Comparative evaluation of interpolation methods for the directivity of musical instruments
Comparative evaluation of interpolation methods for the directivity of musical instruments
复制标题
乐器指向性插值方法的比较评价
DOI：
10.1186/s13636-021-00223-6
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
S. Weinzierl
中科院分区：
文献类型：
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作者：
David Ackermann;F. Brinkmann;F. Zotter;M. Kob;S. Weinzierl
声源指向性的测量几乎在所有情况下都必须进行插值，要么是为了对数据进行更高分辨率的空间上采样，要么是为了对另一个采样网格进行空间重采样，要么是为了模拟声音传播。应用于稀疏采样指向性测量的不同插值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，我们评估了三种从低分辨率采样网格插值的既定方法，使用代表性乐器样本的高分辨率测量作为参考。薄板伪样条插值的平均全局误差最小。对于基于球谐波分解的插值，球谐波阶数和空间采样方式对插值质量的影响较大，且难以预测。分段线性球面三角形插值提供的结果几乎与一阶样条方法一样好，尽管平均计算量要高20倍。因此，对于稀疏采样的乐器指向性测量的空间插值，建议将薄板伪样条法应用于绝对值数据，并在必要时对相位进行后续建模。
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.