S&S Midterm Quiz 1314-1 (Q).pdf

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Page 1 of 2 EE2023 Signals & Systems Midterm Quiz Semester 1 AY2012/13 Date: 4 October 2012 Time Allowed: 1.5 hours Q.1 A signal ( ) x t has a spectrum shown in Figure Q.1 below. You may assume that only signals with frequencies below 3 Hz are important. (a) Without using any anti-aliasing filter, design a sampling frequency to sample ( ) x t such that the sampled signal has no frequency aliasing effects. (b) What is the lowest sampling frequency which can be used to sample ( ) x t in such a way that there is no distortion to the important frequency components? Show how you arrive at your choice of the sampling frequency. (c) If ( ) x t is sampled at 6 Hz, can the important part of ( ) x t be reconstructed from the sampled signal? Justify your answer. (d) Suppose another signal ( ) ( ) ( ) cos 20 y t x t t π = is sampled at 20Hz. Sketch the spectrum of the sampled ( ) y t . Q.2 Let ( ) ( ) 2 1 sinc 2 = x t t π . (a) Determine the phase spectrum and energy spectral density of ( ) x t . Draw a labeled sketch for each.
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