S&S Midterm Quiz 1213-1 (Q).pdf

# S&S Midterm Quiz 1213-1 (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) Determine the appropriate sampling frequency for the signal ( ) x t given by: ( ) ( ) ( ) ( ) 2sin 2 sin 10 6cos 6 x t t t t π π π = + , in order to be completely recoverable from its samples. (b) If ( ) x t above is sampled at 20 rad s π , sketch the amplitude spectrum of the sampled signal. Can ( ) x t be recovered from the samples? Explain your answer. (c) Is ( ) x t a power or energy signal? Explain your answer. Q.2 Let ( ) ( ) ( ) 0 sgn sin 2 x t t f t π = and ( ) ( ) 0 sinc y t f t = where ( ) { 1; 0 sgn 1; 0 t t t + = < and 0 f is a non-zero positive constant. (a) Find the Fourier transforms of ( ) x t and ( ) y t . Your final answers should not contain any unsolved integrals and/or the convolution operator ‘ ’. (b) With ( ) x t and ( ) y t , we form the signal ( ) ( ) ( ) z t x y t d ς ς ς −∞ = . If ( ) z t is an energy signal, find its energy spectral density. If ( ) z t is a power signal, find its power spectral density.

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