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hw5_501_Au2011

# hw5_501_Au2011 - ECE-501 Introduction to Analog and Digital...

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ECE-501 Introduction to Analog and Digital Communications Autumn 2011 Homework #5 Oct. 28, 2011 HOMEWORK ASSIGNMENT #5 Due Fri. Nov. 4, 2011 (in class) Reading: Online lecture notes through page 66; text Ch 6.1-6.7; text Ch. 9.1-9.3 Problems: 1. True or false Let g [ n ] be a pulse shaping filter, q [ n ] be the matched filter for g [ n ], and p [ n ] be the convolution of g [ n ] and q [ n ]. Suppose that p [ n ] is a Nyquist pulse . Finally, let there P = 7 samples per symbol interval. Answer the following as always True or possibly False, and give a very, very brief reason. (a) p [0] = 0 (b) p [0] = 1 (c) p [7] = 0 (d) g [0] = 1 (e) g [7] = 1 2. Eye Diagram: Here you will use the discrete-time baseband model to simulate a real-valued digital communication system and then plot an eye diagram to interpret the outputs. The programs pam.m and srrc.m are available on the course webpage. (a) Using pam , generate a 4-ary PAM symbol sequence with length N = 100 and variance 1. (b) Using srrc , generate { g [ k ] } , a sampled SRRC pulse shape with total time span 4 T , rolloff parameter α = 0 . 5, and oversampling factor P = 16. (c) Implement the discrete-time complex-baseband system below assuming a noiseless and trivial discrete-time channel (i.e., ˜ w [ k ] = 0 and ˜ h [ k ] = δ [ k ]). a [ n ] P a [ k ] g [ k ] ˜ m [ k ] ˜ h [ k ] ˜ w [ k ] ˜ v [ k ] y [ k ] y [ n ] q [ k ] P + Remember than upsampling can be accomplished via a up = zeros(1,P*N); a up(1:P:P*N) = a; and that downsampling can be accomplished via y = y up(1:P:P*N);

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hw5_501_Au2011 - ECE-501 Introduction to Analog and Digital...

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