Analyzing head-related transfer function measurements using surface spherical harmonics

A continuous, functional representation of a large set of head-related transfer function measurements (HRTFs) is developed. The HRTFs are represented as a weighted sum of surface spherical harmonics (SSHs) up to degree 17. A Gaussian quadrature method is used to pick out a set of experimentally efficient measurement directions. Anechoic impulse responses are measured for these directions between a source loudspeaker and the entrance to the ear canal of a head-and-torso simulator (HATS). Three separate SSH analyses are carried out: The first forms a SSH representation from the time responses, with the variable onset delay caused by interaural differences intact, by applying the analysis to each time sample in turn. The second SSH model is formed in exactly the same way, except using impulse responses in which the variable onset delays have been equalized. The final SSH analysis is carried out in the frequency domain by applying the technique on a frequency bin by frequency bin basis to the magnitude and unwrapped phase responses of the HRTFs. The accuracy and interpolation performance of each of the computed SSH models is investigated, and the usefulness of the SSH technique in analyzing directional hearing and, particularly, in spatializing sounds is discussed.