Frequency-domain sound field from the perspective of band-limited functions

A model that approximates the sound field well is useful in various fields, such as acoustic signal processing and numerical simulation. We have proposed an effective model in which the wideband instantaneous sound field is regarded as an element of a spherically band-limited function space, using the reproducing kernel of that space. 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.