{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 12 Communication systems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_1 Pg-12.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "modulation index m=0.8 \n",
      "                 %m=80% \n",
      "\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "Vm=40##peak value of the modulating signal\n",
    "Vc=50##peak value of the carrier signal\n",
    "m=Vm/Vc##modulation index\n",
    "print \"modulation index m=%.1f \\n                 %%m=%.0f%% \\n\"%(m,m*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_2 Pg-12.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Therefore upper side band frequency fusb=234720 Hz \n",
      "\n",
      " Therefore lower side band frequency flsb=224720 Hz \n",
      "\n",
      "\n",
      " required bandwidth BW=10000Hz\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt, pi\n",
    "L=40e-6#\n",
    "C=12e-9#\n",
    "x=2*pi*sqrt(L*C)#\n",
    "fc=1/x##carrier  frequency \n",
    "f=5e3##given audio frequency\n",
    "fusb=fc+f##upper side band frequency\n",
    "flsb=fc-f##lower side band frequency\n",
    "BW=fusb-flsb##required bandwidth \n",
    "print \"Therefore upper side band frequency fusb=%.0f Hz \\n\"%(fusb)\n",
    "print \" Therefore lower side band frequency flsb=%.0f Hz \\n\"%(flsb)\n",
    "print \"\\n required bandwidth BW=%.0fHz\"%(BW)\n",
    "#in the book fc is approximated to 230Khz but the exact answer is 229.72kHz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_3 Pg-12.17 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " for modulation index m=0.75 Vc=1.33 V\n"
     ]
    },
    {
     "data": {
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R5XXDhQDRCgOsLRcAKAWa0GeFGyslKqaMVgEDodu98XKIoFAa1hRDAAaCkFBZRLllAAoq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\nOIGYmVkpTiBmZlbKfznqYwjCFj+zAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1170481c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " for modulation index m=1    Vc=1.00 V\n"
     ]
    },
    {
     "data": {
      "image/png": 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QdElbYRoTeS6Yhkwr5/m2mmnrmbY7YSvJTcu3J7ZHKQPTYIrtlbWJ/T1p4zf6FmIjk3Zu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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11704aab50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " for modulation index m=1.25 Vc=0.80 V\n"
     ]
    },
    {
     "data": {
      "image/png": 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69mYR6QCGtdZaRK4FRGs9Vm3Yhx9+mLe+/wq2Uoyks3zvxFt0RkJETRjPeec/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\nHkE0bG5KsLEphtJCszVGNBB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1c9NEDbloe21bkOJy2gXFmdSl24WSSyrLHDtsKSxT0x4L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2ufGLxadn2BfXKwigbPlL0sa6u0Nc2fOtRUxK7J2s+8WmfZ4aBjXyd2vcebtUXJtI3GU4eaqHJr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\nkd62A68opU4rpdLAv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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f114f315210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy import arange, pi, sqrt, sin\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot, title, xlabel, ylabel, show, grid\n",
    "\n",
    "# NOTE : Don't interrupt the kernel It will take time to output three modulated wave.\n",
    "\n",
    "fm=5e3; #assume modulation frequency f=5kHz\n",
    "fc=1080e3; #assume carrier frequency f=1080kHz\n",
    "time=arange(0,8e-4,2.3148e-7)\n",
    "#Waveform of modulated signal for m=0.75\n",
    "m1=0.75; #modulation index\n",
    "VmbyVc=m1\n",
    "Vm=1; #we assume modulation voltage=1V\n",
    "Vc=Vm/m1; #carrier voltage\n",
    "k=VmbyVc; #modulation index = Vm/Vc\n",
    "print \"\\n for modulation index m=0.75 Vc=%.2f V\"%Vc\n",
    "\n",
    "mt=k*sin(2*pi*fm*time);\n",
    "sam =[]\n",
    "for i in range(0,len(time)):\n",
    "    sam.append(Vc*(1+mt)*sin(2*pi*fc*time[i]))\n",
