Simulations of head-related transfer functions in wideband acoustics

Head-related transfer functions (HRTFs) have been simulated in three dimensions for a head-and-torso model for the entire audio frequency range, from 20 Hz to 20 kHz. As opposed to data acquired through measurements, the results derived from computer simulations are free from the effects of noise and imperfections in the electro-acoustic chain. In addition, the spatial resolution can easily be made better than in any practical experiment. The simulations have been performed using an ultraweak variational formulation method for solving Helmholtz equation. The numerical method with its parallel computing capability is efficient, enabling numerical calculations of large physical systems, e.g., of size 0.4×0.5×0.8 m, at high frequencies. The method uses plane-wave basis functions instead of polynomial basis as in standard finite-element methods (FEM), resulting in the need of much sparser volume mesh than in FEM. For HRTF calculations, a so-called perfectly matched layer has been utilized and the solutions are derived in the far field. Thus, exterior problems often solved using boundary-element method are dealt with. The specific HRTF simulations have been performed using fully reflecting, sound hard, boundaries on the head and torso, and also with complex impedance boundaries on the torso such as clothing.