{ "metadata": { "name": "Windowing" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Introduction\n", "--------------\n", "\n", "In the [prior section](http://python-for-signal-processing.blogspot.com/2013/03/spectral-estimation-using-discrete.html), we discovered that resolving two nearby frequencies depends crucially on the rectangular window and its corresponding sinc Discrete Fourier Transform (DFT). However, our two nearby signals had *equal* amplitudes. What happens when this is no longer the case? The figure below shows the DFT of two nearby signals where one has ten times the amplitude. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "from scipy import signal\n", "\n", "# some useful functions \n", "def dftmatrix(Nfft=32,N=None):\n", " 'construct DFT matrix'\n", " k= np.arange(Nfft)\n", " if N is None: N = Nfft\n", " n = arange(N)\n", " U = matrix(exp(1j* 2*pi/Nfft *k*n[:,None])) # use numpy broadcasting to create matrix\n", " return U/sqrt(Nfft)\n", "\n", "\n", "def db20(W,Nfft=None):\n", " 'Given DFT, return power level in dB'\n", " if Nfft is None: # assume W is DFT \n", " return 20*log10(abs(W))\n", " else: # assume time-domain passed, so need DFT\n", " return 20*log10(abs( fft.fft(W,Nfft)/sqrt(Nfft) ) )\n", "\n", "fs = 64 # sampling frequency\n", "t = arange(0,2,1/fs)\n", "f = 10 # one signal\n", "deltaf = 2.3 # second nearby frequency\n", "\n", "Nf = 512\n", "fig,ax = subplots(2,1,sharex=True,sharey=True)\n", "fig.set_size_inches((9,4))\n", "\n", "x=10*cos(2*pi*f*t) + 10*cos(2*pi*(f+deltaf)*t) # equal amplitudes\n", "X = fft.fft(x,Nf)/sqrt(Nf)\n", "ax[0].plot(linspace(0,fs,len(X)),abs(X),'-o',ms=3.)\n", "ax[0].set_ylabel(r'$|X(k)|$',fontsize=18)\n", "ax[0].set_xlim(xmax = fs/2)\n", "ax[0].grid()\n", "ax[0].text(0.5,0.5,'Same amplitudes',\n", " transform=ax[0].transAxes,\n", " backgroundcolor='Lightyellow',\n", " fontsize=16)\n", "\n", "x=cos(2*pi*f*t) + 10*cos(2*pi*(f+deltaf)*t) # one has 10x the amplitude\n", "X = fft.fft(x,Nf)/sqrt(Nf)\n", "ax[1].plot(linspace(0,fs,len(X)),abs(X),'-o',ms=3.)\n", "ax[1].set_ylabel(r'$|X(k)|$',fontsize=18)\n", "ax[1].set_xlabel('Frequency (Hz)',fontsize=18)\n", "ax[1].set_xlim(xmax = fs/2)\n", "ax[1].grid()\n", "ax[1].text(0.5,0.5,'Different amplitudes',\n", " transform=ax[1].transAxes,\n", " backgroundcolor='lightyellow',\n", " fontsize=16)\n", "ax[1].annotate('Smaller signal',\n", " fontsize=12,xy=(f,abs(X)[int(f/fs*Nf)]),\n", " xytext=(2,15),\n", " arrowprops={'facecolor':'m','alpha':.3});\n", "\n", "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 1, "text": [ "" ] }, { "output_type": "display_data", "png": 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aXMC4OVzi4xPYuDGI3buDiI8vfRCvEEJYGqMqLn/99RcvvviiUQecPHnyPQUk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\n3/nKNVHUA1xV88tdDm8Dc4FP6dFjJr6+XTl79kYlF086hw4lMmjQq5i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0dCQnJ0d5rJBJ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\n", "text": [ "" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the figure above, the top plot shows the two peaks of nearby signals when they both have the same amplitude. The bottom plot shows the case where the higher frequency signal has ten times the amplitude. Note that the two frequencies are no longer resolvable because the weaker signal (smaller amplitude) has descended into the sidelobes of the stronger one. Thus, we need more than just longer sampling durations and denser DFTs to resolve these signals. This is where *windows* (sometimes called *tapers*) come in. \n", "\n", "### What is a window?\n", "\n", "A window is a function that is multiplied sample-by-sample against the input signal (i.e. element-wise). For example, given an input signal, $s_n$, and a window, $w_n$, the new windowed signal is,\n", "\n", "$$y_n = s_n w_n$$\n", "\n", "known in vector notation as the *Hadamard* product,\n", "\n", "$$\\mathbf{y} = \\mathbf{w} \\odot \\mathbf{s}$$\n", "\n", "The following figure compares the the rectangular and triangular windows applied to an input sinusoid." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig,axs = subplots(2,1)\n", "fig.set_size_inches((10,5))\n", "\n", "Nf = 128\n", "nsamp = 64\n", "window = signal.triang(nsamp)\n", "rectwin = ones(nsamp)\n", "ax = axs[0]\n", "\n", "ax.plot(arange(nsamp),window,'m-o',label='triangular')\n", "ax.stem(arange(nsamp),rectwin,basefmt='b-',label='rectangular')\n", "ax.set_ylim(ymax = 1.1,ymin=-0.1)\n", "ax.legend(loc=0)\n", "\n", "x=array(dftmatrix(64,64)[:,5].real).flatten() # convert to numpy array\n", "n = arange(len(x))\n", "window = signal.triang(len(x))\n", "\n", "ax = axs[1]\n", "ax.plot(n,x,'-o',label='signal',ms=3.,alpha=0.3)\n", "ax.plot(n,window*x,'-or',label='windowed\\nsignal',ms=5.)\n", "ax.set_ylabel('Amplitude',fontsize=16)\n", "ax.set_xlabel('sample index',fontsize=16)\n", "ax.legend(loc=0)\n", "ax.grid()\n", "ax2 = ax.twinx()\n", "ax2.fill_between(n,window,alpha=0.2,color='m')\n", "ax2.set_ylabel('Window function',fontsize=16);\n", "\n", "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 2, "text": [ "" ] }, { "output_type": "display_data", "png": 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D+rJ4cQQREX8EICLijyxePPiBJtjUxDV8fX0B+PHHH9m4cSMeHh7Gn2+//ZbU\n1FRSUlJo0qQJjRqZ2YLzPpcuXeLpp5+mVatWNGrUiLfeesvY43lXy5Ytjb87OzuTk5MDwI0bN4x1\nAvDx8an0c7nfjh076N27N02bNsXDw4Pt27eb1KN58+Y0aNCgyte3JTYx+/vatWtlXvzDhw+XOWbz\n5s3Ex8dz5MgRs13VUVFRxt/DwsIICwt7GFUWvzA3ZnLV2FUs6LOAEX8cgV8DPzb9W2ZvCyGsh9rs\n8alzptLTpyfX/3WddX9ex4v6F03OmZg0kU1LN1nd59ewYX0ZNqwvGg3Exf3FIte4+53cunVrIiMj\nTcYd3nXjxg3u3LlDZmZmmcBS7Tt91qxZdO/enQ0bNuDi4sJHH33EV199Van6tGrVymQm+f2zyl1c\nXMjNzTXeTk1NVb1OYWEho0ePJiYmhpEjR2JnZ8ezzz5r0rNZXur8fjqdDp1OV+njrY1NBJWVeUHm\nz5/P+++/j0ajQVEUs13V9waVomZUZUkg967udNN1A2AgAxn4zEBZnFwIYVXMLa7e4d8d8DjrAd+o\nnFTHliSqaZMmTSI0NJRdu3YxYMAAiouLOXToEAEBAXh7ezNkyBBeeeUVPv74Y1xcXDh48CB9+/bF\n09OT27dvk5WVhbu7OwA5OTm4ubnh7OzMhQsX+Ne//kWLFi3MPva9scHYsWNZvHgxw4YNw9nZmUWL\nFpnEGt26dWP9+vUMGTKEkydP8tVXXzFkyJAy1ywqKqKoqIhmzZqh1WrZsWMHu3btonPnzlVqn/s7\nuxYuXFil61iKTaS/vb29y/xFcX9X9bFjxxg3bhxt27blq6++4pVXXmHLFtuapWeLylt2Q5+hJz81\nX/U8uyaVn3kohBDWRnFW77jI/SGXnNM5VrskkUZTvZ/q8vHxYfPmzbz77ru0aNGC1q1b8+GHHxpn\nXa9duxYHBwcCAwPx9PRkyZIlAAQGBjJ+/HjatWtHkyZNSE1N5e9//zuff/457u7uvPTSS4wbN67c\nyTX3Tr6ZMWMGgwYNokuXLnTv3p1hw4ZhZ2eHVmsIi/7yl7+QlJSEh4cHUVFRTJw4scy1ANzc3Fiy\nZAljx46lSZMmxMbGMnLkSNVj6wONYgMzWvR6PR07dmTPnj14eXnRs2dPYmNjCQoKUj1+6tSpDB8+\nnFGjRpncf7cX0xyNBsprDSkvWz43Yq7xQ7M/YexFB8A6n3VMyZnC5S6XOXD5AJHXI43lMf4xqjO4\nrfH51VbYaZEhAAAgAElEQVS5NddNyqVcysuW37uF7N3PtrVt1jLw8YG00bXh07xPmZIxBTD9bNwU\nsalMRqYm6gflf7+J8u3YsYNZs2aRnJxskcc3F59UFLdYG5voqbS3t2fZsmVEREQQHBzM888/T1BQ\nEMuXL6/z0/OtQXkzHM2lt+0c7Oh5vicv7HuBiZ9MlCWBhBB1itqSRBM/nsj4dePpndwbZ29n9RPv\nS49b++zxuqqgoIDt27ej1+u5du0aCxcuLNMRJR6cTfRU1hTpqayZv8bX+a9j/OLxhA8LZ3bf2Yw5\nMAaonb/G62q5NddNyqVcymsui/NF9y/4OOFj9u7YW+5n64M+vvRUPpj8/Hz69evHhQsXaNiwIU8/\n/TSLFy/G1dXVIvWRnkpRL5ibvf3ln77k9NOnCTwRyOpGq03KZccbIUR9p7Yk0Zrma+h2uxsJHRPY\n8NsNdWLHHlvVsGFDEhISyMrKIi0tjRUrVlgsoKxLJKgU5TKX3i68VEiz0c2YlTaLyetkxxshhLiX\nWno8clUkM36YQWB0IEqmmd4nG9uxR4h7SVApqrbjzeNutJraCjtnO9nxRgghVKju2KPR0KhPI5y6\nqu+sojSwrR17hLiXBJX1nNkdb77azY3PbtDpcidW2Jfd8UbS20IIUXVq6fGVzisJOBRA0u+SiPss\nziqXJBKiPDax+Ll4eMzueDNuFa8NeY0xH4/Bv9ifTR/LjjdCCFFT1HbseWHOC/QJ7MP15df5/JXP\nebG48jv2eHh41Kv1EOsaDw8PS1ehRkhQWQ9UZcebRt0b0XmLYUeAAQxgwPABsuONEELUIHM79vh/\n4I/HIQ84oHKSmR17JoVOUt2xxxpnxtdmuahdElTWcfcuCbQUQwplXZIh5fL4o4+TdzVP9TxtYxkZ\nIYQQlqI0VI+Uci7lkPltJkfTj7J+/nrVz3bJJAlLkcihjjOX3v582uccCT7CkwFPstZnrUm5jJkU\nQgjLUhtzGeMXw6Bhg7gw9QJrx6+VJYmE1ZGgsg6oyo43Dm4O9E7uTeSOSCb+W3a8EUIIa6K2JNGE\nZRMY++lYel7oiWs7M2sq/pIel5njwhIk/W3jyktvhw8Lp7i4WPU8R39H7BvZG49TG9cjhBDCcsx9\nNmu0GrQttXCq7DmFGYXs3rybDa9ukNS4qHXSU2njzKW3N765kRN9TxB8IZg1HmtMyiW9LYQQtk11\nxx7PNXTXdyd6bLSkxoVFSFBp48ylt4t/KsZnng+zUmcRuTZS0ttCCFGHqO7YsyKS6Wem06hLI/WT\nZLce8ZDZTFAZFxdHYGAgAQEBLFq0qEz5unXr6Nq1K126dOHxxx/n1CmVvICNqsqON669XGk+ujla\nB63seCOEEHWQuc92TRP19SoL0grQZ+gBGXMpHg6bGFNZUlLC7Nmz2b17N97e3oSGhjJixAiCgoKM\nx7Rr1479+/fTqFEj4uLieOmllzh06JAFa10zzI2ZLMkuIfB6IEGng1jZYCUvFv26SG6MfwwT5kyw\nXKWFEEJYzDNzn2Fd0jqTFHi0VzR9W/TlUNtDXOl1Bd1ZHZFXI2XMpahRNtFTmZCQQPv27fHz88PB\nwYFx48axefNmk2P69OlDo0aGLv9evXpx9epVS1S1xpkbMxkzKYac4zlM+HICU76aIultIYQQgHpq\nfNInk3hh3wv0PN+TA0kHiLwaaXKOjLkUNcEmeiqvXbuGr6+v8baPjw+HDx82e/yKFSsYOnSoallU\nVJTx97CwMMLCwmqqmlVWlR1vGvdqTFCMoad2AAMY8LTseCOEEMLA3MzxBi0b4OztDJfLnlOa8etw\nqvK+l8TDo9Pp0Ol0lq5GldlEUPkg+5nu3buXlStX8u2336qW3xtUWoPylgTqE9iH3ORc1fM0brLH\nqxBCiAdnbix+5rFMTg8/zQ89fmDr2q2yJJEF3N/ZtXDhQstVpgpsIv3t7e1NSkqK8XZKSgo+Pj5l\njjt16hQzZsxgy5YtNrM5u7n09roX1nG893H6d+9PTOsYk3JZEkgIIURVqe7W4x9D5PpImj3bjP9+\n+F9ZkkhUiU0ElT169CAxMZHk5GSKiorYsGEDI0aYBlU//fQTo0aNIiYmhvbt21uopuqqsuONYzNH\nev/UmwlfTWDC/02QMZNCCCFqhOpuPYsnMHD0QFq92IrGjzZWP/GeJYlk9rhQYxPpb3t7e5YtW0ZE\nRAQlJSVMmzaNoKAgli9fDsDMmTP585//THp6OrNmzQLAwcGBhIQES1YbKD+93X9of4rz1Xe8adCm\nAXYN7QDZ8UYIIUTNKu97xWx6/HgmN1bc4Gzjs2x4XXbsEWVpFEVRLF2J2qLRaCjv6Wo0UF5rVKV8\nbsRcRu0aBUB/wtiLDoD1weuZ7jCdIzePkFCUwJTbU4zlMf4xqr2RD6N+Um4d5dZcNymXcim33fKq\nnHtvZ8i930vDI4fT7lg7/rbjb7yoNyxjd+/32qaITWUCVEu3ja2rKG6xNjaR/rZ2VUlvl9wsod3f\n2vHy1ZeJXCM73gghhLAO5tLjI98eSectnWncXdLjQp1NpL+tWXnp7fBh4ZQ2UE8juHR3oclTTYzH\nSXpbCCGEtSj3e8nMLpD51/IpvFHIt8e/Lfd7UdRd0lNZTeZmb//3b//lyttX6Hi0IyudVpqUy+xt\nIYQQtkpt9vhan7U84f8ER4KPsG7aOpk9Xk9JT2U1mUtv53ybQ/Ejxbyw/wWCfgxi09JNsDPMkEaY\nI+ltIYQQtunu99e932sT50wkfFg4+kw963qsgzSVEwtU7hN1ivRUVkJ5Y0PMzZJz6+dGh4874NLJ\nhfBh4cb0wUdxH0lAKYQQwqaZ+16zb2SPQzsH1XP0er3xdxlzWTdJUFmBu2Mm787gHrVrFLHzYonf\nFk/OyRxCNaGs0KwwOSfGP4ZnFjxjieoKIYQQFqWWHl/tsZqg80Gc6HuC//7+v8TOVf9eFbZN0t8V\nMDdmMnpiNA3dG9J3Zl88J3qyaZ2kt4UQQgi19PjkOZMJGxTG7S23WTJjCVPSp5icMzFpIpuWbpLv\nThsnPZVUbUmghr4N6f1Db9q81YZBkYMkvS2EEEL8Qi09rnXQ0nx0cxp1MTN9XJYksnn1vqey3B1v\nhvSnMLtQ9TwHbwc09pparKkQQghh+8zNRchIyCDlHylc8LrAF3/4QpYkskH1vqfSXHp7w283cLj9\nYUIyQohuHm1SLksCCSGEEFWjNuYyxj+G0QtHk3M8h7WT1sqSRDaq3gWVlU1vK5kKweuDmXF5BpNW\nTZIdb4QQQogaYG7HnuG/G05QTBAevTzUT5T0uNWrd+nvMjve2Kt3wzt3c8a9p7vxONnxRgghhKgZ\n5X2vKq7qe13n/ZhHflI+By8clB17rJTN9FTGxcURGBhIQEAAixYtUj1m7ty5BAQE0LVrV06cOGH2\nWhOTJvLfRf/l8oLLdDjcgVXOq0zKJb0thBBCWIbqjj2t1xL2aBjHex8nZkqMpMetlE0ElSUlJcye\nPZu4uDjOnTtHbGws58+fNzlm+/btXL58mcTERD755BNmzZpV7jVzDuWgbahl+unpTPliiqS3hRBC\nCCuglh6f+H8TmfDVBHr/1Bun5k7qJ8qOPRZnE+nvhIQE2rdvj5+fHwDjxo1j8+bNBAUFGY/ZsmUL\nU6YY1r3q1asXGRkZpKWl4enpqXpN9zB32r3bDoBwP0lvCyGEENbCXHrcrqEd9q3t4YLKSWZiTVF7\nbCKovHbtGr6+vsbbPj4+HD58uMJjrl69Wiao7I/O8Mv/PFii0QFhJuWaClYJknIpf1jl1lw3KZdy\nKbfdcmuuW9XKl7D0vnti/GOYMGdC+ReyATqdDp1OZ+lqVJlNBJWait5xv1AU08G9aufNi8hgxJwR\nkt4WQgghbFT8tnjDGMoC2OREndnJLiwsjLCwMOPthQsXWq4yVWATQaW3tzcpKSnG2ykpKfj4+JR7\nzNWrV/H29i5zLUlvCyGEELbtbnpcWBebmKjTo0cPEhMTSU5OpqioiA0bNjBihOns7BEjRhAdbVik\n/NChQzRu3NjseEohhBBCCFGzbKKn0t7enmXLlhEREUFJSQnTpk0jKCiI5cuXAzBz5kyGDh3K9u3b\nad++PS4uLqxataqCqwohhBBCiJqiUe4fiFiHaTSaMuMuhRBCCCGska3FLTaR/hZCCCGEENZNgkpR\naba8zIE1kParOmm76pH2qx5pv6qTtqtfJKgUlSYfDtUj7Vd10nbVI+1XPdJ+VSdtV79IUCmEEEII\nIapNgkohhBBCCFFt9W72txBCCCGErbClMM0m1qmsKbb0wgghhBBC2BJJfwshhBBCiGqToFIIIYQQ\nQlSbBJVCCCGEEKLa6k1QGRcXR2BgIAEBASxatMjS1bF6L774Ip6ennTu3Nl43507d3jqqafo0KED\ngwYNIiMjw4I1tF4pKSn079+fRx55hE6dOrFkyRJA2q+yCgoK6NWrF926dSM4OJg33ngDkPZ7UCUl\nJYSEhDB8+HBA2u9B+Pn50aVLF0JCQujZsycg7VdZGRkZjBkzhqCgIIKDgzl8+LC0XSVdvHiRkJAQ\n40+jRo1YsmSJTbVfvQgqS0pKmD17NnFxcZw7d47Y2FjOnz9v6WpZtalTpxIXF2dy3/vvv89TTz3F\npUuXGDBgAO+//76FamfdHBwc+Oc//8nZs2c5dOgQH3/8MefPn5f2qyQnJyf27t3LyZMnOXXqFHv3\n7uWbb76R9ntAixcvJjg42LjqhbRf5Wk0GnQ6HSdOnCAhIQGQ9qusefPmMXToUM6fP8+pU6cIDAyU\ntqukjh07cuLECU6cOMGxY8dwdnbm2Wefta32U+qB7777TomIiDDefu+995T33nvPgjWyDVeuXFE6\ndepkvN2xY0clNTVVURRFuXHjhtKxY0dLVc2mjBw5Uvnf//4n7VcFubm5So8ePZQzZ85I+z2AlJQU\nZcCAAUp8fLzy9NNPK4oi/38fhJ+fn3Lr1i2T+6T9KpaRkaG0bdu2zP3Sdg9u586dyhNPPKEoim21\nX73oqbx27Rq+vr7G2z4+Ply7ds2CNbJNaWlpeHp6AuDp6UlaWpqFa2T9kpOTOXHiBL169ZL2ewCl\npaV069YNT09P41ACab/KW7BgAX/729/Qan/9iJf2qzyNRsPAgQPp0aMHn376KSDtVxlXrlyhefPm\nTJ06lUcffZQZM2aQm5srbVcF69evZ/z48YBtvffqRVApi57XPI1GI+1agZycHEaPHs3ixYtxc3Mz\nKZP2K59Wq+XkyZNcvXqV/fv3s3fvXpNyaT/ztm7dSosWLQgJCTG7Nq+0X/m+/fZbTpw4wY4dO/j4\n4485cOCASbm0nzq9Xs/x48d55ZVXOH78OC4uLmVStdJ2FSsqKuLrr7/mueeeK1Nm7e1XL4JKb29v\nUlJSjLdTUlLw8fGxYI1sk6enJ6mpqQDcuHGDFi1aWLhG1qu4uJjRo0cTGRnJM888A0j7VUWjRo0Y\nNmwYx44dk/arpO+++44tW7bQtm1bxo8fT3x8PJGRkdJ+D6BVq1YANG/enGeffZaEhARpv0rw8fHB\nx8eH0NBQAMaMGcPx48dp2bKltN0D2LFjB927d6d58+aAbX131IugskePHiQmJpKcnExRUREbNmxg\nxIgRlq6WzRkxYgRr1qwBYM2aNcZgSZhSFIVp06YRHBzM/PnzjfdL+1XOrVu3jLMb8/Pz+d///kdI\nSIi0XyW9++67pKSkcOXKFdavX094eDhr166V9qukvLw8srOzAcjNzWXXrl107txZ2q8SWrZsia+v\nL5cuXQJg9+7dPPLIIwwfPlza7gHExsYaU99gY98dlh7UWVu2b9+udOjQQfH391feffddS1fH6o0b\nN05p1aqV4uDgoPj4+CgrV65Ubt++rQwYMEAJCAhQnnrqKSU9Pd3S1bRKBw4cUDQajdK1a1elW7du\nSrdu3ZQdO3ZI+1XSqVOnlJCQEKVr165K586dlQ8++EBRFEXarwp0Op0yfPhwRVGk/Srrhx9+ULp2\n7ap07dpVeeSRR4zfF9J+lXPy5EmlR48eSpcuXZRnn31WycjIkLZ7ADk5OUrTpk2VrKws43221H4a\nRZENsYUQQgghRPXUi/S3EEIIIYR4uCSoFEIIIYQQ1SZBpRBCCCGEqDYJKoUQQgghRLVJUCmEEEII\nIapNgkohhBBCCFFtElQKIYQQQohqk6BSCCGEEEJUm9UFlXFxcQQGBhIQEMCiRYvKlF+4cIE+ffrg\n5OTEhx9+aFLm5+dHly5dCAkJoWfPnrVVZSGEEEKIWvHiiy/i6elJ586dzR4zd+5cAgIC6Nq1KydO\nnKi1ullVUFlSUsLs2bOJi4vj3LlzxMbGcv78eZNjmjZtytKlS3nttdfKnK/RaNDpdJw4cYKEhITa\nqrYQQgghRK2YOnUqcXFxZsu3b9/O5cuXSUxM5JNPPmHWrFm1Vjf7WnukSkhISKB9+/b4+fkBMG7c\nODZv3kxQUJDxmObNm9O8eXO2bdumeg3ZdVIIIYQQddWTTz5JcnKy2fItW7YwZcoUAHr16kVGRgZp\naWl4enqWe12dTkdsbCwpKSkUFBQY71cUBY1GQ3x8fIV1s6qg8tq1a/j6+hpv+/j4cPjw4Uqfr9Fo\nGDhwIHZ2dsycOZMZM2aUKRdCCCGEsBUP2lmmFktdvXq13KBy+fLlzJo1iyZNmtChQwcaNGhQpbpa\nVVBZ3aDv22+/pVWrVvz888889dRTBAYG8uSTT5ocIz2ZVRcVFUVUVJSlq2GzpP2qTtqueqT9qkfa\nr+qk7aqnqnHR/bFORdf58MMPGT9+PKtWrapyQAlWFlR6e3uTkpJivJ2SkoKPj0+lz2/VqhVgSJE/\n++yzJCQklAkqRdWV190uKibtV3UVtV1JTgnFGcXlHqN11OLQzKFeZizkvVc90n5VJ21X++6Ppa5e\nvYq3t3e551y7do1//etf1Qoowcom6vTo0YPExESSk5MpKipiw4YNjBgxQvXY+6PwvLw8srOzAcjN\nzWXXrl3lzowSQtg+fbae7O+zyTiQQd7ZPPLOmf/JPppN5oFMCtMKUUolYyGEqJtGjBhBdHQ0AIcO\nHaJx48YVjqd89NFH+eGHH6r92FbVU2lvb8+yZcuIiIigpKSEadOmERQUxPLlywGYOXMmqamphIaG\nkpWVhVarZfHixZw7d46bN28yatQoAPR6PRMnTmTQoEGWfDp1zgsvvGDpKtg0ab+qu7/t9Nl68n/I\np+hGEVoHLQ1aVO6v69KCUnKO52DnYkfDDg1p0KIBGm3d77mU9171SPtVnbRdzRs/fjz79u3j1q1b\n+Pr6snDhQoqLDZmamTNnMnToULZv30779u1xcXFh1apVFV5z6dKlTJgwgQ4dOtCvX78q102j1KNB\nhhqNRsZUCmHD9Nl68pN+CSYdtdg3qtrfxaUFpeiz9Ng529GwY/0JLoUQtqW24hZfX1+ysrLIzs7G\nxcUFDw8P46zvu//+9NNPFV7HqnoqhXXT6XSEhYVZuho2S9qv6nTbdXT36m4MJivbM2mO1klLA6cG\nhp7LEzl1PriU91711KX2a9KkCenp6ZauhriPh4cHd+7csdjjDxgwoNzyyo5Fl6BSCGG19FmGnklO\ng95JX+1g8n7G4LKwfgSXQqSnp0vGzgpZegLh6tWra+Q6kv4WQlidu8FkUdovaW732vn7t7SwFH2m\nHm1DLc4dnWngKcGlqFvke9A6mXtdbO31sqrZ30KI+k2fpSf7eDaZ32aiz9DToHmDWgsoAWNqXdtA\nS87JHDL2Z1B4Q2aLCyHqvlOnTjF69GiaNWuGnZ0dzZs357nnnuP06dOVvka9Cyrj4y+YbD8kKk+n\n0z20axcUFLB37wX27q27r8/DbD9bp8+8J5jMNKS57w0mjx09Vqv1qWvBpbz3qqe89qsPn12i7jty\n5Ai9e/dGp9MxfPhwfve73zFs2DDi4+Pp3bs3R48erdR16t2YyoSEAIqLE4mICLR0VcQ9du9O5sqV\nAJo1g4MHE+nfX14fa1FQUMDBg8kA9Onjh5OTU41dW595T5q7YfUn4NS0u8FlaVEpOd/noHXS0rBD\nQxw9HdHY1U5a/GG2v6i+775L5uzZAFxdQVESCQ+Xzy5he9544w06derEnj17cHNzM96fnZ3NwIED\neeONN/jf//5X4XXqXVDp7g6nT0PPnuDhYena2JaHMfvxzh24fBnOn4cGDeDSpbr7uljr7NH7g5YG\nDZzIycH4s3dvMrduBaDVQklJIgMHVv9LU5+pJ/9yPkU3KxdMdu/RvdqPWR3aBloaNDcEl7nf55Lv\nlE/DjrUTXB48mMy5cwHcuQMXLiTSr18grq4Yf0pLKw46rfW9ZyvMtZ+iGD6z8vMhN9fweda+Pfj4\ngLbe5QEfnvfee48ffviBTz/99KE+zurVq1mxYgUHDhx4qI9jjQ4dOkR0dLRJQAng5ubG66+/zuTJ\nkyt1nXoXVAYFJdKunR9HjkCHDuDnZ+k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Qzp0DOX06BS8vaNqkVW09rTrD17cViYkpNGsG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\nMibTHToLr77FUSjk2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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the figure above, the top plot shows the $w_n$ sequences for the rectangular and triangular windows. The bottom plot shows the input signal before (light blue line) and after (red line) applying the triangular window. The amplitudes are noted on the vertical scale on the left. The triangular window is drawn in the background with scale noted on the right side. Basicially, the red line is the product of the blue line and the pink background window function. As shown, because the triangular window slopes to zero at the beginning and at the end, the amplitude of the input signal drops away from the middle. This means that we lose precious signal energy at the start and end of the signal. We certainly want something in exchange for this! \n", "\n", "The following figure shows the two input signals with rectangular, triangular, and Hamming windows applied." ] }, { "cell_type": "code", "collapsed": false, "input": [ "Nf = 512\n", "fig,ax = subplots(3,1,sharex=True,sharey=True)\n", "fig.set_size_inches((10,6))\n", "\n", "x=cos(2*pi*f*t) + 10*cos(2*pi*(f+deltaf)*t)\n", "X = fft.fft(x,Nf)/sqrt(Nf)\n", "ax[0].plot(linspace(0,fs,len(X)),db20(X),'-o',ms=3.)