    "\n",
    "\n",
    "plot(time[0:500],sam[0:500]);\n",
    "title(' Waveform of modulated signal m=0.75');\n",
    "xlabel('Time (sec)');\n",
    "ylabel('Amplitude (Vc=1.33V)');\n",
    "\n",
    "#xgrid(color(\"gray\"));\n",
    "show()\n",
    "\n",
    "\n",
    "\n",
    "#Waveform of modulated signal for m=1\n",
    "m1=1;\n",
    "VmbyVc=m1\n",
    "Vm=1; #we assume modulation voltage=1V\n",
    "Vc=Vm/m1; #carrier voltage\n",
    "k=VmbyVc; #modulation index = Vm/Vc\n",
    "print \"\\n for modulation index m=1    Vc=%.2f V\"%Vc\n",
    "\n",
    "mt=k*sin(2*pi*fm*time);\n",
    "sam =[]\n",
    "for i in range(0,len(time)):\n",
    "    sam.append(Vc*(1+mt)*sin(2*pi*fc*time[i]))\n",
    "\n",
    "\n",
    "plot(time[0:500],sam[0:500]);\n",
    "title(' Waveform of modulated signal m=0.75');\n",
    "xlabel('Time (sec)');\n",
    "ylabel('Amplitude (Vc=1.33V)');\n",
    "\n",
    "#xgrid(color(\"gray\"));\n",
    "show()\n",
    "\n",
    " #Waveform for modulated signal for m=1.25\n",
    "m1=1.25;\n",
    "VmbyVc=m1\n",
    "Vm=1; #we assume modulation voltage=1V\n",
    "Vc=Vm/m1; #carrier voltage\n",
    "k=VmbyVc; #modulation index = Vm/Vc\n",
    "print \"\\n for modulation index m=1.25 Vc=%.2f V\"%(Vc)\n",
    "\n",
    "mt=k*sin(2*pi*fm*time);\n",
    "sam =[]\n",
    "for i in range(0,len(time)):\n",
    "    sam.append(Vc*(1+mt)*sin(2*pi*fc*time[i]))\n",
    "\n",
    "\n",
    "plot(time[0:500],sam[0:500]);\n",
    "title(' Waveform of modulated signal m=0.75');\n",
    "xlabel('Time (sec)');\n",
    "ylabel('Amplitude (Vc=1.33V)');\n",
    "\n",
    "#xgrid(color(\"gray\"));\n",
    "show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_4 Pg-12.22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "modulation index m=0.2 \n",
      "     ie          %m=20 % \n",
      "\n",
      "\n",
      " Therefore upper side band frequency fusb=100.5 kHz \n",
      "\n",
      " Therefore lower side band frequency fusb=99.5 kHz \n",
      "\n",
      "\n",
      " amplitude of upper and lower side bands=5 V \n",
      "\n",
      "\n",
      " required bandwidth BW=1000Hz\n",
      "\n",
      "\n",
      " power delivered to the load 2.125 W \n",
      " \n",
      "\n",
      " transmission efficiency n=1.96 % \n",
      "\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import pi\n",
    "#modulation index\n",
    "Vm=10##peak value of the audio frequency signal\n",
    "Vc=50##peak value of the carrier signal\n",
    "m=Vm/Vc##modulation index\n",
    "print \"modulation index m=%.1f \\n     ie          %%m=%.0f %% \\n\"%(m,m*100)\n",
    "#sideband frequencies\n",
    "wm=2*pi*500#\n",
    "fm=wm/(2*pi)#\n",
    "wc=2*pi*1e5#\n",
    "fc=wc/(2*pi)#\n",
    "fusb=fc+fm##upper side band frequency\n",
    "flsb=fc-fm##lower side band frequency\n",
    "print \"\\n Therefore upper side band frequency fusb=%.1f kHz \\n\"%(fusb*1e-3)\n",
    "print \" Therefore lower side band frequency fusb=%.1f kHz \\n\"%(flsb*1e-3)\n",
    "#amplitude of each sinusoidal frequency\n",
    "A=m*Vc/2#\n",
    "print \"\\n amplitude of upper and lower side bands=%.f V \\n\"%(A)\n",
    "#bandwidth required\n",
    "BW=fusb-flsb##required bandwidth \n",
    "print \"\\n required bandwidth BW=%.0fHz\\n\"%(BW)\n",
    "#power delivered to the load\n",
    "R=600##load resistance\n",
    "P=Vc**2/(2*R)*(1+m**2/2)\n",
    "print \"\\n power delivered to the load %.3f W \\n \"%(P)\n",
    "#transmission efficiency\n",
    "n=m**2/(2+m**2)*100#\n",
    "print \"\\n transmission efficiency n=%.2f %% \\n\"%(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_5 Pg-12.23"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Therefore total power in the modulated wave is 528 W\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "Pc=400##power of the carrier signal\n",
    "m=0.8##modulation index\n",
    "P=Pc*(1+m**2/2)\n",
