Question

Find the Laplace transform of the signal x(t) = te^-αt.

(a) \(\frac{1}{s^2}\)

(b) \(\frac{1}{(s+α)^2}\)

(c) \(\frac{1}{α}\)

(d) \(\frac{1}{s+α}\)

The question was asked in an online interview.

Query is from Properties of the Laplace Transform topic in division Laplace Transform and System Design of Signals and Systems

Answer 1

Right option is (b) \(\frac{1}{(s+α)^2}\)

For explanation I would say: We know that L{e^-αt} = \(\frac{1}{s+α}\)

Differentiation in s-domain property states that (-t)^n f(t) ↔ \(\frac{d^n F(s)}{ds^n}\)

L{te^-αt} = –\(\frac{d}{ds} [\frac{1}{s+α}] = \frac{1}{(s+α)^2}\).