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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 4 Sampling Process"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example4.1 page 164"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Aliasing error cannot exceed max|g(t)| = 2.0\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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H6upn9dXDBHou3aTQWF6qsTeuaUqky62kiYS2iumS1gNeMrOCc69KGgAsMLNr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\nYII=\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7f1df4d30f10>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from numpy import arange,ones,sinc\n",
+ "%matplotlib inline\n",
+ "from matplotlib.pyplot import plot,xlabel,ylabel,show,title,subplot\n",
+ "\n",
+ "\n",
+ "t = arange(-1.5,0.01+2.5,0.01)\n",
+ "g = [2*sinc(2*tt-1) for tt in t]\n",
+ "print 'Aliasing error cannot exceed max|g(t)| = ',max(g)\n",
+ "f = arange(-1,0.01+1,0.01)\n",
+ "G = [0,0,0,0]+[xx for xx in ones(len(f))]+[0,0,0,0]\n",
+ "f1 = arange(-1.04,0.01+1.04,0.01)\n",
+ "subplot(3,1,1)\n",
+ "plot(t,g)\n",
+ "xlabel(' t')\n",
+ "ylabel(' g(t)')\n",
+ "title('Figure 4.8 (a) Sinc pulse g(t)')\n",
+ "subplot(3,1,3)\n",
+ "plot(f1,G)\n",
+ "xlabel(' f')\n",
+ "ylabel(' G(f)')\n",
+ "title('Figure 4.8 (b) Amplitude spectrum |G(f)|')\n",
+ "show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example4.3 page 165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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aM+tyH30EX/0qrLBCuny73m+u56SmPNynpn2WBXaOiOnNjZS0NDCophGZmdXQ\nJ5/AN74BvXt3/8cfWM/jmpoScU2NmXWlCPjud2HsWLjjDlh88aIj6hyuqSkP31G4AySdJWkZSX0k\n3SPp7axpysystH7yE3j8cbjllvIkNFYuTmo6ZrfsRnt7kzoJr026f42ZWSmdfTbcdFOqoVlqqaKj\nMWue+9R0TNN62xu4ISKmSXK7j5mV0qWXwp/+BKNGpc7BZt2Va2raQdI/spe3ShoLbA7cI2kl4IPi\nIjMz6xrXXQeDB8M//gFrrFF0NGatc0fhdpA0JiI2zV4vD0yNiE8kLQksFRFvFhyfOwqbWae59VY4\n5hi4+27YuMUHu9Q/dxQuDzc/tc8ykr5GujdNwNxHGJC9H1FUYGZmnenuu