    "print \"  Therefore total power in the modulated wave is %.0f W\"%(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_6 Pg-12.23"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "therefore carrier power in the modulated wave is 15.6 kW\n",
      "\n",
      " Pusb=2.2 kW \n",
      " Plsb=2.2 kW\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "m=0.75##modulation index\n",
    "P=20##total power in kW\n",
    "Pc=P/(1+m**2/2)#since P=Pc*(1+m**2/2)\n",
    "print \"therefore carrier power in the modulated wave is %.1f kW\"%(Pc)\n",
    "Psb=Pc*m**2/4##side band power\n",
    "Pusb=Psb#\n",
    "Plsb=Psb#\n",
    "print \"\\n Pusb=%.1f kW \\n Plsb=%.1f kW\"%(Pusb,Plsb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_7 Pg-12.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Therefore total antenna current when only the carrier is sent Ic=4.6 A\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt\n",
    "m=0.6##modulation index\n",
    "Itotal=5##total antenna current\n",
    "#Ic=total antenna current when only the carrier is sent\n",
    "Ic=Itotal/sqrt(1+m**2/2)#since Itotal=Ic*sqrt(1+m**2/2)\n",
    "print \"Therefore total antenna current when only the carrier is sent Ic=%.1f A\"%(Ic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_8 Pg-12.26."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "modulation index m=0.8 \n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols, sqrt\n",
    "Ic=symbols('Ic')##unmodulated carrier signal\n",
    "Itotal=1.15*Ic##total rms current when the signal is modulated \n",
    "x=Itotal/Ic#\n",
    "y=2*((x)**2-1)\n",
    "m=sqrt(y)\n",
    "print \"modulation index m=%.1f \"%(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_9 Pg-12.28"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total modulation index m=0.781 \n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "m1=0.6##first modulation index\n",
    "m2=0.3##second modulation index\n",
    "m3=0.4##third modulation index\n",
    "mt=sqrt(m1**2+m2**2+m3**2)#\n",
    "print \"total modulation index m=%.3f \"%(mt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_10 Pg-12.28"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total radiated power P=12.25 kW \n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "from __future__ import division\n",
    "Ptotal=11.8##radiated power in kW when the carrier is modulated\n",
    "Pc=10##radiated power in kW when the carrier is unmodulated\n",
    "m=sqrt(2*((Ptotal/Pc)-1))\n",
    "#when another sine wave of 30% of the \n",
    "#initial modulation is transmitted simultaneously then\n",
    "m1=0.3##added sine wave signal is 30% \n",
    "mt=sqrt(m1**2+m**2)#\n",
    "P=Pc*(1+mt**2/2)##total radiated power \n",
    "print \"total radiated power P=%.2f kW \"%(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_11 Pg-12.30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " carrier power Pc=7.8 kW \n",
      "\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "Ptotal=10##radiated power in kW when the carrier is modulated\n",
    "m=0.75##modulation index\n",
    "Pc=Ptotal/(1+m**2/2)#since Ptotal=Pc*sqrt(1+m**2/2)\n",
    "print \"\\n carrier power Pc=%.1f kW \\n\"%(Pc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_12 Pg-12.30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fusb1=1000.3 kHz \n",
      " flsb1=999.7 kHz\n",
      "\n",
      " fusb2=1000.8 kHz\n",
      "\n",
      " flsb2=999.2 kHz \n",
      "\n",
      " fusb3=1001.0 kHz \n",
      " flsb3=999.0 kHz \n",
      "\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "fc=1000e3##carrier  frequency \n",
    "fm1=300##first audio frequency\n",
    "fm2=800##second audio frequency\n",
    "fm3=1e3##third audio frequency\n",
    "fusb1=fc+fm1##upper side band frequency\n",
    "flsb1=fc-fm1##lower side band frequency\n",
    "fusb2=fc+fm2##upper side band frequency\n",
    "flsb2=fc-fm2##lower side band frequency\n",
    "fusb3=fc+fm3##upper side band frequency\n",
    "flsb3=fc-fm3##lower side band frequency\n",
    "print \"fusb1=%.1f kHz \\n flsb1=%.1f kHz\\n\\n fusb2=%.1f kHz\\n\"%(fusb1*1e-3,flsb1*1e-3,fusb2*1e-3)\n",
    "print \" flsb2=%.1f kHz \\n\\n fusb3=%.1f kHz \\n flsb3=%.1f kHz \\n\"%(flsb2*1e-3,fusb3*1e-3,flsb3*1e-3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_13 Pg-12.30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Therefore total sideband power radiated Psb=130.500 W\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt\n",
    "m1=0.55##first modulation index\n",
    "m2=0.65##second modulation index\n",
    "mt=sqrt(m1**2+m2**2)#\n",
    "Pc=360###power radiated by the carrier signal\n",
    "Psb=Pc*mt**2/2#total sideband power radiated\n",
    "print \"Therefore total sideband power radiated Psb=%.3f W\"%(Psb)\n",
    "#in the question Pc is taken as 360W but in the answer it is taken as \n",
    "#300W I have taken Pc=300W so that Psb=150.5W"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_14 Pg-12.30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Therefore total antenna current It=13.41 A\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt\n",
    "\n",
    "m=0.5## modulation index\n",
    "It=12##antenna current when AM transmitter is 50% modulated\n",
    "Ic=It/sqrt(1+m**2/2)##carrier current \n",
    "m=0.9##when modulation depth is increase to 0.9 \n",
    "It=Ic*sqrt(1+m**2/2)\n",
    "print \"Therefore total antenna current It=%.2f A\"%(It)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_15 Pg-12.31"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Therefore total antenna current It=1.67 A \n",
      "\n",
      "Ptotal=Pc+Pc*m**2/4+Pc*m**2/4 => Total power radiated\n",
      "\n",
      " Therefore percentage power saving %P=89 %\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt\n",
    "from sympy import symbols\n",
    "## m1=0.6## modulation index\n",
    "It=1.5##antenna current when AM transmitter is 50% modulated\n",
    "Ic=It/sqrt(1+m1**2/2)##carrier current \n",
    "m2=0.7#when another modulated signal is added \n",
    "m=sqrt(m1**2+m2**2)##total modulation index\n",
    "It=Ic*sqrt(1+m**2/2)\n",
    "\n",
    "print \"\\n Therefore total antenna current It=%.2f A \\n\"%(It)\n",
    "print \"Ptotal=Pc+Pc*m**2/4+Pc*m**2/4 => Total power radiated\"\n",
    "Pc=symbols('Pc')#\n",
    "Ptotal=Pc+Pc*m**2/4+Pc*m**2/4 #\n",
    "P=Pc+Pc*m**2/4 #Total power if one of the side band is suppressed \n",
    "per_P=P/Ptotal*100##percentage power saving\n",
    "print \"\\n Therefore percentage power saving %%P=%.0f %%\"%(per_P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_16 Pg-12.32"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Output voltage of the transmitter Vam=400(1+0.4sin6280t)sin3.14*10**7t\n",
      "\n",
      " carrier frequency Fc=5 MHz \n",
      " modulating frequency =999 Hz \n",
      " \n",
      "\n",
      " carrier power Pc=133.33 W \n",
      " Total power output Ptotal=144.0 W \n",
      "\n",
      "\n",
      " Peak output voltage P=261.33 W \n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt,pi\n",
    "\n",
    "print \" Output voltage of the transmitter Vam=400(1+0.4sin6280t)sin3.14*10**7t\"\n",
    "Vc=400##amplitude of carrier voltage \n",
    "m=0.4##modulation index\n",
    "R=600##load resistance\n",
    "wm=6280#\n",
    "wc=3.14e7#\n",
    "fc=wc/(2*pi)#\n",
    "fm=wm/(2*pi)#\n",
    "Pc=Vc**2/(2*R)#\n",
    "Ptotal=Pc*(1+m**2/2)#\n",
    "print \"\\n carrier frequency Fc=%.0f MHz \\n modulating frequency =%.0f Hz \\n \"%(fc*1e-6,fm)\n",
    "print \"\\n carrier power Pc=%.2f W \\n Total power output Ptotal=%.1f W \\n\"%(Pc,Ptotal)\n",
    "#peak power output results when modulating signal\n",
    "#is at the peak of the +ve half cycle \n",
    "Vm=m*Vc#\n",
    "V=Vc+Vm##peak output voltage\n",
    "P=V**2/(2*R)##peak power output \n",
    "print \"\\n Peak output voltage P=%.2f W \"%(P)\n",
    "#The exact value of fc is 4997465 Hz but in the book the \n",
