Frequency-Domain Sound Field from the Perspective of Band-Limited Functions

TL;DR

This paper models frequency-domain sound fields as band-limited functions using reproducing kernels, enhancing representation and simplifying wavenumber spectrum estimation, validated through numerical simulations.

Contribution

It introduces a novel representation of frequency-domain sound fields as band-limited functions with reproducing kernels, generalizing existing models and simplifying spectrum estimation.

Findings

Effective representation of sound fields demonstrated in simulations

Simplified formula for wavenumber spectrum estimation

Model generalizes previous Helmholtz-based approaches

Abstract

In this paper, the frequency-domain sound field is regarded as an element of some band-limited function space, and a representation of the field as a linear combination of the reproducing kernel in that space is proposed. This model has the strongest representational capacity of all function systems when we know only the sound pressure information at arbitrary positions. The proposed model can be considered a generalization of the existing three-dimensional sound field model using the reproducing kernel of the solution space of the Helmholtz equation to the spatial dimension. One of the advantages of capturing the frequency-domain sound field in this way is the simplicity achieved for the estimation formula of the wavenumber spectrum. Two numerical simulations were conducted to validate the proposed methods.