fall2003exam2

fall2003exam2 - Department of Electrical and Computer...

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Department of Electrical and Computer Engineering University of Maryland College Park, Maryland ENEE 322 A. Tits Signal and System Theory November 18, 2003 Second Mid-Term Examination Please make sure you answer all the questions. Question 1 (4 pts): Consider a continuous-time stable LTI system S with frequency response given by H F ( ω ) = n 1 if | ω | < 5 0 otherwise . When the input to this system is a periodic signal x with fundamental period T = π and Fourier series coe±cients a k it is found that the output y is identical to x . For what values of k is it guaranteed that a k = 0? Explain. Question 2 (11 pts): Consider a continuous-time LTI system whose input x and output y are related via the di²erential equation y ( t ) + 5 ˙ y ( t ) + 2 y ( t ) = a ˙ x ( t ) + bx ( t ) , where a and b are to be determined (see below). (a) (2 pt) How many di²erent LTI systems satisfy this input/output relationship (for given a and b )? Explain. One of these systems is stable. Is it causal? Explain.
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