9OdgkeOLHdCY+XipKZ9\nlgH2aWW8kxozq3ujRsFhh8GIEbDFFkVHY1Y9Nz+1Q775qTty85OZLaxHH4W994ZrrkmPQegJ3PxU\nHu4obGZmADzzDOyzDwwd2nMSGisXJzXtM1XS9yWtX3QgZmad6fnnYffd4YILUk2NWT1y81M7SFoV\n2APYHVgPGA3cAfwzImYWGRu4+cnMOmbsWNhpJzjrrNSXpqdx81N5OKnpIEm9gK2BPYGdSPepuSsi\nfldgTE5qzKxd/vtf2HFHOPPM9KDKnshJTXm4+akdJB3X9DoiPomIhyLijIj4EnAw8Hob8w+VNEnS\nsy2MX1/Sw5I+kHRyxbg9JI2V9F9JP+qM8phZz/bSS7DzzvDzn/fchMbKxTU17bCwVz9J2h6YAVwZ\nEQvc+UHSisCawFeAKRFxTja8F/BvYBdS4vQYcEhEvFgxv2tqzKwq48dDQwOcdhp861tFR1Ms19SU\nh2tqaigiRgFTWhk/OSIeBz6uGLUVMC4iXomIj4Frgf26LlIzK7PXXks1ND/8oRMaKxfffK99NpE0\nvYVxERFLd9Hnrg5MyL2fSOrPY2bWLq+8kjoFn3gifO97RUdj1rmc1LTPMwXdfM9tSma20MaPTwnN\nSSfB8ccXHY1Z53NSUx9eB/rn3vcn1dYsYMiQIXNfNzQ00NDQ0JVxmVmdePnllNCccopraBobG2ls\nbCw6DOsC7ijcDpJOi4hfLeQyBgC3NtdRODfNEGB6rqNwb1JH4Z2B/wGP4o7CZlall15KCc2PfgTf\n/W7R0XQ/7ihcHq6paZ9FJa0cEZOaG5ndnO/bETG4hfHDgR2AFSRNAAYDfQAi4mJJq5CubFoamCPp\nRGDDiJjmEXnDAAAc7UlEQVSRXU5+F9ALuKwyoTEza864cSmhOf10dwq28nNNTTtI2hs4GVgUeBJ4\nAxCwCrAZ8CFwdkSMLCg+19SY2Vz//nd6htMZZ8CxxxYdTfflmprycFLTAZL6A18CPp0NehV4MCKa\n7edSK05qzKzJc8+lZzmdeSYMGlR0NN2bk5rycFJTIk5qzAzgySdh4EA47zw4+OCio+n+nNSUh2++\n1w6SPp97vaikMyTdKulXkpYoMjYzM4DRo2HPPeHCC53QWM/jpKZ9Ls+9/g2wNnAOsARwUREBmZk1\nGTUK9tkHhg2Dr3616GjMas9XP3XczsCWEfGRpPuBZ4oOyMx6rn/+Ew49FIYPT49AMOuJnNS0zzKS\nvka64ulTEfERpOcjSHJnFjMrxN//nq5uuvFG2H77oqMxK46TmvZ5ANgne/2gpFUi4s3s/jSTC4zL\nzHqoq65KD6a8807YbLOiozErlq9+KhFf/WTWs/zpT/Db38Jdd8EGGxQdTf3y1U/l4ZqaTtJUa1N0\nHGZWfhHw61+nDsEPPAADBhQdkVn34KufOs9lRQdgZuUXkZ7hNHy4ExqzSm5+KhE3P5mV2+zZ6flN\nzz0Hd9wByy1XdETl4Oan8nDzUwdIWhlYAwjg9ZYecGlm1lnefz/dTO/DD+Gee6Bv36IjMut+nNS0\ng6RNgQuBfkDTc57WkDQV+G5EPFlYcGZWWlOnwr77whprwPXXw6KLFh2RWffk5qd2kPQ0cGxEjK4Y\nvg1wcUR8vvk5a8PNT2bl88YbsMcesMMO6VlOi7gnZKdz81N5+PBonyUqExqAiHgEWLKAeMysxMaN\ng+22g4MOgvPPd0Jj1hY3P7XPHZJGAlcAE0h3Fu4PHAncWWRgZlYujz0G++0HgwenzsFm1jY3P7WD\nJAF7AvsCq2eDXwduiYiRVcw/FNgLeCsiNm5hmj9knzELGBQRY7LhpwKHA3OAZ4GjIuLDinnd/GRW\nAiNHwje+AZddlvrSWNdy81N5OKmpIUnbAzOAK5tLaiQNBI6LiIGStgbOj4htJA0A7gU2