\n", "ax[0].set_xlim(xmax = fs/2)\n", "ax[0].grid()\n", "ax[0].text(0.5,0.5,'rectangular window',\n", " transform=ax[0].transAxes,\n", " backgroundcolor='lightyellow',\n", " fontsize=16)\n", "ax[0].annotate('Smaller signal',\n", " fontsize=12,xy=(f,db20(X)[int(f/fs*Nf)]),\n", " xytext=(1,30),\n", " arrowprops={'facecolor':'m'})\n", "\n", "w = signal.triang(len(x))\n", "X = fft.fft(x*w,Nf)/sqrt(Nf)\n", "ax[1].plot(linspace(0,fs,len(X)),db20(X),'-o',ms=3.)\n", "ax[1].set_xlim(xmax = fs/2)\n", "ax[1].grid()\n", "ax[1].text(0.5,0.5,'triangular window',\n", " transform=ax[1].transAxes,\n", " backgroundcolor='lightyellow',\n", " fontsize=16)\n", "ax[1].annotate('Smaller signal',\n", " fontsize=12,xy=(f,db20(X)[int(f/fs*Nf)]),\n", " xytext=(1,30),\n", " arrowprops={'facecolor':'m'})\n", "\n", "w = signal.hamming(len(x))\n", "X = fft.fft(x*w,Nf)/sqrt(Nf)\n", "ax[2].plot(linspace(0,fs,len(X)),db20(X),'-o',ms=3.)\n", "ax[2].set_xlabel('Frequency (Hz)',fontsize=18)\n", "ax[2].set_xlim(xmax = fs/2)\n", "ax[2].grid()\n", "ax[2].set_ylim(ymin=-20)\n", "ax[2].text(0.5,0.5,'Hamming window',\n", " transform=ax[2].transAxes,\n", " backgroundcolor='lightyellow',\n", " fontsize=16)\n", "ax[2].annotate('Smaller signal',\n", " fontsize=12,xy=(f,db20(X)[int(f/fs*Nf)]),\n", " xytext=(1,30),\n", " arrowprops={'facecolor':'m'});\n", "\n", "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 3, "text": [ "" ] }, { "output_type": "display_data", "png": 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9u/egMzrDF77wf+yPmdNnAng5unV1dUGfPgkYNYoZUP7+QGZm+fuVSMSFO1NT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\n8VqJ9FLpHFhYxMPEZDIUikd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m8GBW52vwYAV5eOj2gNWqJaUGDdgzqmtX7efcpUvs+WNr\nK6WPPtL9DNy/nz1vzMykdPSo7jYlraupqYvgYMN5ycri0XtZHruXmRtXWpuXNU5pdgs3pqohZbkx\nyhKis7AofQZdy5ZS2riRqEULbRkcHYUZVnI5+9FSN2o2biQKDha2L11SkImJlDp3FuRu0EA8y05T\n7unTiWJjtcdu35790Pz9t0L1A6SL0pJqOZVDWRP/69YlqlGDzf7TxZw5zMBo0oQZI5oUF7Pz8/PZ\nvbhpk3abb79lRhkRS/ZWXzNQSb16RJcusfcBASz0p86//wpGv1zOyh106SL+fvbsydoR6Q5j3bhB\n5ODAjuvTz5w5whqGJRltBw8KsjRvLi4ZceoUUaNGYvlnzyZ6/31he/p0lvyvzrhxRMolVuVyBVlZ\nSal9e/E19upFtGxZyZ+vjw/R3r362xQUsNm516/rL5miLH9S0vd7wwYWwt2/nxlVwcHaz8tvvmGz\nKaOiWBFWXc/UwYMVVL++lIyNx1GbNtrlK+Rytri2vb2UwsN1P48vXGDPPnNzKa1apbtNx44lzyxW\n15evb+lGUJcuL25M6fujrauP0NCqb9hVRBtuTFVDSjOWSvvQMzIyqFOnslUMt7Nji/6qV5bW7P/J\nE/ZvVzPfyc2NPdSUMtvaiqevz51L9MEH+uW+f5/90D15or9N//5sxpcuwsIUZG0tJReXl5erUFXi\n99UdXZ+Lpm7lcgXZ2Gh7UdT56y+isDCimjX1G1ze3kQnTxLZ2DCDRZOVK9nsvOJiInt7ouxs7TbK\nvKqnT9lY9+6Jj//3nzArMS+PeYKUpTqUjBnDyiUQEaWmsntX/fqLipgH7NEj/d/xpUuJhgxh7/W1\n6d6dzf4Tt0lTtbl9m82IJRI+B1tbKS1ZIuj4xx+JRo8Wt7GwkFJ6utCma1fB8JTLFdStGysRcfKk\nQrVtZKTtAXNxYdcqlyvojTe0v79r17JcuZKucc4c5gksyVsTFcUM5ZKel61bs2vQZ7Q9ekRkZ0d0\n9SqRj4++zySDnJyITp9WkIWFlNq00b5fV61ii3snJjLDS9fzKCZGQV5e7LP45hvdHhhHR5azZmen\noLt3tZpQVhYz5J2cpBQZqfs7s2sXMy4tLKS0bp3uNt9/z2r3WVpK6fJl3bJ4erLP+8MPS/9D3769\nbgNGXe/6StM0aVJyWQ/1cdq0Kd1QCgsrXRZuTFUDyutV0jyu+e9DLldQq1bDyNJyHHl7TyArKyn9\n9Zd4HM1/cxER4hCJXK6gBg2k5O0tyBgVpaCGDQW5NcsN6JI5MlLcr2abvXu1k4aVoQszMxbe8PYm\nOnFCty7bt3/5XiduTBkOTd2W5d/knj3MANFXHJSI/YglJbEfcX19tGjBjCh7e20jiIho4EBm1F+4\nIBQbVefaNcGrpOxPk2nTiD7/nL1fvpyof3/tNvXqEWVlCTWxGjQQPye2bhXKgCgTwv39xW2iooRk\neF3GVHExW6rnwQP9xsjq1US9e2v2If4chg0jWrJEfxvlOPn5gryNG0vJw0OQNzWVGcPK4+HhUnJ1\nldL06QrVvnr1pOTnp/SAsza1a0tp2TJh28xMSv/9J+igsJAZQVeu6Jf/0iX2mT15or/N2rXCMlT6\nvDVRURk0fnzJ92vfvmwihb42RUVEHh7Mu7pmDTPKNJcounaN/SHIzyfq31/8PFaSksK+C0eO6PfG\nxcWxP7kJCYpn3jTtNqGhRH/8wWr6qRc7VlJQwL4rW7YwPeflabfZuJFdR+PG+j128fHsHraxEZcj\nUadVq5VUvz4LZ2vWciMiuniRGZCenlIKCdHdx8aNzDh0dJTSzJm623z+OZvYZGoqpd27X2KYb8WK\nFeTr60tGRkZ0UOlTfsbMmTOpYcOG1LhxY9qow2f+qhpTFWEoEdGzgof6c5l8fcdRzZoTqF49Kb3/\nfsm5TAsXEvXrJ+5/61YF1awpyLl4MfMAqMsdHi7MsiIiatdO3K9MJp6JpOuhHBAgrJOmlF9pKG3f\nrqCkJGZw6eLzz9kxTc/V8+qSU30py+erUBABLNdJH5GRzDAID9d9XFm4UzMsrc7EiczTum4d8/xo\nou5VWryY6O23tdskJbGQEhFRfDyRVMcltWrFZiYSsaKgSqNIycmT4hBdy5bMeFMnNpZoxgz2/soV\nBUkk2j/MHh7Mq6xPx+qV4fW1UeqkpDbq4VFdbf77jz0nNI937iz08dlnTF+abdQ9GU2bEh05wt7L\n5Qpq2ZL9QCsNsOBg5olR6kAuZ8VQ69UT2vj6Coae8llbt66UvvxSOMfeXkotW4rbWFpKac0ahc7r\nk8sVFBoqeOz06Wn7diI/v5Jrps2dK8z2DAnR3WbgQOZVLMloc3dnRps+4zArixlIDx8S/fUX+63o\n0UN8/yxfzjyTRESDBuk27MaOZeHiM2eYsdOxo/h4cTGRry9RRgbR4sXanloi9v22tWWe4IED2R8M\nzSgO3bAAACAASURBVDbLlxOFhDADz9FRQR06aLcZNYroyy+Znhs2FM+qJWLbnp4sfP/JJ+KIihKD\nGVOnTp2iM2fOUHBwsMiYOnHiBDVv3pwKCwvp0qVL1KBBAyrSqJZYHY2pijKUSnMl3r1LVKcO8wzV\nrCmlrCzd4bc335Sqbvrbt/XLcOYM+4einqe0ZAlL8FSiK+/A1VV4COrqd8ECovfe09aPnZ2Ufv5Z\nQU+eCLkqmnz0EUtCHT+e5Szo4r//2I+A+vRyTfh041ebsny+SmNBMyFcnS++YMU9P/1U9zjKBPOE\nBP1G2dy5LIF99mx2/+rC3Z0ZKFKp8OOvTkqK4IUZMUJczkNJRAQrh0DElsLRdITevs08wkrs7bWL\nmS5YwPKbiJi3zdFRe5zWrZnRpjQ8HBzE+lNf7keflywhgWjyZKGNeg6lkqAg4Q+Vrufj5cssXUDf\ncSI2wUCZ06avTXAw89rpa3P3LpGVlXD9utroC6F27SqMM2QI89jo6kN5vxobC2kTutpoTgBQet8a\nNxb60NWvtbWUVqzQ329oKPPenDih37Br1Yr1U9I4DRsKIUJ9bezsBE9ScLB2m7AwJsuBA/pladOG\nGaJXr+qXxdtbSsOHs3HUc8rU29jaSmnRItamcWP9esnMVNDVq8xxEBgo1n9QkGB8HzjA8tuUxW8F\nXRk4zKdpTM2cOZNmzZql2g4LC6M9Gn+dqqIxVd48Jc026l9AdYYPV5CbG/uXpB5+U47v6SmlwYMV\nVFxM1K6dgpo2lYpuHM0bxdVVSo0aCTKfPq0giWQYde+u+xwi4UdB37VpLs+ilK9+feGBOno0m8Gk\nyQ8/sAfOyZPsH4Aujh1jxlr79roTgsuq78qAh/kMx4votiz3SVIS816tXKm/n3r12A/yokW6j//5\nJ1vfMTJS21ukRJlX1bcvq2quifpsvTZtWFtNxo4lSkxk752dWa6OOsXFzDDMz2f/1mvW1A5Lrlgh\neKOVHiZN3b71luB5/uEH8fI5RCwEaG4u9D16tJDvpeTXX5n3TIm/v/asyx49mDePiCVhSyTiZ+zD\nh8I4crmCWrfWzpFbupQtC0TE2jRqpG3YDRggzArWdU8UFwueQ31tNmxg4S19x4nEn4/QJk3Uxt2d\neXf09XP0KPPIKNH1XPfxEZY90meM2NkJS2bp6iMsTEoSiXq0QbtNYKCUnJ21+1DmOGmeoysCUVIb\nXdvPe06zZsNKPUfppdR0VlSsLCXbLSYVXWohOzsbbdq0UW27ublBoV4a+BkjR46E57OSvjY2NvD3\n90fws1LIMpkMACpse9WqVZg7dzXs7d2RlBSDc+fOarWXSn/Cvn0/AwD69x+NWbPGiI7funVFJfuR\nI6fRps3bWv0NGRIDmSwelpansXevCcLDY/HTT+x4bm4uvvvuIPbvBxYtCsKpU0BUVCIWLwZGjQrC\n3LmrVePb24/Gtm1jIJFsxPHjcTh+fDv695+Mv/+eA3//eNjZXUFUVF9ERydCoYgDsB39+k3Gvn1/\n4Pp1F7i7t8SUKf5qtWi2i3S/dasMkZEAwK4vKioIWVmjcfUqu54lS2Tw8AAkErE+//gjAe++C5w7\nJ8OOHWcxcqS2vvv1Az7+mJ3frJnuz+P06VW4c2c1du50h4NDDGQy7c9DXd+3bl2BTCYz2P3Bt6vG\ntpLnPV/z/lY/rlBk45tvJgMA6tSZA8BFZ3/W1sDOncGYOVP3eDk5gFwejOJioGVLGWQybXlcXYOh\nUAAHD8rQsyeg/H4pj/v6suMymQwnTwLe3trX4+IC7NkjQ4MGwN27bFv9uEQC2NjIsGYN+355eQHb\ntonlvXZNhjNn2PhZWUDNmjJkZmaK5C0uBq5fZ9s7dshgYaEtr6lpMO7dAw4fluHoUSAiQnzc2TkY\nN28K23J5MNzcxPI6OQHbt8tgZQV4eATD3T0BkyfLcO7cWbi6uqBGDcDISPasVlYwPvggAT/9JBwH\ngOxsGc6eZfK5urrAzy8Mrq5QHZfJZCgsBHJzmXxRUUHIyBiNwED2PFPKY28fjFu3gLNnZRg6NAhp\nafHo3p21l8lkquMymQxRUUHIyYnHpUvC8eDgYNjbs89XJmN1vTp2jMf9+wcQFfWe6v4zM5Nh0yZg\nzJhgJCXFwMdnNNzdgaSkOQCAM2dkuH5d0Hdu7hWwe7gjAODcubMIDw/DvXvBcHXFs2ehcFx5PR06\nJCAykj2PNZ+X586dxYYNCTA3B06ckKl+oxjbcevWFbi6uuDrrxPw8cfax588Yf0lJcWgZcvRMDVl\n8rMaWez7plxRQqnvoCCm7/79J4vkjYoKwvXro3H8uPB5aMr78cd9IZfH49Yt1n7uXKEg4dOnNyCT\nyZ7JEg9LS/b7t3jxQZW8eXmsv8WLY+DhMRr+/tryql+fOpr6FbaBc+d24uHDuwBKKTQHlGxqde3a\nlZo2bar1Wrt2raqNpmdq/PjxtFRt0apRo0bR30q/9TM0hy2LO19fG+X+kJBx1Lmz9rRVIvHsNQeH\nCJ1t2rQR2tjYaLfJzGThslatpGRuPkHLwu/Rg7ksFy9W6AybVYT1/uQJm4WTk6N5XcIaaF9/LY73\nKvVjbs7ylHRVFCdieUn29ixhU3MWnpKiIjZV/cQJ9o9Y12wSIhZL9/UlmjpV9/GyeBN4CI9TFirC\no0zEaiMB2rP0lGRlMW+qtbU4rK7Ohx8yj6+5OfO4aKLMq8rO1j3bj4h5eyIjWf5Pkya6x3nzTZb7\nsXq1UN1dnXPniOrXZ+8TEog+/li7TVyc8P18+22i5GTtNg0aCDN4/fyEnCQlBw4I+U4FBWzhas31\nLydPFsop7NzJvHeaeHkRnT/P3s+dy/SozqFD4vUb1b1QSj7/nCX4K6lbV9urp55XdfEiyxtT58IF\n8b7kZKLhw8Vt5s0TPxtHjdL2ZnbuzBKzlTRsyBblVqL0+ik5eJDlFKnfwytWCBMU5HIF+fuz/C31\nezwyUggVK0OFTZuK2zg6CmFguZzlP3XqJLQ5cECYBCSXs0Xnzc3FfcyYIYTI5XLdMzDbtRM8rcqI\niXro/d49IktL4ZrlcpacHhKi/5o7dZJSjRrauU9JSUIbPz8h702JmxsLHyvb1KkjpYAAIWTXsSP7\nrVYP85maisN6TZqwKJFym012KodnavPmzaVbYxq4urriqlpJWrlcDldXV51tFYpsREcn4sCB08jJ\nWQYAiI6OR0pKgug4AOTkPMKBAzO12igrywJTAUzXOg6oV+/+Ebm5y5CaKm5TXAw8fBiD5s3jkZV1\nGnfuCG2SkmIQHZ2IY8eAd96Jwc8/u6Bz51hkZAjXER2diA0b4gAAK1fGQyIRjinXpxLWoNNNUlIM\ngoLiUbcuVNWXk5JiEBYWj9u32ftjx1ilZQcH4Zzo6HicOQO0aMHO2bcP6NdP6FdZjXr0aLZGnbMz\nYG8vrigOACYmrNLy+vVsrbvOnbVlNDJiVcznzmX91Kql+1pCQ7MxZUoi1q0DxoyJ0VsFuySUcnM4\nJVER94lCkY0DBxLx/+ydeVxUdffH38PuggIuKKihKSouqZWKK6Lggpq24JZBpqQ9UpmVYk9U1CO2\nqYVZUbmUWdrTz+VJcsmtzC01zSW3kpRFFFBQEEGY3x+3gRlmBgZmBhg679drXs6993vv99zD9d7P\nnHPu9+viAtnZkbi66l+vmtHJmzUzPt+gt7cy117z5lCnjv52Oztl248/Qrt26NwntPtJTYU//oC7\n7zbcj8aWlBRo00Z/e7NmyjHUamUE+c6dDbc5dkz5fvGiMpK8oTaXL4OvrzLKeIsWuts9PUtGdE9J\nUewqPf9l06Ylo7qnpICXgVtBkybKce6+W7G7dJsmTZT5FzVcvqzYVrrNuXPK96IipX3TprptGjWC\n9HTl+5UrhrdnZJQsX72qHFcbDw9lrkQN6emG22RmlixnZJTcs0G5NtRquHVL+e7k5EXbtrFs2lTS\nxt0drl1Tvnt7ezF1aiynTinXmAY3N7h+vaRNz56xhIbqtmnYUGnj6am0qVs3lrVrS869YUPIyio5\nxnvvxTJunO4xGjSAtDRdW86c0W9z44auLY8+WtKmXj3lfIuKlGvE29sLZ+dY/vvfkmdR/fpw82bJ\nMRYujOWJJ3T7qV8fcnJK2jz+eCwpKbpt6tUred56e3vRo0csM2aUtFm5MpaAgJJlb29lbsv165X5\nPgGefjqWX38tafP227H4+y+gLCwynYxaa0bL0aNH8/XXX5Ofn8+FCxc4d+4cPXv2NLhfycSi7f5e\nk8r+/aeLh6jXHoL/8OFEg8coLNRfp7kINTRqFEmbNjE0aXJOZz/NkPj33huFWg1HjsTSt28HgzZe\nuhTNxYuKsPvii0hatYrB11cRW6Un9NRMnuvmFsOkSYrI6ds3kpYtSybU1Uz94OAQQ0xMJJ6eXuTl\nxbJlS8lUEd7eXiQkxHL7dizNmnmxZw/061fSj+ZBsmJFLHv2KPscPAhq9S49n4wYoUw7ceQI9Ohh\n0JWMHKlMKVHWxMEDBqSwfHkUubnGpxH44Yc4IJojRwxPnWDLkwuXTkkJlsMavjXlWouIiOPChWjy\n8oxP9eHkpDyQ/PyM9+XtDbt3Q/v2ZbfZtUsRU4bw8lJER3liKjUVLlyA1q31t9evr0zgfOOGMh3T\nXXfp+1YjlMC4mPL0VB6i2dlw547ygNemaVNFlKjVylQ6hn4za9qA0saQmGratEQspaYq56dN48aK\naNHcZw2JKU0bUISMq6vyNyvdRiOW0tL0xVSDBsrk0/n5yrIhMVVacKWnw6VLu3TauLuXiKk7dxT/\naQtwlUoREJrnVEaGclxttIWS5pxK+9/dXbfNtWv6bdzcSsSSWq2017ZFW0yB/nZQ/JKdXbKclaXs\np42rq26b7GzdH9t2dopw1AghtVoRTq6uusfQiClQvtevr3vt1qtXcgxQvterp2tL3bq6bXJzddvU\nqaMb3CgqUgIuSqq7pM2tWyXL2t+NUemaqXXr1vH000+Tnp5OSEgI3bt35/vvv8fPz4/Q0FD8/Pxw\ncHBg6dKlqAz9BEP7hKfTuPFEbt2CzMySqJD2fEoDB3pjbx/Djz/eIDnZkcDAmahUjpw/X0CTJvPo\n3LkAlWoeGRku3LwZSVERpKamMG5cHL/8AseOReLqqhz38GHo0ydSK6oFvXvHYGcXS3x8JE88EcOO\nHfDvf0fyxhslN1dHR+Vfb28v1qyJJTxcuTmMHx/Jzz/H0K+fcvPWiJx331Vmjp80CX74wYtPP40l\nOLjknBISYpk4EQ4dUv6YPj76/8FbtVJuUgcOwJ49/F2LoUvv3spN88gR5QI0dMMaMgTCwpQbtDEx\nNWwYTJ2qCE1jD43PP1eEUlqafgSwtJ+MIVEnoaqw1LWWnJxCbm4c589DcrLhaKu3t/IQKUtMKTVQ\n8PDDxrdrxJSx/4MaMfXnnzB4sOE2muhUYqJyX9EIDe3tly8r/9dTU/WjTlAippKSlDkOS9/GnZ2V\nB9e1a0obQ8fQFlOlIwgatCNPhsSUi4sijG7cUB7Q5YmptDTF9tJotzEUmdKInIwMxYYrV6BtW902\npaNOV6/qCwvtNteuKeLE3l63jSby5OWltC2dKdCOTIHSpmVL3TZubsp1osGQmNJEpkAREE5OuiKz\nQQNFHKnVyvkbEkqGxJR2pE3TRhOZAn0xBYpYunFD+ffWLeU5of2s0I5MQYmY0qZePd1+bt7Ut6Vu\nXV2xlJNTEnECfaGUl6dcy9pRVRcXZb12m/KotJgaO3YsY8eONbht3rx5zJs3r8z9AwOj+P33R+jS\nJYaWLSE+/oO/xQ1AKj/9dJoGDbxp0mQe99/vQnz8PLy9vejdO4oDB3TTeoMHx/DDD4sAuHQpha5d\n4+jWDVSqPH77TUkNzp4dUzz56qZNKTz8cBz1658utkdzMXt7e7F5cyzPPadMuDt+fCS7d8cwYAA6\nv2x79VIU7S+/wNq1XixapBRna/Pww3DvvfDSS0oIetAgfT+MGQMrVig3iKAgw74aOVJJv+3ZA7EG\nngsODhAcDK+9Bj17wqBBAXptGjRQtq1YAd9+a7ifmzdTcHKK+7uY0/ADw4gu1kGTftR8r02UFD0L\nlqa6fGvK9RoREUd2djTZ2cZ/RGjERIcOepuK8fZW/v8Zi0w1aqQ8IE6eVCYdNkTz5vD778YjU5o2\nqalKmu+uu6Bz5wCd7RoxlZqqPIxKR3GgRExduqT/INduc+WKaZGplBTo0qXsNobEFJQILjs7RQBq\nRzTANDFVXppP00YjpoylCktHpkJCAnTaeHiUiENDUSfQjV4ZamNITN1zj26b0tGr8iJTGmGnjYuL\nck/Py1NEhqHIVMOG+lGn0lHT8iJTmjYaIZSdrf83LC2mNMJL+75Qv35JRBUUoXTXXbrHKR29MhaZ\n0gjIW7d0xZamTZVFpsxl585oOnaM4bffSm5Kmpvavn2nuXZtNTduQFCQ7o3L0IXp7Fzyffr0OK5f\nj+b6dbC3n2iw76VL48jLiyYvLxVn54kEBnbQu4mOHZvCkCFxODrCkiWRhIfrCguVCkaPTmHUqDiu\nXYPFiyMB3TZ33aVcdE8/rdwYDUVsNNGglBR46y3DvgoJUeqg7OyM3zx7905h1qw42rY1/Ms5OTmF\nlJQ4bt2C5s31bQXlgZGZGf33d8MPDFMePBJ5EmwJy12vKUAcK1fC6NGGf4xoosa+voaPoFIpD/KD\nB8uvmUpMNH4/aNYMfvtNeSiUfmiBIjYuX1bElqEUn+YYhw8brpfS0LSpbvTK0HZtMWWsZkrzwnd5\nYgqU7aV/1DVuXLK9rMjUX38p369c0X8Ig65YMlYzpZ3Cy8rSFzAeHvz9NqUitgw9s8pL82kEjKbG\nyFD0yhQxpR2Zun5df7umTVaWcq0Yi0xppwKNtTE1MgUlQkmb+vX1o06GIlPaQslQm/IiU46Oik8L\nCpQfEbm5+jWOdepUPDJlkZqpylL6RqC5qfn7l/y0Ky1ANDUQgwblEhg4r8xaiAEDvMupl2jOoEEd\nSEiI1bvxLVgQR35+NDk50XzzjeE6isOH47hyJZqCgmieeUa/TXJyCtnZUXz3XRQBAYbri27cSMHZ\nOYrffovi7rsNt2nRIoXMzCjU6ihSUgy32bRJSb+dPx/996upukRExHH6dDQQzUsvGT4fU9D8jTZt\n0vfZPwGpmbIeNdm3ptRePf208n/wwAHDtVfJySl89VUUEEX9+ob/H4MiOAoKlPScIZo3V4rH69Y1\nLJQ0bfbvLzlGad/Wras8SI4fNy6mNILLmFDStNFEpgwJLo0IKioqvwA9N1d5aBl64GvEUmqqfopP\ns11TV1XZNB+UL6bc3RUxUVioCBw3N2VoCW20BVfp4nPt42jElCGhZG+viARNtKc8MVVYqAiR0iJH\nOzJlKOoEunVT1qqZ0rQpT0yZUjOl3cZQzZR2ATroR6ZAV3AZiky5uNhQZKqsm1JZ0Y/yfkXq7jvP\n4APfUmmo0n+A0pQIGFizJobwcH27IyLiSE9X2jz9tOFo0IwZcRQURHP5svGIkaEwfUWpzek5QTAH\nS0SvIiLiOHZM+b8+Z47h/8egCKGWLXUj7qW3p6fD/fcb76tZM+Vlku7dy25z8GDZYkqT5tMaOtBg\nm6Qkw2k+Z2flQXb9etmpQG2hZKiUoEkT5Zxv3zYspurWVQRITk7ZaT6NUDJFTF25oi+m7O0VEZCV\nZfhNPtCNOhmLTGmLqYwM/dosUESNJjVXnpjKylLsKl2bpR2ZMpTm07TRCCFDkTZDYqq0UGrQgL/H\nAlOE3a1b+gKmPDFVt66yX2Ghch6lC9TBcGSqvAL00pEpKEnjubmZFpmq0WKqrBuTOTcuU/Y1pY0p\nwqIi4qP0K8OWRteWt8vZLum5yiI1U9bD1n1riR8jyckpHD4cx40bxgvdGzVS6iQNDYugoVkzpaZq\nzBhl2ZBvNWLqyScNH0MjlBo2NF4wr0njGYtMadr88YcSNTIUSdNErwwNi1C6TU6OYTEFJZGntDTD\nKdKKRKY0b/UZGv5FU6Senq4cs7RvS9dDGYpMlY5eGRNc2kLIUD1UWds1bTRDRpgamSqdMSotprKz\ny45MaYRSaVGs/bae5mUCbezsSiJGGuHVsKF+zVRpoWQoFaiJOqnVyvfSYkoj3MC0yJRVC9BrO5YQ\nZZYSZJYQQiKUBMG6WOJ+EBERx19/lV23mJqagoOD8payMcGlqTsylioERZTs2VN+ZKpOnbLTfIcP\nK+lAY0KoaVNluBUvL8NRJ40gM1YvBSViytnZNDFlTgF6enpJis+QvY0aKULo6tXyhVJZkSmNyDEU\nddK0uXZNEQSGhkYwRUyZUjOlXRNlKIVXt64iLAsKlLKb8mqmDKX4QLcmylBkCkoEl+bf0pHM0mm+\n8iJTeXlK1qZ0xE57eARjkamKpvmqtWaqtmNKfZGl2mhTk2tPbB3xrfWo7b61VL1hRITyAs2ffxof\nF0sjOIzVTGnaqNWGC7FBeUg5OChRJWNiqmlTpdDd3d14qYG2mDKEdmSqPDFlaFgEDZq6qrJqpjIy\nlPotYxEjTWTKUL2UBu3IVJMm+r6taM2UsciUJs2Xk6OIGO1xkEARHDk5SiF8WZEpc2umVCrd6FR5\nNVPGxFR5b/OBbt2URlSVN85UWQXohuqlNG3KikzZXAG6YB2OHj1a3SbUWsS31kN8a8kBbVOAKN5+\nWxlc15BvNaLEWGQKFFHi4qL/8NTe/ttvhmuhNDRtis5o0qXRjCN15oxxMaURSmWJKU1dlTExpRmU\nMzVV+W7o7WqNmDJUL6XdJjOzJM1X2rd165bUDVX2bT4oSfMZi1zZ2ZWIHFMiU2XVTJUVmYKSfoqK\nDAsYUyJT5dVMga6YunFDWdb2b+k0n6HIlHaaz1C9FJQfmapMAXqlxdQLL7xAx44dueeee3jwwQfJ\n0np3MjY2lnbt2tGhQwe2bt1a2S6ESnJd+31ZwaKIb62H+Na06JUpgmvePOXNwj17lOhVad8mJ6fw\n9ddR2NlFkZtr/M1CT0/jtVCa7Xl5ZbfRRK+MRaa025QVmUpPNy0ydeWKYTGlGZTz998Np/igYpEp\nTZqvtG+1RzgvKzKVmVmSwisrzWdsO5Sk+kyNTJU1NIKmjSHBpRFTN24oYqV02qyikSlTxJTmbT5t\n/xp6m89QZEojuGwiMhUcHMzJkyc5duwYvr6+xP49muSpU6dYs2YNp06dYvPmzTz11FMUaQ9lLgiC\nIFQaUwRXeYPrKvONRlNUFM2TTxpOFSYnp/DHH1FcvWp86iiNKCkvMpWTU7aYatKkfDFlSprv/Hkl\nqlA6JabdxlwxpR2ZKktwadqU9TZfTo6SSjVkrybNZ46YKl0zZW5kqqztlo5Mlfc2n2ZKGmtEppyd\nlTdHNVMYWTUyFRQUhN3fr6j16tWLpKQkADZs2MCECRNwdHTEx8eHtm3bcvDgwcp2I1SCxMTE6jah\n1iK+tR7iW8tROnpVGd9GRMSRlhZNerrx2ixXV0UIlCemoPzIVHZ22WLqyhXjheOgCKWTJw1HpbTb\nnDpV9jEqUjPVuLHh61Yjpoyl8DSRq8xMw9tBNzJlSChBieCyZM2UMbGUlWX4TT7Ndu3IlLHiclPE\nlKaNJjKl7V8XF6UQ/s4dRew4OCgfbSoTmSotpuzslNSzJiJlSmRKpVaXnqa34owaNYoJEyYwceJE\nIiMj6d27N5MmTQJg6tSpDB8+nIceeqikU1PmJBEEQRAEQaghlCWXyhwaISgoiMvaE+H8zfz58xn1\n98RR//nPf3BycmLiRMNTt4C+eLKAfhMEQRAEQagRlCmmtm3bVubOK1asICEhge3btxev8/b25tKl\nS8XLSUlJeJcVAxYEQRAEQbBhKl0ztXnzZt5++202bNiAi1b13OjRo/n666/Jz8/nwoULnDt3jp49\ne1rEWEEQBEEQhJpGpUdAj4yMJD8/n6CgIAD8/f1ZunQpfn5+hIaG4ufnh4ODA0uXLpUaKUEQBEEQ\nai0WKUAXBEEQBEH4pyIjoAuCIAiCIJiBiClBEARBEAQzEDElCIIgCIJgBiKmBEEQBEEQzEDElCAI\ngiAIghmImBIEQRAEQTADEVOCIAiCIAhmIGJKEARBEATBDERMCYIgCIIgmIGIKUEQBEEQBDMQMSUI\ngiAIgmAGZoupwsJCunfvzqhRowDIzMwkKCgIX19fgoODuX79utlGCoIgCIIg1FTMFlPvvfcefn5+\nqFQqABYsWEBQUBBnz55l8ODBLFiwwGwjBUEQBEEQaipmiamkpCQSEhKYOnUqarUagI0bNxIWFgZA\nWFgY69evN99KQRAEQRCEGoqDOTvPmjWLt99+m+zs7OJ1aWlpeHp6AuDp6UlaWprefpooliAIgiAI\ngi2gCRoZotKRqe+++46mTZvSvXt3ox2oVCqjwkmtVsvHSp9XXnml2m2orR/xrfjWFj/iW/GtrX5q\nin/Lo9KRqb1797Jx40YSEhLIy8sjOzubyZMn4+npyeXLl2nWrBmpqak0bdq0sl0IlSQxMbG6Tai1\niG+th/jWeohvrYf41rrYin8rHZmaP38+ly5d4sKFC3z99dcEBgbyxRdfMHr0aFauXAnAypUrGTNm\njMWMFQRBEARBqGlYbJwpTTpv7ty5bNu2DV9fX3bs2MHcuXMt1YVgIuHh4dVtQq1FfGs9xLfWQ3xr\nPcS31sVW/KtSm5IMtHSnKpVJOUhBEARBEITqpjzdIiOg10J27dpV3SbUWsS31kN8az3Et9ZDfGtd\nbMW/IqZMJDExETs7O4qKigAICAjgs88+s3q/I0aM4IsvvrB6P+Hh4bz88stW70cQBEEQahs2L6b2\n7NlDnz59cHNzo1GjRvTr149Dhw5Zvd+yhn2wJAkJCUyePLlC+wQEBFS4n6o6H1unMr4VTEN8az3E\nt9ZDfGtdbMW/Zg3aWd1kZ2czcuRIPv74Y0JDQ7l9+zY//fQTzs7O1W2aUe7cuYODQ810u9SxnDRm\n5QAAIABJREFUCYIgCELFsenI1NmzZ1GpVIwbNw6VSoWLiwtBQUF06dIFgBUrVtC3b1+ee+453N3d\nadu2LXv37mX58uW0atUKT09PPv/88+Ljbdq0ie7du9OwYUNatWrFa6+9ZrIty5Ytw8/PDw8PD4YN\nG8bFixeLt9nZ2bF06VLatWtH+/bt9fbNy8vj0UcfpXHjxri7u9OzZ0+uXr0K6KYTCwsLmT17Nk2a\nNKFNmzYsWbJEL/UYHR1Nly5daNCgAUOHDiUjI6O4n0ceeYTmzZvj5ubGwIEDOXXqVAW8LYDt5O9t\nEfGt9RDfWg/xrXWxFf/atJhq37499vb2hIeHs3nzZq5du6bX5uDBg9xzzz1kZmYyYcIEQkNDOXLk\nCH/88QerVq1i5syZ5ObmAlC/fn1WrVpFVlYWmzZt4sMPP2TDhg3l2rFhwwZiY2NZt24d6enp9O/f\nnwkTJui1+eWXXwwKmJUrV