Efficient Real Spherical Harmonic Representation of Head-Related Transfer Functions

Several methods have recently been proposed for modeling spatially continuous head-related transfer functions (HRTFs) using techniques based on finite-order spherical harmonic expansion. These techniques inherently impart some amount of spatial smoothing to the measured HRTFs. However, the effect this spatial smoothing has on the localization accuracy has not been analyzed. Consequently, the relationship between the order of a spherical harmonic representation for HRTFs and the maximum localization ability that can be achieved with that representation remains unknown. The present study investigates the effect that spatial smoothing has on virtual sound source localization by systematically reducing the order of a spherical-harmonic-based HRTF representation. Results of virtual localization tests indicate that accurate localization performance is retained with spherical harmonic representations as low as fourth-order, and several important physical HRTF cues are shown to be present even in a first-order representation. These results suggest that listeners do not rely on the fine details in an HRTF's spatial structure and imply that some of the theoretically-derived bounds for HRTF sampling may be exceeding perceptual requirements.