Region-to-region kernel interpolation of acoustic transfer function with directional weighting

TL;DR

This paper introduces a novel kernel-based interpolation method for acoustic transfer functions that accounts for physical properties and directionality, improving estimation accuracy between source and receiver regions.

Contribution

It formulates a new reproducing kernel Hilbert space with directional weighting for better ATF interpolation across regions.

Findings

Outperforms existing methods without directional weighting

Effectively estimates ATFs for both source and receiver regions

Demonstrates improved accuracy through numerical experiments

Abstract

A method of interpolating the acoustic transfer function (ATF) between regions that takes into account both the physical properties of the ATF and the directionality of region configurations is proposed. Most spatial ATF interpolation methods are limited to estimation in the region of receivers. A kernel method for region-to-region ATF interpolation makes it possible to estimate the ATFs for both source and receiver regions from a discrete set of ATF measurements. We newly formulate the reproducing kernel Hilbert space and associated kernel function incorporating directional weight to enhance the interpolation accuracy. We also investigate hyperparameter optimization methods for this kernel function. Numerical experiments indicate that the proposed method outperforms the method without the use of directional weighting.