5KdnU1SUhKZmZl8/PHHuLi4ALrpt08++YTNmzdz7Ngxjhw5wvr16/VS\nc1999RVz587lypUr5Ofn88477xRvCwkJ4fz581y9epUePXowadKkcs9NEARBEISysWkx5erqyp49\ne1CpVEybNo2mTZvywAMPcOXKleI2rVu3JiwsDJVKRWhoKCkpKURHR+Po6EhQUBBOTk6cP38egIED\nB9KpUycAunTpwvjx49m9e3e5dnz00UdERUXRvn177OzsiIqK4ujRo1y6dKm4TVRUFG5ubgZTkE5O\nTmRkZHDu3DlUKhXdu3fH1dVVr93atWt59tln8fLyws3NjaioKJ3UnEql4vHHH2fSpEm4uLgQGhrK\n0aNHi7eHh4dTr149HB0deeWVVzh27Bg3btwwwdOCBlvJ39si4lvrIb61HuJb62Ir/jVLTOXl5dGr\nVy+6deuGn58fUVFRAGRmZhIUFISvry/BwcFcv37dIsYaokOHDixfvpxLly5x4sQJUlJSePbZZ4u3\nayZdBqhTpw4ATZo00Vl38+ZNAA4cOMCgQYNo2rQpbm5ufPzxxzppMmP89ddfPPPMM7i7u+Pu7k6j\nRo0ASE5OLm7TsmVLo/tPnjyZoUOHMn78eLy9vZkzZw537tzRa5eamqpznBYtWui1adasmcFzKyws\nZO7cubRt25aGDRvSunVrANLT08s9P0EQBEEQjGOWmHJxcWHnzp0cPXqU3377jZ07d7Jnzx4WLFhA\nUFAQZ8+eZfDgwSxYsMBS9pZJ+/btCQsL48SJE5Xaf+LEiYwZM4akpCSuX7/O9OnTi+uRyqJVq1bE\nx8dz7dq14k9OTg69e/cublPWm3IODg5ER0dz8uRJ9u7dy3fffadTy6WhefPmOtEu7e/aGMoxr169\nmo0bN7J9+3aysrK4cOECIEXnFcVW8ve2iPjWeohvrYf41rrYin/NTvPVrVsXgPz8fAoLC3F3d2fj\nxo2EhYUBEBYWxvr1683txiBnzpxh4cKFxRGgS5cu8dVXX+Hv71+p4928eRN3d3ecnJw4ePAgq1ev\nNmm4gOnTpzN//vzieqisrCy++eYbk/vdtWsXx48fp7CwEFdXVxwdHbG3t9drFxoaynvvvUdKSgrX\nr1/nzTff1LPPmDi6efMmzs7OeHh4kJOTw7x580zaTxAEQRCEsjFbTBUVFdGtWzc8PT0ZNGgQnTp1\nIi0trTi95unpSVpamtmGGsLV1ZUDBw7Qq1cv6tevj7+/P127duXdd98FDI+dVJY4Wrp0KdHR0TRo\n0IDXX3+dcePGmbTvmDFjmDNnDuPHj6dhw4Z06dKFLVu2mNQnwOXLl3nkkUdo2LAhfn5+BAQEGBxb\natq0aQQHB9O1a1fuvfdeQkJCsLe3x86u5M+oUqmKc8za5//YY49x11134e3tTefOnfH399exS8aZ\nMg1byd/bIuJb6yG+tR7iW+tiK/612Nx8WVlZDB06lNjYWB588EGdN+s8PDzIzMws6VSlIiwsDB8f\nHwDc3Nzo1q1bsdM0YT1ZLnv51q1bzJgxgxUrVtQIe2RZlmVZlmVZlmvDsuZ7YmIioLx1X5ZcsuhE\nx6+//jp16tTh008/ZdeuXTRr1ozU1FQGDRrE6dOnSzqViY4rRV5eHjt27CA4OJi0tDQeeugh+vTp\nw8KFC3Xa7dq1q/jCqChZWVm8Gv0qT818inbt2lnA6tqFOb4VykZ8az3Et9ZDfGtdaop/rTrRcXp6\nevGberdu3WLbtm10796d0aNHs3LlSkBRc2PGjDGnG+Fv1Go1r776Kh4eHvTo0YNOnToRExNj0T5i\nomPY/NFmet3Ti9nPzCYrK8uixxcEQRCE2oZZkanjx48TFhZGUVERRUVFTJ48mRdeeIHMzExCQ0O5\nePEiPj4+rF27Fjc3t5JOJTJVIzl37hy97unFp7c+RY2aFS4rOOh8kNffep0nnnjCYFG8IAiCINR2\nytMtFk3zmYqIqZrJyCEj8d7lzYTCktHbz3CGj+p9xJ3md4j7JK5GhFsFQRAEoSqxappPqJloF9CZ\nSkFBAcdOHOO803nSKHn7sj3tWZizkAfPP8ikkEmMHT6WP//804LW2haV8a1gGuJb6yG+tR7iW+ti\nK/4VMSUA4OjoyOk/TtPnmT5MrzOdFQ4ruMUtAFSoGMQgluUuo9EPjbi3073MnT1XpqIRBEEQBCTN\nJxjg4sWLPB/5PD/98BNP5D5BIIHYaenudNJZVmcZR5yPMP/d+YSHh+uMdSUIgiAItQmpmRIqzc8/\n/8zMqTO5c+kOM3Jm4Iefzvbf+Z2P6n2EqoWKuE/i6N+/fzVZKgiCIAjWQ2qm/oFYKsfct29fDp88\nzHNxz/G62+ssqLOAq1wt3t6RjizOWczIMyMJHRbKw6Me5q+//rJI3zUVW8nf2yLiW+shvrUe4lvr\nYiv+FTEllImdnR2PP/44Zy+epcfMHkTUieALhy+4zW1AqacawhCW5y6nweYGdOvYjX/P/Tc3b96s\nZsv/WSQnpxASEkVISBSHDh0p/p6cnFLdpgmCINR6JM0nVIgLFy7w/Mzn2bdrH1NzpzKIQagomdPv\nClf4rM5nHHc5TuyiWCZPniz1VFVASEgUCQnRADRsOJGsrNUAjBgRw6ZNsdVpmiAIgs0jNVOCVdi9\nezeRUyOxS7VjRs4M2tNeZ/tJTvJhvQ9xucuFuE/j8Pf3ryZLazfJySlERMSxb99prl1TBJSj40QK\nClYDqTRqNJtevToQHx+Jt7dX9RorCIJgo1i1ZurSpUsMGjSITp060blzZ95//30AMjMzCQoKwtfX\nl+Dg4OIpZ4SqoSpyzAMHDuTX078yc/FMohtG87bL22SQUby9E514P+d9gk4FMXbwWCY8OIFLly5Z\n3S5rU9Py9xERcSQkRHPt2ru4uk5kxIgY9u59mWHDYnBxmU1GxmoSEqKJiIirblPLpab5tjYhvrUe\n4lvrYiv+NUtMOTo6smjRIk6ePMn+/fv54IMP+P3331mwYAFBQUGcPXuWwYMHs2DBAkvZK9Qg7O3t\nmTp1KucunsNvuh9TXaay2n41+eQDYIcdQxnK8lvLcfqfE13bd+WVf79Cbm5uNVtu+2hqpPbv10wg\n3pz+/TuwaVMs993Xg++/jyUwsENx+6Ki6rFTEAThn4BF03xjxoxh5syZzJw5k927d+Pp6cnly5cJ\nCAjg9OnTxe0kzVc7+eOPP3juqec4vOcw03KnMYABOvVUl7nMp3U/5XSd07z1/ltMmDABlUpVxhEF\nY5TUSKVSv/5sBgzQT+VpUoD799+gQQNH/PxcJN0nCIJQCaqsZioxMZGBAwdy4sQJWrVqxbVr1wBQ\nq9V4eHgUL2uMCgsLw8fHBwA3Nze6detWPO+bJqwny7a5vHDhQpa+u5SGWQ2ZnjOddrRDm9/4jQ9c\nPsCtnRtLPltCTk5OjbLfFpbnzv2EAwc+BaBXr6ksWDDNaPt7753EkSOPAQMYMSKGF14YWu32y7Is\ny7Is1+RlzffExEQAVq5cWXYQSG0Bbty4oe7Ro4d63bp1arVarXZzc9PZ7u7urrNsoW4FI+zcubO6\nTVDfuXNH/eGHH6qbNGiiHuUySv0t36p3srP4s53t6hd5Ud2kThP1o488qk5KSqpuk02iJvhWrVar\nz59PVjs5zVX37z9XnZSUXGbbESPmqiFXDbnqESPmVpGFFaem+LY2Ir61HuJb61JT/FuebnEwLrNM\no6CggIceeojJkyczZswYgOL0XrNmzUhNTaVp06bmdiPYGPb29kyfPp3x48fz2r9fY+pnUxmXP46x\nRWNxwgk77BjOcAbeGsjq9avp/F1nnnvxOZ6f8zx16tSpbvNrPNu2eREcHMv//ld+2/j4SKZOjWHH\nDnjxxUjrG1ctXASkdMAYAQGtgdo9oK7lUQGtqtsIwUYwK82nVqsJCwujUaNGLFq0qHj9iy++SKNG\njZgzZw4LFizg+vXrOkXoUjP1z+Ps2bPMmjGL4/uPE5EbQV/66tRTpZDCp3U/5Xy987yz5B0eeeQR\nqacyQHJyCtOmxbFrF6xeHcmYMabXP0VHQ2YmLFliPfuqDxEKgjW4q7oNEGoIVq2Z2rNnDwMGDKBr\n167FD77Y2Fh69uxJaGgoFy9exMfHh7Vr1+Lm5mayUULtZevWrTwd8TSu6a7MyJlBG9robD/KUT6s\n9yGNfRsT92kcPXr0qCZLaybag3NWdEDOw4dT6N07jsBAWLasthWii5gSrIGIKUHBquNM9evXj6Ki\nIo4ePcqvv/7Kr7/+yrBhw/Dw8OCHH37g7NmzbN26VUdICdZHu4CuphEcHMyJ8ycIiw1jjusc3nN+\nj+uUjEPWjW4szVmK/1F/hvYbSviEcC5fvlyNFutSk31bHtHRcdy5E83WrTVz3ClL+nb9+q0sWvRZ\nhfZ59dXF2Nm1tpgNVcGKFf/Fzq41Fy8mV7cpBrGza01MzHsWO15N/BvZ8j3BFrAV/5olpgShMjg4\nODAzciZnEs/QIrwFU+pM4Ru7byigAAB77BmpHsnyW8vJ/zYfv7v9iP1PLHl5edVsefXzzjuR2NvH\nEBwcQ3x8ba1/Mp/167eycOGnFdpn2rTx7N+/zkoW/TPZv38dU6eOt+gxJf0v1ERETNVCNK941nQ8\nPDyI+yiOnw//zPl+55lWbxr72If670Li+tQnoiCCuNw4Ns/fTAefDvzf//1ftaaIq9u3R496MWxY\nLFu2xFY4TRcfH8nw4TE4Osbw2ms1T4hVl29v31Ym7fb2bkbPnt2qxYaaQGFhIYWFhRY9Zs+e3fDy\n8rToMWtaiUh13xNqO7biXxFTQrXTsWNHtuzewofffMjylsuJqhdFIonF273x5rXc13g67WnmPDaH\ngb0GcvTo0eozuBpZvx7Gjq3cvt7eXiQkxPLII7EcPlyb6qV0CQ9/ns8//5bk5MvY2bXGzq41bdr0\nB2DXrv3Y2bVm3botTJs2lyZNetCs2f2A4RTSkiUr8fcfS6NG3XB374q//1gSEnbqtElMTMLOrjXx\n8auJjl6Il1dP3N27Mnr0VJKTdVPUubm3mDHjJRo16oaraycefPBJ9u49jJ1da1au/G9xu4CA8Qwa\npB/R8fHpx+OPP1/m+X/99f8IDJxA06b34uraiR49Qvj882/12tnZtebf/36HBQs+pHXrfjg7+3Li\nxBmDx+zSZSjTps0tXs7KysbB4W5attSdc7Nv34cIDf2XTh+vvba4eFnj4/PnEwkJeRxX1074+PTj\n9dff1xNJv/56kv79H6FOnfa0aNGbN96IMyiksrNvMHNmNF5ePXFxaU+HDoNZvHhZ8fbCwkLc3Lry\nn/+UvHlx/Php7Oxa07//IzrHatGiNy++KBODCxVHxFQtxFZyzKUZPnw4J/84yfjXx/N8/edZ4ryE\nLLKKt/egBx/lfMR9h+5jSJ8hTH1sKleuXKlSG6vTt3l5sGULjBpl3nFGjoRNmyxjkyWxlG+jo59m\nxIhBNGnSiP3717F//zrWrftYp01k5CuoVCq+/HIxK1e+W7y+dAopMTGJKVNC+eabpaxd+wH33deV\nkSOnsGXLbr1+Y2OX8uefF1m+/G3ee+8V9u07wqOPPqvTJiIiiuXL/8uLLz7J+vXxtG/fhkmTntHr\nW6UynM4ytl6bP/+8yIMPDmPVqkVs2PAJo0YNYerUuXz88Zd6bVes+C/ff7+LhQtfJiFhOc2bGx7G\nJjCwDzt27C1e3rVrP87OTqSkpHHu3AUAbt7M4dCh4wwe3KeUzfr2jh37JEOG9GPDhk8YMyaYV15Z\nxMqVJYIvPT2TwMAJZGZe5/PPF/LBBzFs3rybZcvW6hyvqKiIkJAprFjxX1544Um+++4zhg0byHPP\nvc5LL70NKMO0DBzYS8f+HTv2UqeOC7/88hu5ubcAOHPmD1JS0vTsLw9bvd/aCrbiX7PHmRIES+Lo\n6Mizs57l0cmPEj03mimrpzDp9iRGF43GAQfssWe0ejSBtwL5Ys0XdPy/jsx9eS7PzHoGJyen6jbf\naiQnpzBmTBx2dlBQEAlUPrI0dCg8+STcugW1cUivNm1a0bixB05OjkbTdr16dSM+Xj8CUTry8c47\nLxV/LyoqYtAgf86evcCHH37J0KEDddq2bt2SVatKojBXr2bywgvzuXz5Ks2aNeHMmT/46quNvPnm\nXJ5/PgKAwYP7kpubR1zcilJ2KMKpMsybVxIZKioqYsCAnqSkpPHhh1/y5JOT9Npv3fo5zs7OZR4z\nIKA3cXEruHQphZYtvdi5cz9DhvTj99/Ps3PnPtq1a82ePYcoKChg0CD/Mo8F8Pzz0wgLexgoEWpf\nfbWR8HBl3aJFn3Hr1m22bv0Cb+9mAAQF9adVK12hk5Cwk59/PsSKFe/w2GMPATBkSD9ycnJ5991P\nmT17Gh4ebgQE9Oall96moKAAR0dHdu7cT1jYQ3z++f+xZ88vBAcPYOfO/Tg4ONC/f89y7ReE0khk\nqhZiKznmsmjcuDFLP13Kj7/8yMneJ3my3pMc5GDx9vrUZ0b+DBblLGJDzAY6+HRg48aNVq+nqC7f\nRkTEcehQNNeumf8mnocH3HMP1LQffFXp27Fjh5rU7vDh44wcOYVmze7H0bEtTk7t2LbtJ86e/VOv\n7YgRg3SWO3f2BSh+0+7AgaOo1WoeeWSETruHHhpWmVMwyrlzF5gwIZIWLXrj5NQOJ6d2fPbZGoM2\nDxs2sFwhBYqYsrOzK47u7Nixl8GD+/wthPYVr/Py8sTXt01ZhwIgJCRQZ7lTp3Y6byTu23eE3r27\nFwspgLp16zBq1GCd/+M//ngQOzs7Jk58QOd4kyaNIT8/n337jgAQGOhPXt5t9u49TFFRET/+eICh\nQwfQr9/9Ovbff39X6tat2C+M2nC/rcnYin9FTAk1mk6dOvHDnh9Y/NVi4r3ieaneS1zkYvH2VrTi\njdw3mJE6g1kTZzG472BOnDhRjRbXfJKTU7h6NYoZM6JITk6pbnOqBWPpLG0uXUph8OBJXL+ezZIl\nr7Fv3//xyy8bGTZsIHl5t/Xae3joDgGjESmatqmpSkq6adPGOu08PXWXy6K83wo3b+YQFDSZ48fP\n8Oabc9mz578cOvQ/pkwJNWizKX4AcHdvyD33dGTHjn2kp2dy8uRZBg3yZ9Cg3uzatR+AnTv3mRSV\nAsO+0rYvNfWKQb94ejbRWc7MvI6HhxsODrpJlmbNmhRvB+jatSONGrmzY8c+fv31JNnZNwkI6M2g\nQb3ZuVMRU7t27ScwsGIpPkHQYJaYmjJlCp6ennTp0qV4XWZmJkFBQfj6+hIcHMz169fLOIJgDWwl\nx2wqKpWKUaNGcerCKR585UFm1ZvFh84fcoMbxW3u534+zvmYrvu7MrDnQKZPmU56errFbaku38bG\nRuLgEMOIEeYPiRAREceZM9H89VfNGm+qKn1ryuv1mzfvJjv7BmvXfsDDD4+gZ89u3HtvF3JyblWq\nT41wuXJF97pMS9O/Tl1cnLl9O19vvUYcGGPfviNcvJhMfHwskyaNoXfv7vTo0ZmCgjsG21dkmIFB\ng/zZuXMfO3fuo1Ejd7p06cCgQf5cuZLO3r2HOXr0lMliqjy8vDy5fPmq3vq0NN11Hh5uZGZe584d\n3fPT7KsRbSqVqrhuaufOfXTv3omGDRswaJA/R46c4OefD5Genlkp+2vb/bamYSv+NUtMPf7442ze\nvFln3YIFCwgKCuLs2bMMHjxYZxoZQTAHJycnZr8wm9MXTtNwfEMer/M4G1QbKER5ndsBB8aox7D8\n1nLSV6fT3qc9ixYuoqCgoJotN5+LF70ICIhl06aKD4lQFvn6z+tagbOzE7dumTcumaYw2cHBvnjd\n2bN/8vPPhyp1vJ49u6FSqVi7Vrf6/5tvEvTa+vi04OzZCzrX7o8/HuDmzZwK23ztWhYbNmwze3ym\nwMA+JCWlEh//VbHoaNq0MZ06+RIdvZDCwkKLiSl//x7s3/8rSUmpxetycnL53/+265xHQEBvioqK\n9Hz65ZfrcXZ2wt+/ZAaFwMA+HDx4jO++21Ecgbr33i7Uq1eXV19djLOzE3373msR+4V/HmaJqf79\n++Pu7q6zbuPGjYSFhQEQFhbG+vXrzelCqAS2kmOuLE2aNCF+RTw79u/gyP1HmF5vOoc5XLy9AQ2Y\neXsm7+a8y9rotfi18SMhQf+BVRmqy7cHDkDv3pY5Vnx8JCNGxODhEUNYWM0Zb8qSvu3UqR2Zmdf5\n6KMv+eWXYxw/frrCxwgK6o+DgwOPPTabrVt/ZOXK/zJ06GPcdZd3pWrzOnS4m4kTH+Dllxfy5psf\nsm3bT0RFvcl3320HwM6u5HY8fvwoMjKuMWXKi/zwwx4++eQrpk9/iYYNXcvsu2/f+2jQwJV//Sua\nhISdrF37HQMHjqNJEw+z6wn7978fOzs7tm//WUc0DRrkz44de7nrLm9at25pVh8aZs16gnr16hAc\nPJm1a79j/fqtBAdPpm7dOjrnMXx4AP363c/06S/x3nvL2LbtJ2bNiuGzz9YUF59r21lQUMCPPx4o\ntt/e3p4BA3qyffvP9O7d3aT6sdLU9vttdWMr/rX423xpaWl4eiqDtHl6epKWlmawXXh4OD4+PgC4\nubnRrVu3YqdpwnqyLMvlLe/av4s33niDhYsXcnfe3UTkRtCCFgD44MP8nPkcyDnA9Iem0+H+Diz+\naHHxcAo1wX5Tl7//Hl57zTLHO3fuLC+8MJSEhAASE2vG+Zm7HBCgOz7U1Knj2b//V+bNe4vr17Px\n8WnBn3/+BBhPbZUedsDPrx1ffrmY6OiFPPDANNq29eHNN+fy/fe72L37gMFj6B9Tt6/4+FhcXevx\n1lsfk59fwODBffngg9cZOXIKDRu6FrcLCOjNRx/9h3fe+YRvv/2eHj06s2rVYh56aLreMbWXGzf2\nYN26j5k9+w0efngG3t7NeOaZx8nIuEZMzPsm2WwMV9f63HdfV3755RiBgSViKjCwD0uWrDQpKmXq\nkA+NGrmzfftqnnnmNcLCZtO4sQfTp0+ioOAOr7/+vtZ+KjZtWsa8eW/z5psfkZFxndatW7Jo0cs8\n88wUnT46dmyLp2djMjOzGDCg5I29wMA+bNq0w6j9NeH6luWqX9Z8T0xMxBTMmugYIDExkVGjRnH8\n+HEA3N3duXbtWvF2Dw8PMjMzdTuViY6tivJwCahuM6qU27dvs3jhYt58402C7wTzaP6j1Kd+8fYC\nCthot5Evnb9k4uSJxMTG4OHhUeF+qsO3RUXKG3jnzkGTJuW3N5U1a+Drr2FdDZlBxTzf2u5Ex++8\nE8+cOQv466+fadGieXWbI+hQ/kTH/8T7bVVSU/xr1YmODeHp6Vk8MW1qaipNm5r2toggmIOzszNz\nouZw6o9T1H24Lo/XeZz/qf5XXE/liCMPFT3E8lvLSVmZgu9dvsS9H6dXuFoTOX0aGje2rJACuO8+\nOFS58h+hknz33XYWLPiQzZt3s3Xrj7z88rtERy9k3LiRIqQEwYaxuJgaPXo0K1euBGDlypWMGTPG\n0l0I5VATVHx10axZM5Z9uYytP2/lQPcDPFXvKY5SMvVMQxry9O2neevmW3wx7ws6t+3Mli1bDB6r\noKCAp6Y/pRNprQ7fHjgAvXpZ/rht2sDNm2AkE1/l/BOu2wYN6rNhw1YmTIhk5Mgn+PLL9TzzzOOs\nWPFOdZsmVJJ/wnVbndiKf81K802YMIHdu3eTnp6Op6cnMTExPPDAA4SGhnLx4kV8fHxYu3Ytbm66\nY4pImk+oCtRqNd9++y2z/zWb1jdbE5EbgZfWyOFq1OxlL/F14/Hr6cfijxbTvn374u3vv/c+s56d\nxeuvv868f8+rjlMgOTkFf/84XF1h69ZIi77JBzBkCDz3HIwYUX7bmo3tpvmEmkz5aT7hn0F5usXs\nmqnKIGLKutSUHHNNIS8vj3ffepd333yX4QXDmVQwibrULd6eTz7r7dbztdPXPDblMV79z6sUFRXh\ne5cvM27O4BO3T/jr8l84OztXuW9DQqJISIgGYMSIGDZtsuwkrHPmQP368PLLFj1spTDPtxcBuacI\nlkQFtCq3ldxvrUtN8W95ukXm5hNqPS4uLrwU/RKPT32cubPmEv6/cMJvhTOUodhjjxNOhBaFEpQX\nxIplK/Bd5YtfFz8GFAxgMIP54c4PfPnll0yZMqX8ziyMtX9z3HcfrFpl3T6qhvIfev9kasoDSRBq\nKxKZEv5xHDp0iJlTZ5J1PosZOTPoSled7ec5zzrHdUQURNCQhhzmMPEt4/k98XedsYCqgr17Uxg8\nOI7AQGV8KEun+fbuTSEwMI7Bg61zfEEQhNqApPkEwQBqtZo1a9bwQuQL+Ob6Mi13Gs1oZrgtambU\nn8G7X79LSEhIldq5dSu8+SZs326d41s7jSgIglAbqPKhEYTqR3vQMcEwKpWK8ePHc+avM/R/rj8z\n6sxgmeMybqE/75oKFQ/ffJg3X32zyn37xx/Qtm2VdlltyHVrPcS31kN8a11sxb8ipoQHeQjHAAAg\nAElEQVR/NHXr1uXV11/l+Nnj5IfkE+4cTj76E9YFEMC5U+c4c+ZMldp3/rx1xVR8fCTNmsXQrZv5\nEygLgiD8U5E0nyD8zaKFi1gbvZb5OfNRoT/lxVq7tXzX+Ce63DeyyuqLHngAwsNh7Fjr9fHii+Du\nDlFR1utDEATBlpE0nyCYQHp6Om9Ev8GTOU/qCalb3OIiF/Eu8ib5yhkSEobTrdu/CAmJIjk5xap2\nWTsyBdC6NZg4/ZQgCIJgABkaoRYir0FXnJfnvIzrLVe22m/lWp1rZNhnkF6UzpXbV8gvKMBB7Y0d\n4ERf8lhFevpqEhJgypQYtmyxTtF2URH8+acyUrk18fGpGfPzyXVrPcS31kN8a11sxb9WE1ObN2/m\n2WefpbCwkKlTpzJnzhxrdSUIZuPd0puQKSG0vLslXl5eeHl54eDgyPz569m//wI3bnwFpNKwYRiu\nTle5elXZb+/eGwQHR+HoaPmhBZKTlfRbvXoWO6RBJDIlCIJgHlapmSosLKR9+/b88MMPeHt7c//9\n9/PVV1/RsWNHpVOpmRJsgJJhA1Jxd5+Nv3+H4iLtiIg4AI4fz+PSpfmA5YcW2LkTXnkFfvzRYoc0\nyK1bimjLzYUqHkZLEATBJqiWEdAPHjxI27Zt8fHxAWD8+PFs2LChWEwJgi1w547mW3P8/TvoCCXN\n95CQKC5dsk7/VVEvBVCnjiKmUlKgRQvr9ycIglDbsIqYSk5OpmXLlsXLLVq04MCBAzptwsPDi8WW\nm5sb3bp1K86LasaVkOXKLS9evFj8aYHlDh0iOXEihpYtL/L442N1tmnax8dHEhIylRMnYMGCty3a\n//nzAbRtWzXn6+EBiYkBtGhRff7WrKspf//atHz06FGeffbZGmNPbVqW+611l6vLv5rviSbWQFgl\nzfftt9+yefNmPvnkEwBWrVrFgQMHiItTUiOS5rMuu3bZRsFeTSU5OYXHHovjp59gz55IevYsqYMy\n5tvw8BR2747Dz89ytVMPPQTjxkFoqNmHKpeJE2H4cJg82fp9GUOuW+shvrUe4lvrUlP8Wy1DI3h7\ne3NJK/dx6dIlWkj+oMqoCReeLRMREceOHdEUFETz2mtxOtuM+TY5OY7ExGgSEqKL66nMparSfKC8\n0VfdRehy3VoP8a31EN9aF1vxr1XE1H333ce5c+dITEwkPz+fNWvWMHr0aGt0JQgWJ19/APRycXKy\nXP/JySmEhERx4kQUdeqkWO7AZdC6NVy4UCVdCYIg1DqsIqYcHBxYsmQJQ4cOxc/Pj3HjxknxeRWi\nnfMVKk6/fpF4ecUwYoT+FCvGfBsfH0mfPjHUrRvDxx+bNy1LREQcCQnRFBVF8/zzlolylUdNGB5B\nrlvrIb61HuJb62Ir/rXaOFPDhw9n+PDh1jq8IFiNDRu8WLkyliFDTN/H29uLPXtiadcOLl/Wfysu\nOTmlOP1XVVPRVAQfH9MjUzX9XARBEKoamZtPELQ4fhxGjFCiNPb2Fd//lVcgOxsWLdJdXzJmFQwZ\nEsO2bcbHo0pOTuGhh+I4dw5++61qxEp+Pri6Qk4OOBj5iaURUfv3nyYzczVg+bG1BEEQaiIyN58g\nmICmTumBB6IYMyalUkIKYMiQFJYujWLECGXePs1x9+07XdzmwIEbDBsWZXRuP29vL2bPjiUgILbK\noj5Xr6ZgZxdFcLDx+QY16cfMzHZ/r0nlwIHTVTJHoSAIQk1GxFQtxFZyzDUJjVC4cCGa48eN1ymV\n59sFC+LIz4/m+++Vt/o0x7127V1cXScyYkQMdes6smVL2W/+ZWRAo0bmnFHFiIiIIy8vmp07jdtU\nUKD5Np0mTSZSt+5sMjJWW+wNRrlurYf41nqIb62LrfhXxJQglMI6c+E1p39/ZRT17t1dym2dkQGN\nG1vDjsozdmwkTZrEMGLEJ/z66wcMHNihuk0SBEGoEUjNlCCgpPkGD47j9m1loM7Kptc0dUX79kFU\nVCRt2sCjj8YxcCB89ply3OTkFPr0iaNePdi2zXBfs2YpReyzZ5t7Zqbb3atXHI0aQUKCYZumTIEe\nPWDmzJJ9Ro2KIykJfv1VCtEFQai9lKdbREwJwt8EBcHTT8OoUeYfa8uWFEaPjsPZGRYsiOSpp3SF\nxqpVsGEDfPON4f0fewwCAyE83HxbTOXpp+Huu+GZZ/S3qdX8PdUMtGtXsv76dWjVSnmDsW7dKjNV\nEAShSpEC9H8gtpJjrknk5cH+/TBgQNntTPXt++8rtVM3bkSzaZN+PVGfPrB3ryJSDFEdab6GDZU3\nEQ1x4gQ4O+uPyO7mpkSrduwwv3+5bq2H+NZ6iG+ti634t9Ji6ptvvqFTp07Y29tz5MgRnW2xsbG0\na9eODh06sHXrVrONFARrs38/+PkpgqIqaN0a7twBrVmXdEhPr9oCdIAGDSAry/C2LVtg6FBQqfS3\nhYTApk3WtU0QBKEmU+lBO7t06cK6det48sknddafOnWKNWvWcOrUKZKTkxkyZAhnz57Fzk6CYFWF\nrcxlVJPYsQMGDy6/nam+jY+PJCIipvh7aVQq8PeHffuUNFlpqvptPlDE1Llzuus0NWAHDsBbb0UC\n+nVRI0cqQkutNiy2TEWuW+shvrUe4lvrYiv+rbTC6dChA76+vnrrN2zYwIQJE3B0dMTHx4e2bdty\n8OBBs4wUBGuhGQdqyZIouna13FhJ3t5ebNoUy6ZNxseK6tNHEVOGqClpPs3QDhkZ0axZY3j4A1fX\nFNLToxgwQMabEgThn4nFp5NJSUmhd+/excstWrQgOTlZr114eDg+Pj4AuLm50a1bt2IFqsmRynLl\nlhcvXiz+NHFZEQvK+hUr4hg/PrbM9tr5e3P79/cPYPZs/e3bt+8iOxvc3KrWHw0aBJCVpb8dfgRK\nRkYvvf3hh1/g1q3H2LNnABERMbzwwtBK9a9ZV5Ouj9qyfPToUZ599tkaY09tWpb7rXWXq8u/mu+J\npk5aqi6DIUOGqDt37qz32bhxY3GbgIAA9eHDh4uXZ86cqV61alXx8hNPPKH+9ttvdY5bTreCmezc\nubO6TbAZRoyYq4ZcNeSqR4yYW257S/r2/PlktZ3dXPXQoXPVSUnJxevT0tTqRo0s1o3J7NmjVvfp\no7suKSlZfd99c9VNmujaqE1FfWgMuW6th/jWeohvrUtN8W95uqXMyNS2bdtMU2RaeHt7c0mrqjYp\nKQlvb+8KH0eoPBqFLZRPfHwkQUEx5OYarm0qjSV9+/TTcRQVRbNlC0RElMxxV10DdjZooJ/m8/b2\n4sknY9m3D4z9N46Pj2TcuBh++800HxpDrlvrIb61HuJb62Ir/rVImk+t9X736NGjmThxIs899xzJ\nycmcO3eOnj17WqIbQbA43t5e9OkTy/33GxcLVU11vMkHxt/mu3wZPD2N7+ft7UVCQizNm0Pz5taz\nTxAEoaZiV9kd161bR8uWLdm/fz8hISEMHz4cAD8/P0JDQ/Hz82P48OEsXboUlTmv+AgVRjvnK5TP\niRPQubNpbS3p2/j4SNq0iaF9+xidiE51vMkHxseZunwZmjUre98GDZSPgfJIg2gK/7UnSZbr1nqI\nb62H+Na62Ip/Kx2ZGjt2LGPHjjW4bd68ecybN6/SRglCVVFUBCdPQqdOVd+3t7cX//pXLBcv6kbF\nqivN5+oKN24oPrHT+pl1+XL5g5kCtG8PZ89Cy5blt9W8JQgwZUoMW7bEVtJqQRCE6qfSkSmh5mIr\nOeaawMWLyijebm6mtbe0bz09IS1Nd111pfns7aFOHcjJ0V2fllZ+ZArA11cRU2WhiUjt23f67zWp\nbN9+msDAKNq1862U3UL5yD3BeohvrYut+NfiQyMIgi1x4kT1RKU0GBJT1ZXmg5JUn6tryTpT0nyg\niKkzZ8puUxKRSsXVdSIuLnD16mp27tQtwhcEQbAlJDJVC7GVHHNN4Phx0+ulwPK+NSamqiPNB4aL\n0E0VU5o0n2k0p3//Dtx/f4fiNRcvXjTZTqFiyD3BeohvrYut+FciU8I/mhMnICio+vqvSWk+0C9C\nv3kTCgt1I1XGMCXNFx8fiZ9fDH5+JcMoRETEcOYMtGljuAZTEAShpqNSq43NW2/FTlUqqqFbQdDj\nnnvgs8/gvvuqp//CQnBxgdxccHRU1vXrB/Pnm1b0bWmCg+H555V/Af74A4YMgQsXyt83P79krCon\nJ8NtbtxQolwZGcp5azh6FB58UOlPXv4VBKGmUZ5ukTSf8I+loECJpHTsWH022NsrUairV0vW1aQ0\nn6kpPlAEVKtWiiAyxr59cO+9ukIKFFFrZwe//lpxmwVBEKobEVO1EFvJMVcnyckpDBkShUoVxfXr\nKSbvZw3flk711aQ0n6lv8mkoL9X344/Qv7/+epUKOnf+L488ojv2lGAZ5J5gPcS31sVW/FtpMfXC\nCy/QsWNH7rnnHh588EGytH7OxsbG0q5dOzp06MDWrVstYqhgOkePHq1uE2o8ERFx/PhjNLduRRMR\nEWfyftbwrbaYKiqCa9fAw8Pi3ZhE6SllKhKZSk5O4dSpKObONS6GfvrJsJgC+O23j/jzz2gSEkz/\nmxga/FPQR+4J1kN8a11sxb+VFlPBwcGcPHmSY8eO4evrS2ys8krzqVOnWLNmDadOnWLz5s089dRT\nFBUVWcxgoXyuX79e3SZUK9oP2EOHjlj0YWsN32qLqawsqF+/pH6qqjEnzRcREceFC9GcPm1YDN2+\nDYcPQ58+hvd3cLhdYXs1Qy1URID9E/mn3xOsifjWutiKfystpoKCgrD7e5jkXr16kZSUBMCGDRuY\nMGECjo6O+Pj40LZtWw4ePGgZawXBBLQfsAEBrxt82MbHR+LtHUOXLjFmTc5rCbTFVHWm+EA/zVcR\nMVUehw4pacAGDQxvHzWqJ+7uMfTqZfrfJD9f8y2VgwdPS4RKEIRqwSJDIyxbtowJEyYAkJKSQu/e\nvYu3tWjRgmRTJ+wSLEJiYmJ1m1BjKCw0vN7b24vWrWOJianYBMfW8K2npyJakpNTCA+PIyMDkpMj\n8fb2snhf5WEoMlXWJMfaxMdHMn58DMeOoSeGkpNTeOKJOG7fNn5uGRkZPPLICrp2Ne1volaDvX0k\nrVrFkJZ2mvT01SQkyOCfhpB7gvUQ31oXW/FvmUMjBAUFcfnyZb318+fPZ9SoUQD85z//4ciRI3z7\n7bcAREZG0rt3byZNmgTA1KlTGTFiBA8++GBJp/LusyAIgiAINkRZQyOUGZnatm1bmQdesWIFCQkJ\nbN++vXidt7c3ly5dKl5OSkrCu9TPTBljShAEQRCE2kKla6Y2b97M22+/zYYNG3DRGjRm9OjRfP31\n1+Tn53PhwgXOnTtHz549LWKsIAiCIAhCTaPSNVORkZHk5+cT9PdcHP7+/ixduhQ/Pz9CQ0Px8/PD\nwcGBpUuXSlpPEARBEIRaS7VMJyMIgiAIglBbkBHQBUEQBEEQzEDElCAIgiAIghmImBIEQRAEQTAD\nEVOCIAiCIAhmIGJKEARBEATBDERMCYIgCIIgmIGIKUEQBEEQBDMQMSUIgiAIgmAGIqYEQRAEQRDM\nQMSUIAiCIAiCGYiYEgRBEARBMAOzxVRhYSHdu3dn1KhRAGRmZhIUFISvry/BwcFcv37dbCMFQRAE\nQRBqKmaLqffeew8/Pz9UKhUACxYsICgoiLNnzzJ48GAWLFhgtpGCIAiCIAg1FbPEVFJSEgkJCUyd\nOhW1Wg3Axo0bCQsLAyAsLIz169ebb6UgCIIgCEINxcGcnWfNmsXbb79NdnZ28bq0tDQ8PT0B8PT0\nJC0tTW8/TRRLEARBEATBFtAEjQxR6cjUd999R9OmTenevbvRDlQqlVHhpFar5WOlzyuvvFLtNtTW\nj/hWfGuLH/Gt+NZWPzXFv+VR6cjU3r172bhxIwkJCeTl5ZGdnc3kyZPx9PTk8uXLNGvWjNTUVJo2\nbVrZLoRKkpiYWN0m1FrEt9ZDfGs9xLfWQ3xrXWzFv5WOTM2fP59Lly5x4cIFvv76awIDA/niiy8Y\nPXo0K1euBGDlypWMGTPGYsYKgiAIgiDUNCw2zpQmnTd37ly2bduGr68vO3bsYO7cuZbqQjCR8PDw\n6jah1iK+tR7iW+shvrUe4lvrYiv+ValNSQZaulOVyqQcpCAIgiAIQnVTnm6REdBrIbt27apuE2ot\n4lvrIb61HuJb6yG+tS624l8RUyaSmJiInZ0dRUVFAAQEBPDZZ59Zvd8RI0bwxRdfWL2f8PBwXn75\nZav3IwiCIAi1DZsXU3v27KFPnz64ubnRqFEj+vXrx6FDh6zeb1nDPliShIQEJk+eXKF9AgICKtxP\nVZ2PrVMZ3wqmIb61HuJb6yG+tS624l+zBu2sbrKzsxk5ciQff/wxoaGh3L59m59++glnZ+fqNs0o\nd+7cwcGhZrpd6tgEQRAEoeLYdGTq7NmzqFQqxo0bh0qlwsXFhaCgILp06QLAihUr6Nu3L8899xzu\n7u60bduWvXv3snz5clq1aoWnpyeff/558fE2bdpE9+7dadiwIa1ateK1114z2ZZly5bh5+eHh4cH\nw4YN4+LFi8Xb7OzsWLp0Ke3ataN9+/Z6++bl5fHoo4/SuHFj3N3d6dmzJ1evXgV004mFhYXMnj2b\nJk2a0KZNG5YsWaKXeoyOjqZLly40aNCAoUOHkpGRUdzPI488QvPmzXFzc2PgwIGcOnWqAt4WwHby\n97aI+NZ6iG+th/jWutiKf21aTLVv3x57e3vCw8PZvHkz165d02tz8OBB7rnnHjIzM5kwYQKhoaEc\nOXKEP/74g1WrVjFz5kxyc3MBqF+/PqtWrSIrK4tNmzbx4YcfsmHDhnLt2LBhA7Gxsaxbt4709HT6\n9+/PhAkT9Nr88ssvBgXMypUryc7OJikpiczMTD7++GNcXFwA3fTbJ598wubNmzl27BhHjhxh/fr1\neqm5r776irlz53LlyhXy8/N55513ireFhIRw/vx5rl69So8ePZg0aVK55yYIgiAIQtnYtJhydXVl\nz549qFQqpk2bRtOmTfn/9u48rKpqfeD49xwEAUWZFBRTNAUUB0RTMQdQ0ZTEgTSHFEfM0ptmmlgO\nYDlkzlcrzJzHujlUajiAZjn8rkkpZjiRCDggDjggAvv3B5ejR0CmczgcfD/PwxN777X3WrzsDq9r\nrb12jx49uH79uqZM7dq1CQwMRKVS0bdvXxISEpg2bRqmpqb4+vpiZmbG+fPnAWjfvj3u7u4ANGrU\niH79+nHw4MF82/Hll18SHByMq6srarWa4OBgoqKiiIuL05QJDg7G2to61yFIMzMzbt68yblz51Cp\nVDRt2hQrK6sc5bZu3cq4ceOoXr061tbWBAcHaw3NqVQqhg4dysCBAzE3N6dv375ERUVpjg8ZMoQK\nFSpgamrK9OnT+eOPP0hJSSlApEU2Yxm/N0YSW/2R2OqPxFa/jCW+xUqmUlNTadmyJR4eHjRo0IDg\n4GAAkpOT8fX1xcXFhc6dO3P79m2dNDY3bm5urFq1iri4OE6fPk1CQgLjxo3THM9+6TKAhYUFAFWq\nVNHad+/ePQCOHTuGj48PVatWxdramq+++kprmCwv//zzD++99x42NjbY2NhgZ2cHQHx8vKbMSy+9\nlOf5gwYNokuXLvTr1w8nJyc+/PBD0tPTc5RLTEzUuk6NGjVylHF0dMz1Z8vIyGDy5MnUrVuXypUr\nU7t2bQCSkpLy/fmEEEIIkbdiJVPm5uZEREQQFRXFn3/+SUREBIcPH2bOnDn4+voSExNDx44dmTNn\njq7a+1yurq4EBgZy+vTpIp0/YMAAevbsyZUrV7h9+zZvv/22Zj7S89SsWZOwsDBu3bql+bp//z6t\nWrXSlHnek3LlypVj2rRpREdH89tvv/Hjjz9qzeXKVq1aNa3erqe/f1puY8wbN25k586d7N+/nzt3\n7nDp0iVAJp0XlrGM3xsjia3+SGz1R2KrX8YS32IP81laWgKQlpZGRkYGNjY27Ny5k8DAQAACAwPZ\nvn17cavJ1d9//82CBQs0PUBxcXFs2rQJLy+vIl3v3r172NjYYGZmxvHjx9m4cWOBlgt4++23mTVr\nlmY+1J07d/j2228LXG9kZCSnTp0iIyMDKysrTE1NMTExyVGub9++LF68mISEBG7fvs3cuXNztC+v\n5OjevXuUL18eW1tb7t+/z5QpUwp0nhBCCCGer9jJVGZmJh4eHjg4OODj44O7uzvXrl3TDK85ODhw\n7dq1Yjc0N1ZWVhw7doyWLVtSsWJFvLy8aNy4MfPnzwdyXzvpecnR8uXLmTZtGpUqVWLmzJm8+eab\nBTq3Z8+efPjhh/Tr14/KlSvTqFEjfv755wLVCXD16lX69OlD5cqVadCgAd7e3rmuLTVy5Eg6d+5M\n48aNadasGX5+fpiYmKBWP/k1qlQqzRjz0z//4MGDqVWrFk5OTjRs2BAvLy+tdsk6UwVjLOP3xkhi\nqz8SW/2R2OqXscRXZ+/mu3PnDl26dGH27Nn07t1b68k6W1tbkpOTn1SqUhEYGIizszMA1tbWeHh4\naIKW3a0n28/ffvjwIaNHj2b16tWloj2yLduyLduyLdtlYTv7+9jYWCDrqfvnpUs6fdHxzJkzsbCw\n4OuvvyYyMhJHR0cSExPx8fHh7NmzTyqVFx0XSWpqKgcOHKBz585cu3aNgIAAWrduzYIFC7TKRUZG\nam6MotSxZs0aBgwYkOsThS+64sRWPJ/EVn8ktvojsdWv0hJfvb7oOCkpSfOk3sOHD9m7dy9NmzbF\n39+fNWvWAFnZXM+ePYtTjfgfRVGYMWMGtra2eHp64u7uTmhoqE7rWLRgEdP/NZ26L9Xliy++yPWp\nQiGEEEI8UayeqVOnThEYGEhmZiaZmZkMGjSIiRMnkpycTN++fbl8+TLOzs5s3boVa2vrJ5VKz1Sp\ndOPGDVydXVn8YDEPeciKCiu4a3eXBcsX0K1bN5lTJYQQ4oWUX96i02G+gpJkqnR6Z8Q73Fh3g3fT\n3gVAQeEIR1hRYQXOjZxZ+MVCPDw8DNxKIYQQomTpdZhPlE5PT6ArqMzMTDZs3oAqU8VDHgKgQkVr\nWrPi/go8jnng29qXwH6BWouRvmiKEltRMBJb/ZHY6o/EVr+MJb6STAkg62XMf5z+A7WfmiEWQ9jF\nLjLIAKAc5eih9GDVw1VkfJ9Bw3oNmRo8VbO6uhBCCPEik2E+kcOxY8cY//Z4bp67ycj7I2lOc63j\nV7nKaovVRJWPYuZnMxk2bFiui4wKIYQQZYHMmRJFoigK27Zt44MxH+B415GR90dSm9paZc5ylrAK\nYaRWTWXhFwvp0qWLgVorhBBC6I/MmXoB6WKMWaVS0bt3b87GnqXvzL5MrDiRheYLSebJ4qtuuDH/\n/nwGXBrAqN6j6NSmE6dOnSp23aVZaR2/j49PwM8vGD+/YP77398138fHJxi6aQVWWmNbFkhs9Udi\nq1/GEl9JpsRzmZmZMW78OM5dPsfLI19muPlw1pVbRyqpQNYk9Ta04esHX+P+mzs+LX0Y/tZwEhMT\nDdzyF0tQ0FJ27ZrGrl3T6NJlpub7oKClhm6aEEKUeTLMJwrl4sWLTHpvEr8e+JUhD4bgiy/qp3Ly\ne9xjo+lGdpfbzXsT3mPi5IlUqFDBgC0u2+LjEwgKWsrRo2dJTt4IgEo1AEXZCCRibz+BFi3cCAsb\ni5NTdcM2VgghjJTMmRJ6ceTIEcaNGsedi3cIuh+EJ55axxNJ5BuLb4g2j+aTzz8hMDBQJqnrgZ9f\nMLt2TQMSsbScQLt2bsyc2YcpU77l0KGzPHqUlWB16xbKTz/NNmxjhRDCSOl1zlRcXBw+Pj64u7vT\nsGFDlixZAkBycjK+vr64uLjQuXNnzStnRMkoiTFmLy8vjv5xlJmrZrLEYQlTK0zlH/7RHK9GNT56\n+BEf3/qYJf9agoebB/v27dN7u/SttIzfZ8+ROno0+52X1fD2dmP37tk0b+5JePhsOnZ005TPzDRM\nOwujtMS2LJLY6o/EVr+MJb7FSqZMTU1ZuHAh0dHRHD16lGXLlvHXX38xZ84cfH19iYmJoWPHjsyZ\nM0dX7RWliEqlok+fPvz9z9/0nN6T9yu8z5LyS7jFLU2ZBjRg4f2F9Dnfh2E9hvGa92tER0cbsNVl\nQ/YcqeTk+VSoMIBu3UIJCxurVSYsbCzduoViZzeR6OhUo5uQLoQQxkKnw3w9e/ZkzJgxjBkzhoMH\nD+Lg4MDVq1fx9vbm7NmzmnIyzFc23bx5k9CpoaxbvY430t4gICOA8pTXHH/MY3aod7Cp/CYC+gYw\nc+5MHBwcDNhi4/VkeC//ITxf32D27StYWSGEEDmV2Jyp2NhY2rdvz+nTp6lZsya3bmX1TiiKgq2t\nrWY7u1GBgYE4OzsDYG1tjYeHB97e3sCTbj3ZNs7tDRs28NXirzgffZ6hD4bSkY5ak9Tvcpf15daz\nz2wf7096n+Ytm2Nubl5q2m8M27GxSQQFneDVV+Hdd5thb2+fZ/lWrQZy7NhgoB3duoUycWIXg7df\ntmVbtmW7NG9nfx8bGwvAmjVr9J9M3bt3j/bt2zN16lR69uyJjY2NVvJka2tLcvKT9YmkZ0q/IiMj\nNTeGIR0+fJhxo8bx4J8HBN0PwgPtlyTHE883lt9w1vwssxbMYtCgQajV6jyuVjqUlthOmwbx8bBy\nZf5ls5/4O3gQvvlmLH37ls6n+kpLbMsiia3+SGz1q7TEV++Ldj5+/JiAgAAGDRpEz549ATTDewCJ\niYlUrVq1uNUII9SmTRuOnzrO1BVTWVBlAdMtpxNHnOa4E05MfTCVycmT+fzdz/Gs76n1rwKRU3x8\nAp07BzNnTjDDhycU6Bwnp+r89NNsFi+ezapVpTOREkIIY1asnilFUQgMDMTOzo6FCxdq9k+aNAk7\nOzs+/PBD5syZw+3bt7UmoUvP1IsnNTWVxQsXM/fTuXRI78CgR4OoTGXNcQWFSDmfec4AACAASURB\nVCJZabmSJq2aMH/ZfNzc3J5zxRdTYeZKPevixQQaNFjKK6/A5s1lbd2py4B8pghdUQE1Dd0IUYro\ntWfq119/Zf369URERNC0aVOaNm3Knj17mDx5Mnv37sXFxYUDBw4wefLk4lQjygBzc3M+DP6QmNgY\nHAY7MNR8KJtNNpNGGpC1kroPPnzz4BtqRdaitWdrRo8YzY0bNwzc8rJj7NilPHo0jcOHy+LK6JJI\nCV2S+0kUTrGSqTZt2pCZmUlUVBQnT57k5MmTvPbaa9ja2rJv3z5iYmIIDw/H2tpaV+0VBVCah8rs\n7e1ZFraMI1FHiPeJZ5jlMA5wAOV/H15mmNE3sy+rHq4iaV0Srs6uzP50NqmpqQZueRZDx/add8Zi\naRma61IIhVEa153SZWxXr/4Otbo2Fy9eznEsPT0dtbo2ISGLdFZfSYiMPIpaXZtDh44ZuikFolbX\nJjR0sc6uN2PGItTq2vkXLGGG/kwo64wlvqV7tq8os1xdXflh7w+s/2k9P7j+wL8q/ItTPHlJcmUq\n827auyx+sJifZ/2MS00XNm7cSGZpzAJK0P791ZkwYTY//TS70MN02etO2diE8uabRU/EygqVSmXo\nJhRKs2YNOXp0G02buhu6KQVy9Og2Rozop9NrGtvvTLw45HUywuAyMzPZuHEjk8dNpt7Deox4MAIn\nnLTK/MEfhFUIw7ymOYu+WkTbtm0N1FrDyciAmjVh3z6oX7/o11myBE6ehFWrdNc2w/tHa2v16u8Y\nNmwi588fpE4d7bkv6enpmJnVY8aMcUyb9l5JNlIUw4wZiwgNXUxm5qUSqrFWCdUjjIHen+YTorjU\najVvvfUW5+LO4TvZl7GWY/mi/Bfc5a6mTBOasPT+Urr+1ZU3X3uTHl16EBMTY8BWl6z4+ARefTWY\nlJRgKlUq2FN8eenVC374AR4/1lHjyoCkpGRGjZqCq2sHKlSoT82arRk48D0SEq5plcseajp79gK+\nvm9RoUJ9nJ3bsGrVtwCsWvUtLi4+WFm506FD/xzDjM7ObRg0aDxr1/4HFxcfLC3daNeuL+fOXSIl\n5R7Dh0/Czs4DR8dXmDhxFhkZGZpzcxvm8/buR9u2fdi37zCenn5UqFCfRo26sH17eI6fcdOmnbi5\ndcTCwpXGjV9j5869eHv3w8fn+b1HjRp1YeTIJ/Ne79y5S7lyL/PSS15a5V59NYC+fd/VbD87lJod\nu/PnY/HzG4qVlTvOzm2YOXNJjj9SJ09G07ZtHywsXKlRoxWffLI01z9kd++mMGbMNKpXb4G5uStu\nbh1ZtOgbzfGMjAysrRvz6af/1uw7deosanVt2rbto3WtGjVaMWmSLGgrikaSqTLIWMaYn2VhYcGU\nqVM4e+ksNgNsGGI+hG/V32omqatR04lOrH6wGsf9jrRq0oqxb48lKSmpxNpoqNgGBS3l2LFppKQU\nf/L4Sy/Byy9DabtN9BHb9PT0HF9PJyjZkpNvU768GZ9++gF79qzh88+ncO5cLK++GsCjR49ylO/T\n5x169PBl586v8fR0Z/jwSUyY8Alff72Zzz+fwqpV8/j774sMGKDd86VSwaFDx/nqq418/vkU1qyZ\nz4UL/xAQMJo33xyDnZ0NW7cuIyioP/PnryAsbNNzfz6VCi5c+Idx40L54IMgvv/+S6pVq0qfPu9w\n4cKT3rq9e39h4MD3aNCgLtu2hfHBByMZP34m585dynforEOH1hw48JtmOzLyKOXLm5GQcI1z57J6\nie7du89//3uKjh1bP9O+nNfu1WsUnTq1YceOFfTs2Znp0xeyZs1/NMeTkpLp0KE/ycm3Wbt2AcuW\nhbJnz0G++War1vUyMzPx8xvG6tXfMXHiKH78cSWvvdae99+fyUcfzQPAxMSE9u1barX/wIHfsLAw\n5//+708ePHgIwN9/XyAh4VqO9heEsX7eGgujia9iAAaq9oURERFh6CboRHR0tNLVp6tSw7KGMp3p\nygEOKBFEaL62sU3pXb63YlvBVvlszmdKamqq3ttkqNh26zZZgQcKPFC6dZtcrGtduRKvuLlNVmrW\nnKxcuRKvoxYWX/FiG6v1tWrV54pKpXruV0jI+BznZX+lp19QLl/+TVGpVMq2bWGa/dOnj1NUKpWy\nbt1Czb5bt/5UTExMFHt7WyUlJVqzf8mSGYpKpVIuX/5Ns69WrRqKnZ2Ncvfu6RzlRo7sr9UGT8+G\nio+Pl2Y7ImKzolKplIMHt2j2tW/fSjEzM1POnz+o2Xf9+gnFxMREmTVrkmafl5en0qiRm9b1T5z4\nUVGpVFp15Pb1/fdfaf0c7703TPH391Xq1autfPXVLEVRYpXdu9coKpVK+fvvA5rzno1xduxWr/5c\n6/qNGrkpnTu302xPmfKuUr58eeXKlaOafffv/6XY2dkoarVas++HH1YqKpVKWbNmvtb1Rozop5Qv\nX165eTNKUZRYZcGCqYqFhbmSlnZOUZRYpUePzsro0W8pFSpYKj//vFZRlFjliy8+VUxNTZX79/96\n6loFU1Y+b0ur0hLf/PIW6Zkqg0rDarG60KBBA3Yd2MXqnav5vu73jKswjmievCTZGmvGPhrLwvsL\n2Rm6E9earmzZskWv8/EMFduPPhpL+fLFf4oPsnq5zp6dxuXLpWuJBH3Edvv2MP773x+0vo4e3ZZr\n2S++WE+TJl2xsnLH1LQutWq9CkBMzMUcZbt2fdJWa+tKODjY06pVUypWrKDZ7+paB4C4uEStc728\nPLGyqpijXJcu7bTKubrWyXFuburVc+bll5/M76lSxY6qVe2Ii8saDs7IyODEidMEBLymdZ6nZ0Nq\n134p3+t7e7dCrVZrencOHPiNjh1b/6/H6ohmX/XqDri41Mn3en5+HbS23d3rcflyvGb7yJHfadWq\nKU5Ojpp9lpYWdO/eUev/7UOHjqNWqxkwoIfW9QYO7ElaWhpHjvwOQIcOXqSmPuK3306QmZnJoUPH\n6NKlHW3avKLV/ldeaYylpUW+7X9WWfm8La2MJb7lDN0AIfLTsWNHov6OYu3atXw04SPqp9Zn+IPh\nVKMaADWpycwHMzn54CQhw0P4fObnLA5bTOvWhe+yL63Onq1O796z2bhRt9d98EC31yttGjZ0zXUC\n+rOWLl3Ne++FMGHCSLp0aYeNTWUyMjJo1aoXqak5h/lsbCprbZuZmeayzwxA63yVKrdzzfK4plmu\ndT/L1jbn0jPlyz85NykpmcePH1O1qn2OclWr2uV7fRubyjRpUp8DB47g59eB6OgYfHy8cHCw5733\nQgGIiDiCj49XPlfKvb3ly5fX+jkTE6/TuHHOJywcHKpobScn38bW1ppy5bT/jDk6VtEcB2jcuD52\ndjYcOHCEihUrcPfuPby9W3H27AW+//5nIGvoctSoAQVqvxC5KVbP1LBhw3BwcKBRo0aafcnJyfj6\n+uLi4kLnzp25fft2sRspCsdoxpgLQa1WM2TIEM7FnaP9xPa8a/kuX5p9SQopmjJNacq/7/+bTtGd\nCOgUQIBfABcuXNBpOwwV28hI0NU/0LKXSKhWLRR//9KzRIIh79vNm3+gU6c2zJs3hU6d2tCsWSOq\nVMk/0TAG9va2mJqacv16zrmF164VbL6hj48XERFHiIg4gp2dDY0aueHj48X160n89tsJoqLOFDiZ\nyk/16g5cvZpzsd5r17T32dpak5x8O0dynH1udtKmUqk086YiIo7QtKk7lStXwsfHi99/P82vv/6X\npKTkIre/LH7elibGEt9iJVNDhw5lz549WvvmzJmDr68vMTExdOzYUes1MkIUl6WlJVNnTOXMhTNU\nfLMiQy2G8r36ex6T9WiaGjVd6MKqh6uw/dmW5g2bM+7dcVov2jY2igIREbpLprLf1RccPJszZ8rS\nK2WK7uHDVMqVM9Hal/2EniHpYl0lExMTmjdvxHff7dbaf+LEKWJjrxToGh06tObKlUTCwjZpko6q\nVe1xd3dh2rQFZGRk6CyZ8vLy5OjRk1y58mSI8/79B/zww36teHh7tyIzM5OtW3/SOn/Dhu2UL2+G\nl5enVvuPH/+DH388QIcOWT3WzZo1okIFS2bMWET58ma8+moznbRfvJiKlUy1bdsWGxsbrX07d+4k\nMDAQgMDAQLZv316cKkQRGMsYc3E4Ojry9dqviTweydlXzzKiwgh+4RfNSurmmDMwYyArU1cS+00s\nLrVcWDB/AWlpacWq1xCxvXgxa42pevV0e902beDXX3V7zeIw5H372mvt+fnnQ8yevZx9+w4zZcpn\nbNnyY4HPL+g0vcJO5yvI/L/cyjy7KyRkPNHRMfTqFcSuXRGsXfsf+vZ9F0fHKqjV+f8ZaNv2FdRq\nNfv3/6qVNPn4eHHgwG/UquVUoPlXBTF+/HAqVLCgc+dBbN36I9u3h9O58yAsLS20ftauXb1p0+YV\n3n77IxYv/oa9e39h/PhQVq7cwoQJI7WGE318vHj8+DGHDh3TtN/ExIR27Vqwf/+vtGrVlPLlyxep\nvS/C560hGUt8dT4B/dq1azg4OADg4ODAtWvX8jlDiKJr2LAh4YfCWfH9CjbX2cyEihM4y1nNcVts\nGZc6js/vfc5/pv8Ht1pufPfdd0a1aGxkJPj4ZM230aVGjSA+Hoy40+65CtOrM23ae4waNYCFC1fS\nu/fbnD4dw88/r83lmrlfN6+qni1b0HJ51ZXb9QrSnk6d2rBhw2L++usCvXu/zbx5YSxY8DGOjlWo\nXNkq90Y9xcqqIs2bN0alUtGhw5NkKruXpyC9Us9r69P77exs2L9/I/b2tgQGTmDs2Ol06+bDsGF9\ntcqpVCp++ukbAgMDmDv3S15/fTi7dx9k4cKpfPLJB1p11K9fFwcHe0xNTWnXroVW+1Uqlc561cSL\nq9groMfGxtK9e3dOncp6FYiNjQ23bt3SHLe1tc0xxKJSqQgMDMTZ2RkAa2trPDw8NBlo9hipbBdt\ne9GiRS9kPNu2bcuqVasIHh9Mk8dNGPFoBI48eSII4AQn+ML8CyycLPh6w9e0bNmyUPU9PX5fEj9f\nfHwCTZpMpFIl+OWXeTg5Vdfp9X19oUOHSLy8DP/7y95XlPO9vUvfO9tKuytXEqlXz5uPPx7LRx+N\nMXRzSqGsJyTl89aw24aKb/b3sbGxAKxZs+a5/wjXeTLl5uZGZGQkjo6OJCYm4uPjw9mzZ7XOkdfJ\n6FfWHxdvQzfDYO7du8e8OfNYsmAJ3dK70f9xfyry5FH0DDIIJ5w1lmto27Etny3+jNq1c/4xfvTo\nEVM/mkroJ6GYm5sDJR9bP79gdu2aBkC3bqH89JNuV2gOCYGHD6E0TG0sXmz/yb/ICyw19RHjx4fS\nqVMb7O1tuHgxjs8++5IbN5KJjg7P8aScgIK+TuZF/7zVt9IS3xJ/nYy/vz9r1qwBsjK5nj176roK\nkY/ScOMZUsWKFQn5JITo89GYvWHGUIuhbFdtJ52sp35MMKErXVn1YBWVdlfCs4EnE96bkOPJ02VL\nlzFv/jzWrn0y3FPSsS3mFK98ubomEBYWjJ9fMPHxxXtNTXG96PetPpmYqLl2LYmxY6fTufNgJkz4\nBFfXlzl0aKskUsUk961+GUt8i9Uz1b9/fw4ePEhSUhIODg6EhobSo0cP+vbty+XLl3F2dmbr1q1Y\nW2uvKyI9U6Ik/fHHH4wfPZ5Lf15ixP0RtKY1Kp7MvbjJTdaYr+GI6RGmzpzK6HdGk5KSgkstFwbd\nG8TO6juJuRyDiYnJc2rRj61bE3j77aV4eWUtaeDkpNun77p0CSY8XH89XyVHeqaErsmLjsUTeu2Z\n2rRpEwkJCaSlpREXF8fQoUOxtbVl3759xMTEEB4eniOREvr39JivgCZNmrD/1/0s/3Y562qtY2KF\nifzN35rjdtjxfur7zE2Zy8aPNlLfuT6DBwym3eN2+OOP5V1LzVOpJR3bq1er8+abs/npp9k6T6QA\nypWiZXvlvhXGSO5b/TKW+Op8mE+I0kilUtG1a1dOnz/NyPkjmVZ5GnMt5nKd65oydajDnPtzGJUw\nijsH7zDo0SBUqOh7ry+ffvypQXpTT53KeupOX8LCxuLoGIqHR/FfU2NYOn7UUbzg5H4ShVPsCehF\nqlSG+YSBpaSkMPfTuSxbsozu6d3p97gflljmWjaTTIZXGM7KnSvp0KFDrmX0pVUr+PzzrDWh9GXa\ntKzH00NC9FeHEEIYsxKfgC6EMbCysuKTOZ9wKuYUSk+FIRZD2KnaSQYZOcqqUdPnfh9mTZ1Vom3M\nzITTp6FhQ/3WU78+nDmj3zqEEKIsk2SqDDKWMebSoEaNGqzbuo49h/dw4pUTjLIYRSqpOcp1ohOn\nTp5ixYoVJda2S5fA1hb0Pe2wfn346y/91lEQct/qj8RWfyS2+mUs8ZVkSgjA09OT0eNHY6Y2wwyz\nHMfNMKP3o95MmzS3xJYROHUKGjfWezW4usKFC/DM+2KFEEIUkMyZEgJITU3FtZYr46+PxwMPrWNp\npHGd61ziEjOYSSbh2NsvpkULN70sV5Bt5kx48ABml8BqBS+/DLt2ZSVWQgghtOWXt5SiB6OFMJwl\ni5aQkZzBBS5wxPQIN8xvcEN9g8S0RG6n3sFMqY6acpjSh0dsJilpI7t2wYgRoezerZ9s588/oVcv\nvVw6h+yhPkmmhBCi8GSYrwwyljHm0iTpWhJNXm1C5ohMmn/anLe/fptZ62bRxKs/5cz8eMhZ7rMX\n88qXqVLlycu7jx1LoWtX3a4gHh+fgJ9fMLt3B+PgUDKrkpeGeVNy3+qPxFZ/JLb6ZSzx1VvP1J49\nexg3bhwZGRmMGDGCDz/8UF9VCVFsny38LMc+P79gDhz4DEjE3n4ALVq4MXToe3h5tSYoKBRFgRMn\nTNmzJ2sF8aAg3awgHhS0VPM+vvnzQ+nYUf/jfA0aQESE3qsRQogySS/JVEZGBmPGjGHfvn04OTnx\nyiuv4O/vT/369fVRnXiGsbzLqLRLTs7+rhotWrhpJUrZ33frFszu3fprg6qE1g6sXx+WLSuZuvIi\n963+SGz1R2KrX8YSX71MQD9y5AghISHs2bMHgDn/eyX95MmTsyqVCeiiFIuPT2DkyKVERqZQp44p\ntWqZ5znRPD4+gQEDlnLkCBw9OhZPz+JPRo+PT6BXr6VcvAh//KG/Ce5Pu3MHnJzg7l1Qy+C/EEJo\nMcgE9Pj4eF566SXNdo0aNTh27JhWmSFDhuDs7AyAtbU1Hh4emgw0e4xUtou2vWjRIolnMbYDAiZy\n7NhgoB21aoUycWIXzp2Lwcmputb4vbe3N05O1QkJ6cKiRUm8/vpSmjaFoUObYW9vX+T6z52Lwdu7\nC+7u3jg5lczPn5SURHr6CTp1gnfeKV77i7qdvc/Qv/+yuB0VFcW4ceNKTXvK0rZ83up321Dxzf4+\nNjaWAlH04LvvvlNGjBih2V63bp0yZswYzbaeqhX/ExERYegmGLUuXSYr8ECBB0q3bpO1juUV2+ed\nUxQhIYry8cfFvkyBdeum2/YXhdy3+iOx1R+JrX6Vlvjml7fopWfKycmJuLg4zXZcXBw1atTQR1Ui\nF9kZtiiazp3HcvJkKM2bk+Plv3nF1sREt22Ii4PmzXV7zdJO7lv9kdjqj8RWv4wlvnqZM5Weno6r\nqyv79++nevXqtGjRgk2bNmkmoMucKVGaeXnBlCnQvXvBz4mPT2Do0KVERMD//d9YPDyKN8+pa1cY\nMwb8/Ip1mQKLj0+gXbulmJrC/v0lM09LCCGMhUFedFyuXDn+/e9/06VLFxo0aMCbb74pT/KVoKfH\nfEXh/PlnVq9Q1665H88rtk5O1QkPn83QobP58cfiJyJXrsBT0w71zsmpOu++O5uuXWcbLJGS+1Z/\nJLb6I7HVL2OJr97WmeratStd8/qLJEQpEx+fQFDQUqKjoU+fsZQrV7SE4o03EvD3X8pvv8GKFUXv\n4blyBUp6ZNzREf7v/0q2TiGEKAvk3XxCkLVAZ/ZCmT4+oRw4ULSFMp++TrduRVvE8949qFoV7t8v\nuXWmAA4cyHofoCzeKYQQ2gwyzCeEMbOwMGz92b1SJZlIQVbP1NWrJVunEEKUBZJMlUHGMsZcmoSF\njaVOnVDq1g3N8QTf0/KLbVjYWDp0CMXUNJTly/O+zvMYYogPoFo1wyZTct/qj8RWfyS2+mUs8dXb\nnCkhjImTU3UqVZrNsmVZK4EX5zr798+mWTOIjYVatQp/jZKefJ7N2hoePsz6MnTvnBBCGBOZMyUE\ncO0auLpCUhKU08E/MUJCsl7NMn9+4c/95JOshObTT4vfjsKqVQsOHoT/vZxACCEEMmdKiALZtw98\nfHSTSEHWGlU//FC0c+PiDDPMBzJvSgghikKSqTLIWMaYS5PwcOjcOf9yBY1t1aoJXL4cjLd3MPHx\nCYVqi6HmTIFhkym5b/VHYqs/Elv9Mpb4FjmZ+vbbb3F3d8fExITff/9d69js2bOpV68ebm5uhIeH\nF7uRQuhLfHwCfn7BbN4cTOPGhUt6nmfUqKU8ejSNgwenERS0tFDnvqjJlBBCGKsiJ1ONGjVi27Zt\ntGvXTmv/mTNn2LJlC2fOnGHPn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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "To enhance detail, the figure above shows the the $20\\log_{10} | X_k |$ of the DFT of the input signal with noted windows applied on the same scale. The top plot shows the rectangular window and we can barely make out the smaller signal in the sidelobes of the dominant larger signal. The middle plot shows the triangular window and we can see that there is definitely something peeking out from the sidelobes, but we can see this most clearly using the Hamming window (bottom plot), which shows a peak at the nearby frequency. Note that the width of the mainlobe widened as the second weaker signal emerged from the sidelobes of the stronger signal. This is one of the trade-offs involved when using windows for spectral analysis. " ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Summary" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this section, we demonstrated that window functions can help resolve nearby frequencies that have different amplitudes. As the plots showed, we traded precious signal energy for resolution, but we need a systematic framework for evaluating different window functions. This framework will be the topic of our next section.\n", "\n", "As usual, the corresponding IPython notebook for this post is available for download [here](https://github.com/unpingco/Python-for-Signal-Processing/blob/master/Windowing.ipynb). \n", "\n", "Comments and corrections welcome!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "References\n", "---------------\n", "\n", "* Oppenheim, A. V., and A. S. Willsky. *Signals and Systems* Prentice-Hall, (1997).\n", "* Proakis, John G. *Digital signal processing: principles algorithms and applications* Pearson Education India, 2001." ] } ], "metadata": {} } ] }