The aim of this paper is to clarify the effect replicated sources in two-dimensional radiation problems. In fact, it will be shown that the discrete pressure computed by using the angular spectrum approach is equal to the analytical pressure plus error terms arising from the convolutions of replicated spectra of the original spectrum and the Green’s function. A similar result is obtained for the far-field discrete pressure. For the later case, it will be shown that errors can be eliminated by choosing a sampling step smaller to that given by the Nyquist criterion.