GATE EC 2015 Set 2 — Question 53
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Electronic Devices → Carrier Transport → Diffusion & Drift Current
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Question
Input and output of an LTI system are related by the differential equation . If the system is neither causal nor stable, the impulse response of the system is
Correct answer
(B) -(1)/(5)e^(3t)u(-t) + (1)/(5)e^(-2t)u(-t)
Solution
Taking the bilateral Laplace transform:Poles are at and . The possible ROCs are (causal, unstable), (non-causal, stable since it contains the axis) and (non-causal, unstable). Neither causal nor stable means ROC , so both terms are left-sided:ThereforeOption A has the wrong sign on the first term. Options C and D contain the right-sided term , i.e. ROC to the right of : D is the stable, non-causal response for , and C has the wrong signs.Answer: (B)
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