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path: root/Digital_Communications_by_S._Haykin/Chapter3.ipynb
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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 3 Detection & Estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example3.1 page 120"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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SZmYpSpqTGJVOly9dAeyU398JWBMRDUt8u5Mws7Gq3zqJlKzAy4FXSVoOLAM+2qxRdxJm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\nOO4C4GayK5VCed8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88T3AMRGxsqotdxxmZiMw2tVNZeZJbEqkA5aTJdLNrjpmLln1umvz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3eb2943610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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YDFyQXjjxeJJwzqWtVZJE2mMSrxIGpHNGEa4mNiNpL+AGYIKZvV2soUbOk/Ak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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3eb26e6d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from numpy import arange, ones, sqrt\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot, subplot, xlabel,ylabel,title, show\n",
    "\n",
    "#using Gram-Schmidt orthogonalization procedure\n",
    "T = 1#\n",
    "t1 = arange(0,0.01+T/3,0.01)\n",
    "t2 = arange(0,0.01+2*T/3,0.01)\n",
    "t3 = arange(T/3,0.01+T,0.01)\n",
    "t4 = arange(0,0.01+T,0.01)\n",
    "s1t = [0]+[x for x in ones(len(t1)-2)]+[0]\n",
    "s2t = [0]+[x for x in ones(len(t2)-2)]+[0]\n",
    "s3t = [0]+[x for x in ones(len(t3)-2)]+[0]\n",
    "s4t = [0]+[x for x in ones(len(t4)-2)]+[0]\n",
    "t5 = arange(0,0.01+T/3,0.01)\n",
    "phi1t =  [sqrt(3/T)*x for x in [0]+[x for x in ones(len(t5)-2)]+[0]]\n",
    "t6 =arange(T/3,0.01+2*T/3,0.01)\n",
    "phi2t = [sqrt(3/T)*x for x in [0]+[x for x in ones(len(t6)-2)]+[0]]\n",
    "t7 = arange(2*T/3,0.01+T,0.01)\n",
    "phi3t = [sqrt(3/T)*x for x in [0]+[x for x in ones(len(t7)-2)]+[0]]\n",
    "\n",
    "#figure\n",
    "title('Figure3.4(a) Set of signals to be orthonormalized')\n",
    "subplot(4,1,1)\n",
    "plot(t1,s1t)\n",
    "xlabel('t')\n",
    "ylabel('s1(t)')\n",
    "subplot(4,1,2)\n",
    "plot(t2,s2t)\n",
    "xlabel('t')\n",
    "ylabel('s2(t)')\n",
    "subplot(4,1,3)\n",
    "plot(t3,s3t)\n",
    "xlabel('t')\n",
    "ylabel('s3(t)')\n",
    "subplot(4,1,4)\n",
    "plot(t4,s4t)\n",
    "xlabel('t')\n",
    "ylabel('s4(t)')\n",
    "show()\n",
    "\n",
    "\n",
    "#figure\n",
    "title('Figure3.4(b) The resulting set of orthonormal functions')\n",
    "subplot(3,1,1)\n",
    "plot(t5,phi1t)\n",
    "xlabel('t')\n",
    "ylabel('phi1(t)')\n",
    "subplot(3,1,2)\n",
    "plot(t6,phi2t)\n",
    "xlabel('t')\n",
    "ylabel('phi2(t)')\n",
    "subplot(3,1,3)\n",
    "plot(t7,phi3t)\n",
    "xlabel('t')\n",
