GATE EE 2019 Set 1 — Question 17
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Signals & Systems → LTI Systems → LTI, Causal & Stable Systems
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Question
The symbols, and , represent positive quantities, and is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?
Correct answer
(C) 1 + e^(-at)u(t)
Solution
A causal linear time-invariant (LTI) system must have an impulse response that is zero for all .(A) : Since for , for . This is causal.
(B) : Since for , for . This is causal.
(C) : For , , so . Since for , this system is non-causal.
(D) : Since for , for . This is causal.Therefore, option (C) is the correct answer.
(B) : Since for , for . This is causal.
(C) : For , , so . Since for , this system is non-causal.
(D) : Since for , for . This is causal.Therefore, option (C) is the correct answer.
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