GATE 2014 EE (EE2) – Question 20

Signals and Systems · Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform · 1 mark · Multiple choice

An LTI system has $h(t)=e^{-5t}u(t)$ and output $y(t)=e^{-3t}u(t)-e^{-5t}u(t)$. Find input x(t).

$e^{-3t}u(t)$
$2e^{-3t}u(t)$
$e^{-5t}u(t)$
$2e^{-5t}u(t)$

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Correct answer: (B) $2e^{-3t}u(t)$

Explanation

H(s)=1/(s+5),while Y(s)=1/(s+3)−1/(s+5)=2/[(s+3)(s+5)]. Divide to obtain X(s)=2/(s+3). Inverse transformation gives **x(t)=2e^(−3t)u(t),B**. This also follows by convolving two causal decaying exponentials.