Question

The Laplace transform of the signal u(t-1) * e^-2t u(t-1) is ___________

(a) \(\frac{e^{-2(s+1)}}{2s+1}\)

(b) \(\frac{e^{-2(s+1)}}{s+1}\)

(c) \(\frac{e^{-(s+2)}}{s+2}\)

(d) \(\frac{e^{-2(s+1)}}{s+2}\)

This question was posed to me during an online interview.

I want to ask this question from Common Laplace Transforms topic in section Laplace Transform and System Design of Signals and Systems

Answer 1

Correct option is (d) \(\frac{e^{-2(s+1)}}{s+2}\)

The best explanation: p (t) = u (t)

Laplace transform of p (t), p(s) = \(\frac{1}{s}\)

Again, q (t) = u (t-1)

Laplace transform of q (t), q(s) = \(\frac{e^{-s}}{s^2} \)

Again, r (t) = e^-2t u (t)

Laplace transform of r (t), r(s) = \(\frac{1}{s+2}\)

Again, v (t) = e^-2t u (t-1)

Laplace transform of v (t), v(s) = \(\frac{e^{-(s+2)}}{s^2}\)

Again, x (t) = q (t) * v (t)

Laplace transform of x (t), x(s) = \(\frac{e^{-2(s+1)}}{s+2}\).