GATE EE 2014 Set 2 — Question 20
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Signals & Systems → Laplace & Z Transforms → Impulse Response & Convolution
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Question
Consider an LTI system with impulse response . If the output of the system is then the input, , is given by
Correct answer
(B) 2e^(-3t) u(t)
Solution
The transfer function of the system is the Laplace transform of the impulse response:
The Laplace transform of the output is:
The input in the s-domain is given by:
Taking the inverse Laplace transform to find :
The Laplace transform of the output is:
The input in the s-domain is given by:
Taking the inverse Laplace transform to find :
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