hw3_sol_501_Au2011

# hw3_sol_501_Au2011 - ECE-501 Introduction to Analog and...

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ECE-501 Introduction to Analog and Digital Communications Autumn 2011 Homework #3 Oct. 17, 2011 HOMEWORK SOLUTIONS #3 1. The code and plots for the coherent QAM experiment appear below. % generate message Ts = 1/1000; t_max = 1.0; t = 0:Ts:t_max; W = 25; to = 50e-3; h = fir2(2*to/Ts,[0,0.25*W*2*Ts,W*2*Ts,1],[1,1,0,0])/Ts; mI = filter(h,1,randn(1,t_max/Ts+1))*Ts; mQ = filter(h,1,randn(1,t_max/Ts+1))*Ts; % QAM modulate without pilot fc = 200; s = mI.*cos(2*pi*fc*t) - mQ.*sin(2*pi*fc*t); % QAM demodulate coherently Bp = W; Bs = 2*fc-W; to = 10e-3; b = fir2(2*to/Ts,[0,Bp*2*Ts,Bs*2*Ts,1],[1,1,0,0])/Ts; po = pi/2; vI = filter(b,1, s.*cos(2*pi*fc*t+po)*2 )*Ts; vQ = filter(b,1, -s.*sin(2*pi*fc*t+po)*2 )*Ts; % plot results figure(1) plottf(s,Ts); title(QAM) figure(2) subplot(211); plottf(vI,Ts,t); hold on; hh = plottf(mI,Ts,t); hold off; set(hh,LineStyle,--,Color,Red); title(recovered I signal) subplot(212); plottf(vQ,Ts,t); hold on; hh = plottf(mQ,Ts,t); hold off; set(hh,LineStyle,--,Color,Red); title(recovered Q signal) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 time [sec] amplitude QAM -500 -400 -300 -200 -100 0 100 200 300 400 500 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 frequency [Hz] magnitude 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.6 -0.4 -0.2 0 0.2 time [sec] recovered I signal 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 time [sec] recovered Q signal (a) The transmitted signal is a bandpass signal centered at f c = 200 Hz and approximate band- width 2 W = 50 Hz. As expected, the passband spectrum is not symmetric around its center (as is the case with AM). (b) The recovered signals looks just like the original messages, but delayed by 10 ms (i.e., t o , the group delay of the receiver LPFs). (c) With a carrier phase o±set of π/ 2 radians, the recovered signals no longer look like like the corresponding messages. Instead, it can be seen that v I ( t ) = m Q ( t ) and v Q ( t ) = - m I ( t ): ECE501, Au2011 1

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.4 -0.2 0 0.2 0.4 time [sec] amplitude recovered I signal 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 time [sec] recovered Q signal 2. The code and plots for the Complex-Baseband QAM experiment appear below. % generate messages
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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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hw3_sol_501_Au2011 - ECE-501 Introduction to Analog and...

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