    "ylabel('phi3(t)')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example3.2 page 121"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa3f2804950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 3.8 (b).Representation of transmitted dibits\n",
      "Loc. of meg.point| (-3/2)asqrt(T)|(-1/2)asqrt(T)|(3/2)asqrt(T)|(1/2)asqrt(T)\n",
      "________________________________________________________________________________\n",
      "Transmitted dibit|         00    |      01      |   11        |   10\n",
      "\n",
      "\n",
      "Figure 3.8 (c). Decision intervals for received dibits\n",
      "Received dibit     |     00          |      01       |   11          |   10\n",
      "________________________________________________________________________________\n",
      "Interval on phi1(t)| x1 < -a.sqrt(T) |-a.sqrt(T)<x1<0| 0<x1<a.sqrt(T) | a.sqrt(T)<x1\n",
      "0.0049504950495\n"
     ]
    },
    {
     "data": {
      "image/png": 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hw4YoWbIk7rvvPuzbty9LXz755JObfRk4cCASExPRuXNnFC9eHB06dMC5c+d0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\nYu4Hg8Oe35fgT0ujDXd5RikG+nvgAWDMGEY3TUw0b1gKvYmNZWTJHTv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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa40942a910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from numpy import sqrt,arange,random,sin,pi,zeros,multiply\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot,subplot,xlabel,ylabel,title,show,grid\n",
    "\n",
    "#Signal constellation and Representation of dibits\n",
    "a =1#  #amplitude =1\n",
    "T =1# #Symbol duration in seconds\n",
    "#Four  message points\n",
    "Si1 = [(-3/2)*a*sqrt(T),(-1/2)*a*sqrt(T),(3/2)*a*sqrt(T),(1/2)*a*sqrt(T)]\n",
    "plot(Si1,[0,0,0,0])\n",
    "xlabel('phi1(t)')\n",
    "title('Figure 3.8 (a) Signal constellation')\n",
    "grid()\n",
    "show()\n",
    "print 'Figure 3.8 (b).Representation of transmitted dibits'\n",
    "print 'Loc. of meg.point| (-3/2)asqrt(T)|(-1/2)asqrt(T)|(3/2)asqrt(T)|(1/2)asqrt(T)'\n",
    "print '________________________________________________________________________________'\n",
    "print 'Transmitted dibit|         00    |      01      |   11        |   10'\n",
    "print ''\n",
    "print ''\n",
    "print 'Figure 3.8 (c). Decision intervals for received dibits'\n",
    "print 'Received dibit     |     00          |      01       |   11          |   10'\n",
    "print '________________________________________________________________________________'\n",
    "print 'Interval on phi1(t)| x1 < -a.sqrt(T) |-a.sqrt(T)<x1<0| 0<x1<a.sqrt(T) | a.sqrt(T)<x1'\n",
    " \n",
    "#Implementation of LMS ADAPTIVE FILTER\n",
    "#For noise cancellation application\n",
    "order = 18#\n",
    "t =arange(0,0.01+1,0.01)\n",
    "x = [sin(2*pi*5*tt) for tt in t]\n",
