The angular spectrum method (ASM) is an effective tool for propagating wave fields between parallel planes through decomposition of the field into a series of independent plane waves. One source of error is interference from mirror sources introduced through the inherent periodicity of the fast Fourier transform (FFT) used to implement this method numerically. Here, spatial filters attenuate waves propagating at large angles, which are sensitive to mirror sources. Simulations show that this suppresses the ripple artifact whilst preserving the accuracy of the ASM-computed fields. To achieve comparable performance without filtering requires up to a 13.5-fold increase in computation time.