S&S Midterm Quiz 1112-1 (Q).pdf

# S&S Midterm Quiz 1112-1 (Q).pdf

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Page 1 of 2 EE2023 Signals & Systems Quiz Semester 1 AY2011/12 Date: 6 October 2011 Time Allowed: 1.5 hours Q.1 Consider the periodic signal ( ) x t given by the expression ( ) ( ) ( ) 3 2 2 3 2 2 3 5 3 2 2 j t j t j t j t x t j e je je j e = + + + + (a) What is the fundamental period and fundamental frequency of ( ) x t ? (b) Sketch the amplitude and phase spectra of ( ) x t . (c) Is ( ) x t a real signal ? Justify your answer. (d) What is the power of ( ) x t ? Q.2 Derive the Fourier transform of the signal ( ) x t shown in Figure Q2-1. Derive the Fourier transform of the periodic signal ( ) y t shown in Figure Q2-2. Q.3 A signal is modeled by ( ) ( ) ( ) 2rect rect 2 2 t t x t = where denotes convolution. Determine the spectrum, ( ) X f , of ( )

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