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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 10: Digital Signal"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.1, Page 272"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable Declaration\n",
      "\n",
      "PR=0.01  #The Average power received(watts)\n",
      "Tb=0.0001  #Bit period(seconds)\n",
      "N0=10**-7  #Noise power(joule)\n",
      "\n",
      "#Calculations\n",
      "\n",
      "\n",
      "Eb=PR*Tb  #Energy per bit received (joule)\n",
      "x=math.sqrt(Eb/N0)\n",
      "\n",
      "from scipy import integrate\n",
      "f=lambda t:math.exp(-t**2)\n",
      "erf=integrate.quad(f,0,x)\n",
      "erf1=erf[0]*(2/math.pi**0.5)\n",
      "BER=(1-erf1)*(10**6)/2\n",
      "BER=round(BER,2)\n",
      "\n",
      "print \"The Bit error rate is\", BER,\"*10^-6\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Bit error rate is 3.87 *10^-6\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "EXample 10.2, Page 274"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#Variable Declaration\n",
      "Rb=61   #Transmission rate (Mb/s)\n",
      "ENR=9.5 #Required Energy to noise ratio(dB)\n",
      "\n",
      "#Calculation\n",
      "\n",
      "Rb=10*math.log10(61*10**6)  #Converting Transmission rate to dB\n",
      "CNR=Rb+ENR  #Carrier to noise ratio\n",
      "CNR=round(CNR,2)\n",
      "#Results\n",
      "\n",
      "print \"Required Carrier to noise ratio is\", CNR,\"dB\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Required Carrier to noise ratio is 87.35 dB\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.3, Page 275"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable Declaration\n",
      "BER=10**-5  #Maximum allowable bit error rate\n",
      "\n",
      "#Calculation\n",
      "\n",
      "import math\n",
      "from pylab import*\n",
      "%pylab inline\n",
      "x=linspace(8,10,11)  #Eb/N0 ratio represented by x\n",
      "x1=x**0.5\n",
      "for i in range(0,11):\n",
      "   x[i]=10*math.log10(x[i])  #Converting x into decibels\n",
      "\n",
      "\n",
      "erf=linspace(0,0,11)  #Initialization for erf function\n",
      "Pe=linspace(0,0,11)   #Initialization for Probablity of error\n",
      "\n",
      "from scipy import integrate\n",
      "f=lambda t:math.exp(-t**2)\n",
      "for i in range(0,10):\n",
      "   k=integrate.quad(f,0,x1[i])\n",
      "   erf[i]=k[0]*(2/math.pi**0.5)    \n",
      "   Pe[i]=(1-erf[i])/2       #Probability of error\n",
      "\n",
      "y=linspace(9,9.59,5)\n",
      "z=linspace(BER,BER,5)\n",
      "a=linspace(9.59,9.59,5)\n",
      "b=linspace(0,BER,5)\n",
      "plot(x,Pe)\n",
      "plot(y,z)\n",
      "plot(a,b)\n",
      "xlabel('xdB')\n",
      "ylabel('Pe(x)')\n",
      "show() \n",
      "x=9.6   #The Eb/N0 ratio for Maximum BER(dB) from the graph\n",
      "EbN0=x+2 #Eb/N0 ratio with implementation margin\n",
      "#Results\n",
      "\n",
      "print \"The Eb/N0 ratio with allowable BER of 10^-5 and implementation margin of 2dB is\",EbN0,\"dB\"\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['linalg', 'draw_if_interactive', 'random', 'power', 'info', 'fft']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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X3G431q9fj/T09BbbOBwOrF27FgDgdDq99486autwOFBUVAQAKCoqgsPh8L6/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\nUBQF/fr1w/PPP99hW0BL5Ky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       "text": [
        "<matplotlib.figure.Figure at 0x3733c90>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Eb/N0 ratio with allowable BER of 10^-5 and implementation margin of 2dB is 11.6 dB\n"
       ]
      }
     ],
     "prompt_number": 1
    }
   ],
   "metadata": {}
  }
 ]
}