Interpolation of Head-Related Transfer Functions

Abstract : Using current techniques it is usually impractical to measure head-related transfer functions (HRTFs) at a spatial resolution that does not exceed the minimum audible angle, i.e. 1-2 degrees for a source directly in front, by a considerable amount. As a result, measured HRTFs must be interpolated to generate a display in which auditory space is rendered smoothly. The spatial resolution at which it is necessary to measure HRTFs for the display to be of high spatial fidelity will depend on the quality of the interpolation technique. This report describes an interpolation technique that involves the application of a novel, inverse-distance-weighted averaging algorithm to HRTFs represented in the frequency domain. The quality of this technique was evaluated by comparing four listeners' abilities to localize virtual sound sources generated using measured or interpolated HRTFs. The measured HRTFs were shown to be of sufficiently high fidelity to allow virtual sources to be localized as accurately as real sources. Localization error measures, i.e. lateral errors, polar errors and proportions of front/back confusions, for HRTFs interpolated across up to 30 degrees of either lateral or polar angle, or 20 degrees of both lateral and polar angle, did not differ noticeably from those for measured HRTFs. On the basis of this finding we recommend that HRTFs be measured at a 20 degrees lateral- and polar-angle resolution.