Sound Field Recording Using Distributed Microphones Based on Harmonic Analysis of Infinite Order

Abstract

A sound field recording method based on spherical or circular harmonic analysis for arbitrary array geometry and directivity of microphones is proposed. In current methods based on harmonic analysis, a sound field is decomposed into harmonic functions with a center given in advance, which is called a global origin, and their coefficients are obtained up to a certain truncation order using microphone measurements. However, the accuracy of the reconstructed sound field depends on the predefined position of the global origin and the truncation order, which makes it difficult to apply this technique to an asymmetric array since the criterion to determine the position of the global origin and the truncation order is not obvious. We formulate an estimate of the harmonic coefficients on the basis of infinite-order analysis. This formulation enables us to estimate the harmonic coefficients at an arbitrary desired position independently of the position of the global origin without truncation errors. Numerical simulation results indicated that the proposed method makes it possible to avoid performance degradation caused by inappropriate setting of the global origin.