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"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1> Chpater 7: PERFORMANCE ANALYSIS OF DIGITAL COMMUNICATION SYSTEMS<h1>"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.15, Page No 414"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#initialisation of variables\n",
"T=1.0*10**-6 #ms\n",
"A=10.0*10**-3\n",
"N=1*10**-11\n",
"\n",
"#CALCULATIONS\n",
"Eb=((A**2)*T)/2.0\n",
"Epb=math.sqrt(Eb/N)\n",
"Pb=(1.0/2)*math.erfc(Epb)*(1.0/4)\n",
"\n",
"#RESULTS\n",
"print(\"Bit error probability = %.2f X 10^-4 \" %(Pb*(10**4)))\n",
"print('Approximation error')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Bit error probability = 1.96 X 10^-4 \n",
"Approximation error\n"
]
}
],
"prompt_number": 44
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.16, Page No 420"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#initialisation of variables\n",
"Br=25*10**6 #bits/sec\n",
"N=2*10**-20 #Power spectral density of noise\n",
"A=1.0*10**-6\n",
"Ps=1*10**-12 # Normalized power\n",
"\n",
"#CALCULATIONS\n",
"Tb=1.0/Br\n",
"Ps=(A**2)/2.0\n",
"Pe=1.0/2*(math.erfc((0.6*Ps*Tb)/N))\n",
"#RESULTS\n",
"print(\"Average probability of bit error is Pe= %.2f X 10^-4 \" %(Pe*10))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Average probability of bit error is Pe= 1.98 X 10^-4 \n"
]
}
],
"prompt_number": 45
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.17, Page No 423"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Find probability of error\n",
"\n",
"#initialisation of variables\n",
"A=2.0\n",
"N0=2.0*10**-4 #power sepctral density\n",
"\n",
"#CALCULATIONS\n",
"Tmin=(6.76*N0)/4\n",
"\n",
"#RESULTS\n",
"print(\"The min time for which the signal should be extended is Tmin= %.3f X 10^-3 msec \" %(Tmin*10**3))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The min time for which the signal should be extended is Tmin= 0.338 X 10^-3 msec \n"
]
}
],
"prompt_number": 46
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.20, Page No 428"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#The average carrier\n",
"\n",
"#initialisation of variables\n",
"Pe=10**-4\n",
"N0=2*10**10\n",
"T=1.0/10**6\n",
"\n",
"#CALCULATIONS\n",
"E=6.76*N0\n",
"P=E/T\n",
"Eb=8.5171*N0\n",
"P2=Eb/T\n",
"\n",
"\n",
"#RESULTS\n",
"print(\"The average carrier = %.3f X 10^-3 mW \" %(P2/10**17))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The average carrier = 1.703 X 10^-3 mW \n"
]
}
],
"prompt_number": 47
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.21, Page No 430"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#The average carrier\n",
"\n",
"#initialisation of variables\n",
"A=0.2*10**-3 #V\n",
"T=2*10**-6\n",
"N0=2*10**-15\n",
"\n",
"#CALCULATIONS\n",
"Pe=(math.sqrt((A**2*T)/4*N0))\n",
"\n",
"#RESULTS\n",
"print(\"The average carrier = %.3f X 10^-4 mW \" %(Pe*10**15))\n",
"print(\"Approximation error\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The average carrier = 6.325 X 10^-4 mW \n",
"Approximation error\n"
]
}
],
"prompt_number": 48
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.29, Page No 447"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#initialisation of variables\n",
"A=1.0\n",
"N0=2.0*10**-5 #power sepctral density\n",
"\n",
"#CALCULATIONS\n",
"T=((3.71**2)*2*N0)/(A**2)\n",
"Br=1/T\n",
"#Results\n",
"print(\"Bit rate Br= %.2f k bits/sec\" %(Br/(10**3)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Bit rate Br= 1.82 k bits/sec\n"
]
}
],
"prompt_number": 49
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.31, Page No 448"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#initialisation of variables\n",
"Pe=10.0**-4 #probability of error of PSK\n",
"N0=2.0*10**-10\n",
"Br=10**6 #Bit Rate\n",
"\n",
"\n",
"#CALCULATIONS\n",
"T=1.0/Br\n",
"E=N0*6.76\n",
"P=E/T\n",
"Eb=8.5171*N0\n",
"Pb=Eb/T\n",
"#Results\n",
"print(\"i) PSK system The required carrier power = %.2f mW\" %(P*10**3))\n",
"print(\"ii) DPSK system The required carrier power = %.2f mW\" %(Pb*10**3))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"i) PSK system The required carrier power = 1.35 mW\n",
"ii) DPSK system The required carrier power = 1.70 mW\n"
]
}
],
"prompt_number": 50
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.32, Page No 450"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#initialisation of variables\n",
"A=0.2*10**-3 #V\n",
"T=2*10**-6 #Sec\n",
"N0=2*10**-15\n",
"\n",
"\n",
"#CALCULATIONS\n",
"x=math.sqrt((A**2*T)/(4*N0))\n",
"Pe=(1.0/2)*math.erfc(x/math.sqrt(2.0))\n",
"\n",
"#Results\n",
"print(\"Probability of error = %.2f X 10^-4\" %(Pe*10**4))\n",
"#print(\"Channel Bandwidth = %.5f MHz\" %BW)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Probability of error = 7.83 X 10^-4\n"
]
}
],
"prompt_number": 51
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.36, Page No 453"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#initialisation of variables\n",
"Ap=1 #mV\n",
"En=192.3 #mV\n",
"Arms=707 #mV\n",
"\n",
"\n",
"#CALCULATIONS\n",
"Z=Arms/En\n",
"Pe=1.0/2*(math.erfc(math.sqrt(2)*(Z/math.sqrt(2))))\n",
"\n",
"#Results\n",
"print(\"Probability of error is %.7f \" %Pe)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Probability of error is 0.0000001 \n"
]
}
],
"prompt_number": 52
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.37, Page No 454"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#initialisation of variables\n",
"Br=2.08*10**-6 #Bit Rate\n",
"N0=2*10**-8\n",
"\n",
"#CALCULATIONS\n",
"Eb=(math.sqrt(3.3))/(5*10**7) #Eb=bit energy\n",
"Ps=Eb*Br\n",
"BW=2*Br #Bandwidth\n",
"Es=286.39*N0\n",
"Ps2=(Es*Br)/2\n",
"BW2=(2*Br)/4\n",
"\n",
"#Results\n",
"print(\"i) BPSK THe transmission bandwidth = %.2f MHz\" %(BW*10**6)) \n",
"print(\"ii) For 16 ary PSK THe transmission bandwidth = %.2f MHz\" %(BW2*10**6)) \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"i) BPSK THe transmission bandwidth = 4.16 MHz\n",
"ii) For 16 ary PSK THe transmission bandwidth = 1.04 MHz\n"
]
}
],
"prompt_number": 53
}
],
"metadata": {}
}
]
}