20092ee132A_1_hwk4

20092ee132A_1_hwk4 - to the noise power for the following...

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EE132A, Spring 2009 Communication Systems Prof. John Villasenor Handout #9 TA: Pooya Monajemi and Erica Han Homework 4 Assigned: Monday, April 20, 2009 Due: Monday, April 27, 2009 Reading Assignment: Proakis & Salehi, Chapter 8 (8.3), Chapter 9 (9.1, 9.2) 1. P(f) = [sin( 2 π fT )/ 2 π fT ] 2 , for all real f , is the power spectral density function. What is the corresponding autocorrelation function? 2. A communication system transmits binary data at 64kbit/sec. The data are transmitted using PAM with a raised cosine spectrum. Calculate the bandwidth required for transmission for roll off factors 0.3, 0.5, 1.0 in the following cases: (a) Data are transmitted using binary PAM. (b) Data are transmitted using 16-level PAM by grouping each set of 4 consecutive bits into one symbol. 3. Find and sketch the impulse response of the matched filter that maximizes the ratio of the signal power
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Unformatted text preview: to the noise power for the following pulse shapes: (a) ≤ ≤ = otherwise for ) ( T t t t g (b) ≤ ≤ =-otherwise for ) ( T t e t g t (c) ≤ ≤ = otherwise for 2 sin ) ( T t T t t g π For each case, Compute the value of ) ( T p produced by sampling the matched filter output at time T , the output noise power )] ( ˆ [ 2 t n E , and the signal to noise ratio at the output of the matched filter. 4. (a) Show that sinc( t ) is a Nyquist pulse shape for symbol period 1 = s T . (b) Show that sinc 2 ( t ) is a Nyquist pulse shape for symbol period 1 = s T . 5. Problem 7.2 in Proakis and Salehi....
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