    "#value is taken as 5 MHz  same is the case for fm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_17 Pg-12.33"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " equation of the Am sine wave =Vc(1+m*sinwm*t)*sinwc*t\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f18359ff610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy import arange\n",
    "from math import pi,sin\n",
    "from __future__ import division\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot,title,show,grid,xlabel,ylabel\n",
    "print \" equation of the Am sine wave =Vc(1+m*sinwm*t)*sinwc*t\"\n",
    "Vc=12##amplitude of carrier voltage \n",
    "m=0.5##modulation index\n",
    "fc=10e6##carrier frequency\n",
    "fm=1e3##modulated frequency\n",
    "wc=2*pi*fc#\n",
    "wm=2*pi*fm#\n",
    "t=arange(0,8e-4,2.3148e-7)\n",
    "Vam =[]\n",
    "for tt in t:    \n",
    "    Vam.append(Vc*(1+m*sin(wm*tt)*sin(wc*tt)))\n",
    "fusb=fc+fm##upper side band frequency\n",
    "flsb=fc-fm##lower side band frequency\n",
    "A=m*Vc/2##amplitude of side bands\n",
    "\n",
    "#plotting of the graph\n",
    "x=[ flsb ,flsb  ]##x-coordinate\n",
    "y=[  0   , A  ]##y-coordinate\n",
    "\n",
    "plot(x,y)\n",
    "x1=[10e6 , 10e6]##x-coordinate\n",
    "y1=[ 0   ,  12]##y-coordinate\n",
    "plot(x1,y1)\n",
    "x2=[fusb , fusb]##x-coordinate\n",
    "y2=[ 0   ,  A]##y-coordinate\n",
    "plot(x2,y2)\n",
    "x5=[flsb-1e3, flsb-1e3]##x-coordinate\n",
    "y5=[    0   ,    4    ]##y-coordinate\n",
    "plot(x5,y5)\n",
    "x6=[fusb+1e3 ,fusb+1e3]##x-coordinate\n",
    "y6=[  0      ,   4 ]##y-coordinate\n",
    "plot(x6,y6)\n",
    "\n",
    "xlabel('Frequency(Hz)')#\n",
    "ylabel('amplitude of carrier signal(V)')#\n",
    "title(\"Frequency Spectrum of AM wave\")\n",
    "grid()\n",
    "show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_18 PG-12.18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " When modulation index m=100%% \n",
      " Now Pdsbfc=1.5*Pc or Pdsbfc/Pc=1.5\n",
      "  %Power saving %P :75.000000 %\n",
      "\n",
      "\n",
      " When modulation index m=50%% \n",
      "  Now Pdsbfc=Pc*(1+m**2/2) \n",
      "  Pdsbfc=1.125*Pc  or Pdsbfc/Pc=1.125\n",
      "\n",
      "  %Power saving %P :94.44 %\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols\n",
    "print \" When modulation index m=100%% \"\n",
    "m=1#\n",
    "print \" Now Pdsbfc=1.5*Pc or Pdsbfc/Pc=1.5\"\n",
    "Pc=symbols('Pc')\n",
    "Pdsbfc=Pc*(1+m**2/2)##power required for double sideband with full carrier transmission\n",
    "Pssb=Pc*m**2/4#\n",
    "per_P=(Pdsbfc-Pssb)/Pdsbfc*100\n",
    "x=per_P\n",
    "print \"  %%Power saving %%P :%f %%\\n\\n\"%(x)\n",
    "\n",
    "print \" When modulation index m=50%% \"\n",
    "m=0.5#\n",
    "Pdsbfc=Pc*(1+m**2/2)##power required for double sideband with full carrier transmission\n",
    "print \"  Now Pdsbfc=Pc*(1+m**2/2) \\n  Pdsbfc=1.125*Pc  or Pdsbfc/Pc=1.125\\n\"\n",
    "Pssb=Pc*m**2/4#\n",
    "per_P=(Pdsbfc-Pssb)/Pdsbfc*100\n",
    "x=per_P\n",
    "print \"  %%Power saving %%P :%.2f %%\"%(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_19 Pg-40"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Therefore frequency deviation f=40 kHz \n",
      "\n",
      "    modulation index m=10 \n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "R=2##frequency deviation constant in KHz/V\n",
    "V=20##amplitude of the modulation signal\n",
    "fd=R*V## frequency deviation\n",
    "f=4##frequency applied in kHz\n",
    "print \"\\n Therefore frequency deviation f=%.0f kHz \\n\"%(fd)\n",
    "m=fd/f##modulation index\n",
    "print \"    modulation index m=%.0f \"%(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_20 Pg-40"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "when modulating voltage V=2.5 V\n",
      "\n",
      " frequency deviation constant R=2 KHz/V \n",
      "\n",
      "when modulating voltage V=7.5 V\n",
      "\n",
      " Therefore frequency deviation f=15 kHz \n",
      "\n",
