hw5_sol_501_Au2011

hw5_sol_501_Au2011 - ECE-501 Introduction to Analog and...

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Introduction to Analog and Digital Communications Autumn 2011 Homework #5 November 4, 2011 HOMEWORK SOLUTIONS #5 1. Nyquist pulses and the root-raised cosine. (a) False; p ( nT ) = δ [ n ] (b) True; p ( nT ) = δ [ n ] (c) True; zero crossings at sampling times (d) False; holds for p ( t ), but not necessary for g ( t ). (e) False. 2. The MATLAB code for 4-PAM transmission, along with a plot of the output signal and the eye diagram, appears below. % design SRRC P = 16; % oversampling factor alpha = 0.5; % SRRC rolloff param D = 2; % truncation to [-DT,DT] g = srrc(D,alpha,P); % SRRC pulse Ng = length(g); % pulse length % generate symbols N = 100; % # symbols M = 4; % alphabet size sig2a = 1; % symbol variance a = pam(N,M,sig2a); % symbol sequence % pulse-amplitude modulate a_up = zeros(1,N*P); a_up(1:P:end) = a; % upsampled symbols m = conv(a_up,g); % PAM % matched-filter demodulate y_up = conv(m,g); % use SRRC again % remove causal filtering delay dly = (Ng-1)/2+(Ng-1)/2;% delay due to pulses y_up = y_up([1:P*N]+dly);% remove delay y = y_up(1:P:P*N); % downsample % plot received signal figure(1) plot([0:P*N-1]/P,y_up,’r’,[0:N-1],y,’.’); axis(’tight’) title([’SRRC (\alpha=’,num2str(alpha),. .. ’) truncated to \pm’,num2str(D),’T’]) xlabel([’symbol index’]) % plot eye diagram figure(2) Y_up = reshape(y_up(P/2+[1:P*(N-1)]),P,N-1); % extract N-1 segments plot([0:P-1]/P-1/2,Y_up) % superimpose segments title([’SRRC (\alpha=’,num2str(alpha),. .. ’) truncated to \pm’,num2str(D),’T’]) xlabel([’relative symbol index’]) 0 10 20 30 40 50 60 70 80 90 -1.5 -1 -0.5 0 0.5 1 1.5 SRRC ( α =0.5) truncated to ± 2T symbol index -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 SRRC ( α =0.5) truncated to ± 2T relative symbol index In the plots above, where α = 0 . 5, it can be seen that the recovered symbols y [ m ] match the transmitted symbols a [ m ] closely (though not perfectly); the eye is seen to be “open.” The plots on the next page show that the eye is nearly closed when α = 0 . 25, while there is a near-perfect
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This note was uploaded on 11/11/2011 for the course ECE 501 taught by Professor Schniter,p during the Fall '08 term at Ohio State.

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hw5_sol_501_Au2011 - ECE-501 Introduction to Analog and...

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