Computation of the head-related transfer function via the boundary element method and representation via the spherical harmonic spectrum

The head-related transfer function (HRTF) is computed using the fast multipole accelerated boundary element method. For efficiency, the HRTF is computed using the reciprocity principle, by placing a source at the ear and computing its field. Analysis is presented to modify the boundary value problem accordingly. To compute the HRTF corresponding to different ranges via a single computation, a compact and accurate representation of the HRTF, termed the spherical spectrum, is developed. Computations are reduced to a two stage process, the computation of the spherical spectrum and a subsequent evaluation of the HRTF. This representation allows easy interpolation and range extrapolation of HRTFs. HRTF computations are performed for the range of audible frequencies up to 20 kHz for several models including a sphere, human head models (for the “Fritz” and “Kemar”), and head and torso model (the Kemar manikin). Comparisons between the different cases and analysis of limiting cases is provided. Comparisons with the computational data of other authors and available experimental data are conducted and show satisfactory agreement for the frequencies for which reliable experimental data is available. Our results show that, given a good mesh it is feasible to compute the HRTF over the full audible range on a regular personal computer