Question

Find the Laplace transform of the following

a) Finite support signals, and indicate their region of convergence:
i) x(t) = δ(t - 1)

Answer 1

The Laplace transform of a finite support signal is given by the formula F(s) = ∫[0 to ∞] f(t)e^(-st) dt. In this case, the signal is x(t) = δ(t - 1), where δ(t) is the Dirac delta function. The Laplace transform of the Dirac delta function is F(s) = e^(-s).

Step-by-step explanation:

The Laplace transform of a finite support signal is given by the formula:

F(s) = ∫[0 to ∞] f(t)e^(-st) dt

In this case, the signal is x(t) = δ(t - 1), where δ(t) is the Dirac delta function. The Laplace transform of the Dirac delta function is F(s) = e^(-s). The region of convergence depends on the value of s. If Re(s) > 0, the Laplace transform converges.