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.

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乐器指向性插值方法比较评价

几乎所有情况下都必须对声学声源的方向性的测量进行插值，无论是将空间上采样到数据的更高分辨率表示，还是将空间重新采样到另一个采样网格，或者用于声音传播的模拟。应用于稀疏采样方向性测量的不同内插技术的性能取决于所使用的采样网格，但也取决于源本身的辐射方向图。因此，我们使用代表性乐器样本的高分辨率测量值作为参考，评估了从低分辨率采样网格进行插值的三种既定方法。平均而言，最小的全局误差发生在薄板伪样条插值中。对于基于球谐函数 (SH) 分解的插值，所应用的 SH 顺序和空间采样方案对插值质量有很强且难以预测的影响。分段线性球面三角形插值提供几乎与一阶样条方法一样好的结果，尽管平均计算量高 20 倍。因此，对于乐器的稀疏采样方向性测量的空间插值，建议将薄板伪样条方法应用于绝对值数据，并在必要时对相位进行后续建模。尽管平均计算量要高 20 倍。因此，对于乐器的稀疏采样方向性测量的空间插值，建议将薄板伪样条方法应用于绝对值数据，并在必要时对相位进行后续建模。尽管平均计算量要高 20 倍。因此，对于乐器的稀疏采样方向性测量的空间插值，建议将薄板伪样条方法应用于绝对值数据，并在必要时对相位进行后续建模。