Beamforming with Optimal Aliasing Cancellation in Spherical Microphone Arrays

Spherical microphone arrays facilitate three-dimensional processing and analysis of sound fields in applications such as music recording, beamforming and room acoustics. The frequency bandwidth of operation is constrained by the array configuration. At high frequencies, spatial aliasing leads to side-lobes in the array beam pattern, which limits array performance. Previous studies proposed increasing the number of microphones or changing other characteristics of the array configuration to reduce the effect of aliasing. In this paper we present a method to design beamformers that overcome the effect of spatial aliasing by suppressing the undesired side-lobes through signal processing without physically modifying the configuration of the array. This is achieved by modeling the expected aliasing pattern in a maximum-directivity beamformer design, leading to a higher directivity index at frequencies previously considered to be out of the operating bandwidth, thereby extending the microphone array frequency range of operation. Aliasing cancellation is then extended to other beamformers. A simulation example with a 32-element spherical microphone array illustrates the performance of the proposed method. An experimental example validates the theoretical results in practice.