgINDsbj+/fjUKwK1c3zIvCXz/Ho2yZ0Eu2vD4kHm9PiELFisCbbwbPlo61o3BsSTxCUdgWreKsYUPu4eQtbcpuBrWKQnhKPCjfuy3uxMcD1apx806nbGlwNB7QYYsnmrCyK4F9UKso9I6Mh8ozYEv//vzQidZyQRLYBUEQSi8Bk9eJ6EsAPQBUJ6IDAP4BIAwAlFIzACwBt1pIB7dbuEfPwBXKlcGap3tixw6g6fvABx94zwd3glOngAULgAceiEJyfZ6s8efRBeGc0aPZnmnTuJeU0yxYAJzbHoW2D0WiQoXCtmgMHgw89hiwezcLLafIygLSfohCg/aRaNDAuy0aRNxbatUq5+w5siEKFftFIi7Ovy2eVK3K3dFTUuyzpdKJKOQcjUS3bjpt2bmTlzobU2kTO+/fz6JVEARBKH0E9FgppYYrpWorpcKUUnWVUh8ppWa4RBUU87BSqqFSKj5QbpUnTZqwN+aTT4BgNbKdOxe4cIEFlDfuvpvXf/VVcOz5+mu+9lao4HubQYN4uXChs7asW8fvg15B2bUri73DunyUxrh4kYsH/Z0XfzRtCmzfbp89mZmBp9QpxNix/NCJJqwyM/1vJwiCIJRcSsSUNvfcA6SnOzcNiSdz5gDNmgGtW3tf37YtCx0DBV2mOXcOWL06cMQoOpqnk/HskmA369dzD6hKlfRt37UrL1ev9r+dGX7/HcjNNS+smjXjSaTz8+2xx7CwMsjVV3O15f79zo0hCIIgOEuJEFZDhnBzRKe9MQCHAVetAgYO9N0xnIhtWrWKt3eS1avZM3PDDYG3veEG9ihlZwfe1izr17OAC9H5yWjViltnrVljvy1aGM+Kx+qvv+wTKk4Lq9BQbgcmwkoQBKH0UiKEVeXKwPXXA99+63w4cNkyIC+P+0X64+abeTunKt40li9nUalnHryePTlE6ZRnLy+Pp4Pp2FH/PmFhLK42GQoA6yM1lcVGRIS5/Zs142VamnVb8vN52hknhRXA4UAJBQqCIJReSoSwAoABA3iKFC3f1ykWL+ZKtg4d/G/XsSNw1VXOh96WL+dm7nq8Ml27stD46SdnbElL41J/I8IKANq04eq7PJv7vKakAI0a6feeedK0KS/tyLP64w8gJ8d5YVWvnnisBEEQSjMlRlhpOUZLljg3hlLsserXjwWKP0JDgb592WPllBft5Enus9Srl77tK1UC2rd3TlitX8/L664ztl/bthxy27HDXntSUoDmzc3vX60aNwe1w2N14AAvw8MN7PT88/wwQP36PJbdIlUQBEEIDiVGWNWrx96JlSudGyMtDTh2jENqeujRgz0VntPa2cWGDbzs1En/Pl26AFu2cEjQCXuuusp4O4c2bXhpZzgwO5urDeOK9Po3hl2VgVp4zpDH6oYb9CXPuVG/PifsHzliaDdBEAShhFBihBXAeVa//soXFifQGll266Zv++7defnLL87Ys24dh7nat9e/T8eOnOxuV+NLdxITOV/KV1K/L7RWEZs322dLWhp7Cq14rADOs9q+3brX0ZSwSkw03Pq9Xr3C4wmCIAilixInrP780xnRALCwqlMHuOYafds3asQl8E51Fl+3jhtBVqyofx8t/0nzdtlFbi6H3lq2NL5vaKj9Cey7dvGySRNrx4mNBU6ftj7/XmYmhwHDwgzs9Oij/DCAe5NQQRAEofRRooSVwTlrDaEUC6Ru3fR7ZIjYa/XLL/bnWeXnszgyms9Upw57NbR8KLv4/Xfg/PmCqWCMkpAAJCfb1zMqPZ2XekWwL669tvDxzJKZWeBNchIRVoIgCKWbEiWsatViD4MTU6Ts3cvl8nrDgBrdunEysd0XurQ09s4ZrcADuKLRbmG1bRsvzXisAPa8nT0L7Ntnjz3p6UDt2uZ7WGlowkrzgJklM5N7TDlNlSpcpCChQEEQhNJJiRJWAAuNDRvs9xCtW8fLzp2N7aflP23caK89ZivwAD5HGRmcWG8XiYkc5jIbetPmtrNrbr709AJRZIWYGM5jKy0eK4C9VuKxEgRBKJ2UOGHVoQNw9CgLBzvZuJEbTWpNI/XSogU38LRbWCUlcW6VGfGgVeEZzIv2y7ZtnChetqy5/bUk8+Rke+zZvdseYVW2LNCggTVhlZsLHDokwkoQBEEIjC5hRUR9iWgnEaUT0dNe1tcnopVEtJWIkojoJrMGaY077U7O3rSJ5wYsU8bYfuXKcXjst9/stSclhUWemeaXWh6UncIqMdF8GBDg7vkNGtgjrM6d40md7RBWAB/HSijw8GHOHTMsrF57jR8GkSahgiAIpZeAl3UiCgUwDUA/AM0ADCciT7/P8wDmKaVaAbgDwLtmDYqP5+orO4VVbi73fmrb1tz+7dtzKwE7mzampJjv0RQZyZMy21U9eeQIhxXNJq5rxMXZEwrcvZuXdgmrRo1YWJkNL2v5ToaFVadOxpqUuahfn6sYnZwTUhAEQXAGPf6S9gDSlVJ7lFIXAcwBMNBjGwWgsuvvKgAOmTUoLIxDXXYKq7Q0vki1a2du/3bteKoXu6bbOXaMw51Wml8mJNjnsdK8TFqelFni47n7+sWL1o6jhe3s9FidPg1kZZnbX+u6blhYrV1ramJHrTJQEtgFQRBKH3qEVRQA95/4A67n3JkEYAQRHQCwBMAj3g5ERGOIaBMRbcrJyfE5YIcO7GGyeoHW0PKjrHisAPvCgampvLQqrH7/ncNmVtGmfLHajDM+nr2DVjvVa8LKaAd4X1htuWDaY/Xss/wwiDaOhAMFQRBKH3Ylrw8HMFMpVRfATQA+J6Iix1ZKva+UaquUahvmp9Ni27Y8ZYtdc89t2sQ5QI0amds/NpYTzbdsscceLVxmRci0asWhraQk6/akpXF48eqrrR1HE4pWw4Hp6UD16tx6wA60992KsKpY0T57AuF0L6vsbOChh3gexQ4dTDnVBEEQBB/oEVYHAbjfq9d1PefOfQDmAYBSah2AcADVzRpld3L2xo0cXjSTKA7wfvHxBb2erJKSAlStyn2azGLnOUpL4zn1jE5l40njxnwMqyFTuyoCNWJi2C6zCexaqwWr50cvUS5/sBaCtJP8fOC224AZM3jOzD/+4OkM7a56FQRBuFLRIzU2AmhERDFEVBacnP6dxzb7AfQCACJqChZWx8wa1bgxt0awQzTk5nIOUevW1o7TsiULKzv6a2mJ61Yu1PXqsTiz4xxt3268DYU3wsM5qd6qp9GuHlYa5cqxF0hLijdKsJqDapQrB9SowQ1t7eb994ElS4B33gHmzOHwds2awN132xd6FwRBuJIJKKyUUrkAxgNYBiANXP2XSkQvEdEA12YTADxARNsAfAlgtFLmJUhoKHuI7BANu3ZxWLFFC2vHadGCE6CthmeUslYRqEHEx9DytcySlcXJ9E2bWjuORpMm1jxW58+zkLFTWAHstdq719y+wWwOqhEVZb+wys4GXnyRZxN4+GF+rmZNYPp0FsPvmq7lFQRBEDR0dXVSSi0BJ6W7PzfR7e/tAAz2NPdPQgLw1VcsRKx4drSKN6vCSuvxlJTE/ZrMcugQCzSrwgrgHK05c6ydIy1x3S5hFRvLcyvm55sLve7dy6/HbmEVHQ38+KPx/S5e5HCZKWE1daqJnZi6de2vCvzkE26tMWdO4c9Lv34stt56i3OvzDaJFQRBEEpg53WNhATg5EnrF5ekJPaAWRUOWisCq3lWdiSuazRvDpw6xQ0szbJ9Oy/tCAUC7LH66y/z3ha7Wy1oxMSwqD1/3th+Bw+y0DMlrBISTDcHc8Jj9eGHXPTQvXvRdU89xTldCxbYO6YgCMKVRokWVoD1cGByMntRypWzdpxKlbj8v6QJK6BAHJkhLQ0oX76gEs0qsbG8NJtnZXerBY3oaF4aDeWabrUAAMuX88MEdetyk1CjQtAX27ZxQ9l77vG+vm9ffo2ffmrPeIIgCFcqJVZYxcdzuMKqsEpKst74UkNLYLdCSgpQqxa3E7CK5mWykmeVlsZeJrMVk55okzibzbPavZvbGlSrZo89GjExvDSaZ2W6OSgAvPIKP0ygVQYeMt1qtzBz5vB0Tnfe6X19SAgwciSHS+0aUxAE4UqkxAqrihW5/5CVaVv+/JMnc7aaX6XRsiV7VKw05UxNtSe/CuDE42rVrAsru/KrAO6FVbmyNY/Vtdfa39pAE1ZGJ/e25LGygFaFaFfLhcWLOY/Kn2AdOZJz4yQcKAiCYJ4SK6wAFkRWmk1q+9rlsWrRgvNtzAqZ/Hze144wIMDio3lz86HAs2c5NGansCKyVhlod6sFjdq1ebokox6rzExunlqxov02+UPzWNmRZ5WRwd+FW27xv12TJhzKXbTI+piCIAhXKiVaWMXFcWjor7/M7W/XHHgamiAyK6wyMvi12OWxAtim1FRz/bU0r5JdiesaTZqY81jl5PA5ckJYhYZyNacZj1Uwe1hp2Omx+v57XgYSVgDQvz+wciV7ewVBEATjlHhhpVRBSwCjJCVx0rmV9gjuXHMNN8E0K6w0D5rdwspsZaDdrRY0YmNZEJw9a2y/ffuAvDxnhBXACexmPFbBDgMCHE6tWNEej9WPP3IxgJ4pnfr3Z4FrpjWFIAiCUMKFlVUPUXJyQRK8HYSGsjfGbOhNE1Z2eoi0Y5mxKS2NE5rtrsDTKgONTsbsVKsFjZgYcx4r08Lqvff4YZK6da17rPLzgdWrvbdY8EanTlw8IMJKEATBHCVaWF17LTcrNJNnpU1QbFfiukazZuaFXmoqe88qV7bPHivic+dOFlV+5sM2hVlhpU05Y7fQ04iJAY4e1V98kJ3NLQ9MC6vY2IKTYQI7ellt3w6cOAF07apv+zJlOMl95Upr4wqCIFyplGhhVaYMe4jMiIYDB7jDuV35VRrNm3PC95kzxvdNSbEvcV2jZk1u3WDGY/X77zwvo91oVX1GE9jT07mnVq1a9tsEFPSy2rdP3/aWWi0AnAVuIRO8bl3rwmrVKl5266Z/n549+b2wu/O7IAjClUCJFlYA5yOZ8Vg5kc8EFITejOZ95eRwQrfd9mg2GRVWeXk8j6IFh4pPwsPZM2cmFOhEqwUNo72sLLdaeOstfpgkKop7SuXlmT4EVq0C6tQpeO16uP56XorXShAEwTglXlhpHiKjVUqal8tuD5HZ0Ft6Os8755SwMloZuH8/T07thLAC+LhmPFZO5VcBxoWVZY+VRerWZVF19Kj5Y6xezWFAI2I1Pp77XYmwEgRBMI4uYUVEfYloJxGlE9HTPrYZSkTbiSiViL6wy0BNiBj1yKSmcrNKuzt4X3MNT49jxh7AGWHVtCnPq2jkAqyJHqeEVePG7LHSK/by8oA9e5wVVjVrAhER+hPYNY9VcbRbAAp6WZlNYP/jD34N7dsb2y8khMXY6tXmxhUEQbiSCSisiCgUwDQA/QA0AzCciJp5bNMIwDMAOiulmgN41C4DzXqI7GzE6Y5WGWjUnpQUvmBpU77YiZnKQKeFVWws56EdOaJv+wMH2KPnpLAiMtZyITOT89ciIpyzyR+aoDObZ7VlCy/btDG+73XXsQfx+HFzYxvh7Flg9mzgk0+AY8ecH08QBMFJ9His2gNIV0rtUUpdBDAHwECPbR4AME0pdRIAlFIWgheFiYnhC5uRPKv8fBYZTggroKAppxFSUrjazYmLtJm8r507uaN4jRr22wMUJMXrzbPSKgKdFFYACysjHqvi8lYB1j1WmzfzslUr4/t27MjLDRvMja2XxEQW4SNGAPfey+//Dz84O6YgCIKT6BFWUQDc64MOuJ5zpzGAxkS0hojWE1FfbwciojFEtImINuXk5OgzMMS4kNm/n0vqnRJWzZoZrwxMSXEmDAjwdC1Vqhj3WMXGOpcornnC9OZZaT2snGq1oGGkl5Xl5qCff84Pk9Sowa0wzHqsNm9mgWumvUebNuydXb/e3Nh6OHQI6N2bx/n5Z/awNWwIDBpUIAoFQRBKG3Ylr5cB0AhADwDDAXxARJGeGyml3ldKtVVKtQ0z0DypeXNjHiunEtfd7QH0e4jOn2fh4JSwIjJeGagJK6eoW5e9c3o9VunpnLvmtIcoOpr7OukphrAsrOrVs3SAkBCu6LPisTITBgSAChW4B5yTwuqBB/gGaNkybmDaqhXwv/9xbuTw4RwaFgRBKG3oEVYHAbhfHeq6nnPnAIDvlFI5Sqm9AH4HCy1biIvjKVtOnNC3vdPCSgu96fWi7dzJydlOCSvNJr3C6uxZ9oI4KaxCQngKFSMeq2uu4f2cRKsMDOS1OnuWpwqyJKzmzuWHBcz2sjp2jIWhWWEFcDhwwwZr7R58sXIlsGQJMGlS4SmVqlXjZvW7dgH/+Y/94wqCIDiNnsvYRgCNiCiGiMoCuAPAdx7bLAR7q0BE1cGhwT12GWk0gT01lcNjVavaZUFhGjY0VhmoeducEnoAX5z++APIygq8reZFclJYAQWVgXpwutWChtYkNFACu+UeVgAwfTo/LGC2+7qWuN66tfmxO3bkcLfZuTr9MXEin9tHHim6rl8/oE8fYPJk7n4vCIJQmggorJRSuQDGA1gGIA3APKVUKhG9REQDXJstA5BFRNsBrATwpFJKxyVeH5qnR2840KmKQA2jlYEpKZwro2cSXLMYSWDXvEhOdF13p3FjbqEQKJ1OKU5eD6awCuSxskVY2YA2X6CRHmUAz5MJAC1bmh+7XTte2p3vlJjIrRwee4ybyXrjmWe4IvGzz+wdWxAEwWl0BV6UUkuUUo2VUg2VUq+6npuolPrO9bdSSj2ulGqmlIpXSs2x08i6dTk5W7tY+CM/n8WFk8IKMDZnYEoKe4fKlnXWHkCfF23nTs7LclrIxMYCubmBvUNHjgB//RUcYVWtGlCxYukRVlFRfG5Onza2X2oqTw101VXmx27cmKcY2rrV/DG8MX0659+NHu17m27dgLZtgbffNi4qBUEQipMS33kdYBEQH69PWGVk8IXIaWEVH6+/I3xqqrP5VQALgAoV9AurBg2c78+kecQC5VkFqyIQ0N/LSksYj/Ksfw0yWjK/0QR2Oz5zoaHs8dLCinaQnQ188QVwxx3+Q/VEwJgxfJO0caN94wuCIDhNqRBWQIGwCnT36nTiuoZ20QrktTp7li/iTgurkBDOs9IbCnQ6vwrQ38tKE1bB8FgB+npZZWZydZqTXkY9aMLOSJ6VnX3cWrXi0F1+vvVjAdyj6uxZ4K67Am87dCiHCj/91J6xBUEQgkGpElanTwe+c9eETrNm/rezit68L82D5LTQA/RVBirFQicYwuqqq7hzuR6PVZky7EULBjExLHb9iXTLrRYAYP58fljAjMdq3z77+ri1asUJ7HtsKkX56iv+THTvHnjbKlW4p9WXXwbO07OLbds49+v++4EFCyQMKQiCcUqVsAIChwNTU/kuP7JIFy17adCAQ2+BhJW23mmPFcAeqwMH/IcnDx7ki24whBXA4wTyWO3axV6kMmWCYhKio/kcnTrlextbhFX16vywQO3avDTisbLTa6t1bbcjzyo7G1i0CBgyRP97PWwYz4P566/Wxw/EtGncnmLGDOCbb4Bbb+XH+fPOjy0IwuVDqRFW2kVCj7AKhncoJITFkh57IiIK+ic5iZ7KQKfnCPSkcePAHqtdu5ytmPREey985VkpZZOwmjmTHxYoW5YnjzYjrOzw2sbFsQiyI8/q559Z1A8Zon+f3r35+7NwofXx/fHVV8D48cBNN3FH+GPHgDffZIF1333iuRIEQT+lRlhVrcphEX9CJi8P2LEjOMIK4ItOII9VcjJ7kkJDnbdHT2VgsIVVbCxX/fnyoikVfGEVqOXCqVOcB1S/vsWBbBBWgPFeVnZ6bcuV4++THR6rH3/knKlu3fTvU748i6uFC50TN4cOAWPHct+ur77i35qQEOCJJ4CXX+ZkewszEwmCcIVRaoQVELgyMD2dww0tWgTHnrg4vrM96mfK6eTk4NkTExO4cen27dxuIFjVboES2I8cYS9GSRJW+/fz0rKwsgkzwsrOm4tWrewRVsuWsagyWo06eDCHuO2sTnTn2We5kvjTT/n747muY0fg73833vJCEIQrk1InrNLSfCeyJibyMiEhOPYESmA/epSFQ7CElda41J+w0i66Tk2+7EmgyZh37eJlMIVV1aqcGO0rFKgJq2Al0wfCiLBSir227tPEWKVlS/4s+7uBCERmJn93+/Qxvm+/frxctsz8+L7YsYO9UQ8/7L1hbkgIT63zxx/AW2/ZP74gCJcfpU5Y5eT49n4kJnKHc6crAt3tAXx70bTngyWsAH7t/nKsgpWDptGwIV+cfL1nxSGsAP8tF0qix+rYMeDChcDbHjrE3hc7Q71GZz7whiaKzAirmjVZ3P3vf+bH98Vrr7EH7emnfW/Tti1XJ/7nP1whGSz++AP48ENg6lR9PfwEQSgZlDphBfj+kdm2jYVFsHoP1azJRV++LjhJSbwMprBq2pQFw7lzRdcdO8aPYAqrcuVYxPjzWIWFBV/EaC0XvLF/f0HSeElAC9seOhR4WyeEqh3C6qefuMLR7E3PjTcCa9d6/1yb5fhxniN79GigRg3/2z7zDOfeffihfeP7Y9Ys7uv2wAPc/qFFC2DcuOC1nRAEwTylSlg1acLhLl/CKjHR2txoRiHyn8CelMTTigT60baTZs04HORNyGjVYsFo/eCOv8mYd+0CrrkmeK0WNDSPlbeE6P37uSIwxOq3Y8kSfljESJNQ7TzbKayuvpqnArIirNasAbp2NR+CvvFG4OJFYNUq8zZ4MnMmH3PcuMDbtm8PdOoEvPee8xWCn38OjBzJrR+2bWNBPWECj33XXfY1axUEwRlKlbDSKpQ2bSq67uhR4PDh4OVXaWjCytuPXVJSgZctWPirDAxWV3pPtF5W3i5Iwa4I1IiOZu/H8eNF1+3fb5MHrXx5fljEiLDatYu/J3bOcRjoBiIQ+/fzo0sX8zZ07cqvy65woFLA+++zTXpvNO6/n29YVq+2xwZvJCXxVD7XX8/h0xYt2NM3ZQrwxhtctThlinPjC4JgHV3Cioj6EtFOIkonIp/ZCER0KxEpImprn4mF6dAB+O23okJGS1wPpscK4PyLs2eLeohycljIBDMMCHD4oEwZ38KqShWgTp3g2tS4MYsYz1CWUlzJWRzCSutl5S3PyjZh9e67/LCIUY/Vtdfa4G3zID6ehZUZb82aNbzs3Nn8+BERvP9PP5k/hjtbtrAIHTVK/z5DhwKVKzsXDszPZ+9ZpUrAnDlFKxSffJJ7gE2cCOze7YwNvsjL48rQ9es5h08QBN8E/PklolAA0wD0A9AMwHAiKpIpQUSVAPwfgA12G+lOhw6c66DlkmisX8931m0dk3Tead+el7/9Vvj5lBRONg62PWFhLGS8CauUlOBWBGr4qgzcv5/bYwSrp5Y7vlou5OSwALRFWM2bxw+LREaysNDrsfJW3WaVuDhO3NYS+42wZg23+LB6k9GtG4fG7Gh7MG8e34AMHqx/nwoVgNtv56ahTnRj/+ILYN064J//9J7fR8QJ9GXLAo8+av/4vli+nL+jrVsD113H/QSnTZOmqYLgCz33te0BpCul9iilLgKYA2Cgl+1eBvAGAEcngOjQgZcbPOTb2rX841+5spOjFyU2lu8wPYWVZp9mbzDxNmdgfj7fcbZuHXx7fPWyCuZ0P55owsozgf3QIT5XJaUiEOALqp6WC3l57MlwwgNoJYF99Wq+IFvNo+valS/m69ZZO45SLKxuuIFzx4wwdCgLzB9/tGaDJ3l5wEsvcc+wu+/2vV2dOpxIv3hx0d8cJ/jyS67kLFuW+3wtXMg3i+PHs7gTcSUIRdEjrKIAZLr9f8D13CWIqDWAekqp7/0diIjGENEmItqUY7K8pWlTvvt1F1b5+eyx6tTJ1CEtERICtGtX9Efut9+4YlC7gAeT+HgOsbl3O//9dw5ZBtuDBrAoKF++qMequHK+ABbgV11V1GO1bx8vS0oPKw09wmr/fk7GdkJYae+RUWF1+jTnDVkJA2p06MDizGoC+6ZN/L4PHWp83+uv58+NDY7IQnzzDXsbn302cBh3/Hi24eWX7bXBk3XrOFTatSv/nt19NzBwILB0KYuqd95hD1qwOX+exWWX2GMAACAASURBVPrPPwe3/YUg6MVyJgYRhQD4F4AJgbZVSr2vlGqrlGobFhZmarzQUP6Bdf9xTU3lH/DrrjN1SMu0b88hiuzsgufWr+fngx12A7hTtFKFxZ6W8F8cwiokhC/23jxWwZgw2xfR0UU9VprQKkkeK4DDL4GElRYedyIUGBnJNhgVVhs38mfRjpueChXY42o1eXzRIv5MDhhgfN+wMM5z+vZbe8OBb77J3xE9oclKlYD/+z/2WgWah9Msf/3FoqpOHfZSVaxYsC4kBPjXv4D+/TnvK1g9tpQCPvqIfzO6dmWRW6cOJ/Xn5QXHBkHQgx5hdRCAe41RXddzGpUAxAH4mYgyAHQE8J2TCex9+vCX+cAB/n/pUl726uXUiP7p3p1zc379lf8/fJibdHbvXjz2dOjAgm7t2oLnNm1ir1GTJsVjU2xs0YtASkrxhAE1YmKKeqx27+YLRzAmzTZCVBSHKf2FXpxutmqmMtBuQd+lC3ur9TRL9cXSpfwdMRoG1LjtNvb+rlxp3gZ3tm3jm6Dx4/XPKTpmDIu8GTPsscGT117jz9PHH3u/8SHidZUqAY884nxIUCkOgd5/P3vkFy4EfvgB6NmTm7uOHl084io/n3/Xfv9dxJ1QgB5htRFAIyKKIaKyAO4A8J22Uil1WilVXSkVrZSKBrAewACllJemCPagTXHxww+8XLKEE2Pr1nVqRP90786Ty2r2aCXhvXsXjz1VqnDoxj0X5Zdf2IMWjMmgvdG8ObBnT0F4MjeXxWdxhAE1vPWySk/nMKAtTWZ//pkfNhAVxWIiK8v3Nr//zp6FWrVsGbIIcXH8nuXm6t9n0ybuvl+1qj02dO3K58FbyxU9HDvG+2q/IWbo3p1vUmxoUQYA+OQT/rzddZf+fWrVYs/ZzJn2V+n98Qfw738Dw4axcPFF9erAK6/wb8uCBfba4MmMGeyZGjeOK0MHDgT69mWB9cor3FD1+eedtcEdpfjc16/PN6uxsfw5nz07eDYIJZeAwkoplQtgPIBlANIAzFNKpRLRS0RkwplunebN+UP8+ed8YfzlF55yoriIiOAf20WL+A7mm2/4hy/YrRbc6dyZq7EuXOBeTYmJnKxbXGjhyY0b+f+UFA6lFEdoUiM6mm04cqTgufR0bldQ0tDTckGz3anwc/Pm/Hnas0f/Pps3c6NLu9B6YWktHIzy44/8ObQirMLD2Tv+/ffWPTUXLvDv2KBBxj1oDz7IFdJff23NBk9ee43t0pPD9cADnPf64ovOea2Sk7n7fN++XI3onoNGBDz3HNsxebL9RQXeyM9n7+I997Cw+ugjflx9NTBiBPD448FP6j92jN+DPn04RPuf/0hbjOJEV46VUmqJUqqxUqqhUupV13MTlVLfedm2h5PeKoC/TA89xHlWAwbwF+2++5wcMTB33cUXnI8/5tyHu+6yv5eQEfr358TOlSsL5mkrrlApUNCWYv36wsuOHYvHHqAgF2nHjoLnbBVWU6bY1s1Rj7Dau9fZEKY2sbO/uSjdycriGx87xXP16nxT5VkVrJelS3kmBKvVsTfdxOfbao7TkiXAiRPAvfca37drV/aufvmlNRvcOXmS+3SNHKkvpBwayqG45GQWmnajFP/WV6rEVYm+flPfeYe/zw89VDjX1QlefJHb0z3xBOf73XsvP9au5bDov/8NvPqqsza488MP/NpffJEFVno68Le/cU/H4phjMjGR8/Pi4jjk/uKL/LkqDrQq4vff54ITfx5/OylVndfdGTeO74STk4FJk4o/2XjoUP6Re+AB/rEZP7547enVi3+MPvuMXdYNGhSIm+IgMpIvzFp4cv16vsAVR9WkhhaG1KoTT5zgh23CavFifthAIGGlFIsYJ4WVlp/nLkT9sXkzL+30WAEFTYKNkp/PNxl9+li/6dE8XlbDgfPns6fKzE1PSAgwfDh7aY4ds2aHxkcfsafDSJ+s4cP59+WNN+yxwZ2vvmLx8uqr/ufuDA9nsbN7N/DWW/bbobF0KbfFGD2a+425f45CQ4G33+ab6okT7Wtm64/Fi/kmOjqaowBbtvCNz4oV/D726GFtKiojKMWfgdatubijYUNucjtpEufFmb0ZMktqKt+4d+oEjB3Loe369dkj6/S0UKVWWJUvzxfpzMzgxtZ9Ua4c37Hddx/w3XfFKxgA/qF58EG+m12+nP8uTg8awA0ef/mFv/BLl3JVT3FUTWrUqcP5aJqw0pK/S2IosFYtPle+hNUff/CdupPCqkoVnl5Fr8dKy4Oyu3da+/ZcuKJnUmp3tm9nAWKH57ZBAxbmVoTVhQt8YRw40HyPr7vu4qRpO9o/5OUB//0vpzUYmcEiLIw9NatX23sRz8vjMF98vL6IRK9eHMF46y0OkdrNX3/x72jTpizivP12EXE+WKNGnGjvpPcsNZVFbUICF065T3DesydHdMqVY+HlxPnw5OWX2Xs5dCh7c7/9lu3atIlzCG+8sSAVxGlWreIuARkZ7K3at49v5vv25c/UnXcayxU1SqkVVgB/oYsrYd0bzZuzG724ktY9eeEF/nKPH885CsXNrbdyNdVzz7EQ6N+/eO0h4vdME1ZJSbwszkpFX4SFcQ6HL2GltY1wupqxaVNjHqtGjexvp+FrtoNA/PILL+2q1u3dm8WE2bYLy5dzMcett5q3IS6OhcecOeaPobFsGV+AzHjbR43ii+d771m3Q2PBAg5rTZyov+hm0iQWEe+8Y58dGq+9xhfqGTM4r9YXFSsC06fzd3LyZPvtAFgUjBrFdnz7LUcnPLnmGs6/y8zkEKmTfPUV8I9/cK+zL74oXKzSpg0LrGrVOJfQLu+qL9LSWGDXqcO/QQ88wJ6qDh3YQzx5MjB3LrcscYpSLawE/1SsCHzwQcE0GMVNjx584Z86lRscFmfBgYYmrJRiYVWpUvF7G30RFVXQYsSTYAmrJk34h0tPcu6mTfaHAQG+Qy9Txriw+vVXnpzarve3Z0/2OpntBP/119yo1qoH7dZbOZn/6FFrx5k1i7+XZvp7Va/ObSg+/9yepGktrKS3t5dGq1bsAXz7bXu9RUePcu+uO+9kz3sgevbk0NOUKdbfF29MncqiYdq0gjQBb1x3HQvTL7+0bwJzTw4f5lBbhw58vfEWGalbl4Xy8ePsfXQquf/CBeCOO/h6t3RpUccLEfDUU8CECex1nDvXGTtEWAlBIyyM72ZuuYW/6O5NB4uLhATOq8rI4H5C8fE2hkwjIvzf2hrEX/d1TVg5LQqbNmUvy+HD/rfLyuJO8E4Iq4gIrrg1IqyUYo9Vt272hZ+7dWNPiplcmrw8Thno37/oZMtGGTiQX5+VdL4zZ7h1wdCh5m/CxozhRs3ffGPeDo1Vq1g4PPmk8RYxjz3G3+kvvrBuh8abb/JF+x//0L/PSy+xN/Of/7TPDoC/Wy+/zL+jt90WePu//53znR55hPst2s0jj7CYnjnT/2enVSvg9de5en7hQvvtAPicJyVxrqC/38LXX+f8q4ceYrFnNyKshKDSsSN/sUpKuFS7+1y2jOP/tib4//BDQXMzGwgkrK6+mnMPnURvArsWVjWSq2OEDh34/dKbhLprF4ef7WzaW7kyC0czjUI3b+YL5M03W7ejZUsOdXz7rfljLFjAHp6RI80fo2tX9hDYUaX44Yd8fo309tLo1o1vkN55xx7PyLFj7Bm66y5jsxo0bsz7vPuuvV6ryZNZCE+erO8mITyc88527mSvpJ2sWcOe1+ef19d8+m9/4/fm0Uftn8g8PZ1F7KhRLDr9ERbG3rU//2QPlt2IsBKuaJo149j/c8/xF704W1IEIiqK78S9hTicbrWgobflglbmHR/vjB3t2/OPot52B1p+lZ4wjhF69uRqp7Nnje23dClfFG+80boNRBy++9//zIfhZs1ir4aVacG0KsVly6yVtZ88yTk7d91l7kaBiC/gSUnm+5258+GH/J17+mnj+z77LO/7/vvW7QC4595//8v9sow0Vx4wgG8CXnnFPq+VUuwNq11bfw5vmTIcxty/375zovHMM+z91ZvXFhfHeVaffGJ/WwoRVsIVTUgI502cOMEJl7YKq5dftnWmXC2Xwls1XLCEVZ06nIemx2NVowZ70ZzAaAL7r7+yLXbPo9izJycSG52/cOlSnry9enV77Bg4kC/gZvJosrLY6zZ0qPUw6fDhfD7mzzd/jC++4Juc++83f4w77uC5JWfONH8MgEO2M2bw++xedaeXJk3YOz99uj2CZto0Dkm+8IKx/Yg4sX/PHvtCpMuWce+uSZP4XOulZ0/Ot339dfvy4DZu5M/cE08Ym3ni2Wc5JeXFF+2xQ0OElXDF8+KLXAk1b56tKVHcTGbFCtsO56uXVW4u3wEGQ1gRFSSw+yMpib1VTrXTiI1lgadXWK1ezaEqu+3p3JnDCkbyrE6eZC9X37722dG9O58PM+0fvv+eBYSRJHFfJCTw58NKOPDjjzkfx0qbjooVOf9o3jxryfSLF/N36+GHzR/jb3/jmyGr0/5kZ7PI69/f3HygN9/MXq6337YnRDplCv8mjR5tfN8XX2Tv24cfWrcD4EKHyEhOSjfCVVext+3rr7mxqV2IsBKueKpW5crJ4pzyRw++hNWBA3xhDNbE0U2b+hdWeXlcaenklE6hoXzx3bIl8LZHjnBxgpUwly/Kl+d8Ly3UqIflyzk3rE8f++wIC2NPwLJlxi+aCxfyZ8uOQgMi9nytWmUur2jXLn5PreR6aYwaVZCUb5Z33+W8MTOVkhr9+nGY9d13zR8D4HkIjx831rzVHSJONN+6lT1NVtiyhe8Z//Y3c8UO3bpxvu0771hv1rlrF4tWrUO/UR57jIX4v/5lzQ53RFgJQinBl7AKVqsFjSZN+A5cm1Dbkz172Evg9FyZrVtzJWegRn9ax+cOHZyxo2tXvtDo9YwsXcp313bPhNCnD/eh0hrd6iE7m8XYwIH2VcMOGsQXSzNVilr5u55qt0B0785J/Z9+am7/gwc5tHrPPeYbuAJ8Xu+5h8PR2nfVKEpxblXLlhxGM8uIEfzZs9rn6623WIyMGWP+GI8+ygnnVmcvmDKFxd0jj5jbPzKSpySaMydwtbNeRFgJQimhcmXOZShuYaUlsPvKs9IqAp1KXNdo3ZqFQaAE9g0b+MJodwd4jc6dWdzpDUuuWMHeJSsXa29olbba3KB6WL6cBeHAgfbZkZBgvkpx3jw+n/XqWbcjJIQT4FesMNeU8ssvWdCMGGHdlpEj2WP02Wfm9t+6lW8ixo61Fs6uUIH7SC1YwFWyZjh2jIsL7r3XWvPfIUP4ZnHqVPPHOHmSz+nIkcZyqzx55BH+Dk+fbv4Y7ugSVkTUl4h2ElE6ERWpjSCix4loOxElEdEKImpgj3mCUIqpVo0fNkHkveXC3r18EbHjYqSHQMIqOZntMZPsa4RWrXgZKBy4fj3f6duaP+dGp0681FOBlpHBXiUrXgdfNGzIjx9/1L/PwoUs2O20h4iFmtEqxbQ0/uwMG2afLbffzqFpMyJv1iz2KtpR8FC/PhfGfPqpudDXzJlc8XbHHdZtufdeFhFmk9hnzeJE/AcesGZHWBiH71asYM+VWVvOn+ephqxw7bWcuzZjBnDxorVjATqEFRGFApgGoB+AZgCGE5HnT+ZWAG2VUi0AzAdgc0s0QSiFfP01P2zEl7CqV49/qILBNdewt8VXnlVSEv9QBaOnVng43837Ii+PK4acCgMCnKMXF6evMlDLxXJCWAHstVq5Ut/FQSkOS/bubf/MDGaqFOfNY1FmRxhQIyGBP69GqxSTk9lDZEeul8bo0fxdXbXK2H4XLnB+1aBBhaeKMUuzZiwYP/nEeD6eUpxw3r69PVN/jRrFN2FmqjeV4l5UrVvb440eO5a9cVYa7Wro8Vi1B5CulNqjlLoIYA6AQo5jpdRKpZR2b7IeQAmawU8QLh+8Cat9+4I7DU9YGFcl+RNWTudXASzuWrb077FKS+MeU04KK4DDV2vXspDzxy+/cCWSkR5ERujTBzh3Tl9ycmoq58rZmUSv0a0bh4mMJI5/8w3QpQv3RbILIvZarVjBLVX0Mns2F0jY6T0bPJhvNozO67h4MdtupvrOF/fcw+LR302JNzZs4MnMrbTCcCcqiqtjZ84M/N3xZONGfg1WPWcaffqwPR9/bP1YeoRVFIBMt/8PuJ7zxX0AvLabJqIxRLSJiDblONFbXxD+v70zD66qTNP48xIIJrKpCAq0oKJBbGUxYBBwQLC4IGsHBK3pxW6Hmp6xZ6yeckqcLmfGcmrGsqpnq55u7dZutadUUAgJW4goS7FJJNBRMDRqTyBNFxBlk4gC7/zx3s/cXO5ykpwly/OrunVz7z14X798Oec579qWWLLEHj4ycKBdDBPDCbW1FmoIk2HDUocCz5yx5PWg86sco0fbxSFdeGXHDnsuKgrWjgkTLJnfDfROx8aNllTt29ikJCZPNsHpJRzojgliCkK3blYNt3att9DXoUPmIQpiMPv8+Rb6Ki31dryqebimTrVebH6Rn28dwZcvz15wkcjLL1v/OD+ayToWLrTQ4q9/3bx/98IL9v/hp+D8/vcbCwWawy9/abY8+KA/duTkmAdt7drUvQKbg69/3iLy5wAKATyb6nNVfV5VC1W1sFtYcQtComL79pZP6E3DwIGW3+DmW124YCelsPKrHLfcYnkRySGnffvswhSmsDp1ysRcKnbutPBJS/r+NIcJE+w5UziwttZCQX6O1UmmVy9rPOplzE55uQnkoET59OmWIL13b/ZjXfglCGF1xx3m0V22zNvx1dXARx9ZcrXfLFhgbSg2b/Z2/MmTFq5duLD5MxMzccUVttZLl3oXeefO2RoWF9s+84tZsywVtTkir6HBKkgXLPDXloceshuBllaSOrwIqzoAiaftQfH3miAiUwH8A4DZqnqudWYRQlKR3HLhyBETV2F7rAoK7HuTBc2+ffYcVKgrGZdbkS4cuGOH5YME1ajUMXiweRUyCaug86sckyZZmCTTmJ2GBru4BxEGdDhP2Lp12Y9dtcoS7wsK/LdDxPKTNmywMGk2VqxoTMD3mxkzzMviVeSVldnNy4IF/tuycGHzRN769Sb0HnjAXztycy0pv6zM+2ioNWusR1lLZklmYuhQu0l65ZXWNVH1Iqx2AbhJRK4XkVwAiwA0caqKyCgAz8FElY/jJgkhiSQLq0PxIH3YHit3AUxudbB/v50ob7ghHDtuvdXCTqmE1enTFpoLOr8KsAvxhAmZKwM3bjRPQdDevMmTTfRmEnlbtlg1VZDCqn9/q9zMJqw+/9xEz8yZwQngWbPM4+JlEMKKFZYzF8Q4puaGA5ctswalQezhGTOs/cLSpd6Of+01yw8MopHywoUm9svKvB3/6qtAv3621/3mwQftPPb++y3/b2QVVqp6HsAjAMoB7AewVFU/EJGnRMT1o30WQA8Ay0Rkj4h4jGYTQppDsrCqrbXnKDxWwKXCat8+K0/3u0dTOrp3t+qkVMJq71676xwzJhxbxo+338ehQ6k/37TJkrqDyq9y3HWXic2NG9MfU15uAtjvodTJxGKWSH/yZPpjNmww0RNEGNAxYYKFjLJduD/5xPaNH+N90uE1HHjqlP2e5s8PZs/k59uav/lmdpF39qzlqBUXB1N9PH68ndu8JPafOmUezvvvD+Y8U1xsYdfmFhkk4unXpaprVPVmVb1RVf8l/t6Tqloa/3mqqvZX1ZHxRysGABDSQRg0yB4+cs01dpI9fNheu4t42MKqTx+7o09OYN+/v7HPVViMHm3CKtl178RWUI1Bk3Ejc1yn90SOHLG8nYkTg7fj8sst/Jkpz2r9erOlOcNzW0IsZhftTLMUV60y0RPk2uTmmndu9erMyfQrVthzkMJqxgzrqZatYrKszARnEGFAx/33W75mJhEOWOjtzBl/+miloksXs2XdOuDEiczHlpTYuvgdknT062c9x157reXhQHZeJyQofvtbe/hI164maBI9Vr16+ZvA6ZVhw5p6rL74wu74wxZWo0YB9fWXeop277a18rN8PxMjRpgHzVUiJuJqGMaPD8eWSZOA995LPXbo6FELc4QxG3PcOJvfli4cqGpiZ9o0/3tpJTNzpgncTC0Gli+33ldBTjHIz7cKv9LSzBfuZcvMixNkRWssZqNpsoUDX3/d/paCLLxYuNDyybIJzldftZzGIGZ/OhYtsvzRysqW/XsKK0LaGYm9rA4dCt9b5SgoaCqsDhwwb0AUHivg0gvm7t32WdCJ647cXKtASyWstm2zz123+KDJlGcVVhI9YGGjqVNNWKUSEe+/b6Xt06cHb8uMGbYX0jWAPH7cfk9z5wZvy+zZ1n+uujr152fO2JoVFwcbOs7LM1sy5XydOWNrtmCBv5WJyYwda9WbmUJwx49bW4YHHgj273rePPt7bWk4kMKKkKB49NGWj6LPQKKwqq0NP3HdUVBgniLX+sE1DA1bWI0YYRefxDyrhgbL9worDOgoKjJPUXIbiu3bgcJC82iFwbhx6fOsNm2yEOAdd4Rjy7Rptk9T9T1zvYv87NGUjr59bV3S5VmtX2/ib8aM4G1xifrpemtVVFi4KwyRN3eu/R2naypbXm7e6OLiYO0QsXDghg02AzAVZWV2w+Bnd/5U9Olj3rylS1sWDqSwIiQo9uyxh88kC6uoPFbDhtmz81rt22cnRz9mqzWH/Hz7zsSlrq62E3BY4sExbpxdhNwgasAukJWVwYYuksnPN5GXSlht3GjJ3GG1EnSiKVVFXkWF7SOfUxHTMnOmCd9UDSDXrLGGoGHsmf79rdIvnbBatQro3buxP1qQxGLmnUk3T7G01KoBw7DlW98yz9nq1ak/X7HCzndh3DAVF1sua0vCgRRWhLQzBg60BE/nLYrSYwU0Cqv9+63NQlDDjjMxalRTYRV24rrD5cMkhgOrqsyD5YY1h4XLs0qsyDt61FpQhBEGdNxwg+UsvfVW0/fPnTPvWRi5Xo777rPn5JyvixfNMxOLBV+16Zg92/qNJYu8ixdNWMRi4Yjfnj0tWXvlyku9M+fPm8i7775wKn3HjLGcyFR5VmfOmFdx7txwwvszZ1ro0xU0NAcKK0LaGe7u3lWfReWxGjLE7nRdiCeKikDHyJHmvauvt9e7d9tddthrM2iQCd9EYeVCLGF6rADLs7p4sWmelSvxD1NYASae3nmnaR7Ptm0Wsg0jDOi47Ta7cJeXN32/stJuUsLI9XLMjtfOJ+d8VVZax/og208kM2eOVa0mj2TautXmFAbRLDUVXbrYd61da3sjkfXrwwuPAnb+mDSJwoqQToHrZeUqzaISVjk5NiqmpsYumAcORCusgMbxKWEnridSVNR0ktH27SZCw6pOdNx5p3k8tmxpfG/jxnDzqxxTpliF4nvvNb5XUWF7KEyRJ2KeoIqKpiJvzRq7qAcxNzEdw4ebNy85HFhWZrbEYuHZ4kRccjhw5Uq7eQpzXebNs75ZyR7OkhJrsBtGy5JEWz78MHV+YCYorAgJiptvDiThyAkr5xWJKhQINFYGfvKJhbuiFlZ79pgd1dXhhwEdRUVWqn30qIVWtm0LPwwIWJ7VmDFNG1Fu2mQtH8Ie1XrPPfaceLGsqLC1CrtVSCxmydG7djW+t3atVaVddVV4doiY1+qtt5qO2lm1yn5HYdoyYID9/ycKK1V7PWWKhQvDYtIkyy9L9BR99ZWty6xZ4TUfBhq9Y831WlFYERIUzz9vD59xwmrnTjs5u9dRMGyYhRCcpygqYdWvn10cqqosif7LL6MVVoD9fg4dshyasMOAjrvvNgFx9ixw7Ji1Nwg7DAhYUviIEY0J7PX15r0KMwzomDrVPEIuz+rYMVujMKoBk5k508JbroHqoUN2czBzZvi2zJnTNOdr3z67QQgrDOjIzbWcrtLSRq/ili0mhoNs3JqKgQNNcFJYEdLB6dnTHqdPW3VRWCX8qSgosJPfmjX2OiphBZjXas+e6BLXHaNH2131jh2N+VVReKwAE1bnz5stUeVXOaZOtZyds2dNSKhGI6yuvNIulk5YuTYLYeZXOSZOtAadrgrOPYeZX+VwAsqFJp33KgpbXAsIN3tzxQorigkzJOmYN88Ep5t24QUKK0KCYvFiewSA81JFlV/lcJWBpaXmMerdOzpbRo2yBPpt20x43nhjNHbk55t3ZscOy6/Kzwduvz0aW+66y7wzmzdbflV+vvXTioKpU82TuHWrhQF79TKBEwWxmF0s6+vtpqBfv2iEeG6uicvVq03clZVZ3pVrZRImw4fb34yryFu50n4/AwaEb0ssZjeMJSW2LiUlJqry88O3xXnJsnWET4TCipCgOHDAHgHghFWU+VVAo7Cqr4/WWwWYx+rCBRsFMmpUeGXzqSgqAt5910IYY8eGmxeSSO/eti6bN0eXX+WYONG++623TFhNnhzdusRidsFet84qBKdNi26/3HefeUN27rRQ6axZ0RRdiJjX6u237bT17ruNlYth07OnCfGSEgsZHz4cXjVgMgUFdm5rTjjQ01YSkZiI1IjIQRF5PMXn3UXk9fjnO0VkiHcTCCHNpa14rNwwZiB6YeXGxZw6FV0Y0FFUZH13qqqiy69y3H23tTqoro4uDAhYNeK4ccBzzwF/+EM0YUBHYaGFBJ9+2m4KosivcrgQ5I9/bPlWUeRXOWbNskTxH/3IXoedX5XI3Lm2T55+2kRvFCHJRFvcKCgvZL1fEJEcAD8DcC+AwwB2iUipqu5LOOwHAD5T1aEisgjAMwAWNsdwQog3SqrqsOvaGlz39w2oyMlDSVUB5o6KJoO9pKoOly+qwXXdG7Cpa7S2/O5EHQb9sAZdejbg7dxobfm8bx0G/mUNcno1YG23PIyN0Jb84Y22LP8qD8MjtGXIn9Xho+E16N2rAS99moeBEdmSkwOMnFuHwuZHwgAACCFJREFUmtwaXDe7Af/5cR4ui8iWAQOA4dPrUDu4BtdNbMCTu/Jw5qpobKnvUYdv/FUNPuzRgME35+H3Xxbgm4hmr3Qdavu2qlcDhlyfhy21BZh7VTS2XDm6Dtf8RQ2OlQz11KjEi8dqLICDqvqxqn4J4DUAyTp2DoCX4j+/AWCKSBTOTEI6NiVVdViyvBpn0QAR4PTFBixZXo2SqrrIbLlwmdly6kK0tjxRUo2cXmbLya+iteU/tlaja2+z5bNz0dry5v812nK8IVpbtl9otOXo59HaUtuv0ZYjp6K15YvbG23548lobCmpqsNPVlajS0+zA5c34IkV0a3JMxsa1+RC92h/Py/sNVu8IpplwqCIzAcQU9WH46+/DeBOVX0k4Zj348ccjr/+KH7M8XT/3aG98nXDnIAnKXpgz59sDsbIa0ZGbAltSUd7teWKSmuU81nhGN++v6r2BM6dv3DJ+9275mDUdX18+x7aQltoS+eypa3Y0ZZt+c7HB3DuyO+zOo1CTR0UkcUAFgPAjT0iGCiWgh65PaI24WtoS2raqy1+CipHqpNNpveDhLakhrakhrakpq3Y0lbsyPSdbcmWTHjxWI0D8E+qOi3+egkAqOq/JhxTHj9mu4h0BfAnAFdrhv94YWGhVrZkbDQhnZjx//Y26k5c6pIe2CcPWx+/h7bQFtpCW9q1HW3ZliMvPerJY+Ulx2oXgJtE5HoRyQWwCEDSdCOUAvhu/Of5AN7OJKoIIS3jsWkFyOuW0+S9vG45eGxaAW2hLbSFtrR7O9qDLdnIGgpU1fMi8giAcgA5AF5U1Q9E5CkAlapaCuAFAK+IyEEAn8LEFyHEZ1yl0LPlNfjjiQYM6JOHx6ZFU0FEW2gLbek4trQVO9qyLUc8/pusocCgYCiQEEIIIe0FEXlPVbPOLohMWInIaQA1kXx556EvgLSVmcQXuMbBwzUOFq5v8HCNgyeMNR6sqldnOyiigQIAgBovyo+0HBGp5BoHC9c4eLjGwcL1DR6ucfC0pTXmrEBCCCGEEJ+gsCKEEEII8YkohdXzEX53Z4FrHDxc4+DhGgcL1zd4uMbB02bWOLLkdUIIIYSQjgZDgYQQQgghPhG4sBKRmIjUiMhBEXk8xefdReT1+Oc7RWRI0DZ1NDys8fdE5JiI7Ik/Ho7CzvaKiLwoIkfjw8ZTfS4i8l/x9f+diIwO28b2joc1niQiJxP28JNh29ieEZFviMg7IrJPRD4Qkb9NcQz3cSvwuMbcx61ARC4TkXdFZG98jf85xTGRa4pAhZWI5AD4GYDpAIYDeEBEhicd9gMAn6nqUAD/DuCZIG3qaHhcYwB4XVVHxh+/CtXI9s9vAMQyfD4dwE3xx2IAPw/Bpo7Gb5B5jQFgS8IefioEmzoS5wH8naoOB1AE4K9TnCe4j1uHlzUGuI9bwzkA96jqCAAjAcREpCjpmMg1RdAeq7EADqrqx6r6JYDXAMxJOmYOgJfiP78BYIqIZB1ySL7GyxqTVqCqm2GjmtIxB8DLauwA0EdErg3Huo6BhzUmrUBVj6jq7vjPpwHsB5A8H4T7uBV4XGPSCuJ780z8Zbf4IzlRPHJNEbSwGgjgUMLrw7h0o319jKqeB3ASwFUB29WR8LLGAFAcd++/ISLfCMe0ToPX3wFpHePiIYC1InJr1Ma0V+KhkVEAdiZ9xH3sExnWGOA+bhUikiMiewAcBVChqmn3cVSagsnrnYMyAENU9XYAFWhU84S0F3bDxkmMAPDfAEoitqddIiI9ALwJ4FFVPRW1PR2RLGvMfdxKVPWCqo4EMAjAWBH5ZtQ2JRO0sKoDkOgdGRR/L+UxItIVQG8A9QHb1ZHIusaqWq+q5+IvfwXgjpBs6yx42eekFajqKRcCUNU1ALqJSN+IzWpXiEg32AX/f1V1eYpDuI9bSbY15j72D1U9AeAdXJqbGbmmCFpY7QJwk4hcLyK5ABYBKE06phTAd+M/zwfwtrK5VnPIusZJeRKzYbF/4h+lAL4Tr6oqAnBSVY9EbVRHQkSucXkSIjIWdu7iDZhH4mv3AoD9qvrTNIdxH7cCL2vMfdw6RORqEekT/zkPwL0APkw6LHJNEegQZlU9LyKPACgHkAPgRVX9QESeAlCpqqWwjfiKiByEJa8uCtKmjobHNf4bEZkNq1r5FMD3IjO4HSIirwKYBKCviBwG8I+wpEmo6i8ArAEwA8BBAGcBPBSNpe0XD2s8H8APReQ8gAYAi3gD1izGA/g2gOp4fgoAPAHgOoD72Ce8rDH3ceu4FsBL8Wr4LgCWquqqtqYp2HmdEEIIIcQnmLxOCCGEEOITFFaEEEIIIT5BYUUIIYQQ4hMUVoQQQgghPkFhRQghhBDiExRWhBBCCCE+QWFFCCGEEOITFFaEkA6BiAwRkTUiUiMiB0RkSdQ2EUI6HxRWhJB2j4h0gc1o+4WqFgC4DUChiCyO1jJCSGeDndcJIe0eEZkO4GFVLU5471oAm1T15ugsI4R0NuixIoR0BG4BsDfxjfgA4V7x4eSEEBIKFFaEkI7ABQA9Et8QEQGQDxs+TgghoUBhRQjpCGwEMCMuphz3AtitqhejMYkQ0hmhsCKEtHtUdS+AKgBPAYCI9AfwUwBPRGkXIaTzQWFFCGn3iMjjAAoB/ERE7gHwcwCDAfyPiAyJ0DRCSCeDVYGEEEIIIT5BjxUhhBBCiE9QWBFCCCGE+ASFFSGEEEKIT1BYEUIIIYT4BIUVIYQQQohPUFgRQgghhPgEhRUhhBBCiE9QWBFCCCGE+MT/Az5j8uYbSq5AAAAAAElFTkSuQmCC\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.signal as sig\n", "\n", "N = 32 # length of filter\n", "Omc = np.pi/3 # corner frequency of low-pass\n", "\n", "# specify desired frequency response\n", "Ommu = 2*np.pi/N*np.arange(N)\n", "Hd = np.zeros(N)\n", "Hd[Ommu <= Omc] = 1\n", "Hd[Ommu >= (2*np.pi-Omc)] = 1\n", "\n", "# compute impulse response of filter\n", "h = np.fft.ifft(Hd)\n", "h = np.real(h) # due to round-off errors\n", "# compute frequency response of filter\n", "Om, H = sig.freqz(h, worN=8192)\n", "\n", "# plot impulse response\n", "plt.figure(figsize = (10,3))\n", "plt.stem(h)\n", "plt.title('Impulse response')\n", "plt.xlabel(r'$k$')\n", "plt.ylabel(r'$h[k]$')\n", "# plot transfer functions\n", "plt.figure(figsize = (10,3))\n", "plt.plot(Om, np.abs(H), 'b-', label=r'designed $|H(e^{j \\Omega})|$')\n", "plt.stem(Ommu, np.abs(Hd), 'g', label=r'desired $|H_d[\\mu]|$')\n", "plt.plot([0, Omc, Omc], [1, 1, 0], 'r--')\n", "plt.title('Magnitude response of desired/designed filter')\n", "plt.xlabel(r'$\\Omega$')\n", "plt.legend()\n", "plt.axis([0, np.pi, -0.05, 1.5])\n", "# plot phase\n", "plt.figure(figsize = (10,3))\n", "plt.plot(Om, np.unwrap(np.angle(H)))\n", "plt.title('Phase of designed filter')\n", "plt.xlabel(r'$\\Omega$')\n", "plt.ylabel(r'$\\varphi(\\Omega)$')\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercises**\n", "\n", "* Does the resulting filter approximate the desired magnitude and phase response well?\n", "* Increase the length `N` of the filter. Does the attenuation in the stop-band improve?\n", "\n", "Solution: The desired magnitude and phase response is an ideal low-pass with zero-phase. The magnitude response of the designed filter approximates this only very coarsely and shows major ringing artifacts. The phase of the designed filter is also not zero for all frequencies. Increasing the length `N` of the filter does not improve the attenuation in the stop-band, it only changes the frequencies of the local minima of the ripples. The reason for the poor performance of the designed filter is the zero-phase of the desired transfer function which cannot be realized by a causal non-recursive system. This was [already discussed for the window method](../filter_design/window_method.ipynb#Zero-Phase-Filters). The frequency sampling method suffers additionally from time-domain aliasing due to the periodicity of the DFT. Again a linear-phase design is better in such situations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Design of Linear-Phase Filters\n", "\n", "The design of non-recursive FIR filters with a linear phase is often desired due to their constant group delay. As for the [window method](../filter_design/window_method.ipynb), the design of a digital filter with a generalized linear