Design issues for eigenbeamforming spherical microphone arrays

Abstract

Approximating an analytic function by orthonormal bases functions has its origins in the theory of least squares developed by Gauss and Legendre. The use of orthonormal bases functions has been a standard tool in soundfield analysis since Rayleigh. One common set of orthonormal bases functions that naturally fit the solution of the spherical wave equation are the spherical harmonics. In this talk we describe the concept of building a microphone array on a rigid spherical baffle. We process the output signals from the spherical array such that we spatially decompose the acoustic soundfield into spherical harmonic Eigenbeam signals. Computationally efficient Eigenbeamforming, or modal beamforming, with these processed Eigenbeam signals will be discussed. Two main design issues are the growth in sensitivity to self-noise for higher-order spherical modes at lower values of k*r where, k is the wavenumber and r is the radius, and spatial aliasing due to the finite number of microphones covering the spherical surface at higher values of kr. We will discuss how to practically handle these design issues and how these design solutions impact the overall performance of the Eigenbeams and the use of these components in the design of modal beamformers.