adequate opportunity to adapt in a closed-loop SE, much of the current concern with detailed characteristics of the HRTFs and with the importance of intersubject differences would disappear. In addition, significant advances are now being made in the modeling of HRTFs and the development of parametric expressions for HRTFs based on abstractions of the head, torso, and pinnae. In fact, in the not-too-distant future, it may be possible to obtain reasonably good estimates of an individual's HRTFs merely by making a few geometric measurements of the outer ear structures. These two factors, combined with the use of models for describing the effects of reverberation, should greatly simplify the HRTF estimation problem.
Given an adequate store of estimated HRTFs, it is then necessary to select the appropriate ones (as a function of source and head position/orientation) and filter the source signal in real time. Although some ability to perform such processing has been achieved with relatively simple analog electronics (e.g., Loomis et al., 1990), the devices available for achieving the most accurate simulations employ digital signal processing. The earliest commercially available systems (e.g. the FocalPoint system from Gehring Research and the Convolvotron) employed simple time-domain processing schemes to ''spatialize" input sound sources. The Acoustetron (successor to the Convolvotron) quadrupled the computational capabilities of these earlier systems. It stores 72 pairs of spatial filters sampled at 50 kHz for spatial positions sampled at 30 degrees in azimuth and 18 deg in elevation. The spatial filters that most closely correspond to the instantaneous position of the source relative to the listener's head are retrieved in real time, interpolated to simulate positions between the spatial sampling points, and then convolved with the input sound source to generate appropriate binaural signals. The system can spatialize up to 32 sources in parallel, enabling simulation of simple acoustic room models (with first- and second-order reflections) in real time.
Another time-domain spatialization system was developed by McKinley and his associates in the Bioacoustics and Biocommunications Branch of the Armstrong Laboratory at Wright-Patterson Air Force Base in order to present three-dimensional audio cues to pilots (R.L. McKinley, personal communication, 1992). The HRTFs incorporated into this system, derived from measurements using the mannequin KEMAR, are sufficiently dense in azimuth (HRTFs are measured at every degree in azimuth) to eliminate the need for interpolation in azimuth. In elevation, the measurements are much less dense and linear interpolation is employed. The researchers at Wright-Patterson, in conjunction with Tucker Davis Technologies of Gainesville, Florida, have recently developed a new time-domain processor based on their earlier efforts. This machine, which is