Question

The Laplace transform of the signal u (t+2) is _________

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

(b) \(\frac{-1}{s}\)

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

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

This question was posed to me by my college director while I was bunking the class.

My enquiry is from Common Laplace Transforms topic in section Laplace Transform and System Design of Signals and Systems

Answer 1

The correct option is (a) \(\frac{1}{s}\)

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

Here, the given signal is u (t+2).

Hence, u (t+2) = 1 for all t>-2 and = 0 for all t<-2.

So, limit is from 0 to ∞

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