Pole-zero approximations for head-related transfer functions using a logarithmic error criterion

Pole-zero approximations of human free-field-to-eardrum transfer functions-i.e., head-related transfer functions (HRTFs)-can be used to synthesize binaural acoustic fields over headphones with fewer parameters, and therefore, lower computational complexity than is typically achieved by all-zero approximations. While standard pole-zero designs minimize 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 the HRTF approximations. The paper proposes a new design algorithm that minimizes an error criterion based on complex logarithms. As a result, both log-magnitude and phase errors are minimized. Slight modifications to the proposed algorithm result in one for which the phase error can be ignored. A comparison of this modified algorithm to others that have been developed to minimize the log-magnitude error shows implementation advantages without sacrificing performance. In achieving comparable errors, application of the proposed algorithm to the HRTF approximation results in pole-zero model orders smaller than those required for approximating the HRTFs using a least-squares error criterion