Range-dependence of the HRTF for a spherical head

This paper examines the range dependence of the head-related transfer function (HRTF) for a simple spherical model of the head in both the time-domain and the frequency domain. The variation of low-frequency interaural level difference (ILD) with range is shown to be significant for ranges smaller than five times the sphere radius. The impulse response explains the source of the ripples in the frequency response, and provides direct evidence that the interaural time delay (ITD) is not a strong function of range. Time-delay measurements confirm the Woodworth/Schlosberg formula. Numerical analysis indicates that the HRTF is minimum phase. Thus, except for the time delay, the impulse response can be reconstructed from a simple principle components analysis of the magnitude response.