Infinite-impulse-response models of the head-related transfer function

Head-related transfer functions (HRTFs) measured from human subjects were approximated using infinite-impulse-response (IIR) filter models. Models were restricted to rational transfer functions (plus simple delays) so that specific models are characterized by the locations of poles and zeros in the complex plane. The all-pole case (with no nontrivial zeros) is treated first using the theory of linear prediction. Then the general pole-zero model is derived using a weighted-least-squares (WLS) formulation of the modified least-squares problem proposed by Kalman (1958). Both estimation algorithms are based on solutions of sets of linear equations and result in efficient computational schemes to find low-order model HRTFs. The validity of each of these two low-order models was assessed in psychophysical experiments. Specifically, a four-interval, two-alternative, forced-choice paradigm was used to test the discriminability of virtual stimuli constructed from empirical and model HRTFs for corresponding locations. For these experiments, the stimuli were 80 ms, noise tokens generated from a wideband noise generator. Results show that sounds synthesized through model HRTFs were indistinguishable from sounds synthesized from original HRTF measurements for the majority of positions tested. The advantages of the techniques described here are the computational efficiencies achieved for low-order IIR models. Properties of the all-pole and pole-zero estimators are discussed in the context of low-order HRTF representations, and implications for basic and applied contexts are considered.