Novel Sampling Scheme on the Sphere for Head-Related Transfer Function Measurements

Abstract

This paper presents a novel sampling scheme on the sphere for obtaining head-related transfer function (HRTF) measurements and accurately computing the spherical harmonic transform (SHT). The scheme requires an optimal number of samples, given by the degrees of freedom in the spectral domain, for the accurate representation of the HRTF that is band-limited in the spherical harmonic domain. The proposed scheme allows for the samples to be easily taken over the sphere due to its iso-latitude structure and non-dense sampling near the poles. In addition, the scheme can be used when samples are not taken from the south polar cap region of the sphere as the HRTF measurements are not reliable in south polar cap region due to reflections from the ground. Furthermore, the scheme has a hierarchical structure, which enables the HRTF to be analyzed at different audible frequencies using the same sampling configuration. In comparison to the proposed scheme, none of the other sampling schemes on the sphere simultaneously possess all these properties. We conduct several numerical experiments to determine the accuracy of the SHT associated with the proposed sampling scheme. We show that the SHT attains accuracy on the order of numerical precision ${(10^{ - 14}})$ when samples are taken over the whole sphere, both in the optimal sample placement and hierarchical configurations, and achieves an acceptable level of accuracy ${(10^{ - 5}})$ when samples are not taken over the south polar cap region of the sphere for the band-limits of interest. Simulations are used to show the accurate reconstruction of the HRTF over the whole sphere, including unmeasured locations.