We have used the Fourier transform for the same purpose, but the Laplace transform, whether bilateral or unilateral, is applicable in more cases, for example, to unstable systems or unbounded signals.

Hilbert transforms (HT) and analytic signals. Bilateral Laplace transforms (LT): convergence properties. Contour integration methods applied to FT, HT and LT. Discrete-time Fourier series and Fourier ...