GATE EC 2015 Set 2 — Question 27
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Signals & Systems → LTI Systems → Laplace Transform & ROC
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Question
Let the signal outside the interval , where and are finite. Furthermore, . The region of convergence (RoC) of the signal's bilateral Laplace transform is
Correct answer
(C) the entire s-plane
Solution
The bilateral Laplace transform is defined as .
Given that is a finite-duration signal ( for and ) and is bounded (), the integral becomes:For any finite value of , the term is finite over the finite interval . Since is also bounded, the integral converges for all finite values of .
Therefore, the Region of Convergence (RoC) for a finite-duration, bounded signal is the entire -plane.Correct option is C.
Given that is a finite-duration signal ( for and ) and is bounded (), the integral becomes:For any finite value of , the term is finite over the finite interval . Since is also bounded, the integral converges for all finite values of .
Therefore, the Region of Convergence (RoC) for a finite-duration, bounded signal is the entire -plane.Correct option is C.
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