phase is considered in the following. For $|\\Omega| < \\pi$ its transfer function is given as\n", "\n", "\\begin{equation}\n", "H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\cdot \\mathrm{e}^{\\,-\\mathrm{j} \\alpha \\Omega + \\mathrm{j} \\beta}\n", "\\end{equation}\n", "\n", "where $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\in \\mathbb{R}$ denotes the amplitude of the filter, $-\\alpha\\,\\Omega$ its linear phase and $\\beta$ a constant phase offset. The impulse response $h[k]$ of a linear-phase filter shows specific symmetries which have already been discussed for the [design of linear-phase filters using the window method](../filter_design/window_method.ipynb#Causal-Linear-Phase-Filters). For the resulting four types of linear-phase FIR filters, the properties of $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ and the values of $\\alpha$ and $\\beta$ have to be chosen accordingly for the formulation of $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ and $H_d[\\mu]$, respectively. This is illustrated in the following for the design of a low-pass filter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example: Linear-phase approximation of an ideal low-pass\n", "\n", "We aim at the approximation of an ideal low-pass as a linear-phase non-recursive FIR filter. For the sake of comparison with a similar [example for the window method](../filter_design/window_method.ipynb#Example:-Causal-linear-phase-approximation-of-ideal-low-pass), we choose a type 1 filter with odd filter length $N$, $\\alpha = \\frac{N-1}{2}$ and $\\beta = 0$. The desired frequency response $H_\\text{d}[\\mu]$ is given by sampling\n", "\n", "\\begin{equation}\n", "H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\mathrm{e}^{\\,-\\mathrm{j} \\frac{N-1}{2} \\Omega} \\cdot \\begin{cases}\n", "1 & \\text{for } |\\Omega| \\leq \\Omega_\\text{c} \\\\\n", "0 & \\text{otherwise}\n", "\\end{cases}\n", "\\end{equation}\n", "\n", "which is defined for $|\\Omega| < \\pi$. Note that for sampling on the unit circle with $0 \\leq \\Omega < 2 \\pi$, the periodicity $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}(\\Omega+ n 2 \\pi)})$ for $n \\in \\mathbb{Z}$ has to be considered." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", 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8+OKLrFmzhtzc3AP7A/j888957rnn+Oc//8l5553Hiy++yEUXXVTisbp06VJsbGVZt24dY8aMOTDVwd69exk+fDg5OTl88cUXtG/fHvAz319++eU89thjHH300SxYsIB7772Xf//733z55Zd06NCBBQsWcPvtt9O5c2euu+46UlNT2b17N127dmXZsmURfCeKp5nXRUREDsN118Hq1ZHdZ8+e8MADpZdZsmQJo0ePpm7dugCMHDkSgEWLFrFixQpOOOEEALKysmjRogUXXHABkydP5vrrr2f48OGcfPLJRfa3dOlSRo0aRXJyMsnJyYwYMeLAtg4dOtCzZ08AevfufWBMUknH2rlzZ7GxlWbz5s00b96cTz/99MC6a6+9lg4dOrB9+3YaNWp0YP2cOXNYt24dZ599NgB5eXmcfPLJTJs2jWOOOQaAa665hmuuuQaANWvWFDlWUlISe/bsoX79+mXGdbiUWImIiNQAzjnGjx/PPffcc8i2lStXsmDBAm6++WYGDhzILbfcEtY+69Spc+D3+Pj4A12BJR3rgbKywmJkZGTQpUuXIus++eQTRo0aRUpKSpFZ0NesWcNdd93FZZddVu7jAOzfv5/k5OTDem64InFVoIiISK3zwAOweHFkl3DyklNOOYU5c+aQlZXFnj17mDdvHgADBw5k9uzZbNvm5+reuXMnX331Fd988w1169bloosuYsqUKaxcubLI/vr168e8efPIzs5m7969zJ8/v8wYSjpWSbGVZu3atXTu3LnIunXr1tGtWzcaN25Mfn7+geSqVatWLFy4kIICP8NTRkYGzrkyjwGwY8cOmjVrdtg3Vw6XWqxERESqkV69enH++efTo0cPWrRocaA7rnPnztx5550MHjyYgoICEhMTmTZtGrt372bKlCnExcWRmJjIww8Xnc/7hBNOYOTIkXTv3p0jjzySbt260bBhw1JjKOlYffv2LTa20mRkZDB8+PADj3fu3IlzjpYtWwIwePBg3n33XQYNGsSll17K22+/TadOnUhJSaFr164888wzYdXb22+/zbBhw8IqWxEWbqYXaenp6W758uUxObaIiMjhWL9+PZ06dYp1GBG3d+9e6tWrx759+zjllFN47LHHilylF2kDBgxg+vTpBwall2blypX89a9/5emnn67QMceMGcO9995Lx44dy4yhuPfZzFY459LLOo5arERERGq5iRMn8sknn5Cdnc348eOjmlSVV69evfjFL35Bfn5+mXNZlSQnJ4ezzjrrQFIVTUqsREREarlnn322Uo83YcKEIlf7leXSSy+t0PGSkpK45JJLKhRDuJRYiYiISKWaMGFCrEOIWgy6KlBEREQkQpRYiYiIiESIEisRERGRCFFiJSIiIhIhZSZWZvaEmW0zs49L2H6hma01swwze8/MekQ+TBEREZGqL5wWq+nA0FK2fwmc6pzrBtwBPBaBuERERESqnTKnW3DOvWNm7UvZ/l7Qww+ANhUPS0RERKT6ifQ8VpcBr5W00cwmAhMBjjrqqAgfWkREpGqZsyqT+xZu4JtdWbRulMKUIWmcdXxqrMOSKIrY4HUz+wU+sbq+pDLOucecc+nOufTmzZtH6tAiIiJVzpxVmdz4UgaZu7JwQOauLG58KYM5qzIjepzbbruNqVOnlvt5J510UtSOO2DAADZt2gTAo48+ylVXXVVke9euXVm/fv0hz9u0aRMpKSn07NmzzONnZWXRs2dPkpKS2L59+yHHjZWIJFZm1h14HBjlnNsRiX2KiIhUZ/ct3EBWbj47Ex9jZ6IffpyVm899CzfEODLvvffeO2Sdc46CgoKIHicjI6PIvQezs7PZtGlTifftO/roo1m9enWZ+01JSWH16tW0bt06YrFGQoUTKzM7CngJuNg591nFQxIREan+vtmVBUCOfUGOfXHI+oq466676NixI/3792fDhoOJ2jPPPEOfPn3o2bMnkyZNIj8/n59++olhw4bRo0cPunbtyqxZswCoV68e4FuJ0tLSuOSSS+jatSubN28udj+lHbc0a9euLZJYZWRk0LFjx7BvqDxgwAA+/fRTAHbs2EHXrl3Del6slDnGysyeAwYAzcxsC3ArkAjgnHsEuAVoCjxkZgB5zrn0aAUsIiJSHbRulEJmMUlU60YpFdrvihUrmDlzJqtXryYvL49evXrRu3dv1q9fz6xZs1i6dCmJiYlcffXVzJgxgyOOOILWrVvz6quvArB79+5D9vn555/z5JNP0rdv3xL306VLl2KPW5Z169YxZswYAjkCe/fuZfjw4WG/3o0bNx5o3Vq7di3dunUL+7mxEM5VgePK2H45cHnEIhIREakBpgxJ48aXMoqsS0mMZ8qQtArtd8mSJYwePZq6desCMHLkSAAWLVrEihUrOOGEEwA/BqlFixZccMEFTJ48meuvv57hw4dz8sknH7LPdu3a0bdv31L3s3PnzmKPW5rNmzfTvHnzAy1OANdeey0dOnQ4pOzChQv56KOPiqz76quvSE1NJS7Od7CtXbuW7t27l3ncWIr0VYEiIiICB67+Gz8vnv15+aRG+apA5xzjx4/nnnvuOWTbypUrWbBgATfffDMDBw7klltuKbL9iCOOKHM/DzzwQLljysjIoEuXLkXWffLJJ4waNQqAnJwcfve739GgQQM+/PBDpk2bdqCrEmDNmjVFEqkVK1Zw/vnnlzuOyqTESmqkvDz45BP4+GPYswfq1oW0NOjdG8Ls1hcRKdW3d9/N/vWfllrmeOCpbwsAo2fL6bAOviqlfJ1Ox9HypptK3ecpp5zChAkTuPHGG8nLy2PevHlMmjSJgQMHMmrUKH77298eaGHas2cPiYmJNGnShIsuuohGjRrx+OOPl7r/kvZT0nFLs3btWjp37lxk3bp16w505z388MOMHz+eE044gf79+1OnTp0iZVevXk12djbguytfeeUV7rzzzlKPGWtKrKRG2bABHnwQXngBvv/+0O3NmsGll8LkydCiReXHJyK1T72kehHdX69evTj//PPp0aMHLVq0ONBl17lzZ+68804GDx5MQUEBiYmJTJs2jd27dzNlyhTi4uJITEzk4YcfLnX/Je2nb9++xR63NBkZGUXGU+3cuRPnHC1btgRg1apVTJo0iT179tCsWbMD47AKrVmzhuTkZHr06EH37t3p3LkzTz75JH/84x/LW22VxpxzMTlwenq6W758eUyOLTVPZib84Q/w3HNQpw6MHOmXnj2hSRP48UdYvRpmz4aXXoKGDeHvf4cLL4x15CJSnaxfv55OnTrFOowqb8CAAUyfPp327duXWu65555j4cKF1K1bl3r16nH11VczfPhwPv7Y35742GOPZeXKldSvX7/EfbRv357ly5fTrFmzsI9bluLeZzNbEc7FeWqxkmqtoAAeeghuuglyc+H3v/dLaGtUq1a+K/D882H9erjsMrjoIli5Eu67D+IiNlWuiIiEa9y4cYwbd/Aauc2bN7N792569uzJkiVLMLMSk6qsrCx+/vOfk5ube2Bwe1WgxEqqrZ9+gvHj4cUX4fTT4eGH4eijy35ep06wZAn87ndw//3www/wr39BSAu0iIgcpgkTJtCoUaNyP69t27Zs3rz5wOPPPit5eszCCUIjcdxIUmIl1dJXX8GoUZCRAVOn+iSpPIlRfDz87W++S/COO6BpU99yJSIiFTdhwoRaddxgSqyk2nn3XRgzBnJy4NVXYejQw9/Xn/4EO3b45KxXLxhX6qxtIiIipas6nZIiYfjXv+C006BRI/jww4olVeBbuR54APr1gyuugE9Lv3JaRESkVEqspFrIy4Pf/AYuvxwGDPBJVVrFJi8+IDERZs3yVxP+8pcQuCWWiEixYnU1vVSOir6/SqykyvvhBzjzTD8/1W9/CwsWQOPGkT1Gaqofc/XBB/CPf0R23yJScyQnJ7Njxw4lVzWUc44dO3aQnJx82PvQPFbVUE4O/O9/fjLML77wE2F+/z3s3u2nHwBITvaTYTZv7q+U69TJt/CkVOzen5Xu009hxAg/WP2RR/zkntHiHAwfDv/9L3z+uZ+iQUQkWG5uLlu2bDkwG7jUPMnJybRp04bExMQi68Odx6rMxMrMngCGA9ucc12L2W7A34AzgX3ABOfcyrIOXKfVsS79N49G9b5JpZmzKpP7Fm7gm11ZtI7y/ZsqEkd+PqxbB++/75cPP/Qf+sHdVQkJPoFq1MjPx2QG+/bB9u1+Yszgcr17+660gQP9z8LzpirUR2gMg1umcf9vUklO9pN69usX/Rj+9z/odVYmrYZuYH98bM8NERGpOiKZWJ0C7AWeKiGxOhP4FT6xOhH4m3PuxLIOXKfVsa7V+AdISYznnjHdIv7B5VzJl9/PWZXJjS9lkJV7MDuJVhylKS6O5IR4xh7djfwvUnn/ffjoI3+vO/AtUH37Qo8evvXpuON8a1TjxiW/1uxs2LjR3zdv1Sp45x1YtsxPptmokZ+dvP2ATGZ9kUF2DOujuLooyI2n3ifd+M+jqRx1VKWEwZxVmUyemUG+xfbcEBGRqiViiVVgZ+2B+SUkVo8Ci51zzwUebwAGOOe2lrbP4+okuOlH+uni44mneVwj1h53Hkt7XE3B3n1cMedMCgrAFUCB811cr7eawPxmE0j5aTt3rD+HgsA2V+C3/yvpKmZxPs2zN/Pv/IuJM4iL93MWxcfBzNTJrD9mBK7Vk9z25lRyzYeY6Hyfz4yBl/C3f00hbu1quO66Q4O++2446SR47z0/1XeoBx7w91B5800o7iaRjz7qM6J58+Avf2Hl17vIycs/EMcfhk1la4PmnLHiA8a+uYQj6kGDBtCwgf+ZPH821rwZTJ/ul1ALFvi7DT/0EDz//KHbFy8GIOfuqfz43Hy2f+9bteJb7GJ/cgIjL/SJw62L69PvqzUkJcTT66jARGtNm/qZOAFuvNE3nwVr0waeecb/ft11/v4xwTp2hMce879PnAghk749n9uUP5x8KTsTH+Ofc1bQbrcfRHUghp//HArvtH722X6OhGADB0LhvaPOOAOysopuHz7cT8kOvqku1HnnwdVXc9rtC7j78esPOTcWnXgG//fC//MVds45hz7/qqv8tO6bN8PFFx9cf8EF/vWKiEi1Vpm3tEkFNgc93hJYd0hiZWYTgYkAaUkHx83nkc+mr+D1r+HxxdAoCc7KCnRrxfmfceZn2s5v7McPJSYdXF9Ypn93aNwVmmdDu/k+2SrI991m+QU+Odm+Heqn+r5xZ4EP30BuuWNfDklJcFoTuDsL6iRBUhIk1fE/N/4X6sRB+2+hRUH4t0HJy/ctR8vehrX/AZsP/VZCTqN8LDiOgPi6OfTv7xPCohUY3vHKkpQEzZr6pcDBR1/mAwnk2BeBEj0AyMmrvMvj9u7P88e0LyhgL9C40mMA2Lrbvxeh58YP+3LLv7PC5FKJlYhIrRGJFqv5wL3OuXcDjxcB1zvnSh2ZHtc6xR11yWwAWjdMYekNp1XaLUX63fsWmbuy+DbpBgBa5twLQIP4FEbaaWzdClu3wrff+p/bth0cFB6scWM/wLlp04Njm8x8N9vu3bBrl18Ku/IKNWvmu/Mye79Flh0aR2ojXx+VpaT6cHtTGN/kNC6/nKh2xeXlQc8/vsVeV3Xr4rDiKGwZC7QUiohI9VWZLVaZQNugx20C68KSkhjPH4amVep92qYMSePGlzIOieP2MWmcdfyh5fPy/FV3hYlWaOK1Y4cf01VQ4H8mJvqxTw0b+iU1Fdq180uHDv4GwWYwZ1XxcUwZEqEJmsJUXH0kxsXTYmcadz4Ed90Fw4bBlVfCkCHFtKRVwDvvwLXXwpd5aRw5vGrWRZ34w4xj8uQIRSUiItVFJBKrucC1ZjYTP3h9d1njqwqlxuiKq8LjjZ8Xz/68/DLjSEjwLVOtWsHxxSRelRVHtJQWx6a74Z//9DOez5vnk8OJE/20By1bHv4xly3zCdsrr/jWsKf/moq1hwnzq1Zd5P+YwtEcZhwjRkQ4OhERqerCuSrwOWAA0Az4DrgVSARwzj0SmG7hH8BQ/HQLvyyrGxCgfof6bs+Xe8oqFlUDpg8AYPGExYqjjDhycnwS9Mgj8NZbPtk880y/DB3qE64jKtzfAAAflklEQVSybNvm9/Hkk7B0qb8q8brrYMoUP+a+rBgqU2EcnT5czL//DVu2+C7cctmwwf+M1BTxIiISMxHrCnTOlXpbWuczs2vKEZtUQ0lJcO65ftmwwV/g9+KLMHeu356a6i+I7NjRd3XWq+fHmv3wg58bavVqP+UD+Gki7rvPt3w1aBC71xSOX/3KJ5OPPw433FDOJ0+a5H9qjJWISK0Ria5AqWXS0uAvf4GpU/3M6K+/DitW+HmyFi/2V28WiouDtm2hc2e45BI4/XTfnVqZY+oqonNnGDQIpk3zszUk6C9GRERKoY8JOWxm/lY5nToVXf/TT37m96Qk38UXcleAaufXv/YTqb7yip9CS0REpCS6CbNE3BFH+FvsNGxY/ZMq8OPI2rSBJ56IdSQiIlLVKbESKUN8PEyYAP/5D2SGPZGIiIjURkqsRMIwYYKfp+ypp8rxpJtv9ouIiNQaSqxEwnD00X4i9See8JPAhmXQIL+IiEitocRKJEyXXgobN8KSJWE+YfXqQ29GLSIiNZoSK5EwnX22n5/r6afDfMJ11/lFRERqDSVWImGqWxfOOstPjJqTE+toRESkKlJiJVIOY8f62eRffz3WkYiISFWkxEqkHE4/HZo0gZkzYx2JiIhURUqsRMohKQnOOQfmzPGzy4uIiAQLK7Eys6FmtsHMNprZIbeiNbOjzOxtM1tlZmvN7MzIhypSNYwd62/bM39+GQXvvtsvIiJSa5SZWJlZPDANOAPoDIwzs84hxW4GnnfOHQ+MBR6KdKAiVcUpp0CrVmF0B550kl9ERKTWCKfFqg+w0Tn3hXMuB5gJjAop44AGgd8bAt9ELkSRqiU+3k+98NprvuWqRO+95xcREak1wkmsUoHNQY+3BNYFuw24yMy2AAuAXxW3IzObaGbLzWx5bm7uYYQrUjWMHg3Z2bBwYSmFbrrJLyIiUmtEavD6OGC6c64NcCbwtJkdsm/n3GPOuXTnXHpiYmKEDi1S+U45xV8d+PLLsY5ERESqknASq0ygbdDjNoF1wS4Dngdwzr0PJAPNIhGgSFWUkAAjRvgB7Gp8FRGRQuEkVsuAY82sg5kl4Qenzw0p8zUwEMDMOuETq+8jGahIVTN6NOzaBYsXxzoSERGpKspMrJxzecC1wEJgPf7qv3VmdruZjQwUmwxcYWZrgOeACc45F62gRaqCwYP9bW7UHSgiIoUSwinknFuAH5QevO6WoN8/AfpFNjSRqi0lBYYO9ZOF/uMfEBf6NeWBB2ISl4iIxI5mXhepgNGjYetW+OijYjb27OkXERGpNZRYiVTAsGF+Xqu5oaMOAd580y8iIlJrKLESqYDGjaF/f3j11WI23nmnX0REpNZQYiVSQcOGwdq1sHlz2WVFRKRmU2IlUkHDhvmfCxaUXk5ERGo+JVYiFdSpE7RvX0J3oIiI1CpKrEQqyMy3Wi1a5O8fKCIitZcSK5EIGDYM9u0LmYX90Uf9IiIitYYSK5EIGDDATxg6f37QyrQ0v4iISK2hxEokAlJSYOBAP87qwM2c5s3zi4iI1BpKrEQiZNgw2LQJ1q8PrPjLX/wiIiK1hhIrkQgpnHZBVweKiNReYSVWZjbUzDaY2UYzu6GEMueZ2Sdmts7Mno1smCJVX9u20K0bvPZarCMREZFYKTOxMrN4YBpwBtAZGGdmnUPKHAvcCPRzznUBrotCrCJV3pAh8O67sHdvrCMREZFYCKfFqg+w0Tn3hXMuB5gJjAopcwUwzTn3A4BzbltkwxSpHoYOhdzckGkXRESk1kgIo0wqEHwXtC3AiSFlOgKY2VIgHrjNOfef0B2Z2URgIkCd1DqHE69Ilda/P9StCwsXwvCnn451OCIiUskiNXg9ATgWGACMA/5pZo1CCznnHnPOpTvn0hMTEyN0aJGqo04dP6fVwoX4QVdt28Y6JBERqUThJFaZQPCnQ5vAumBbgLnOuVzn3JfAZ/hES6TWGTIEPv8ctv19FsyaFetwRESkEoWTWC0DjjWzDmaWBIwF5oaUmYNvrcLMmuG7Br+IYJwi1caQIf5n3t8fhocfjm0wIiJSqcpMrJxzecC1wEJgPfC8c26dmd1uZiMDxRYCO8zsE+BtYIpzbke0ghapyjp2hHbtYOfOWEciIiKVLZzB6zjnFgALQtbdEvS7A34XWERqNTPfavXDv6DAaRZeEZHaRP/zRaJgyBDIz4cff4x1JCIiUpmUWIlEwcCBYKg7UESktgmrK1BEyqdhQ7jvxNlkZcOiWAcjIiKVRi1WIlHSd3gz3l7bjO+/j3UkIiJSWZRYiUTJBbnTucRN5403Yh2JiIhUFiVWIlHSYfF0rkiY7mdhFxGRWkGJlUiUmEHjxv72NgUFsY5GREQqgxIrkShq0gS++w7Wro11JCIiUhmUWIlEUeMm/qe6A0VEagclViJRVCcJundXYiUiUlsosRKJlgULYMEChg6Fd9+FPXtiHZCIiESbEiuRaKlbF+rWZehQyM2Ft9+OdUAiIhJtYSVWZjbUzDaY2UYzu6GUcmebmTOz9MiFKFJNPfQQPPQQ/frBEUeoO1BEpDYoM7Eys3hgGnAG0BkYZ2adiylXH/gN8GGkgxSplp5/Hp5/nqQkOO00eO01cC7WQYmISDSF02LVB9jonPvCOZcDzARGFVPuDuDPQHYE4xOpEYYOhS+/hI0bYx2JiIhEUziJVSqwOejxlsC6A8ysF9DWOfdqaTsys4lmttzMlufm5pY7WJHqasgQ//M//4ltHCIiEl0VHrxuZnHA/cDksso65x5zzqU759ITExMremiRauPoo+GYYzTOSkSkpgsnscoE2gY9bhNYV6g+0BVYbGabgL7AXA1gFylq6FB/ZWC2OstFRGqscBKrZcCxZtbBzJKAscDcwo3Oud3OuWbOufbOufbAB8BI59zyqEQsUl0sXuyXgCFDYN8+P6eViIjUTGUmVs65POBaYCGwHnjeObfOzG43s5HRDlCkphgwAJKS1B0oIlKTJYRTyDm3AFgQsu6WEsoOqHhYIjXA1Kn+5+9/D0C9enDyyX4A+333xTAuERGJGs28LhIt8+f7JcjQofDxx7BlS4xiEhGRqFJiJVKJCqddeP312MYhIiLRocRKpBJ17QqtW2s+KxGRmkqJlUglMvPdgW+8AXl5sY5GREQiTYmVSLSkpPglxJAhsGsXfPRRDGISEZGoCuuqQBE5DK+9VuzqQYMgLs5Pu3DSSZUck4iIRJVarEQqWZMmcOKJGmclIlITKbESiZY77vBLMYYMgWXLYPv2So5JRESiSomVSLQsWuSXYpxxBjinVisRkZpGiZVIDKSnQ8uWMHdu2WVFRKT6UGIlEgNxcTB8uG+xysmJdTQiIhIpSqxEYmTECNizB955J9aRiIhIpISVWJnZUDPbYGYbzeyGYrb/zsw+MbO1ZrbIzNpFPlSRaqZpU7+UYNAgSE5Wd6CISE1SZmJlZvHANOAMoDMwzsw6hxRbBaQ757oDs4H/F+lARaqdF1/0Swnq1vXJ1bx5fiC7iIhUf+G0WPUBNjrnvnDO5QAzgVHBBZxzbzvn9gUefgC0iWyYIjXTiBGwaRN8/HGsIxERkUgIJ7FKBTYHPd4SWFeSy4Bip5w2s4lmttzMlufm5oYfpUh1dOONfinF8OH+57x5lRCPiIhEXUQHr5vZRUA6cF9x251zjznn0p1z6YmJiZE8tEjV8/77filF69Z+6gUlViIiNUM4iVUm0DbocZvAuiLMbBDwf8BI59z+yIQnUvONGAEffgjffRfrSEREpKLCSayWAceaWQczSwLGAkWuYzKz44FH8UnVtsiHKVJzjRzpB6/r6kARkeovoawCzrk8M7sWWAjEA08459aZ2e3AcufcXHzXXz3gBTMD+No5NzKKcYvUGD16wM9+BrNnwxVXVGxfn34Ks2b5+xD+8IO/4XP37r5V7MQTwf95iohItJSZWAE45xYAC0LW3RL0+6AIxyVS/bUJ7+JYMzj3XJg6FXbsKHXqqxJlZsKvfw0vveT316ULtGgBX38Nr70Gd98NJ5wAd94JgweXf/8iIhIezbwuEi3PPOOXMJxzDuTnwyuvlP8wixZB164+gbr1Vti6FTIy/Po1a2D7dnjkEZ+0DRkCF10Eu3eX/zgiIlI2JVYiVUDv3tC+ve8OLI8XXoChQ33j2Nq1cNttcOSRRcs0agSTJsEnn8Att/iuwhNOgHXrIhW9iIgUUmIlEi3XXeeXMBR2B775ph8bFY4334QLL/Rjp5YuhWOOKb18nTrwpz/BW2/Bjz/Cz3+u+xSKiESaEiuRaFm92i9hOvdcyM0N7+rAL77w3YedOsH8+dCgQfhhnXwyLF8Oqam+a/C1YqfzFRGRw6HESqSKSE+Hdu18915p9u+H88/3rVxz5viuvvJq08a3VnXqBKNGweuvH17MIiJSlBIrkSqisDvw9df9gPOS3H23b3F64gno0OHwj9e8uR/g3qkTjB4N7713+PsKlpMDr74KV10FffpAy5ZwxBF+7FevXn5KiRkzYM+eyBxPRKQqUWIlUoVcfLHvDpw1q/jtn34K99zjx1aNHl3x4zVu7BO51q1h2DA/AP5w7d7tk77UVH8PxBkzoF49PwHqlVfCWWf5ZO7FF/2ViS1awIQJflC9iEhNEdY8ViJyGDp2LPdTunf3E4Y+9RRcc03Rbc75VqB69eD++yMUI74l6c03oV8/n1x9+KFPtMLlnE8Er7vO35bnjDN87KefDklJh5YvKPC3UJwxA5580i9jx8Kf/wxHHRW511Xoxx9hwwY/p9e+fX5ds2b+WGlpkKD/giISQfqXIhItjz12WE+75BKYPNm3Th133MH18+fD4sXw0EO+tSeS2rXz3Xf9+/vWpnfe8QlcWX78ES67zE8T0bu3v5n0CSeU/py4OJ/E9esHt98ODzwAf/mLn8Pr5pvhD3+oeLKzZo1P3F5/3f9ekuRk3105YoRvATz66IodNxzOQVaWf43FJZ4iUr2pK1CkirngAp98PP30wXX5+XDTTXDssXD55dE5bo8evuVpzRofQ35+6eXXr/dJycsvw733+pauspKqUM2a+dngP/0UzjwT/u//4KST/OPyKiiA55/3MfTs6RO2xo3hjjt8jKtXw+efw2ef+fFkTz3luyh374YpU/x0FQMH+iQxL6/8xy/ODz/4/V17LQwY4MebJSb6MWd16vjEqkMHf3XmlCk+uY325K15ebB5s7/t0dKlsGSJn1D2u+/Kfs9FpGxqsRKJlokT/c9ytly1bOk/aJ9+2icFcXHw7LPw8cc+8UlMjEKsAWeeCQ8+6BOB3/8e/vrX4su9/77vNkxK8gPgTz21Ysdt184nIM8/D1dfDccf77s7r7wyvPsbvvoq3HCDr6PjjoO//c2PQyvp9kDHHuvn8br4Yv/4q698C9ejj/oLCDp2hD/+0XdRlrf1bN8+n8j9+9/w9ts+4atXD7p1862BRx7pp8fIz/cD+L/+2ndVPvigv61RQoK/7dDYsX5cWv365Tt+qM2bff28/z589JFPLAsKii+bkuJn8e/ZE37xCxg0yI+Li5ScHP8erVvnE/PvvvN3BMjK8ud1nTrQqhW0bevfg/R0fwVrtO5x+eOP8L//+bsV7Nnj37s6daBuXX/utG/vxwzGVUITREEB7Nrl6yI7258HDRr4JT4++seXyFFiJRItn3122E+95BIYN86PfRo40CdYxx/v566KtmuugY0bfYvPz34Gv/pV0e0LF8KYMX4c1htv+A+fSDnvPDjlFPjlL32CtWSJT3ZKSi62bPH3SHz5Zf9B/Oyzfh/l/SBq1863CF5/ve+S/NOffNJ1550+2Rk2rOwP9x07fHL097/7lqr27eHGG32y2qdP2QlaVhZ88IGfV2zWLH8ONGjgB/hfc035hux9950fuzZzJqxa5dcdeaSP4+yz/fiyVq18YhwX5z/Qt23zScbatX7Kj3/+0z/vxBN9C+Z55/mkv7w++8y/P2+9Be++e3CcW0KCj6lJE5/I5Ob6Oli0qGirXYsW/m9g6FD/hSP0zgLhysvzLZXvvut/LlvmX3NZkpJ8UnziiX45/XRfdxXxzTf+vV6+HFas8PPSbd7sp1IJZeYTzWOO8Vfwnngi9O3rH1c04fzpp4PT7a1eDZs2+fuOfvutT+5ycvz71KiRX446yp+HaWm+Zfj4430iWlH79/tEe+1av3z1lU92t23z2/Lz/XnauLE/X9q29TGkpR2cpiYSyff+/f5imowMv2ze7OP4/nt/bobLnHNlFzIbCvwNiAced87dG7K9DvAU0BvYAZzvnNtU2j7rd6jv9nwZ2+utB0wfAMDiCYsVRxWJoyrEELE4Bvh9sLj8+9i/3//z6NfPf8Cffbb/sKuMxAr8P7Kzz/aTlc6e7RMp8InU8OHQuTP85z+H/yFXloICP5j95pt969ILL/gPt0LO+Rah3/zGf2DecosflxapMUsFBX6OsJtu8q1Jgwf7FrQuXQ4tu2uXvxryoYf8B9VZZ/lk79RTD7+lwzn/4f/ww74VLzfXjwO7+WafHJX0nP/+F/7xD58c5uX5D+DRo/2VmWlp4X/45Of7D/zXX/dXca5e7V/L0KE+4R06tPTkdetW39U6a9bBxK5rV98KdvLJ/vdjjim59XXPHt+qtWKFb2l74w3/IWvm/6wuvNCfn2XN4ZaV5ccmvvIKLFhw8K4GnTr5ujnuOB9H69Y+eT/iCJ9M/PST/zD98kv/JWPlSp+IFU4R0quXT5jPPdefl2XVa16e/5Lw2mv+7yYjw69PSPB1kZbmk5bWrQ92E+fl+Ra1nTsPxrFu3cEYWrb0F4qceaZP9ho2LD0G8Of1smX+fX3jDV+3hd3eTZv6ukhN9YljSor/e8rL8+f4zp0+8frsMx8X+DjT033CO2yYT7TCOccK43jrrYMJd3a235ac7L+UtGzp/78kJ/t6Koxjxw4fx5YtB/fXurUfQjBokI+jTZuyYwC/z/ff9y3Lb7/tfy9MbuvU8e9Jy5Y+ua9bF55+2lY459LL2m+ZiZWZxQOfAacDW4BlwDjn3CdBZa4GujvnrjSzscBo59z5pe1XiZXiqKoxRCyOCiRWAGNvyOTd3RtIaJAF+1K4f0IaY3qnHn485bRvn28pWL8vk6PHbGBHVhb5P6ZQ74s03nsulcaNox/D4sW+5W73brjizkyW52zgm11ZJOamkPlaGn2OTOVf//Ita9GQm+sTpttu8x9okybBiedl8uj7Po768SlseyONbctTufBC3x1ZXPJVEd9952+i/eCD/sNt8GA47ZeZzN3kY2jVKIVBzdN44/FUPvjAj1sbP96PxQu++KEiPvnEd5U+8YRvzejQwXfTtuqbySPv+ThaN0phRLs0Vs1J5aWX/IdWnz6+S/Pcc8P/sCtOQYFP7l55xbdKbtzoP/SHDfNTd+S3yeSBtw7GMfqYNDa+mcrMmf7cadrUfyEYOdL/WTZpUv4Y8vN9QvTaaz5Je+89H1eXLv4cHTcO1u7O5L6FB+M4+9g0vl7i4/juO59InnyyT0xPPdVfBZycXL4Y1q/3CcCiRb71eNcuv98hQ3wMI0fCm58XjWP00WlkvpfKCy/4FikznxwOGuS/vB1/vE+owkmKnDvY4vb++/5Cl+XL/fpWrXyiN2IEZB+ZyYOLD8Yw+fQ0muxJZfZseOkln3yDT0xPO813zffo4ZO7cLrf9+71X3o++MC/F0uW+BYm8PsZNsy/51uTMvnLGwfj+O1padTdnsqLL/rzaccO/7qPP94n/iee6GMqLg6zyCVWPwduc84NCTy+0VeuuyeozMJAmffNLAH4FmjuStm5EivFUVVjiFgcFUis5qzK5PoXM9ifd3A0cUpiPPeM6cZZx1decvX0O5n8cW4GJByMIzkhnnvPrrw4vv0WRv06k61tM4hLPBhHAvH8v3O7VUqyuX073HorPPXfTJoMycCC4rD8eK7r143fnBXdOPbs8UneAy9nktivaF0U5MYTt7wb149N5Ze/LN+HdXnk5vpuvWnTYPn3mTQ949A4sv/bjYtOSeWqq3xrY6Q551uyZszwXZ0/Ns6k2RlF35OC3Hj2LOrGiO6pjB/vk5hIT6vx/fe+JfW553yLS91OmTQflgHxRePY/UY3Bh6TygUX+IQqnKttw1XY4jJnjm/Z3LIFGvXIpPHgDAriDo3jFz9L5dxzfRLWrFnk4ti2zSecr77qk7281EPPDZcXz/YF3Sj4MpUzz/St4IMHR24Mn3M+6Xz1Vb+8+y7U6XjoueFy49n+WjcSMlMPXA182mmE9UUxkonVOcBQ59zlgccXAyc6564NKvNxoMyWwOP/BcqUOH/0MQ3qukWjKqlfowSrv/X3cevZsqfiqCJxVIUYIhVH4+XLAPghvZyXygGrvt5VJKkqVCchnuOPOox72BymqhLHyq93kVMF4ljx1S5yi7l0rjLjKKkukhLi6VUF6qIy43DOx5FXENs4svdDxje7yHexi8MBP+6GDTt2UUDs4ihwsOqrXeQW854kxMVzfNtGlTIYPzcP1mwp/txIiIunV7tGxJVzXFb7Z54OK7Gq1MHrZjYRmAhwdL2Uyjx0seolRfCrQwUojqoVA0QmjsNJqAoVl8yUtj5aqkocxSUSsYijuESisuMoqS5KWh8tJdVFZcZhRrEfnJUdR3Idik2qKjMOw4+zKtgR2zjijGKTKvDvVWVd4ZiYUPK5kVeQX+6kqjxi1hWYnp7uli9fHoGXIFLz9Lv3LTJ3HXoZSmqjFJbecJriqMVxVIUYFIfiqOoxRCOOcLsCw7lmZRlwrJl1MLMkYCwwN6TMXGB84PdzgLdKS6pEpHRThqSRklj0q11KYjxThqQpjloeR1WIQXEojqoeQyzjKLMr0DmXZ2bXAgvx0y084ZxbZ2a3A8udc3OBfwFPm9lGYCc++RKRw1Q4MDz4yp4pQ9IqdeC64qiacVSFGBSH4qjqMcQyjrDmsYoGdQWKiIhIdRGxqwKjxcz2ABticvDaoxlQ4pWZEhGq4+hTHUeX6jf6VMfRVxl13M45V+YEEbG8pc2GcDI/OXxmtlx1HF2q4+hTHUeX6jf6VMfRV5XquBJuLSkiIiJSOyixEhEREYmQWCZWj8Xw2LWF6jj6VMfRpzqOLtVv9KmOo6/K1HHMBq+LiIiI1DTqChQRERGJkKgnVmY21Mw2mNlGM7uhmO11zGxWYPuHZtY+2jHVNGHU8QQz+97MVgeWy2MRZ3VlZk+Y2bbAzcaL225m9mCg/teaWa/KjrG6C6OOB5jZ7qBz+JbKjrE6M7O2Zva2mX1iZuvM7DfFlNF5XAFh1rHO4wows2Qz+8jM1gTq+E/FlIl5ThHVxMrM4oFpwBlAZ2CcmXUOKXYZ8INz7hjgr8CfoxlTTRNmHQPMcs71DCyPV2qQ1d90YGgp288Ajg0sE4GHKyGmmmY6pdcxwJKgc/j2SoipJskDJjvnOgN9gWuK+T+h87hiwqlj0HlcEfuB05xzPYCewFAz6xtSJuY5RbRbrPoAG51zXzjncoCZwKiQMqOAJwO/zwYGmlkU7ztd44RTx1IBzrl38LdqKsko4CnnfQA0MrNWlRNdzRBGHUsFOOe2OudWBn7fA6wHQu/rofO4AsKsY6mAwLm5N/AwMbCEDhSPeU4R7cQqFdgc9HgLh55oB8o45/KA3UDTKMdVk4RTxwBnB5r3Z5tZ28oJrdYI9z2Qivl5oAvgNTPrEutgqqtA18jxwIchm3QeR0gpdQw6jyvEzOLNbDWwDXjDOVfieRyrnEKD12uHeUB751x34A0OZvMi1cVK/O0kegB/B+bEOJ5qyczqAS8C1znnfox1PDVRGXWs87iCnHP5zrmeQBugj5l1jXVMoaKdWGUCwa0jbQLrii1jZglAQ2BHlOOqScqsY+fcDufc/sDDx4HelRRbbRHOeS4V4Jz7sbALwDm3AEg0s2YxDqtaMbNE/Af+DOfcS8UU0XlcQWXVsc7jyHHO7QLe5tCxmTHPKaKdWC0DjjWzDmaWBIwF5oaUmQuMD/x+DvCW0+Ra5VFmHYeMkxiJ7/uXyJkLXBK4qqovsNs5tzXWQdUkZtaycJyEmfXB/+/SF7AwBeruX8B659z9JRTTeVwB4dSxzuOKMbPmZtYo8HsKcDrwaUixmOcUUb0Js3Muz8yuBRYC8cATzrl1ZnY7sNw5Nxd/Ij5tZhvxg1fHRjOmmibMOv61mY3EX7WyE5gQs4CrITN7DhgANDOzLcCt+EGTOOceARYAZwIbgX3AL2MTafUVRh2fA1xlZnlAFjBWX8DKpR9wMZARGJ8CcBNwFOg8jpBw6ljnccW0Ap4MXA0fBzzvnJtf1XIKzbwuIiIiEiEavC4iIiISIUqsRERERCJEiZWIiIhIhCixEhEREYkQJVYiIiIiEaLESkRERCRClFiJiIiIRIgSKxGpEcysvZktMLMNZvaZmd0Y65hEpPZRYiUi1Z6ZxeHv0faIcy4N6Aakm9nE2EYmIrWNZl4XkWrPzM4ALnfOnR20rhXwX+dcx9hFJiK1jVqsRKQm6ASsCV4RuIFwg8DNyUVEKoUSKxGpCfKBesErzMyAuvibj4uIVAolViJSEywGzgwkU4VOB1Y65wpiE5KI1EZKrESk2nPOrQFWAbcDmNmRwP3ATbGMS0RqHyVWIlLtmdkNQDpws5mdBjwMtAMeMrP2MQxNRGoZXRUoIiIiEiFqsRIRERGJECVWIiIiIhGixEpEREQkQpRYiYiIiESIEisRERGRCFFiJSIiIhIhSqxEREREIkSJlYiIiEiE/H/FZO/3ItrrSwAAAABJRU5ErkJggg==\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 33 # length of filter\n", "Omc = np.pi/3 # corner frequency of low-pass\n", "\n", "# specify desired frequency response\n", "Ommu = 2*np.pi/N*np.arange(N)\n", "Hd = np.zeros(N)\n", "Hd[Ommu <= Omc] = 1\n", "Hd[Ommu >= (2*np.pi-Omc)] = 1\n", "Hd = Hd * np.exp(-1j*Ommu*(N-1)/2)\n", "\n", "# compute impulse response of filter\n", "h = np.fft.ifft(Hd)\n", "h = np.real(h) # due to round-off errors\n", "# compute frequency response of filter\n", "Om, H = sig.freqz(h, worN=8192)\n", "\n", "# plot impulse response\n", "plt.figure(figsize = (10,3))\n", "plt.stem(h)\n", "plt.title('Impulse response')\n", "plt.xlabel(r'$k$')\n", "plt.ylabel(r'$h[k]$')\n", "# plot frequency response\n", "plt.figure(figsize = (10,3))\n", "plt.plot(Om, np.abs(H), 'b-', label=r'designed $|H(e^{j \\Omega})|$')\n", "plt.stem(Ommu, np.abs(Hd), 'g', label=r'desired $|H_d[\\mu]|$')\n", "plt.plot([0, Omc, Omc], [1, 1, 0], 'r--')\n", "plt.title('Magnitude response of desired/designed filter')\n", "plt.xlabel(r'$\\Omega$')\n", "plt.legend()\n", "plt.axis([0, np.pi, -0.05, 1.5])\n", "# plot phase\n", "plt.figure(figsize = (10,3))\n", "plt.plot(Om, np.unwrap(np.angle(H)))\n", "plt.title('Phase of designed filter')\n", "plt.xlabel(r'$\\Omega$')\n", "plt.ylabel(r'$\\varphi(\\Omega)$')\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercises**\n", "\n", "* Does the designed filter have the desired linear phase?