Computation of the head-related transfer function via the fast multipole accelerated boundary element method and its spherical harmonic representation

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 [the Neumann KU-100 (“Fritz”) and the Knowles KEMAR (“Kemar”) manikins], and head-and-torso model (the Kemar manikin). Comparisons between the different cases are 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 are available. Results show that, given a good mesh, it is feasible to compute the HRTF over the full audible range on a regular personal computer.