Accurate time-domain simulation of spherical microphone arrays

Hahn, Nara, Schultz, Frank and Spors, Sascha (2023) Accurate time-domain simulation of spherical microphone arrays. In 10th Convention of the European Acoustics Association. European Acoustics Association. pp. 599-606 .

Abstract

The simulation of spherical microphone arrays is commonly performed in the frequency domain, where the spatial transfer function is expressed in the spherical harmonics domain. Each modal spectrum is described by the spherical Hankel function and its derivative. Although the resulting simulation is accurate in the frequency domain, the corresponding time-domain signal exhibits temporal aliasing and pre-ringing. Also, evaluating the spherical Hankel functions at a larger number of frequencies requires heavy computations. In this paper, we propose a time-domain approach, where each modal transfer function is realized as a parallel combination of IIR filters and a single FIR filter. The poles of the IIR filters correspond to the roots of the spherical Hankel functions’ derivative, and thus can be pre-computed. The moving average coefficients of the IIR filters and the FIR filter coefficients are obtained by the least-squares solution, where the squared spectrum errors are minimized at logarithmically spaced frequencies. While the number of poles are fixed for each harmonic order, the FIR length is a free design parameter, with which we can adjust the simulation accuracy. The presented approach is numerically compared with the frequency-domain model and a previously proposed time-domain method.

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Contributors

Author: Nara Hahn

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