GATE EE 2020 Set 1 — Question 13
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Signals & Systems → Laplace & Z Transforms → Laplace Transform & ROC
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Question
Which of the following statements is true about the two sided Laplace transform?
Correct answer
(B) It has no poles for any bounded signal that is non-zero only inside a finite time interval.
Solution
Statement (B) is true. A signal that is bounded and has a finite duration (non-zero only for ) has a Laplace transform given by:Since the integrand is bounded and the integration interval is finite, this integral converges for all finite values of in the complex plane. Such a function is called an entire function and has no poles in the finite -plane.
(A) is false as some signals have neither transform.
(C) is false as the number of finite poles and zeros depends on the specific transfer function.
(D) is false as exponentials typically introduce poles in the -domain.
(A) is false as some signals have neither transform.
(C) is false as the number of finite poles and zeros depends on the specific transfer function.
(D) is false as exponentials typically introduce poles in the -domain.
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