Efficient representation of head-related transfer functions in continuous space-frequency domains

TL;DR

This paper compares 4D continuous functional models, including hyperspherical and spherindrical harmonic representations, for efficient, accurate, and compact representation of head-related transfer functions across space and frequency domains.

Contribution

It introduces and evaluates 4D continuous models for HRTFs, demonstrating improved compression and accuracy over traditional spherical harmonic methods.

Findings

HSHs and SHs with Fourier-Bessel series outperform other models

HSHs offer better compression and slightly higher accuracy at low coefficients

Models are applicable to various directivity functions beyond HRTFs

Abstract

Utilizing spherical harmonic (SH) domain has been established as the default method of obtaining continuity over space in head-related transfer functions (HRTFs). This paper concerns different variants of extending this solution by replacing SHs with four-dimensional (4D) continuous functional models in which frequency is imagined as another physical dimension. Recently developed hyperspherical harmonic (HSH) representation is compared with models defined in spherindrical coordinate system by merging SHs with one-dimensional basis functions. The efficiency of both approaches is evaluated based on the reproduction errors for individual HRTFs from HUTUBS database, including detailed analysis of its dependency on chosen orders of approximation in frequency and space. Employing continuous functional models defined in 4D coordinate systems allows HRTF magnitude spectra to be expressed as a small set of coefficients which can be decoded back into values at any direction and frequency. The best performance was noted for HSHs and SHs merged with reverse Fourier-Bessel series, with the former featuring better compression abilities, achieving slightly higher accuracy for low number of coefficients. The presented models can serve multiple purposes, such as interpolation, compression or parametrization for machine learning applications, and can be applied not only to HRTFs but also to other types of directivity functions, e.g. sound source directivity.