Maximal azimuthal resolution needed in measurements of head-related transfer functions.

The head-related transfer function (HRTF) is a continuous function of sound source position. Measurement of the HRTF can only be undertaken at discrete positions in space, however. Determination of angular resolutions so as to reconstruct HRTFs at unmeasured positions has been an open problem. Azimuthal Fourier analysis was proposed to analyze the variation in the HRTF in each elevation plane. As a result, an azimuthal sampling theorem and a corresponding interpolation formula were derived. It was proved that the maximal azimuthal resolution of measurements is 360 degrees /(2Q+1), where Q represents the highest order in the truncation of the azimuthal Fourier expansion of the HRTF. The maximal azimuthal resolutions for the HRTF with and without arrival time correction were investigated. Results show that the arrival time correction can reduce the burden of measurements, since a larger azimuthal resolution is possible without introducing obvious interpolation error. A psychoacoustic experiment was also conducted to evaluate the proposed theorem.