Incorporating directivity in the Pseudospectral time-domain method by using spherical harmonics

A technique to incorporate directivity in the Pseudospectral time-domain method (PSTD) for auralization purposes is presented. The Pseudospectral time-domain method is a numerical method for solving the wave equation that requires only two spatial points per wavelength, making it more efficient compared to other wave based methods. The effect of source directivity as well as the head-related directivity have a clear influence on the perceived sound field and have to be included for the purpose of auralizations. In the less efficient finite difference time-domain method, directivity has been incorporated. Thus far, no such developments to incorporate directivity in PSTD have appeared. In this paper, directivity has been modeled by composing initial spatial distributions from spherical harmonic profiles and with the use of filters in order to achieve a frequency dependent directivity. The method is described in detail, drawbacks of the method and suggestions for further improvements are included.