Sound Field Analysis along a Circle and Its Applications to HRTF Interpolation*

The sampling and interpolation of a sound field in two and three dimensions along a circle is discussed. The Fourier domain representation of the sound field is used, and an angular sampling theorem is developed for the sampling of the sound field along a circle. Based on these results, HRTF sampling and interpolation are discussed. This method achieves very precise interpolation in terms of mean square error. However, these results are only possible if very finely spaced HRTF measurements are available. A method is proposed to improve interpolation results when the HRTF measurements are more coarsely spaced than dictated by the angular Nyquist theorem. The proposed method interpolates the HRTFs in a subband domain. In subbands where small angular aliasing occurs, the previous method is applied. In the other subbands, interpolation is carried out in a complex temporal envelope domain to avoid aliasing. Simulations with models and measured data show that the proposed algorithm performs significantly better than previous methods in a mean square error sense.