Spherical correlation as a similarity measure for 3-D radiation patterns of musical instruments
Spherical correlation as a similarity measure for 3-D radiation patterns of musical instruments
复制标题
球面相关性作为乐器 3D 辐射图的相似性度量
DOI：
10.1051/aacus/2023033
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发表时间：
2023
期刊：
影响因子：
1.4
通讯作者：
Carpentier T
中科院分区：
文献类型：
--
作者：
Carpentier T
我们调查使用球面互相关作为声辐射模式的相似性度量，其研究，组织和操纵的潜在应用。本研究的动机是将基于语料库的合成技术应用于基于管弦乐器辐射模式的空间投影。为此，我们希望得到空间描述符，以补充其他音频功能可用于组织的样本语料库。考虑球面上的两个方向性函数，它们的球面相关性可以由它们的球谐系数来计算。此外，可以搜索使互相关最大化的3-D旋转矩阵，即，其提供最佳球形匹配。这些工具的数学基础在文献中得到了很好的建立;然而，它们在声学领域的实际应用仍然相对有限和具有挑战性。作为一个概念的证明，我们应用这些技术来模拟辐射数据和测量来自现有的数据库的3-D方向性图案的管弦乐器。使用这些例子，我们提出了几个测试案例，比较球面相关的数学和声学期望的结果。一系列的可视化方法被应用到分析测试用例，包括多维缩放，作为一种有效的技术，用于数据减少和导航。这篇文章是以前发表在[Carpentier和Einbond.第16届法国声学大会（CFA），马赛，法国，2022年4月，pp. 1-6. https://openaccess.city.ac.uk/id/eprint/28202/].
We investigate the use of spherical cross-correlation as a similarity measure of sound radiation patterns, with potential applications for their study, organization, and manipulation. This work is motivated by the application of corpus-based synthesis techniques to spatial projection based on the radiation patterns of orchestral instruments. To this end, we wish to derive spatial descriptors to complement other audio features available for the organization of the sample corpus. Considering two directivity functions on the sphere, their spherical correlation can be computed from their spherical harmonic coefficients. In addition, one can search for the 3-D rotation matrix which maximizes the cross-correlation, i.e. which offers the optimal spherical shape matching. The mathematical foundations of these tools are well established in the literature; however, their practical use in the field of acoustics remains relatively limited and challenging. As a proof of concept, we apply these techniques both to simulated radiation data and to measurements derived from an existing database of 3-D directivity patterns of orchestral instruments. Using these examples we present several test cases to compare the results of spherical correlation to mathematical and acoustical expectations. A range of visualization methods are applied to analyze the test cases, including multi-dimensional scaling, employed as an efficient technique for data reduction and navigation. This article is an extended version of a study previously published in [Carpentier and Einbond. 16th Congrès Français d’Acoustique (CFA), Marseille, France, April 2022, pp. 1–6. https://openaccess.city.ac.uk/id/eprint/28202/].
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