iIgPJf0N\nGBkRV1TM76TGrM5ddhmcfjrcdBNsu23R0fQMTmrKwy207SBpqKQtWxm/taRhLY2PiFHAlFY+Yl9S\n0xZZ351+2eXj7wEfA0tI6g0sQaohMrOSiICf/QzOPDPdVM8JjVn7uU9N+5wLnJJd7fRv4A1Sv5pV\ngPWAh4CzF2L5q5P66jSZCKweEU9KOgd4DXgfuCsi/rkQn2Nm3cjs2fCd78CYMfDQQ7DKKkVHZFaf\nnNS0Q0Q8CxwpaTFgU2BN0g34XgWejogPOuFjFqgClbQ28H/AAGAacL2kwyLir53weWZWoOnT09VN\nAI2Nvqme2cJwUtMxvYHHsku5kdQLWKwTlvs66WqqJmtkwxqAhyLinezzRgBfBBZIaoYMGTL3dUND\nAw0NDZ0Qlpl1hYkTYa+9UlPTH/8IvX1GronGxkYaGxuLDsO6gDsKd4Ck0cDOETEje78UqUnoi1XM\nOwC4tYqOwtsA52Udhb8AXA1sCXwAXA48GhF/qpjfHYXN6sRTT8E++8AJJ8APfgByN9XCuKNwefh3\nQccs1pTQAETEdElLtDWTpOHADsAKkiYAg4E+2TIujoiRkgZKGgfMBI7Kxj0l6UrgcdIl3U8Cf+ns\nQplZbYwcCYMGwZ//DAccUHQ0ZuXhmpoOkPQgcEJEPJG93wK4ICIKvV7BNTVm3d+f/wy/+AWMGOEr\nnLoL19SUh2tqOub/gOskvZG9XxX4eoHxmFk3N3s2nHQS3H03/OtfsPbaRUdkVj6uqekgSYuSLuMO\n4N8R8XHBIbmmxqybmjYNvv71dC+av/0N+vUrOiLLc01Nefjmex23BbAJsDlwiKQjC47HzLqhl19O\nzUzrrAO33+6ExqwrufmpAyRdDXwGeAr4JDfqymIiMrPuaNQoOPBAOOMM+N73io7GrPyc1HTM5sCG\nbusxs5YMGwY/+hFcfTXstlvR0Zj1DE5qOuY5Uufg/xUdiJl1L7Nnw8knwx13pGc4rb9+0RGZ9RxO\najpmReAFSY8CH2bDIiL2LTAmMyvYO++kRx4suig8+qj7z5jVmpOajhlSdABm1r089xzstx/svz/8\n+tfQq1fREZn1PL6ku0R8SbdZMf7+dzj2WDj3XDjssKKjsfbyJd3l4ZqadpD0YER8SdIM0v1p8iIi\nli4iLjMrxiefwM9+Bpdfnh59sMUWRUdk1rM5qWmHiPhS9r9v0bGYWbGmTEm1MrNmwWOPwcorFx2R\nmfnmex0gaW1Ji2evd5R0giR3CTTrIZ55BrbcMl3ZdPfdTmjMugsnNR0zApgtaR3gYqA/cE2xIZlZ\nLVxzDey8M/z85/D730OfPkVHZGZN3PzUMXMiYrakr5Gezn2BpDFFB2VmXeejj+CHP4Rbb4V77oFN\nNik6IjOr5KSmYz6SdChwJLBPNsy/18xKauLEdP+Z5ZeHxx+HZZctOiIza46bnzrmaGBb4MyIGC9p\nLeCqgmMysy5w992p/8y++8LNNzuhMevOfJ+adpD0F+AO4J8RMb0D8w8F9gLeioiNW5jmD8CewCxg\nUESMyYb3Ay4FNiJdTn50RDxSMa/vU2PWSebMgV/+Ei66CP76V9hxx6Ijsq7i+9SUh5uf2mcoKeE4\nSdLHwF3AnRHxdJXzDwMuoIWneUsaCKwTEZ+VtDVwIbBNNvp8YGREHCCpN7DkQpTDzFrx9ttwxBEw\nc2ZqblpttaIjMrNquPmpHSLikYgYHBHbAwcBE4CTJT0laZikg9qYfxQwpZVJ9gWuyKYdDfSTtLKk\nZYDtI2JoNm52REzrjDKZ2fweeAA23TR1BL7nHic0ZvXENTUdFBFvky7jvkaSgFOAzy7kYlcnJUpN\nJgJrAJ8AkyUNAz4PPAGcGBGzFvLzzCzzySfpmU1//CMMGwZ77ll0RGbWXk5qOkFEhKTjI6J/Jyyu\nsl03SNtpM+C4iHhM0nnAj4GfVs48ZMiQua8bGhpoaGjohJDMym3SJDj8cPjwQ3jiCVh99aIjsq7U\n2NhIY2Nj0WFYF3BH4XaQ9Gwro9eLiEWrWMYA4NbmOgpLughojIhrs/djgR1Iic7DEbFWNnw74McR\nsXfF/O4obNZO99wDRx4JRx8NgwdDb//U63HcUbg8fPi2z0rAHjTfL+ahTlj+LcBxwLWStgGmRsQk\nAEkTJK0bEf8BdgGe74TPM+uxPv4YzjgDrroqPZBy112LjsjMFpaTmva5HejbdJl1nqT725pZ0nBS\nzcsKkiYAg8lu2hcRF0fESEkDJY0DZgJH5WY/HvirpEWBlyrGmVk7jBsHhx4KK60EY8ak/2ZW/9z8\nVCJufjJrXUSqmTn5ZPjpT+G440BudOjx3PxUHq6pMbMeYdo0+O53U82Mn91kVk6+T42Zld7998Pn\nPw9LL51upueExqycXFNjZqX14YepM/DVV8Mll8BeexUdkZl1JSc1ZlZKzz2X7j2z1lrw9NOw4opF\nR2RmXc3NT2ZWKnPmwO9/nx5AeeKJMGKEExqznsI1NWZWGi+9BEcdla5yGj0aPvOZoiMys1pyTY2Z\n1b05c+DPf4att4avfAUaG53QmPVErqkxs7r22mvpEQfTp8O//gXrr190RGZWFNfUmFldioBLL4XN\nN4edd4YHH3RCY9bTuabGzOrO+PFwzDHphnr33gsbL/B4WDPriVxTY2Z145NP4PzzYcstYbfd4OGH\nndCY2TyuqTGzujB2LHzzm7DIIvDQQ7DuukVHZGbdjWtqzKxb++gj+OUvYbvt4JBD0iMPnNCYWXNc\nU2Nm3daDD8Kxx6a7Aj/5JHz600VHZGbdmZMaM+t2pk6FU0+Fm29OfWgOOACkoqMys+7OzU9m1m1E\nwA03wEYbpdcvvAAHHuiExsyq45qaGpI0FNgLeCsimr1mQ9IfgD2BWcCgiBiTG9cLeByYGBH71CBk\ns5oZNw6OOw4mToS//S31oTEzaw/X1NTWMGCPlkZKGgisExGfBY4FLqyY5ETgBSC6LEKzGvvgAxgy\nBLbZBnbZBcaMcUJjZh3jpKaGImIUMKWVSfYFrsimHQ30k7QygKQ1gIHApYAr460U7roLPvc5eO65\nlMz84AfQp0/RUZlZvXLzU/eyOjAh935iNmwScC5wCrB0AXGZdarx4+Gkk+CZZ+CPf4Q99yw6IjMr\nAyc13U9lLYwk7U3qhzNGUkNrMw8ZMmTu64aGBhoaWp3crKZmzYLf/Ab+9KeU1AwfDosvXnRU1tM0\nNjbS2NhYdBjWBRTh7hm1JGkAcGtzHYUlXQQ0RsS12fuxQANwAnAEMBtYnFRbc2NEHFkxf3h7WncU\nATfeCCefDNtuC2edBf37Fx2VWSKJiHCzfgm4pqZ7uQU4DrhW0jbA1Ih4Ezgt+0PSDsAPKhMas+7q\n6adTrczkyXDllbDDDkVHZGZl5aSmhiQNB3YAVpA0ARgM9AGIiIsjYqSkgZLGATOBo1pYlKtjrNt7\n80044wy49VYYPDg9Vbu3zzhm1oXc/FQibn6y7uCDD+Dcc+Gcc+Coo+D006Ffv6KjMmuZm5/Kw7+b\nzKxTzJmTbpp36qmw2WbwyCOwzjpFR2VmPYmTGjNbaPfdB6ecAossAldc4X4zZlYMJzVm1mHPPQc/\n+hGMHQu//rWf02RmxfIdhc2s3V57DY4+GnbeGXbfHV58EQ46yAmNmRXLSY2ZVe2tt+D//g823RRW\nXRX+8x844QRYdNGiIzMzc1JjZlWYOjVdnr3BBulGei+8AGeeCcssU3RkZmbzOKkxsxbNmJEea7Du\nujBxIjz5JJx/Pqy8ctGRmZktyB2FzWwBM2em5zOdcw7suCPcf3+qpTEz686c1JjZXLNmwYUXpmcz\nffnLcO+9sNFGRUdlZlYdJzVmxowZcNFFqWbmS1+Cu++GjRd45KqZWffmpMasB5s6FS64IP3ttBPc\ndRdssknRUZmZdYw7Cpv1QJMnp2cyrb02vPwyjBoF117rhMbM6puTGrMeZPx4OO44WG89eOcdePxx\nGDYsvTczq3dOasx6gDFj4NBDYcstYaml0n1mLroI1lqr6MjMzDqPkxqzkopIHX533x323jvdBfjl\nl9MzmlZZpejozMw6nzsKm5XMBx/ANdfAueemxOakk+CWW2CxxYqOzMysa7mmpoYkDZU0SdKzrUzz\nB0n/lfS0pE2zYf0l3SfpeUnPSTqhdlFbvXjrLfjZz2DAALj+evj97+HZZ9ODJ53QmFlP4KSmtoYB\ne7Q0UtJAYJ2I+CxwLHBhNupj4PsRsRGwDfA9Sb6/qwHw2GPwjW+kzr6vv55umHfHHbDrrn5qtpn1\nLE5qaigiRgFTWplkX+CKbNrRQD9JK0fEmxHxVDZ8BvAisFpXx2vd14cfwtVXwzbbwIEHprv+jhsH\nf/kLbLhh0dGZmRXDfWq6l9WBCbn3E4E1gElNAyQNADYFRtcyMOsexo+HSy6BoUPTHX9POw322gt6\n9So6MjOz4jmp6X4qGwxi7gipL3ADcGJWY7OAIUOGzH3d0NBAQ0ND50doNTV7Ntx+e7oE+7HH4PDD\n4b77/IBJs45qbGyksbGx6DCsCygi2p7KOk1W03JrRCzwZB1JFwGNEXFt9n4ssENETJLUB7gNuCMi\nzmth2eHtWR6vvppqZC67DNZcE771rdTU9KlPFR2ZWblIIiLcA60E3Keme7kFOBJA0jbA1CyhEXAZ\n8EJLCY2VwwcfwPDhqZPv5pvDu++mTr8PPghHHumExsysNa6pqSFJw4EdgBVI/WQGA30AIuLibJo/\nkq6QmgkcFRFPStoOeAB4hnnNUadGxJ0Vy3dNTR2KgCeegMsvT89f2nzzdBn2fvvB4osXHZ1Z+bmm\npjyc1JSIk5r68tpr6Qqmq66Cjz5KNTGDBqWmJjOrHSc15eGOwmY1NHUqjBiREplnnkl9ZC67DLbd\n1veUMTNbWK6pKRHX1HRPM2fCbbelpqV774WddoIjjkiXYvtOv2bFc01NeTipKREnNd3H++/DP/4B\nf/sbjByZbpJ38MHw1a/CMssUHZ2Z5TmpKQ8nNSXipKZYM2akK5VuuAHuuis9Ffugg2D//WGllYqO\nzsxa4qSmPJzUlIiTmtp7++1UE3PTTXDPPalvzP77w1e+4kTGrF44qSkPJzUl4qSmNsaNg5tvhltu\ngTFjYOed0+XX++4Lyy1XdHRm1l5OasrDSU2JOKnpGh99BKNGpaalkSNhyhTYZ5+UxOy8s2+IZ1bv\nnNSUh5OaEnFS03leew3uvDMlMvfeC+uvDwMHwp57whZbwCK+F7dZaTipKQ8nNSXipKbjpk6Fxka4\n++70N3Uq7LJLSmR23x1WXLHoCM2sqzipKQ8nNSXipKZ6M2ak5yndf3964vVzz6VOvrvumv422cS1\nMWY9hZOa8nBSUyJOalo2dSo8/DA88ECqkXn2WdhsM2hogB12gC99yc9ZMuupnNSUh5OaEnFSk0TA\n+PGpJqbp75VXUl+Y7beHHXdMN8NzB18zAyc1ZeKkpkR6alLz7rvw2GMwejQ8+mj669071b40/X3h\nC9CnT9GRmll35KSmPJzUlEhPSGreeivdG+bJJ+f9f+st2Hxz2Hpr2Gqr9Lf66n5ApJlVx0lNeTip\nKZEyJTUffghjx6a+L88+mzryPv106uC72WbpEQRN/9dbD3r1KjpiM6tXTmrKw0lNDUkaCuwFvBUR\nG7cwzR+APYFZwKCIGJMN3wM4D+gFXBoRv21m3rpLaqZNg3//OyUw+b/x4+Ezn4GNN4bPfS7933hj\nWGst18CYWedyUlMeTmpqSNL