      "when modulating voltage V=10 V\n",
      "\n",
      " Therefore frequency deviation f=20 kHz \n",
      "\n",
      " \n",
      " modulation index \n",
      " mf1=10 \n",
      " mf2=30 \n",
      " mf3=80 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "print \"when modulating voltage V=2.5 V\"\n",
    "V=2.5##modulating voltage\n",
    "fd1=5## frequency deviation in kHz\n",
    "R=fd1/V##frequency deviation constant in KHz/V\n",
    "print \"\\n frequency deviation constant R=%.0f KHz/V \\n\"%(R)\n",
    "print \"when modulating voltage V=7.5 V\"\n",
    "V=7.5##new value amplitude of the modulating voltage\n",
    "fd2=R*V#new frequency deviation in kHz\n",
    "print \"\\n Therefore frequency deviation f=%.0f kHz \\n\"%(fd2)\n",
    "print \"when modulating voltage V=10 V\"\n",
    "V=10##new value amplitude of the modulating voltage\n",
    "fd3=R*V#new frequency deviation in kHz\n",
    "print \"\\n Therefore frequency deviation f=%.0f kHz \\n\"%(fd3)\n",
    "fm=0.5##modulation frequency in kHz ie 0.5kHz=500Hz\n",
    "mf1=fd1/fm#           \n",
    "mf2=fd2/fm#\n",
    "fm1=.25#new modulation frequency in kHz ie 0.25kHz=250Hz\n",
    "mf3=fd3/fm1#\n",
    "print \" \\n modulation index \\n mf1=%.0f \\n mf2=%.0f \\n mf3=%.0f \\n\"%(mf1,mf2,mf3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_21 Pg-41"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "maximum deviation fd_max=24 kHz \n",
      "\n",
      "when modulating voltage V=3.2 V\n",
      " \n",
      " modulation index mf=128\n"
     ]
    }
   ],
   "source": [
    "mf=60##modulation index\n",
    "fm=0.4##modulation frequency in kHz ie 0.4kHz=400Hz\n",
    "#fd_max=maximum frequency deviation\n",
    "fd_max=mf*fm##since mf=fd_max_/fm \n",
    "print \"maximum deviation fd_max=%.0f kHz \\n\"%(fd_max)\n",
    "V=2.4##modulating voltage\n",
    "R=fd_max/V##frequency deviation constant in KHz/V\n",
    "print \"when modulating voltage V=3.2 V\"\n",
    "V=3.2#\n",
    "fd=R*V##frequency deviation\n",
    "fm=0.25#modulation frequency in kHz ie 0.25kHz=250Hz\n",
    "mf=fd/fm#\n",
    "print \" \\n modulation index mf=%.0f\"%(mf) \n",
    "#in the book the final answer for modulation mf=80 \n",
    "#is wrong the correct answer is mf=128"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_22 Pg-41"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " maximum frequency deviation  fd=75 KHz/V \n",
      "\n",
      " \n",
      " modulation index mf=7.0\n"
     ]
    }
   ],
   "source": [
    "R=5##frequency deviation constant in KHz/V\n",
    "fm=10##modulation frequency in kHz \n",
    "V=15##amplitude of the modulating signal\n",
    "fd=R*V##frequency deviation\n",
    "print \"\\n maximum frequency deviation  fd=%.0f KHz/V \\n\"%(fd)\n",
    "mf=fd/fm#\n",
    "print \" \\n modulation index mf=%.1f\"%(mf) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_23 Pg-41.43"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "equation of a frequency modulated v=A*sin(wc*t+mf*sin(wm*t))\n",
      "or v=A*sin(wc*t-fd/fm*cos(wm*t)) where fd=frequency deviation\n",
      "Now v=50*sin(5e8*t-10*cos(1000*t))\n",
      "\n",
      " carrier frequency fc=79.58 MHz \n",
      "\n",
      " modulating frequency fc=159.15 Hz \n",
      "\n",
      " \n",
      " modulation index mf=10\n",
      "\n",
      " maximum deviation fd_max=1591.55 Hz \n",
      "\n",
      "\n",
      " Power dissipated by the wave in resistance P=16.67 W\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import pi,sqrt\n",
    "print \"equation of a frequency modulated v=A*sin(wc*t+mf*sin(wm*t))\"\n",
    "print \"or v=A*sin(wc*t-fd/fm*cos(wm*t)) where fd=frequency deviation\"\n",
    "print \"Now v=50*sin(5e8*t-10*cos(1000*t))\"\n",
    "A=50##peak value of the modulating signal\n",
    "wc=5e8#\n",
    "mf=10#\n",
    "wm=1000#\n",
    "fc=wc/(2*pi)##carrier frequency\n",
    "print \"\\n carrier frequency fc=%.2f MHz \\n\"%(fc*1e-6)\n",
