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GATE EC 2015 Set 2 — Question 55

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NAT+2 / -0MediumLaplace Transform & ROCLTI SystemsSignals & Systems

Signals & Systems → LTI Systems → Laplace Transform & ROC

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Question

Let x(t)=αs(t)+s(−t)x(t) = \alpha s(t) + s(-t) with s(t)=βe−4tu(t)s(t) = \beta e^{-4t} u(t), where u(t)u(t) is unit step function. If the bilateral Laplace transform of x(t)x(t) isX(s)=16s2−16,−4<Re{s}<4;X(s) = \frac{16}{s^2 - 16}, \quad -4 < \text{Re}\{s\} < 4;then the value of β\beta is _______.
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