Range dependence of the response of a spherical head model

The head-related transfer function (HRTF) varies with range as well as with azimuth and elevation. To better understand its close-range behavior, a theoretical and experimental investigation of the HRTF for an ideal rigid sphere was performed. An algorithm was developed for computing the variation in sound pressure at the surface of the sphere as a function of direction and range to the sound source. The impulse response was also measured experimentally. The results may be summarized as follows. First, the experimental measurements were in close agreement with the theoretical solution. Second, the variation of low-frequency interaural level difference with range is significant for ranges smaller than about five times the sphere radius. Third, the impulse response reveals the source of the ripples observed in the magnitude response, and provides direct evidence that the interaural time difference is not a strong function of range. Fourth, the time delay is well approximated by well-known ray-tracing formula due to Woodworth and Schlosberg. Finally, except for this time delay, the HRTF for the ideal sphere appears to be minimum-phase, permitting exact recovery of the impulse response from the magnitude response in the frequency domain.