Time domain radial filter design for spherical waves

Hahn, Nara, Schultz, Frank and Spors, Sascha (2022) Time domain radial filter design for spherical waves. In ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE. pp. 1076-1080 . (doi:10.1109/ICASSP43922.2022.9747104).

Abstract

Signal processing based on spherical harmonic representations requires an efficient and accurate modeling of the radial functions whose spectrum is commonly described by spherical Bessel and Hankel functions. In this paper, the time-domain radial functions for spherical waves are realized as FIR filters. The filter design exploits the continuous-time representations of the radial functions which have a finite temporal support and are described by the Legendre polynomials. Since the discontinuities occurring in the time domain exhibit infinite temporal bandwidth, a direct time-domain sampling results in frequency-domain aliasing. In order to reduce the aliasing artifacts, the time-domain discontinuities of different orders are replaced with band-limited functions that are analytically derived from the Lagrange interpolation kernel. The FIR coefficients are then obtained by sampling the band-limited representations which leads to a considerable reduction in spectral aliasing. The coefficients are given in closed form expressed solely by polynomials which makes the proposed method suited for real-time applications.

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Contributors

Author: Nara Hahn

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