Question

The necessary condition for convergence of the Laplace transform is the absolute integrability of f(t)e^-σt.

(a) True

(b) False

I have been asked this question in unit test.

My enquiry is from The Laplace Transform in division Laplace Transform and System Design of Signals and Systems

Answer 1

Right answer is (a) True

The explanation: The necessary condition for convergence of the Laplace transform is the absolute integrability of f(t)e^-σt.Mathematically, this can be stated as

\(\int_{-∞}^∞|f(t) e^{-σt}|\)dt<∞

Laplace transform exists only for signals which satisfy the above equation in the given region.