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fall2003exam1 - -t u t ∀ t(a(5 pts Compute the output y 1...

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Department of Electrical and Computer Engineering University of Maryland College Park, Maryland ENEE 322 A. Tits Signal and System Theory October 7, 2003 First Mid-Term Examination Please make sure you answer all the questions. Question 1 (7 pts): For a given discrete-time LTI system S it is known that when the input is x [ n ] = δ [ n ]+ δ [ n - 1], the output is y [ n ] = u [ n ]. Determine the following two responses for S , thus establishing that the given data completely specifies S . (a) (4 pts) Determine and plot the unit step response for S , i.e., determine the output signal s [ n ] = y 1 [ n ] that results when the input signal x 1 [ n ] = u [ n ] is applied. (b) (3 pts) Determine and plot the unit impulse response h for S . (If you need the result of (a) to answer (b) but are unable to answer (a), just refer to the unit step response as s [ n ]—and do not plot h —, for partial credit.) Question 2 (8 pts): Consider a continuous-time LTI system S 1 with unit impulse response h 1 ( t ) = exp(
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Unformatted text preview: -t ) u ( t ) ∀ t. (a) (5 pts) Compute the output y 1 obtained when input signal x given by x ( t ) = exp( t ) u ( t ) ∀ t is applied to S 1 . (b) (3 pts) Is S 2 stable? Explain. Also comment on how your answer possibly relates to bounded-ness/unboundedness of the given x and resulting y 2 . Question 3 (2 pts): Obtain and plot the unit pulse response h for the discrete-time LTI system, with the initial rest property, whose input x and output y are related by y [ n ] = x [ n ] + x [ n-2] ∀ n. Question 4 (8 pts): Consider the system whose input x and output y are related by y ( t ) = Z t-∞ x ( τ + 1) dτ ∀ t. Indicate whether (yes or no) the system is (a) linear; (b) time-invariant; (c) causal; (d) (BIBO) stable. Justify all answers. Be precise in your explanations. (An incorrect justification results in no credit for the answer.)...
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