Optimal Series Truncation of the Rigid-Sphere Head-Related Transfer Function for Accurate Binaural Perception

A formula is derived for computing the order at which the infinite series representation of the rigid-sphere head-related transfer function (RS-HRTF) must be truncated to minimize the time required to compute the HRTF to a sufficiently high accuracy based on binaural perception metrics. Quick and accurate computation of this HRTF may be useful for implementing spatial audio in computationally limited and portable devices. Using a brute-force approach, the lowest truncation order, N_min, that yields the RS-HRTF that differs from the benchmark (i.e., the RS-HRTF computed with the highest possible accuracy) by less than just-noticeable difference thresholds in interaural time and level differences is approximately computed for a wide range of source distances. By fitting power and rational functions to these computed values, a formula that approximates N_min as a function of frequency and source distance is derived. It is shown that truncation order varies significantly with source distance and that the proposed formula, unlike a previous one, accurately captures this variation. Consequently, using the proposed formula instead of the previous one results in a more accurate RS-HRTF that is also computed 48% faster on average.