\n", "* Increase the length `N` of the filter. What is different to the previous example?\n", "* How could the method be modified to change the properties of the frequency response?\n", "\n", "Solution: The designed filter has the desired linear phase in the pass-band, here below $\\Omega = \\frac{\\pi}{3}$. Increasing the length `N` of the filter results in a better approximation of the desired ideal low-pass, especially in a higher attenuation in the stop-band." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparison to Window Method\n", "\n", "For a comparison of the frequency sampling to the [window method](../filter_design/window_method.ipynb) it is assumed that the desired frequency response $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ is given. For both methods, the coefficients $h[k]$ of an FIR approximation are computed as follows\n", "\n", "1. Window Method\n", "\\begin{align}\n", "h_\\text{d}[k] &= \\mathcal{F}_{*}^{-1} \\{ H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\} \\\\\n", "h[k] &= h_\\text{d}[k] \\cdot w[k]\n", "\\end{align}\n", "\n", "2. Frequency Sampling Method\n", "\\begin{align}\n", "H_\\text{d}[\\mu] &= H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j} \\frac{2 \\pi}{N} \\mu}) \\\\\n", "h[k] &= \\text{DFT}_N^{-1} \\{ H_\\text{d}[\\mu] \\}\n", "\\end{align}\n", "\n", "For finite lengths $N$, the difference between both methods is related to the periodicity of the DFT. For a desired frequency response $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ which does not result in a FIR $h_\\text{d}[k]$ of length $N$, the inverse DFT in the frequency sampling method will suffer from time-domain aliasing. In the general case, filter coefficients computed by the window and frequency sampling method will hence differ.\n", "\n", "However, for a rectangular window $w[k]$ and $N \\to \\infty$ both methods will become equivalent. This reasoning motivates an oversampled frequency sampling method, where $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ is sampled at $M \\gg N$ points in order to derive an approximation of $h_\\text{d}[k]$ which is then windowed to the target length $N$. The method is beneficial in cases where a closed-form inverse DTFT of $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$, as required for the window method, cannot be found." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example: Oversampled frequency sampling method\n", "\n", "We consider the design of a linear-phase approximation of an ideal low-pass filter using the oversampled frequency sampling method. For the sake of comparison, the parameters have been chosen in accordance to a [similar example using the window method](../filter_design/window_method.ipynb#Example:-Causal-linear-phase-approximation-of-ideal-low-pass). Using $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ from the previous example in this section, the filter is computed by\n", "\n", "1. (Over)-Sampling the desired response at $M$ frequencies\n", "\\begin{equation}\n", "H_\\text{d}[\\mu] = H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j} \\frac{2 \\pi}{M} \\mu})\n", "\\end{equation}\n", "\n", "2. Inverse DFT of length $M$\n", "\\begin{equation}\n", "h[k] = \\text{DFT}_M^{-1} \\{ H_\\text{d}[\\mu] \\}\n", "\\end{equation}\n", "\n", "3. Windowing to desired length $N$\n", "\\begin{equation}\n", "h[k] = h_\\text{d}[k] \\cdot w[k]\n", "\\end{equation}\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 33 # length of filter\n", "M = 8192 # number of frequency samples\n", "Omc = np.pi/2 # corner frequency of low-pass\n", "\n", "# specify desired frequency response\n", "Ommu = 2*np.pi/M*np.arange(M)\n", "Hd = np.zeros(M)\n", "Hd[Ommu <= Omc] = 1\n", "Hd[Ommu >= (2*np.pi-Omc)] = 1\n", "Hd = Hd * np.exp(-1j*Ommu*(N-1)/2)\n", "\n", "# compute impulse response of filter\n", "h = np.fft.ifft(Hd)\n", "h = np.real(h) # due to round-off errors\n", "h = h[0:N] # rectangular window\n", "# compute frequency response of filter\n", "Om, H = sig.freqz(h, worN=8192)\n", "\n", "# plot impulse response\n", "plt.figure(figsize = (10,3))\n", "plt.stem(h)\n", "plt.title('Impulse response')\n", "plt.xlabel(r'$k$')\n", "plt.ylabel(r'$h[k]$')\n", "# plot frequency response\n", "plt.figure(figsize = (10,3))\n", "plt.plot(Om, 20 * np.log10(abs(H)), label='rectangular window')\n", "plt.plot([0, Omc, Omc], [0, 0, -100], 'r--')\n", "plt.title('Magnitude response of designed filter')\n", "plt.xlabel(r'$\\Omega$')\n", "plt.ylabel(r'$|H(e^{j \\Omega})|$ in dB')\n", "plt.axis([0, np.pi, -100, 3])\n", "plt.legend()\n", "plt.grid()\n", "# plot phase\n", "plt.figure(figsize = (10,3))\n", "plt.plot(Om, np.unwrap(np.angle(H)))\n", "plt.title('Phase of designed filter')\n", "plt.xlabel(r'$\\Omega$')\n", "plt.ylabel(r'$\\varphi(\\Omega)$')\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercises**\n", "\n", "* Compare the designed filter and its properties to the [same design using the window method](../filter_design/window_method.ipynb#Example:-Causal-linear-phase-approximation-of-ideal-low-pass)\n", "* Change the number of samples `M` used for sampling the desired response. What changes if you increase/decrease `M`?\n", "\n", "Solution: Comparison of above results to the window method (with a rectangular window) reveals that both give a similar performance in terms of achievable stop-band attenuation. Increasing `M` in above example does not result in obvious changes since the initial choice constitutes already a high amount of oversampling. However, decreasing `M` till it is the range of the filter length `N` results in a smooth degradation of the performance towards the original frequency sampling method." ] }, { "cell_type": "markdown", "metadata": { "nbsphinx": "hidden" }, "source": [ "**Copyright**\n", "\n", "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples, 2016-2018*." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 1 }