2wAzgyuaSGkkDgeMiYqCkrYHzI2IbSb2AfwO7AK8DjwGHRMSLFfN3\nu6Rmzhx480149VV46aV5f+PGpf8zZ6aalvXXn/e33nrpb7HF5l9WY2MjDQ0NhZSjFly++lbm8pW5\nbOCkpkx6Fx1ATxIRoyQNaGWSfYErsmlHS+onaRVgLWBcRLwCIOlaYD/gxZYWVAuzZ8OkSfC//8Eb\nb6T///sfTJiQkphXX4WJE6FfP1hzTVh77fS3445wzDHp9aqrVl/zUvYTq8tX38pcvjKXzcrFSU33\nsjowIfd+YjZstWaGb90ZHxgBs2alviozZsB776V7ukydmp5x1PT/7bdh8uT5/6ZOhRVWgNVWS3+r\nrpr+ttsODj00JTL9+/vSaTMzqw0nNd1Pp1aBXnopXH89vP9+Sl7ef3/e65kz0//FF4cll4S+fWGp\npWDZZVPtSr9+6fUyy6R+LSuuOP/f8sunS6fNzMy6A/epqbGs+enWFvrUXAQ0RsS12fuxwA6k5qch\nEbFHNvxUYE5lZ2FJ3phmZh3gPjXl4N/Z3cstwHHAtZK2AaZGxCRJ7wCfzRKi/wFfBw6pnNkHpZmZ\n9WROampI0nBSzcsKkiYAg4E+ABFxcUSMlDRQ0jhgJnBUNm62pOOAu0iXdF9WeeWTmZlZT+fmJzMz\nMyuFRYoOwNpP0h6Sxkr6r6QftTDNH7LxT0vatNYxLoy2yidpfUkPS/pA0slFxLgwqijfYdl2e0bS\ng5I2KSLOjqqifPtl5Rsj6QlJOxURZ0dUc+xl020pabakr9UyvoVVxbZrkDQt23ZjJP2kiDg7qspz\nZ0NWtuckNdY4RFtYEeG/OvojNT+NAwaQmq6eAjaomGYgMDJ7vTXwSNFxd3L5VgS2AH4JnFx0zF1Q\nvm2BZbLXe5Rw+y2Ze70x6R5MhcfeGWXLTXcvcBuwf9Fxd/K2awBuKTrWLixfP+B5YI3s/QpFx+2/\n9v25pqb+bEV2I76I+BhouhFf3nw38QP6SVq5tmF2WJvli4jJEfE48HERAS6kasr3cERMy96OBtao\ncYwLo5ryzcy97Qu8XcP4FkY1xx7A8cANwORaBtcJqi1fvV6QUE35DgVujIiJABFRL/umZZzU1J+W\nbtDX1jT18sVYTfnqWXvL901gZJdG1LmqKp+kr0h6EbgDOKFGsS2sNssmaXXSF+WF2aB66rRYzbYL\n4ItZ8+FISRvWLLqFV035PgssJ+k+SY9LOqJm0Vmn8NVP9afak2Tlr6l6ObnWS5wdVXX5JO0IHA18\nqevC6XRVlS8i/g78PXse2lXAel0aVeeopmznAT+OiJAk6qtWo5ryPQn0j4hZkvYE/g6s27VhdZpq\nytcH2AzYGVgCeFjSIxHx3y6NzDqNk5r68zrQP/e+P+kXR2vTrJENqwfVlK+eVVW+rHPwJcAeETGl\nRrF1hnZtv0jPQ+stafmIeKfLo1s41ZRtc9J9pgBWAPaU9HFE3FKbEBdKm+WLiOm513dI+rOk5SLi\n3RrFuDCq2X4TgLcj4n3gfUkPAJ8HnNTUCTc/1Z/HyW7EJ2lR0o34Kk+YtwBHAuRv4lfbMDusmvI1\nqadfwU3aLJ+kTwMjgMMjYlwBMS6Masq3dlaLgaTNAOogoYEqyhYRn4mItSJiLVK/mu/USUID1W27\nlXPbbivSbUHqIaGB6s4tNwPbSeolaQnShRYv1DhOWwiuqakz0cKN+CR9Kxvf4k386kE15VN6cvlj\nwNLAHEknAhtGxIzCAq9SNeUDfgosC1yYfX98HBFbFRVze1RZvv2BIyV9DMwADi4s4Haosmx1q8ry\nHQB8R9JsYBZ1su2g6nPnWEl3As8Ac4BLIsJJTR3xzffMzMysFNz8ZGZmZqXgpMbMzMxKwUmNmZmZ\nlYKTGjMzMysFJzVmZmZWCk5qzMzMrBSc1JiVlKRPJI2R9JykpySd1HTjtDbmO60W8VV85gBJz1Y5\n7fJZucZIekPSxNz73tk0F0m6Nxv2vKRZuWm+1rWlMbOi+D41ZiUlaXpELJW9XhG4BngwIoZUO1+t\nSBoA3BoRG7dzvsHA9Ij4fcXwMcBm2TOY1gRua++yzaz+uKbGrAeIiMnAscBxAJIGSbqgabyk2yTt\nIOk3wKeyGo2rJf0su2Nz03RnSlrgqdqSjsye3PyUpCsk9ZX0cq7mZOnsfS9J60j6ZzbtE5LWqlhW\nL0lnSXo0W+axbRRvvtonSRsA/4l5v9iUG7eRpNFZ+Z6WtE4168/M6oMfk2DWQ0TE+CxhWIkFn1gc\naZL4saTvRcSmAFktxwjgfEmLkJ6Xs2V+RkkbAacD20bEu5L6RcQMSY3AXqTn6RwM3BgRn0j6K/Cr\niLg5ewZPL2Dl3CK/SXpe2VaSFgP+JekfEfFKlUXdE7ijhXHfBs6PiGuyhMvnQLMScU2NWc8TVPkw\n0Ih4FXhH0heA3YAnm3lq+E7AdU0PNoyIqdnwS5n33LFBwDBJSwGrRcTN2bQfZU9EztuN9GyoMcAj\nwHJAe2pUdgPubGHcQ8Bpkn4IDIiID9qxXDPr5vwrxayHkPQZ4JOImJw9kDD/o2bxVmZtSk5WBoY2\nM77ZJCkiHso6ADcAvSLihSypqcZxEXF3ldPOlT1ZuV9EvNnc+IgYLukRYG9gpKRvRcR97f0cM+ue\nXFNj1gNkHYUvApr60YwHvqCkP5B/CvjHTX1hMjcBewBbkJ5wXOle4EBJy2WftVxu3JXAX8mSoYiY\nDkyUtF827WKSPlWxvLuA7+b646ybJSvV2DGLp1mSPhMR4yPiAlKzmDsPm5WIa2rMyutTWRNOH2A2\nKcE4FyAiHpQ0HngBeBF4IjffX4BnJD0REUdExMeS7gWm5DrfzpXVwJwJ3C/pE+BJ4Ohs9DXAL4Hh\nuVmOAC6W9HPgY+CApkVl/y8FBgBPZpegvwV8tZVy5mPaE7iulWkOknR49rlvAGe2slwzqzO+pNvM\nWpV1EH4COCAiXmrnvAcA+0TEN7okuAU/7wlgq4j4pBafZ2bdi2tqzKxFkjYEbgVGdCChuQDYHRjY\nFbE1JyI2r9VnmVn345oaMzMzKwV3FDYzM7NScFJjZmZmpeCkxszMzErBSY2ZmZmVgpMaMzMzKwUn\nNWZmZlYK/x9BcGdXqAyYrQAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7f05d85531d0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from numpy import arange,ones,sinc,pi,sin\n",
+ "%matplotlib inline\n",
+ "from matplotlib.pyplot import plot,xlabel,ylabel,show,title,subplot\n",
+ "\n",
+ "T_Ts = arange(0.01,0.01+0.6,0.01)\n",
+ "#E = 1/(sinc_new(0.5*T_Ts))#\n",
+ "E=[1]\n",
+ "for i in range(1,len(T_Ts)):\n",
+ " E.append(((pi/2)*T_Ts[i])/(sin((pi/2)*T_Ts[i])))\n",
+ "\n",
+ "plot(T_Ts,E)\n",
+ "xlabel('Duty cycle T/Ts')\n",
+ "ylabel('1/sinc(0.5(T/Ts))')\n",
+ "title('Figure 4.16 Normalized equalization (to compensate for aperture effect) plotted versus T/Ts')\n",
+ "show()\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}