{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 3 Detection & Estimation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example3.1 page 120" ] }, { "cell_type": "code", "execution_count": 40, "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, ones, sqrt\n", "%matplotlib inline\n", "from matplotlib.pyplot import plot, subplot, xlabel,ylabel,title, show\n", "\n", "#using Gram-Schmidt orthogonalization procedure\n", "T = 1#\n", "t1 = arange(0,0.01+T/3,0.01)\n", "t2 = arange(0,0.01+2*T/3,0.01)\n", "t3 = arange(T/3,0.01+T,0.01)\n", "t4 = arange(0,0.01+T,0.01)\n", "s1t = [0]+[x for x in ones(len(t1)-2)]+[0]\n", "s2t = [0]+[x for x in ones(len(t2)-2)]+[0]\n", "s3t = [0]+[x for x in ones(len(t3)-2)]+[0]\n", "s4t = [0]+[x for x in ones(len(t4)-2)]+[0]\n", "t5 = arange(0,0.01+T/3,0.01)\n", "phi1t = [sqrt(3/T)*x for x in [0]+[x for x in ones(len(t5)-2)]+[0]]\n", "t6 =arange(T/3,0.01+2*T/3,0.01)\n", "phi2t = [sqrt(3/T)*x for x in [0]+[x for x in ones(len(t6)-2)]+[0]]\n", "t7 = arange(2*T/3,0.01+T,0.01)\n", "phi3t = [sqrt(3/T)*x for x in [0]+[x for x in ones(len(t7)-2)]+[0]]\n", "\n", "#figure\n", "title('Figure3.4(a) Set of signals to be orthonormalized')\n", "subplot(4,1,1)\n", "plot(t1,s1t)\n", "xlabel('t')\n", "ylabel('s1(t)')\n", "subplot(4,1,2)\n", "plot(t2,s2t)\n", "xlabel('t')\n", "ylabel('s2(t)')\n", "subplot(4,1,3)\n", "plot(t3,s3t)\n", "xlabel('t')\n", "ylabel('s3(t)')\n", "subplot(4,1,4)\n", "plot(t4,s4t)\n", "xlabel('t')\n", "ylabel('s4(t)')\n", "show()\n", "\n", "\n", "#figure\n", "title('Figure3.4(b) The resulting set of orthonormal functions')\n", "subplot(3,1,1)\n", "plot(t5,phi1t)\n", "xlabel('t')\n", "ylabel('phi1(t)')\n", "subplot(3,1,2)\n", "plot(t6,phi2t)\n", "xlabel('t')\n", "ylabel('phi2(t)')\n", "subplot(3,1,3)\n", "plot(t7,phi3t)\n", "xlabel('t')\n", "ylabel('phi3(t)')\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example3.2 page 121" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Figure 3.8 (b).Representation of transmitted dibits\n", "Loc. of meg.point| (-3/2)asqrt(T)|(-1/2)asqrt(T)|(3/2)asqrt(T)|(1/2)asqrt(T)\n", "________________________________________________________________________________\n", "Transmitted dibit| 00 | 01 | 11 | 10\n", "\n", "\n", "Figure 3.8 (c). Decision intervals for received dibits\n", "Received dibit | 00 | 01 | 11 | 10\n", "________________________________________________________________________________\n", "Interval on phi1(t)| x1 < -a.sqrt(T) |-a.sqrt(T)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from __future__ import division\n", "from numpy import sqrt,arange,random,sin,pi,zeros,multiply\n", "%matplotlib inline\n", "from matplotlib.pyplot import plot,subplot,xlabel,ylabel,title,show,grid\n", "\n", "#Signal constellation and Representation of dibits\n", "a =1# #amplitude =1\n", "T =1# #Symbol duration in seconds\n", "#Four message points\n", "Si1 = [(-3/2)*a*sqrt(T),(-1/2)*a*sqrt(T),(3/2)*a*sqrt(T),(1/2)*a*sqrt(T)]\n", "plot(Si1,[0,0,0,0])\n", "xlabel('phi1(t)')\n", "title('Figure 3.8 (a) Signal constellation')\n", "grid()\n", "show()\n", "print 'Figure 3.8 (b).Representation of transmitted dibits'\n", "print 'Loc. of meg.point| (-3/2)asqrt(T)|(-1/2)asqrt(T)|(3/2)asqrt(T)|(1/2)asqrt(T)'\n", "print '________________________________________________________________________________'\n", "print 'Transmitted dibit| 00 | 01 | 11 | 10'\n", "print ''\n", "print ''\n", "print 'Figure 3.8 (c). Decision intervals for received dibits'\n", "print 'Received dibit | 00 | 01 | 11 | 10'\n", "print '________________________________________________________________________________'\n", "print 'Interval on phi1(t)| x1 < -a.sqrt(T) |-a.sqrt(T)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from __future__ import division\n", "from numpy import arange,sqrt,cos,pi,convolve\n", "%matplotlib inline\n", "from matplotlib.pyplot import plot,subplot,title,show\n", "\n", "\n", "fc =4# #carrier frequency in Hz\n", "T =1#\n", "t1 = arange(0,0.01+T,0.01)\n", "phit = [sqrt(2/T)*xx for xx in cos(2*pi*fc*t1)]\n", "hopt = phit#\n", "\n", "phiot = convolve(phit,hopt)#\n", "phiot = [yy/max(phiot) for yy in phiot]\n", "\n", "t2 = arange(0,0.01+2*T,0.01)\n", "subplot(2,1,1)\n", "plot(t1,phit)#\n", "title('Figure 3.13 (a) RF pulse input')\n", "subplot(2,1,2)\n", "plot(t2,phiot)#\n", "title('Figure 3.13 (b) Matched Filter output')\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example3.4 page 124" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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AJeEm/Pdf6NkTPvggakkcx/zzNWvCNdfYhGzVqlFL5CRCutMlNAG6q2qL4H0X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\n6tvAr0CuZbiFQg2s20uxieR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raITyICKCPS2nqmqfKGXJRVW7qmodVd0Tm2z8\nTFXbRyzTfOBPEdk72NQcmBKhSLlMB5qIyHbBd9kcm9TOBoYClwT/XwJEbkgEKcpvA85Q1TVRy6Oq\nk1W1hqruGdzvc7DJ9qgfjO8BJwAE93wFVf0nWpEAmCEixwX/n4BNsueNqkb2wvLc/wzMALpEKUsg\nz/+3d8coCENBFEVvY624EREsBS3dhi7CpbgBC3tLsbcQMWIpuA+tLOYLYmEnPzD3QCohPMLPS8gk\nOCaeizfAuWyz2rk+8k2Abe0cJcsAOAIX4q6nWztTybUkLjxXYhDaqZBhQ8wMnsRcag70gX05IXdA\nr3KmBXAj3nh5r/VVpUyP93H6+v0O9GtnAjrAuqypEzBtyZoaETPFBjgAw1/78KMqSUqgFX84Lkn6\nL8tekhKw7CUpActekhKw7CUpActekhKw7CUpActekhJ4AYYH4nN9SeHqAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from __future__ import division\n", "from numpy import random,convolve\n", "%matplotlib inline\n", "from matplotlib.pyplot import plot,subplot,title,show\n", "\n", "\n", "phit = [0.1*xx for xx in random.uniform(0,1,10)]\n", "hopt = phit\n", "phi0t = convolve(phit,hopt)\n", "phi0t = [yy/max(phi0t) for yy in phi0t]\n", "subplot(2,1,1)\n", "plot(range(0,len(phit)),phit)\n", "title('Figure 3.16 (a) Noise Like input signal')\n", "subplot(2,1,2)\n", "plot(range(0,len(phi0t)),phi0t)\n", "title('Figure 3.16 (b) Matched Filter output')\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example3.6 page 127" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Predictor-error variance 0.64\n", "1 Predictor input variance 1\n", "The predictor-error variance is less than the variance of the predictor input\n" ] } ], "source": [ "from __future__ import division\n", "\n", "Rxx = [0.6, 1, 0.6]\n", "h01 = Rxx[2]/Rxx[1]# #Rxx(2) = Rxx(0), Rxx(3) = Rxx(1)\n", "sigma_E = Rxx[1] - h01*Rxx[2]\n", "sigma_X = Rxx[1]\n", "print 'Predictor-error variance',sigma_E\n", "print sigma_X,'Predictor input variance',sigma_X\n", "if(sigma_X > sigma_E):\n", " print 'The predictor-error variance is less than the variance of the predictor input'\n" ] } ], "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 }