Kernel interpolation of acoustic transfer function between regions considering reciprocity

A method for interpolating the acoustic transfer function (ATF) between predetermined source and receiver regions is proposed. A previous work has shown that the region-to-region ATF can be estimated by separating it into a reverberant component added to a given direct component and representing the reverberant component with a finite sum of spherical wavefunctions. Our proposed method is based on the kernel ridge regression for estimating the reverberant component with a reproducing kernel Hilbert space defined to include acoustic properties into the interpolation. The proposed method based on the infinite dimensional expansion into spherical wavefunctions is independent of the empirical truncation used in the previous method. Furthermore, by taking the acoustic reciprocity into consideration, more accurate estimations are possible with a limited set of measurements compared to the truncation-based method. The advantages of the proposed method were validated by experiments based on a three-dimensional acoustic simulation.