Aliasing-free time-domain simulation of spherical microphone arrays

Abstract

This paper proposes an improved time-domain simulation of rigid spherical microphone arrays. The spatial transfer function of an external sound source evaluated on a rigid sphere can be represented as a spherical harmonics expansion. Each harmonic mode is described by the spherical Hankel function and its derivative, where the corresponding spectrum is characterized by Laplace-domain poles and zeros. We convert the continuous-time transfer function into the z-domain by using a recently proposed discretization technique, called the band-limited impulse invariance method. The resulting discrete-time system has a parallel structure of digital IIR filters and a single FIR filter, where the FIR part is designed to cancel the aliasing introduced by the IIR filters. The captured signals are simulated by applying the filters to any given source signal. The filter coefficients are given in closed form which are derived analytically. Numerical evaluations of the proposed method reveals its superiority to the conventional Laplace-to-z mappings (such as bilinear transform and impulse invariant method) in terms of spectral accuracy which comes at the cost of slightly increased computations. A comparison is also carried out with the commonly used frequency-domain approach which not only is computationally more demanding but also exhibits time-domain aliasing artifacts.

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ORCID for Nara Hahn: orcid.org/0000-0003-3564-5864

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