Comparative evaluation of interpolation methods for the directivity of musical instruments

Measurements of the directivity of acoustic sound sources must be interpolated in almost all cases, either for spatial upsampling to higher resolution representations of the data, for spatial resampling to another sampling grid, or for use in simulations of sound propagation. The performance of different interpolation techniques applied to sparsely sampled directivity measurements depends on the sampling grid used but also on the radiation pattern of the sources themselves. Therefore, we evaluated three established approaches for interpolation from a low-resolution sampling grid using high-resolution measurements of a representative sample of musical instruments as a reference. The smallest global error on average occurs for thin plate pseudo-spline interpolation. For interpolation based on spherical harmonics (SH) decomposition, the SH order and the spatial sampling scheme applied have a strong and difficult to predict influence on the quality of the interpolation. The piece-wise linear, spherical triangular interpolation provides almost as good results as the first-order spline approach, albeit with on average 20 times higher computational effort. Therefore, for spatial interpolation of sparsely sampled directivity measurements of musical instruments, the thin plate pseudo-spline method applied to absolute-valued data is recommended and, if necessary, a subsequent modeling of the phase.