Cylindrical Radial Filter Design With Application to Local Wave Field Synthesis

Abstract

The cylindrical radial filters refer to the discrete-time realizations of the radially dependent parts in cylindrical harmonic expansions, which are commonly described by the cylindrical Bessel functions. An efficient and accurate design of the radial filters is crucial in spatial signal processing applications, such as sound field synthesis and active noise control. This paper presents a radial filter design method where the filter coefficients are analytically derived from the time-domain representations. Time-domain sampling of the cylindrical radial functions typically leads to spectral aliasing artifacts and degrades the accuracy of the filter, which is mainly attributed to the unbounded discontinuities exhibited by the time-domain radial functions. This problem is coped with by exploiting an approximation where the cylindrical radial function is represented as a weighted sum of the radial functions in spherical harmonic expansions. Although the spherical radial functions also exhibit discontinuities in the time domain, the amplitude remains finite, which allows application of a recently introduced aliasing reduction method. The proposed cylindrical radial filter is thus designed by linearly combining the spherical radial filters with improved accuracy. The performance of the proposed cylindrical radial filters is demonstrated by examining the spectral deviations from the original spectrum.