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   "source": [
    "# Chapter 12 : Digital Modulation and Modems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1 : pg 407"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a)The theoretical max data rate is 50.278 kb/s\n",
      "b)The data rate for 4 states is 40.0 kb/s\n"
     ]
    }
   ],
   "source": [
    " \n",
    "# page no 407\n",
    "# prob no 12_1\n",
    "#calculate the data rate and theoretical max\n",
    "#A radio channel with BW=10KHz and SNR=15 dB\n",
    "from math import log\n",
    "#given\n",
    "B=10.*10**3;\n",
    "snr=15.;\n",
    "#calculations and results\n",
    "#converting dB in power ratio\n",
    "SNR=10**(snr/10);\n",
    "#a)Determination of theoretical max data rate\n",
    "C1=B*log(1+SNR) /log(2);\n",
    "print 'a)The theoretical max data rate is',round(C1/1000,3),'kb/s'\n",
    "#b)Determination of data rate with 4 states i.e M=4\n",
    "M=4.;\n",
    "C2=2*B*log(M) / log(2);\n",
    "print 'b)The data rate for 4 states is',C2/1000,'kb/s'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2 : pg 408"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The baud rate is  10.0 kbaud\n",
      "The bit rate is  60.0 kb/s\n"
     ]
    }
   ],
   "source": [
    " \n",
    "# page no 408\n",
    "# prob no 12_2\n",
    "#calculate the baud and bit rates\n",
    "from math import log\n",
    "#A modulator transmit symbol with symbol rate=10k/sec with 64 states\n",
    "#given\n",
    "M=64.;\n",
    "S=10000.;\n",
    "#calculations and results\n",
    "#Baud rate is simply symbol rate\n",
    "print 'The baud rate is ',S/1000,'kbaud'\n",
    "#Determination of bit rate\n",
    "C=S*log(64) / log(2);\n",
    "print 'The bit rate is ',C/1000,'kb/s'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 3 : pg 411"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a)The frequency shift is 135416.5 Hz\n",
      "b)The maximum frequency is 880067708.25 Hz\n",
      "The minimum frequency is 879932291.75 Hz\n",
      "The bandwidth efficiency in b/s/Hz is 1.354 b/s/Hz\n"
     ]
    }
   ],
   "source": [
    " \n",
    "# page no 411\n",
    "# prob no 12_3\n",
    "#calculate the frequency shift, max, min frequency\n",
    "#given\n",
    "f=200.*10**3;\n",
    "fb=270.833 *10**3;\n",
    "data_rate=270.833 *10**3\n",
    "fc=880*10**6;\n",
    "bandwidth=200*10**3;\n",
    "#calculations and results\n",
    "freq_shift=0.5*fb;\n",
    "print 'a)The frequency shift is',freq_shift,'Hz'\n",
    "# The shift each way from the carrier frequency is half the freq_shift\n",
    "f_max=fc+0.25*fb;\n",
    "print 'b)The maximum frequency is',round(f_max,3),'Hz'\n",
    "f_min=fc-0.25*fb;\n",
    "print 'The minimum frequency is',round(f_min,3),'Hz'\n",
    "bandwidth_efficiency=data_rate/bandwidth;\n",
    "print 'The bandwidth efficiency in b/s/Hz is',round(bandwidth_efficiency,3),'b/s/Hz'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 4 : pg 412"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The channel data rate is 48.6 kb/s\n"
     ]
    }
   ],
   "source": [
    " \n",
    "# page no 412\n",
    "# prob no 12_4\n",
    "#calculate the channel data rate\n",
    "#given\n",
    "baud_rate=24.3;# in kilobaud\n",
    "#calculations\n",
    "# In this problem dibit system is used.\n",
    "#Therefore symbol_rate=baud_rate=0.5*bit_rate\n",
    "bit_rate=2*baud_rate;\n",
    "#results\n",
    "print 'The channel data rate is',bit_rate,'kb/s'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 5 : pg 413"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The no. of bits per symbol is 6.0\n"
     ]
    }
   ],
   "source": [
    " \n",
    "# page no 413\n",
    "# prob no 12_5\n",
    "#calculate the no. of bits per symbol\n",
    "from math import log\n",
    "#given\n",
    "no_of_phase_angles=16;\n",
    "no_of_amplitudes=4;\n",
    "#calculations\n",
    "no_of_states_per_symbol=no_of_phase_angles*no_of_amplitudes;\n",
    "bit_per_symbol=log(no_of_states_per_symbol)/ log(2);\n",
    "#results\n",
    "print 'The no. of bits per symbol is',bit_per_symbol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 6 : pg 415"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shannon limit 29901.68 b/s\n"
     ]
    }
   ],
   "source": [
    " \n",
    "# page no 415\n",
    "# prob no 12_6\n",
    "#calculate the shannon limit\n",
    "from math import log\n",
    "#given\n",
    "B=3.*10**3;SNR_dB=30.;\n",
    "#calculations\n",
    "SNR_power=10**(30./10);\n",
    "C=B*log(1+SNR_power)/ log(2);\n",
    "print 'Shannon limit',round(C,2),'b/s'"
   ]
  }
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