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 analysed 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.

Distance-varying filters to synthesize head-related transfer functions in the horizontal plane from circular boundary values

“…10(a) and 10(b). This is because Fourier-Legendre transforms are applied along two hemi-circumferences separated by the interaural axis and, unfortunately, differ- Overall accuracies obtained with the method in interaural coordinates, calculated with (13) and (14), are displayed in Fig. 12.…”

“…Resulting overall accuracies of the proposal in spherical coordinates, calculated with (13) and (14), are displayed in Fig. 13.…”

“…(11) and proposed magnitudedependent threshold in (12). Overall accuracies were calculated using the spectral distortion (SD) in (13) and normalized circular correlation (CC) in (14).…”

“…This is a useful result, since spherical datasets are typically obtained for only one far distance [12]. Nevertheless, optimally distributing sound sources on the sphere is a non-trivial problem [13,14], and obtaining the HRTFs for all required initial positions might not be feasible for many applications.…”

Spatial accuracy of binaural synthesis from rigid spherical microphone array recordings

“…Recently, a perceptual study [22] has reported that low-order HRTF representations might be sufficient to approximate an individual space, whereas an objective study [23] has identified HRTF features that would require high-order representations. Because the required resolution for characterizing an individual space is still an open question, the performance of binaural systems should be evaluated by considering HRTF datasets with the higher resolution that can be achieved.…”