    "noise =random.rand(len(x))\n",
    "x_n = x+noise#\n",
    "ref_noise = [noise*xx for xx in random.rand(10)]\n",
    "w = zeros([order,1])\n",
    "\n",
    "\n",
    "mu = 0.01*(sum(multiply(x,x))/len(x))\n",
    "\n",
    "print mu\n",
    "\n",
    "N = len(x)#\n",
    "desired=[]\n",
    "for k in range(0,1010):\n",
    "    for i in range(0,N-order-1):\n",
    "        if i < len(ref_noise):\n",
    "            buffer = ref_noise[i]#,i+order-1]\n",
    "            desired.append(x_n[i]-buffer*w)\n",
    "            w = w+(buffer*mu*desired[i])\n",
    "  \n",
    "\n",
    "subplot(4,1,1)\n",
    "plot(t,x)\n",
    "title('Orignal Input Signal')\n",
    "subplot(4,1,2)\n",
    "plot(t,noise)\n",
    "title('random noise')\n",
    "subplot(4,1,3)\n",
    "plot(t,x_n)\n",
    "title('Signal+noise')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example3.3 page 123"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gzXWjJOm0g4iMBRrE2XRr9BtVVRFJdJoPU9UlIlIXGCsic1U17vo6twqxxOPw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\nmVnJuPCbmZXMf3bsm31O2SeyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f527e136a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from numpy import arange,sqrt,cos,pi,convolve\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot,subplot,title,show\n",
    "\n",
    "\n",
    "fc =4# #carrier frequency in Hz\n",
    "T =1#\n",
    "t1 = arange(0,0.01+T,0.01)\n",
    "phit = [sqrt(2/T)*xx for xx in cos(2*pi*fc*t1)]\n",
    "hopt = phit#\n",
    "\n",
    "phiot = convolve(phit,hopt)#\n",
    "phiot = [yy/max(phiot) for yy in phiot]\n",
    "\n",
    "t2 = arange(0,0.01+2*T,0.01)\n",
    "subplot(2,1,1)\n",
    "plot(t1,phit)#\n",
    "title('Figure 3.13 (a) RF pulse input')\n",
    "subplot(2,1,2)\n",
    "plot(t2,phiot)#\n",
    "title('Figure 3.13 (b) Matched Filter output')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example3.4 page 124"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AJeEm/Pdf6NkTPvggakkcx/zzNWvCNdfYhGzVqlFL5CRCutMlNAG6q2qL4H0X\nIEdVHw61eR4Yo6pvBu+nA8eF3Di57boBK1W1V8z2rdIlrF9vMegtWpSMeN/eveGLLywXjuM4TipI\ndejlt0ADEakbpDxoCwyNaTMUaB+cvAmwVFUXiEhFEakcbK8EnAxMTkSo8uXhzTdtBeDo0Yl+lOxk\n1SrLWeI+UcdxoiSduXFqAkPE8iCUA15T1ZGJClarFgwcCBddZP77mjUL/+GygWeesWyEjRpFLYnj\nOKWZrFhBm58M3brB55/b8u+yZTMoWApYsQLq17fRyX77RS2N4zgliWK5gjY/7r3XlHy3blFLUnie\negqaN3dF7zhO9GS9ZQ+2wu/QQ22F36mnZkiwJFm2zKz6L7+EvfeOWhrHcUoaKbfsk0mXEOwrG6RL\nKHLgYY0atgLw0kvhzz8Lbp8N9OkDrVq5onccJztId7oEgM7AVBKP2Y/LscfCjTdaQqf165PpKf0s\nWWIuHM8H7jhOtlCQZb8pXYKqrgdy0yWE2SJdAlBVRGoAiEhtoCXQjwTTJuTH7bdbYqcuXZLtKb30\n6gVnnQX16kUtieM4jpHudAm9gduAlCRNLVPGUgQfcgg0bWoV37ONRYssZfN330UtieM4zmbSlS5B\nROQ04G9VnSgizfI7ODZdQrNmeTffaSdLmNa6NRx4IOy1V4ISZojHHrPc/HXrRi2J4zgliWxNl9AM\n6ARcDGwAtsWs+3dUtX3MOQqMxolHnz4waJBFu2yzTaEPTwsLFliY5aRJULt21NI4jlOSKWw0TkHK\nvhzwM3AiMBcYD7RT1WmhNi2B61W1ZfBw6KOqTWL6OQ64VVVPj3OOIil7VTjnHNhtN0urkA3ccotN\nHj/5ZNSSOI5T0imssk9nuoStuktUqEQQgf79rW7tW29ZlE6UzJ0LL78MP/0UrRyO4zjxKBaLqvLj\n++/hlFOs1uY++6RQsELSqZMlcOvVq+C2juM4yZJSN04mSFbZA7zwgiUc+/prqFgxRYIVgjlz4KCD\nYNo02GWXzJ/fcZzSR6lU9qqWHXPbba3SVaa55hqoUgUeeijz53Ycp3SSNekSRGRbEflGRH4Qkaki\n0jPxj1E4RMy6HzfO/OaZZNYsePttuPXWzJ7XcRynMKQtXYKqrgGOV9X/AI2A40XkmNR/BGP77eG/\n/4XbbsvsJOkDD5hlX7165s7pOI5TWNKaLkFVVwdtKmDRPItTJXg8DjjAFjWdey6sXJnOMxm//Qbv\nvmshl471Ij/KAAAgAElEQVTjONlMQco+r1QIBbWpDZsyXv6ApU4YrapTkxO3YC65BI4+Gq66ynz5\n6eS+++CGGyxfj+M4TjZTkLIvaroEBVDVjYEbpzZwbEFpE1LFU0/B5Mnw4ovpO8cvv8BHH1kmTsdx\nnGynoNw4fwF1Qu/rYJZ7fm1qB9s2oarLROQj4DBgTOxJCpMbJxEqVjT//THHwOGHW+K0VNOjB9x0\nk0XhOI7jpJt058YpcroEEakObFDVpSKyHbYKt4eqjoo5R9Khl3nx1lvQtatloKxaNXX9Tp0Kxx8P\nM2ZA5cqp69dxHCdRUh5nLyKnAn3YnC6hZzhdQtAmN2JnFXCpqn4vIgdiE7dlgterqvponP7TpuwB\nrr/eUhm8846FaKaC886zNA23356a/hzHcQpLqVxUlR9r19qE7UUXpca//uOPlp5hxgyoVCn5/hzH\ncYqCK/s4zJwJRxwBQ4dCkyYFt8+Ps8+2wik33ZQa2RzHcYqCK/s8eP99S1b2/fdWAKUofP89nH66\nWfXbbZda+RzHcQpDytMlBJ0WNWVCHREZLSJTROQnEemUqGCp5owzoE0baN8ecnKK1ke3blb/1hW9\n4zjFjURy4xQ5ZQKwHrhJVfcHmgDXxR6bSXr2hCVL4JFHCn/s+PFWgeryy1Mvl+M4TrpJxLIvcsoE\nVZ2vqj8E21cC04DdUiZ9ISlf3sIx+/SBsWMLd+y998Jdd1lmTcdxnOJGIso+qZQJuYhIXeBg4JvC\nCplK6tSxzJgXXmg1YxPhyy9h+nS4NK8aXI7jOFlOIso+qZQJACKyPTAY6BxY+JHSogV06GAKf+PG\ngtt36wb33AMVKqRdNMdxnLRQULoESDJlgoiUB94BBqnqe/FOkOp0CYnQvTucdBL83/9Z6oO8GDvW\ncta3b592kRzHcfIkrekSIOmUCYL58v9R1biR6ZkKvYzH/Plw6KEwYACcfPLW+1WhWTPo2NGVveM4\n2UXKQy9VdQNwPZbbZirwlqpOE5GrQmkThgG/i8gM4AXg2uDwo4GLsMIlE4NXi8J9pPRRsyYMGmRp\nkf/6a+v9o0bZA+GCCzIvm+M4TiopNYuq8uOBB2D4cPjsM4vYAbPqjz7a8tW3axepeI7jOFuRlkVV\nJZ0uXSzPzd13b942YgQsW2ZJzxzHcYo7ruyBMmXMnfPGG/DBB2bV33OPTdyWLRu1dI7jOMmTSDRO\nqaB6dXjzTTjrLLPw162zpGeO4zglgbTmxgm29xeRBSIyOVVCp4ujjrIc9Z06QZs2YyiTZeOeZMKu\n0oXLlBjZKBNkp1wuU3pId24cgAHBscWCm2+G996D9evHRC3KVmTjDecyJUY2ygTZKZfLlB7SmRun\nZvD+C2BJ6kROLyKWITNVVa0cx3GygXTmxolt4ziO40SFqub7As4B+obeXwQ8FdPmA+Do0PtPgUNC\n7+sCk/PoX/3lL3/5y1+FfxWkv8OvtOfGKYjCLApwHMdxikYibpxvgQYiUldEKgBtgaExbYYC7QGC\n3DhLVTXBBMKO4zhOukl3bhxE5A1gHLC3iPwpIp4V3nEcJ8NEnhvHcRzHST+RLhtKZLFWhuXJugVg\n2VS0PYyIbCsi34jIDyIyVUR6Ri0T2LqQILvqB1HLkouIzBKRHwO5xkctD4CIVBWRwSIyLfj+mkQs\nzz6hzLgTRWRZNtzrItIl+O1NFpHXRWSbqGUCEJHOgUw/iUjnhA4qzGxuKl9AWWAGFqlTHvgBaBiV\nPIFMTbHSiXEjh9J43hVA3Tz21QT+E/y/PVZbINLrFJKtYvC3HPA1cEyS/fXEqpkBNAP+zKftY8DV\ncbbfDLwGDI3getQFcoAyMdtnAjsWob9ZwImFPGYYcHHwfwfgizzaDQQuC31/VaK+n0KylQHmAXUi\nlqMu8DuwTfD+LeCSLLg+BwCTgW0DPfoJUK+g46K07BNZrJVRNM0LwAILb7WIrAhey0WkpqpWVtVZ\neciUsaLtInJ8YIEuEZHFIjJSRPbL55AuwSjoXywaa3FMfzsH1tDSoL9B+Zx7Z+Bi4PkExX0M6BpU\nQsvtozbQEugHVBSRHBH5PuY81UVknYjMTOQkItJBRL5IUKZ8uyrCMbkhdlt3JvKyiKwN3UsrRKSN\nqrZU1VfzOCZHRPYSkSpAU1XtDzYvp6rLiiBfkQkCPnJEJJ4Oag78pqp/xtlXlP6KynJgPXYvlQMq\nkmCUYZrZF/hGVdeo6kZgLFBgJq8olX1pXIilwGmBcq+sqjuo6vxED5ZCFm0PUl0UhinAqapaDagB\nTAT659N+BvYDAJipqlNj9g/BqpvVAXYGHs2nrw7AR6q6NhFBg+s2HVu9nUtv4DbMus5lOxHZP/T+\nAsxay+RklQKfisi3InJFCvt8OHQvVVbV/yZwnAB7AgtFZICIfC8ifUWkYr4HmbJLB/EegucDr6ew\nvyKhqouBXsAf2H28VFU/TVX/SfAT0FREdgy+t1ZYuHu+RKnsfWY4INfiCv7fSUQ+CHyW40XkfhH5\nQqxo+1BMca4OHTtGRDoG/3cQkS9F5HERWQR0E5EKIvKYiMwWkfki8pyIbBtPDlX9W1VzLZcymNKc\nl5fcqjpQVethNYb3EJFmIblOxm7A21V1hapuVNVJ+VyGFpiFEnttuojIQhGZKSKxNcPGYDc6InIa\n8LeqTmTLH/yrwCWh9xcDr4TbiMidIjIjGGlNEZEzg+0NsTxPRwaW8+Jg+3Yi0isYqS0Nvp+wL/ei\n4HovFJGu2ILDg4FTgR4iMkdEFonIWyJSLSTHxcFxi4LjCk34fojZ/nnw7yTgS+BQ4FngXuBM4J/g\n3jkwdMwsEbldRH4EVsSzmkXkKBGZEFyH8SJyZMzxJ4bedxeR3FFHrjxLg+veJLh/xwHtgJ5i8wkn\nFKG/FSJyRGJXLG9EpB5wI+bO2Q3YXkQuTLbfZFHV6cDDwEjgY8woy8n3IKJV9oks1iqJFGR5PIP5\n8GtgSiq3+u07QLyC7bFD/cbAb8AuwIPYTVEfOCj4Wwv7gccXTmR3EVmCPVBaAVspjjisB34BDgtt\na4LNLwwMlNd4ETk2nz4ODNqHqQnshP3QLgFeFJG9Q/unB58L4CigdeCeeSN4L5j//nwx9sPmPWJH\nRjOw+YYdgB7AIBGpoVZn+Wrgq8By3jFo/xg2wjoS2BEbTYS/g6OBvbG6zfcCOwTbLwA2AC8Bu2Iu\nw2cAAtmeBS4MPu9OFGytxbuX4rp+VDX32jcC6mGj6lxZugCjsLDpoRJyjWFW9qlAVVXdQqGIyI7A\nR0Af7Do8DnwUeoDFyhL+v2nwt0owwv06eN8Ym6vYEegGDBGRqoXsr7Jajq5kOQwYp6r/qIWgD8Hu\nq8hR1f6qepiqHgcsZevfzlZEqewTWaxV0hDgPTGf+BIRGbLFTnO7nA10C/xx07CJtL2xNQ75uVRy\nmauqzwQ/zLXAFcDNqro08Pn3xH7AcVHVPwI3TnXMChwQ94OY7zv3R1gWUyATQ01qAycDn2EPrl7A\n+yKyUx6nroo95GK5R1XXq+rnmGIJ1w5bERyHqnZV1Tqqumfw+cZhymAO9kM4CXtwvhLnMw/Odaep\n6tvAr0CuZbiFQg2s20uxieR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GjeCuu6KWxilunHuuReyccw6MGwfPPgvbbRe1VNlLlDVo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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f527df99e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from numpy import random,convolve\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot,subplot,title,show\n",
    "\n",
    "\n",
    "phit = [0.1*xx for xx in random.uniform(0,1,10)]\n",
    "hopt = phit\n",
    "phi0t = convolve(phit,hopt)\n",
    "phi0t = [yy/max(phi0t) for yy in phi0t]\n",
    "subplot(2,1,1)\n",
    "plot(range(0,len(phit)),phit)\n",
    "title('Figure 3.16 (a) Noise Like input signal')\n",
    "subplot(2,1,2)\n",
    "plot(range(0,len(phi0t)),phi0t)\n",
    "title('Figure 3.16 (b) Matched Filter output')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example3.6 page 127"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predictor-error variance 0.64\n",
      "1 Predictor input variance 1\n",
      "The predictor-error variance is less than the variance of the predictor input\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "\n",
    "Rxx = [0.6, 1, 0.6]\n",
    "h01 = Rxx[2]/Rxx[1]#  #Rxx(2) = Rxx(0), Rxx(3) = Rxx(1)\n",
    "sigma_E = Rxx[1] - h01*Rxx[2]\n",
    "sigma_X = Rxx[1]\n",
    "print 'Predictor-error variance',sigma_E\n",
    "print sigma_X,'Predictor input variance',sigma_X\n",
    "if(sigma_X > sigma_E):\n",
    "    print 'The predictor-error variance is less than the variance of the predictor input'\n"
   ]
  }
 ],
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