Spatial Correlation of Radial Gaussian and Uniform Spherical Volume Near-Field Source Distributions

Abstract

In this paper, a pair of analytic expressions describing the correlation functions due to spherically symmetric radial Gaussian and uniform volume near-field source position distributions are presented. An approximate spatial correlation function solution for a radial Gaussian source location distribution is derived and compared with the existing numerical methods. An exact solution for a uniform volume source location distribution is also derived and compared with existing numerical methods. The approximate radial Gaussian solution produces a result consistent with numerical methods for compact source location distributions. The uniform volume solution matches the expected behavior. Finally, the spatial correlation functions were used to design spatially robust beamformers for compact microphone arrays. Both of the spatial correlation function solutions lead to improved spatial robustness for the applications of signal enhancement and suppression.