Question

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

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

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

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

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

The question was asked by my college director while I was bunking the class.

My question comes from Common Laplace Transforms topic in division Laplace Transform and System Design of Signals and Systems

Answer 1

Right option is (a) \(\frac{1}{s+2}\)

Easy explanation: X(s) = \(\int_0^∞ x(t)  e^{-st} \,dt\)

Here, the given signal is u (t+1).

Hence, u (t+1) = 1 for all t>-1 and = 0 for all t<-1.

So, limit is from 0 to ∞

∴ Laplace of signal = \(\int_0^∞ e^{-2t} e^{-st} \,dt  = \frac{1}{s+2}\).