Interpolation and range extrapolation of HRTFs [head related transfer functions]

The head related transfer function (HRTF) characterizes the scattering properties of a person´s anatomy (especially the pinnae, head and torso), and exhibits considerable person-to-person variability. It is usually measured as a part of a tedious experiment, and this leads to the function being sampled at a few angular locations. When the HRTF is needed at intermediate angles, its value must be interpolated. Further, its range dependence is also neglected, which is invalid for nearby sources. Since the HRTF arises from a scattering process, it can be characterized as a solution of a scattering problem. In this paper, we show that by taking this viewpoint and performing some analysis we can express the HRTF in terms of a series of multipole solutions of the Helmholtz equation. This approach leads to a natural solution to the problem of HRTF interpolation. Furthermore, we show that the range-dependence of the HRTF in the near-field can also be obtained by extrapolation from measurements at one range.