Calculation of Head-Related Transfer Functions for Arbitrary Field Points Using Spherical Harmonics Decomposition

The head-related transfer function (HRTF) characterizes the transfer path of sound from a certain position in space to the ear of a listener. Traditionally, HRTFs have been measured for relatively distant sources at discrete positions on a surrounding sphere. It is well known from literature that the HRTF changes significantly for sources in the proximal region, i.e., at distances less than one meter from the head. In practice, the measurement of near-field HRTFs requires a significant number of measurement points at different distances from the head; it may thus not be feasible for many projects. An essential question is whether HRTFs can be calculated for any arbitrary position in space from measurements on a single radius. HRTF data can be represented in the spherical wave spectral domain, thus turning the range extrapolation problem into an acoustic radiation problem. The range extrapolation is then calculated using the corresponding wave propagation terms. This paper presents a comprehensive study of the spherical acoustic method for calculating HRTFs at arbitrary field points. Near-field HRTFs are calculated for two dummy heads and then compared to other range extrapolation methods known from literature. Particular attention is paid to the effect of incomplete spherical data sets on the reproduction accuracy and different regularization methods are discussed. The results are compared to near-field measurements for these dummy heads and numerical boundary-element method (BEM) simulations thereof. The spherical acoustic method shows a good agreement with measurement data, thus providing an efficient method for near-field binaural synthesis using already existing HRTF data sets.