S&S Midterm Quiz 1213-2 (Q).pdf

S&S Midterm Quiz 1213-2 (Q).pdf

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Page 1 of 2 EE2023 Signals & Systems Midterm Quiz Semester 2 AY2012/13 Date: 7 March 2013 Time Allowed: 1.5 hours Q.1 The signal ( ) x t has an amplitude spectrum given in Figure Q.1 below. (a) What is the minimum sampling frequency that will allow ( ) x t to be recovered from its samples? (b) Suppose that ( ) x t is sampled at a rate of 38 kHz s f = . What part of ( ) X f can be recovered without error from the samples? Explain your answer with an illustration of the appropriate spectrum. (c) Is ( ) x t a power or energy signal? Explain your answer. Q.2 Consider the complex signal ( ) ( ) ( ) sinc sinc = + x t t j t . (a) Find the energy spectral density of ( ) x t . Hence, or otherwise, determine the total energy of ( ) x t . (b) Suppose ( ) ( ) 2 = y t x t . Find the 3dB bandwidth of ( ) y t . Q.3 The complex exponential Fourier Series representation of a periodic signal, ( ) x t , is jkt k k c e =−∞ where the Fourier Series coefficients are 0.1 0.1 0.49 0.1 : 2 1.5 : 1 2 : 0 1.5 : 1 0.49 0.1 : 2 0 : j k j j k j e k
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