Circular harmonics beamforming with spheroidal baffles

Abstract

Circular microphone arrays have been well studied when mounted on cylindrical and spherical baffles. In this paper, the oblate and prolate spheroids are explored as a baffle for a microphone array system. It is shown that the prevailing methods for analysis of circular arrays may be easily adapted to this class of baffle, and that the use of these baffles represent a continuously variable geometry with edge cases that are the cylindrical and spherical baffles, and the array in empty space with no baffle. The performance—in the form of directivity index, maximum side-lobe level and main beam resolution—of spheroidally baffled arrays is analyzed with respect to errors created by transducer noise, positioning error, and modal aliasing, for both delay-and-sum and eigenbeamforming arrays. It is shown that the noise and position errors depend strongly on the spheroidal eccentricity while the aliasing error is fairly independent of baffle shape. Simulations of example arrays are used to show that while the prolate spheroidal baffle is of little advantage compared to current systems, the oblate spheroidal baffle can be used to create a significantly smaller array with only a relatively minor performance degradation.