    "fm=wm/(2*pi)##modulating frequency\n",
    "print \" modulating frequency fc=%.2f Hz \\n\"%(fm)\n",
    "#fd_max=maximum frequency deviation\n",
    "fd_max=mf*fm##since mf=fd_max_/fm \n",
    "print \" \\n modulation index mf=%.0f\"%(mf) \n",
    "print \"\\n maximum deviation fd_max=%.2f Hz \\n\"%(fd_max)\n",
    "Vrms=A/sqrt(2)##rms value of the modulating signal\n",
    "R=75##wave resistance\n",
    "P=Vrms**2/R#\n",
    "print \"\\n Power dissipated by the wave in resistance P=%.2f W\"%(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_24 Pg-41.47 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      " modulation index mf=0.333\n",
      "Now we refer from the table-12.2 of Bessel function \n",
      " \n",
      " For modulation index mf=0.333 we take the value of J0,J1,and J2 \n",
      "\n",
      " J0=4.8V\n",
      " J1=0.9V\n",
      " J2=0.1V \n",
      "Now we plot the frequency spectrum\n"
     ]
    },
    {
     "data": {
      "image/png": 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xQJXBV6jvPhURfwdulvTc9LqXA3+oKO6q9b2dyE6u2FHS09L/w5cD11YXeuXy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\nsxHk5G9mNoKc/M3MRtD/Ai/e7pLukjrgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fddec195ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot,title,show,grid,xlabel,ylabel\n",
    "\n",
    "V=5##amplitude of modulating voltage\n",
    "R=1##frequency deviation constant in KHz/V\n",
    "fd=V*R## frequency deviation in kHz\n",
    "fm=15##modulating frequency in kHz\n",
    "mf=fd/fm##modulation index\n",
    "print \" \\n modulation index mf=%.3f\"%(mf)# \n",
    "print \"Now we refer from the table-12.2 of Bessel function \"\n",
    "print \" \\n For modulation index mf=%.3f we take the value of J0,J1,and J2 \"%(mf)# \n",
    "J0=0.96##for carrier frequency\n",
    "J1=0.18##first side frequency\n",
    "J2=0.02##second side frequency\n",
    "A=5#amplitude of the carrier frequency\n",
    "J0=J0*A##for carrier frequency\n",
    "J1=J1*A##first side frequency\n",
    "J2=J2*A##second side frequency\n",
    "print \"\\n J0=%.1fV\\n J1=%.1fV\\n J2=%.1fV \"%(J0,J1,J2)\n",
    "print \"Now we plot the frequency spectrum\"\n",
    "x=[ 89.97,    89.97]##x-coordinate\n",
    "y=[  0   ,    0.1]##y-coordinate\n",
    "plot(x,y)\n",
    "x1=[89.985,   89.985]##x-coordinate\n",
    "y1=[  0   ,   0.9]##y-coordinate\n",
    "plot(x1,y1)\n",
    "x2=[90   , 90]##x-coordinate\n",
    "y2=[ 0  , 4.8]##y-coordinate\n",
    "plot(x2,y2)\n",
    "x3=[90.015, 90.015]##x-coordinate\n",
    "y3=[  0   ,  0.9]##y-coordinate\n",
    "plot(x3,y3)\n",
    "x4=[90.03, 90.03]##x-coordinate\n",
    "y4=[  0   ,  0.1]##y-coordinate\n",
    "plot(x4,y4)\n",
    "x5=[90.04 ,90.04]##x-coordinate\n",
    "y5=[  0   ,  5]##y-coordinate\n",
    "plot(x5,y5)\n",
    "x6=[ 89.96 , 89.96]##x-coordinate\n",
    "y6=[  0     , 5]##y-coordinate\n",
    "plot(x6,y6)\n",
    "xlabel('Frequency(MHz)')#\n",
    "ylabel('amplitude of carrier signal(V)')#\n",
    "title(\"Frequency Spectrum\")\n",
    "grid()\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_25 Pg-41.48"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " For FM broadcast percent modulation is %M=20%\n",
      "\n",
      "\n",
      " For TV broadcast percent modulation is %M=60% \n",
      "\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "fd=15##frequency deviation in kHz \n",
    "f=75##maximum frequency deviation in kHz for FM broadcast\n",
    "per_M=fd/f*100#\n",
    "print \"\\n For FM broadcast percent modulation is %%M=%.0f%%\\n\"%(per_M)\n",
    "f=25##maximum frequency deviation in kHz for TV broadcast\n",
    "per_M=fd/f*100#\n",
    "print \"\\n For TV broadcast percent modulation is %%M=%.0f%% \\n\"%(per_M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_26 Pg-41.48"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Therefore frequency deviation for FM broadcast fd=60 Khz \n",
      "\n",
      " carrier swing=120 kHz\n",
