S&S Midterm Quiz 1112-2 (Q).pdf

# S&S Midterm Quiz 1112-2 (Q).pdf

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Page 1 of 2 EE2023 Signals & Systems Quiz Semester 2 AY2011/12 Date: 8 March 2012 Time Allowed: 1.5 hours Q1. Consider a periodic signal, ( ) x t , modeled by the following equation: ( ) ( ) ( ) 3 2 2 3 2 2 3 5 2 3 2 j t j t j t j t x t je j e j e je = + + + + (a) What is the fundamental frequency of ( ) x t ? (b) By comparing ( ) x t with the Fourier Series expansion equation, ( ) o k k jk t x t c e ω =−∞ = , derive the magnitude, k c , and phase, k c , of the Fourier Series coefficients when k = 0, 1, 2 and 3. (c) An alternative method for evaluating the Fourier Series coefficients, k c , of ( ) x t is ( ) 0 2 1 T k j kt T c x t e dt T π = What is the value of T ? (d) Suppose the Fourier Series coefficients for the signal ( ) ( ) 4sin 3 y t t = is determined using the equation ( ) 0 2 1 T k j kt T c y t e dt T π = , where T is the value determined in part (c). Can the resulting Fourier Series coefficients be used to correctly synthesize ( ) y t via Fourier Series expansion ?

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