Abhijit Kulkarni
H. Steven Colburn
Dept. of Biomed. Eng., Boston Univ., 44 Cummington St., Boston, MA 02215
The head-related transfer function (HRTF) is empirically measured as a finite-impulse-response (FIR) filter e.g., Wightman and Kistler, 1989. In this study we explore reduced-order approximations of measured HRTFs for use in virtual acoustical displays. The HRTFs tested were measured from human subjects and provided by Dr. Fred Wightman. In all model reconstructions it is assumed that HRTFs can be approximated as minimum-phase functions. Theoretical results are derived which allow for two model-order reduction strategies with optimal criteria. First, we demonstrate that the partial energy contained in the first n taps of a minimum-phase FIR filter is optimal in the Parseval sense. Secondly, we demonstrate that the HRTF expressed by its cepstral coefficients (Oppenheim and Schafer, 1979) constitutes a Fourier series. A partial sum from this Fourier series then provides the best mean-square approximation to the log-magnitude function of the HRTF. The validity of the reconstructed HRTFs was assessed psychophysically using a 4I-2AFC procedure. Using a 80-ms white noise stimulus and testing a new position on each trial, for a 64-tap HRTF reconstruction by both methods, subjects performed close to chance for most of the 13 representative positions tested. [Work supported by NIDCD (Grant DC00100).]