{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 5 Waveform Coding Techniques" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example5.1 page 187" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The average transmitted power is:\n", "1.225e-05 W\n" ] } ], "source": [ "from __future__ import division\n", "\n", "sigma_N = 10**-6 #the noise variance\n", "k = 7 # separation constant for on-off signaling\n", "M = 2 # number of discrete amplitude levels for NRZ polar\n", "print 'The average transmitted power is:'\n", "P = (k**2)*(sigma_N)*((M**2)-1)/12#\n", "print P,\"W\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example5.2 page 189" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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XO5SN/J3ZzjnXjEx8eyJfGvol2qn5nJ4LGomk2yQtjo0LZsaNlbRQ0tTYHZmY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\nV7mOkx88mU/Xf8pjxz/WZhK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from __future__ import division\n", "%matplotlib inline\n", "from matplotlib.pyplot import plot,xlabel,ylabel,show,title,subplot\n", "\n", "\n", "from math import log\n", "def log2(x):\n", " return log(x,2)\n", "\n", "\n", "#Channel Capacity theorem\n", "P_NoB_dB = range(-20,30) #Input signal-to-noise ratio P/NoB, decibels\n", "P_NoB = [10**(xx/10) for xx in P_NoB_dB]\n", "k =7# # for M-ary PCM system#\n", "Rb_B = [log2(1+(12/k**2))*yy for yy in P_NoB]##bandwidth efficiency in bits/sec/Hz\n", "C_B = [log2(1+xxx) for xxx in P_NoB]##ideal system according to Shannon's channel capacity theorem\n", "#plot\n", "plot(P_NoB_dB,C_B)\n", "plot(P_NoB_dB,Rb_B)\n", "xlabel('Input signal-to-noise ratio P/NoB, decibels')\n", "ylabel('Bandwidth efficiency, Rb/B, bits per second per hertz')\n", "title('Figure 5.9 Comparison of M-ary PCM with the ideal ssytem')\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example5.3 page 192" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Channel width = 32000.00 Hz\n", "Output Signal to noise ratio = 40.80 dB\n" ] } ], "source": [ "from __future__ import division\n", "\n", "#Channel Bandwidth B\n", "n = 8 # no. of bits used to encode\n", "W = 4000 # the message signal banwidth in Hz\n", "B = n*W#\n", "print 'Channel width = %.2f Hz'%B\n", "SNRo = 6*n - 7.2#\n", "print 'Output Signal to noise ratio = %.2f dB'%SNRo\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 5.5 Page 207" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Maximum output signal-to-nosie = -5.17 dB for Delta Modualtion:\n" ] } ], "source": [ "from __future__ import division\n", "from numpy import pi,log10\n", "\n", "a0 = 1 # The amplitude of sinusoidal signal\n", "f0 = 4000 # the frequency of sinusoidal signal in Hz:\n", "fs = 8000 # the sampling frequency in samples per seconds\n", "Ts = 1/fs##Sampling interval\n", "delta = 2*pi*f0*a0*Ts##Step size to avoid slope overload\n", "Pmax = (a0**2)/2##maximum permissible output power\n", "sigma_Q = (delta**2)/3##Quantization error or noise variance\n", "W = f0##Maximum message bandwidth\n", "N = W*Ts*sigma_Q# #Average output noise power\n", "SNRo = Pmax/N# # Maximum output signal-to-noise ratio\n", "SNRo_dB = 10*log10(SNRo)#\n", "print 'Maximum output signal-to-nosie = %.2f dB for Delta Modualtion:'%SNRo_dB" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 5.13(a) page 215" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from __future__ import division\n", "from numpy import arange,sign\n", "from sympy import log\n", "%matplotlib inline\n", "from matplotlib.pyplot import plot,xlabel,ylabel,show,title,subplot\n", "\n", "#Caption:u-Law companding\n", "#Figure5.13(a)Mulaw companding Nonlinear Quantization\n", "#Plotting mulaw characteristics for different \n", "#Values of mu\n", "\n", "x = arange(0,0.01+1,0.01)# #Normalized input\n", "mu = [0,5,255]##different values of mu\n", "def mulaw(x,mu):\n", " \"\"\"\n", " F(x) = sgn(x) ln(1 + μ|x|) / ln (1 + μ)\n", " -1 <= x <= 1\n", " \"\"\"\n", " f=sign(x)*log(1+mu*abs(x))/log(1+mu)\n", " return f\n", "Cx=[]\n", "\n", "for i in range(0,len(mu)):\n", " Cx.append(mulaw(x[i],mu[i]))\n", " plot(Cx)\n", "title('Compression Law: u-Law companding')\n", "xlabel('Normalized Input |x|')\n", "ylabel('Normalized Output |c(x)|')\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 5.13(b) page 216" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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RiHixyO1vCLwZEVMAJF0P7ARMblHuV8DNuCtws/L33HNw6KHwt7/B0kvnHY2V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\nFSQ9VMQ2pvR2XNa/OTlY3uY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from __future__ import division\n", "from numpy import arange,sign,log\n", "\n", "%matplotlib inline\n", "from matplotlib.pyplot import plot,xlabel,ylabel,show,title,subplot\n", "\n", "#Caption:A-law companding\n", "#Plotting A-law characteristics for different \n", "#Values of A\n", "\n", "x = arange(0,0.01+1,0.01)# #Normalized input\n", "A = [1,2,87.56]##different values of A\n", "\n", "\n", "def Alaw(x,a):\n", " \"\"\"F(x) = sgn(x) A |x| / (1 + lnA) for 0 ≤|x| < 1/A\n", " \n", "= sgn(x) (1+ln A|x|) /(1 + lnA) for 1/A ≤|x| ≤ 1\n", "\"\"\"\n", " if abs(x) >= 0 and abs(x) < 1/a:\n", " f = sign(x)*a*abs(x)/(1+log(a))\n", " elif abs(x) >= 1/a and abs(x) <=1: \n", " f = sign(x)*(1+log(a*abs(x))/(1+log(a)))\n", " else:\n", " f = 'Wrong parameters'\n", " return f\n", "Cx=[]\n", "for i in range(0,len(A)):\n", " #[Cx(i,:),Xmax(i)] = Alaw(x,A(i))#\n", " Cx.append(Alaw(x[i],A[i]))\n", " plot(Cx)\n", " \n", "title('Compression Law: A-Law companding')\n", "xlabel('Normalized Input |x|')\n", "ylabel('Normalized Output |c(x)|')\n", "show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }