Maximum directivity beamformer for spherical-aperture microphones

Spherical microphone arrays have been recently studied for sound analysis and beamforming. These arrays have the advantage of spherical symmetry facilitating three-dimensional analysis. Performance of microphone arrays at the high-frequency range is typically limited by aliasing, which is a result of the spatial sampling process. A potential approach to avoid spatial aliasing is by using continuous sensors, in which spatial sampling is not required. This paper presents an optimal beamforming technique for the spherical-aperture microphone, which is based on a continuous sensor. The proposed beamforming technique is used to compute the optimal real-valued aperture weighting function. Real-valued aperture weighting functions are required to ensure the realizability of the sensor.