In this paper, we present a method for extrapolating a truncated spectrum with the objective of obtaining a causal impulse response. The method is based on solving a set of equations that relates a truncated (known) spectrum with its unknown part. These equations are obtained from a matrix formulation of the Hilbert transform integrals in the Z-domain, which guaranties causality. Finally, the efficiency of the method was tested in two cases of interest for the electromagnetic compatibility community.