Time-Domain Representations of a Plane Wave with Limited Spatial Bandwidth in the Spherical Harmonics Domain
* Presenting author
Spherical harmonics expansion is often used to describe the sound fields captured by microphone arrays or reproduced by multichannel loudspeaker systems. Although the majority of the related sound field analysis and synthesis methods are formulated in the temporal frequency domain, their time-domain implementation can improve the computational efficiency significantly as the computation of the spherical Bessel function and/or the spherical Hankel function is avoided. The goal of this paper is to find an explicit time-domain representation of a spatially band-limited plane wave suited for discrete-time realization. Two derivations, one based on series expansion and the other on plane wave decomposition, are introduced and their equivalence is revealed. The series expansion is used to express the spherical Bessel function in the Laplace domain. The inverse Laplace transform consists of two right-sided signals corresponding to the spherical Hankel function of the first and second kind. In the plane wave decomposition, the sound field consists of an infinite number of plane waves due to the spatial band limitation. The amplitude, time-of-arrival, and propagation direction of the individual plane waves are derived, which provides deeper understanding of the spatial structure of the sound field.