Limitations and Error Analysis of Spherical Microphone Arrays

There has been a strong interest in theory and design of spherical microphone arrays in recent years due to their possible use in recording directional sounds for surround sound creation. The theory of such arrays is based on decomposition of sound fields to spherical harmonics which are the natural basis functions for valid sound fields over three dimensional space. However, due to physical size of practical spherical arrays, number of extractable spherical harmonic components are limited to the third order. This paper investigates the various design issues including the inherent limitations of the spherical microphone, discretization of the theoretical continuous spherical microphone into a microphone array and associated spatial aliasing problems, calibration errors of these microphones and signal processing issues. A fourth order microphone design was presented and analysed, which allowed the verification, integration and evaluation of the design issues mentioned earlier, in the context of this design. Overall, the design was capable of recording a frequency range of [340; 3400]Hz. The work presented in this paper has made the following main contributions to sound field recording: (i) Analysis of the role of rigid spheres in improving microphone design; (ii) Analysis of various microphone arrangements, which are applicable to microphone array design; (ii) A model for analysing the error due to inexact positioning of microphones in a spherical array; (iii) A set of error measures for error analysis of spherical microphones; and (iv) Design and analysis of a fourth order spherical microphone.