Spatially Constrained Anti-Aliasing Filter Using Slepian Eigenfunction Window on the Sphere

Spherical microphone arrays sample the sound field on the sphere in both space and time. The performance of spherical microphone arrays is typically limited by spatial aliasing which introduces side-lobes in the array beam pattern. In order to reduce the aliasing error, anti-Aliasing filters, both ideal and spatially constrained, have been presented in the literature. In this paper, we propose a slepian eigenfunction window which spatially truncate the ideal anti-Aliasing filter used in literature to design a spatially constrained anti-Aliasing filter. We also provide an illustration to show that the aliasing on the beam pattern is reduced by the use of the proposed anti-Aliaisng filter and compare the results with the spatially constrained filters obtained by applying rectangular and hamming windows. Robustness analysis such as measurement of the white noise gain and directivity index shows the superiority of the proposed filter over other spatially constrained anti-Aliasing filters.