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fall2005exam1

fall2005exam1 - Department of Electrical and Computer...

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Department of Electrical and Computer Engineering University of Maryland ENEE 322 A. Tits Signal and System Theory October 11, 2005 First Mid-Term Examination Please make sure you answer all the questions. Question 1 (5 pts): For each of the statements below, indicate whether it is true or false. Carefully justify your answers. (Without justification, you get no credit for a correct answer.) (a) (1 pt) Suppose the input signal x and output signal y of a system S are related by y ( t ) = exp( x ( t )) for all t . Then S is stable. (b) (1 pt) If a signal is not even, it must be odd. (c) (1 pt) The sum of two periodic signals is always periodic. (d) (2 pts) Consider a system S whose input x and output y obey the differential equation ˙ y ( t ) + y ( t ) = x ( t ) + 1 . If appropriate auxiliary conditions are imposed, S can be linear. Question 2 (10 pts): (a) (6 pts) Consider an LTI system S 1 with unit impulse response h 1 ( t ) = n 1 when | t | ≤ 1 0 otherwise. Determine and plot the output signal y 1 when the input signal x 1 is identical to h 1 , i.e., x 1 ( t ) = n 1 when | t | ≤ 1 0 otherwise. Is S 1 causal? Justify. (b) (4 pts) Repeat part (a) but with an LTI system S 2 whose unit impulse response is
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