A model of head-related transfer functions based on principal components analysis and minimum-phase reconstruction

TLDR

The authors measured free‑field to eardrum HRTFs from 10 subjects at 265 positions and modeled the magnitude as a linear combination of five basis functions while assuming minimum‑phase behavior and approximating interaural phase differences by a simple time delay. Principal‑components analysis showed that five basis functions capture ~90 % of HRTF magnitude variance, and sounds synthesized with the model produced localization judgments nearly identical to those from measured HRTFs, whereas using fewer than five basis functions increased large localization errors.

Abstract

Free-field to eardrum transfer functions (HRTFs) were measured from both ears of 10 subjects with sound sources at 265 different positions. A principal components analysis of the resulting 5300 HRTF magnitude functions revealed that the HRTFs can be modeled as a linear combination of five basic spectral shapes (basis functions), and that this representation accounts for approximately 90% of the variance in the original HRTF magnitude functions. HRTF phase was modeled by assuming that HRTFs are minimum-phase functions and that interaural phase differences can be approximated by a simple time delay. Subjects’ judgments of the apparent directions of headphone-presented sounds that had been synthesized from the modeled HRTFs were nearly identical to their judgments of sounds synthesized from measured HRTFs. With fewer than five basis functions used in the model, a less faithful reconstruction of the HRTF was produced, and the frequency of large localization errors increased dramatically.