s2 - c Does the pulse in b have a wider or a narrower...

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Cmpen/EE 362 Asst. 2 Solution Spring 2011 Problem 1 . a) Text, problem 2.22. 4 (Fig. 2-25) or 5 (Fig. 2-23) edition. b) Also answer the bps for th th the 64-QAM system. Modem constellation has points, (1,1), (1,-1),(-1,1).(-1,-1) At 1200 symbols per second, how many bits per second can modem achieve? Solution. a) 2 bits per pulse, so 2*1200 = 2400 bits/second. b) 2 = 64, so 6 bits per pulse, so 7200 bits/second. 6 Problem 2. The Fourier Transform relates a signal’s time shape to its frequency content. The Fourier relation Time function Fourier transform is called the scale change property. a) Draw a triangle pulse, called p(t), versus t, that extends in time from t = -1 to t = 1 and peaks with magnitude 1 at t=0. b) Draw the triangular pulse p(3t) versus t, showing key magnitude and time parameters.
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Unformatted text preview: c) Does the pulse in b) have a wider or a narrower bandwidth than the pulse in a)? Solution. a) Use ë for t. A function p( ) defines its value in terms of what is in the parentheses. b) The function p(3t) falls to zero when 3t = ±1, t = ±1/3 c) The pulse in b) is 1/3 as wide, and requires 3 times the bandwidth. Problem 3 The theoretical channel capacity C relating to bandwidth H, signal power S, and noise power density N /2 is Suppose that at H = 2 megaherz the capacity is 4 megabits/second. If the bandwidth is doubled with no change in S and N , what is the new capacity? Aid for calculating base 2: Solution....
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