GATE EE 2024 Set 1 — Question 16
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Signals & Systems → Laplace & Z Transforms → Laplace Transform & ROC
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Question
If is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal is
Correct answer
(A) -∞ < Re(s) < ∞
Solution
The signal is a finite-duration signal, as it is non-zero only for the interval . For any finite-duration signal that is absolutely integrable, the region of convergence (ROC) of its Laplace transform is the entire -plane. Since is a continuous and bounded function on the closed interval , the signal is absolutely integrable: Therefore, the ROC is .
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