Comparison of spherical harmonics based 3D-HRTF functional models

Abstract

The modeling performance of three models for the 3D Head Related Transfer Function (HRTF) are compared. One of these models appeared recently in the literature whilst the other two models are novel. All models belong to the class of functional models whereby the 3D-HRTF is expressed as an expansion in terms of basis functions, which are functions of azimuth, elevation, radial distance and frequency. The expansion coefficients capture the 3D-HRTF individualization. The models differ in the choice of basis functions and the degree of orthogonality that is possibly given the constraint that for each frequency the HRTF needs to satisfy the Helmholtz wave equation. One model introduced in this paper is designed to provide a functional representation that is orthonormal on a sphere at some nominal radius and approximately so around that nominal radius. This model is shown to be superior to the other two in being able to reconstruct most efficiently the 3D-HRTF derived from a spherical head 3D-HRTF model. For all cases we show that there is a unified technique to estimate expansion coefficients from measurements taken on a sphere of arbitrary radius.