An Investigation of a non-axisymmetric beamformer based on the reproducing kernel representation of sound fields

This study investigates a non-axisymmetric beamforming approach based on the reproducing kernel representation of sound fields in the frequency domain. In recent years, beamformers in the spherical harmonic domain have been actively studied, but most of them assume axisymmetry. However, in scenarios where it is necessary to extract signals arriving from several specific directions—such as in spatial filtering, source localization, or speech enhancement—non-axisymmetric beamforming becomes essential.When forming non-axisymmetric beams within conventional framework, complex computations such as the use of rotational actions (Wigner-D matrices) are typically required, which increase computational cost and implementation complexity. On the other hand, we have proposed a sound field representation using reproducing kernels of bandlimited spaces in general spatial dimensions and have demonstrated its effectiveness. In this study, we propose a beamformer based on the observation that spatial derivatives of reproducing kernels from nonaxisymmetric polynomials can be expressed in a simple form using Hobson’s formula. Leveraging this property, we develop a beamformer that enables more efficient computation of nonaxisymmetric directivity patterns. The validity and performance of the proposed beamformer is verified through numerical simulations that form complex beam patterns.