      "\n",
      "\n",
      " Therefore frequency deviation for TV broadcast fd=20 Khz \n",
      "\n",
      " carrier swing=40 kHz\n",
      "\n"
     ]
    }
   ],
   "source": [
    "per_M=80## percent modulation in %\n",
    "f=75##maximum frequency deviation in kHz for FM broadcast\n",
    "fd=f*per_M/100##frequency deviation in kHz since %M=fd/f*100#\n",
    "print \"\\n Therefore frequency deviation for FM broadcast fd=%.0f Khz \\n\"%(fd)\n",
    "cs=2*fd##carrier swing\n",
    "print \" carrier swing=%.0f kHz\\n\"%(cs)\n",
    "f=25##maximum frequency deviation in kHz for TV broadcast\n",
    "fd=f*per_M/100##frequency deviation in kHz since %M=fd/f*100#\n",
    "print \"\\n Therefore frequency deviation for TV broadcast fd=%.0f Khz \\n\"%(fd)\n",
    "cs=2*fd##carrier swing\n",
    "print \" carrier swing=%.0f kHz\\n\"%(cs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_27 Pg-41.51"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " carrier swing=80 kHz\n",
      "\n",
      "\n",
      " Therefore highest frequency reached fh=93.24 MHz\n",
      " \n",
      "Lowest frequency reached fl=93.16 MHz\n",
      "\n",
      "\n",
      " modulation index m=8 \n"
     ]
    }
   ],
   "source": [
    "fd=40##frequency deviation in kHz \n",
    "cs=2*fd##carrier swing\n",
    "print \"\\n carrier swing=%.0f kHz\\n\"%(cs)\n",
    "fc=93.2e3###carrier frequency in kHz\n",
    "fh=fc+fd##highest frequency reached\n",
    "fl=fc-fd##lowest frequency reached\n",
    "print \"\\n Therefore highest frequency reached fh=%.2f MHz\\n \"%(fh*1e-3)\n",
    "print \"Lowest frequency reached fl=%.2f MHz\"%(fl*1e-3)\n",
    "fm=5##modulating frequency in kHz\n",
    "m=fd/fm##frequency modulation\n",
    "print \"\\n\\n modulation index m=%.0f \"%(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_28 Pg-41.51"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Therefore frequency deviation produced fd=5 Khz \n",
      "\n",
      "\n",
      " carrier swing=10 kHz\n",
      "\n",
      "\n",
      " Therefore lowest frequency reached fl=50.395 MHz\n"
     ]
    }
   ],
   "source": [
    "fc=50.4e3###carrier frequency in kHz\n",
    "fh=50.405e3#highest frequency reached in kHz\n",
    "fd=fh-fc##frequency deviation in kHz \n",
    "print \"\\n Therefore frequency deviation produced fd=%.0f Khz \\n\"%(fd)\n",
    "cs=2*fd##carrier swing\n",
    "print \"\\n carrier swing=%.0f kHz\\n\"%(cs)\n",
    "fl=fc-fd##lowest frequency reached\n",
    "print \"\\n Therefore lowest frequency reached fl=%.3f MHz\"%(fl*1e-3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_29 Pg-41.52"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "    Modulation index m=5 \n"
     ]
    }
   ],
   "source": [
    "cs=70##carrier swing in kHz\n",
    "#since cs=2*fd\n",
    "fd=cs/2##frequency deviation in kHz  \n",
    "fm=7#modulating frequency in kHz\n",
    "m=fd/fm#\n",
    "print \"\\n    Modulation index m=%.0f \"%(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex 12_30 Pg-41.52"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Carrier swing=24 kHz\n",
      "\n",
      "\n",
      " Therefore frequency deviation fd=12 Khz \n",
      "\n",
      "\n",
      " Therefore carrier frequency fc=99.035 Mhz \n",
      "\n",
      "\n",
      " Modulation index m=1.714 \n"
     ]
    }
   ],
   "source": [
    "fh=99.047e3##highest frequency reached in kHz\n",
    "fl=99.023e3##lowest frequency reached in kHz\n",
    "fm=7#modulating frequency in kHz\n",
    "cs=fh-fl##carrier swing\n",
    "print \"Carrier swing=%.0f kHz\\n\"%(cs)\n",
    "fd=cs/2##frequency deviation in kHz  \n",
    "print \"\\n Therefore frequency deviation fd=%.0f Khz \\n\"%(fd)\n",
    "fc=fh-fd###carrier frequency in kHz\n",
    "print \"\\n Therefore carrier frequency fc=%.3f Mhz \\n\"%(fc*1e-3)\n",
    "m=fd/fm#\n",
    "print \"\\n Modulation index m=%.3f \"%(m)"
   ]
  }
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