Question

For the signal given below, the region of convergence is ____________

(a) ω1 < ω < ω2 in s-plane

(b) Entire s-plane

(c) Imaginary axis

(d) Entire s-plane except imaginary axis

This question was addressed to me in final exam.

My question is based upon Characterization and Nature of Systems topic in section Laplace Transform and System Design of Signals and Systems

Answer 1

Correct choice is (b) Entire s-plane

Explanation: We know that, if x (t) is of finite duration and is absolutely integrable, then the region of convergence is the entire s-plane. Here since x (t) is of finite duration and is also integrable in the given range, so the ROC is the entire s-plane.