POLE-ZERO APPROXIMATIONS FOR HEAD-RELATED TRANSFER-FUNCTIONS USING A LOGARITHMIC ERROR CRITERION

Pole-zero approximations of human free-held-to-eardrum transfer functi ons-i.e., head-related transfer functions (HRTF's)-can be used to synt hesize binaural acoustic fields over headphones with fewer parameters, and therefore, lower computational complexity than is typically achie ved by all-zero approximations. While standard pole-zero designs minim ize the squared difference between the desired and designed frequency responses, the synthesis of binaural acoustic fields is more likely to be sensitive to relative, rather than absolute, differences in HRTF a pproximations. The following paper proposes a new design algorithm tha t minimizes an error criterion based on complex logarithms, As a resul t, both log-magnitude and phase errors are minimized, Slight modificat ions to the proposed algorithm result in one for which the phase error can be ignored, A comparison of this modified algorithm to others tha t have been developed to minimize the log-magnitude error shows implem entation advantages without sacrificing performance. In achieving comp arable errors, application of the proposed algorithm to HRTF approxima tion results in pole-zero model orders smaller than those required for approximating HRTF's using a least-squares error criterion.