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引用次数: 2
摘要
我们研究了使用球形互相关作为声辐射模式的相似性度量,以及它们的研究、组织和操作的潜在应用。这项工作的动机是将基于语料库的合成技术应用于基于管弦乐乐器辐射模式的空间投影。为此,我们希望派生空间描述符来补充样本语料库组织可用的其他音频特征。考虑球面上的两个指向性函数,可以通过它们的球谐系数计算它们的球相关关系。此外,还可以搜索使相互关系最大化的三维旋转矩阵,即提供最佳球形匹配的三维旋转矩阵。这些工具的数学基础在文献中得到了很好的确立;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。作为概念的证明,我们将这些技术应用于模拟辐射数据和从管弦乐器的三维指向性模式的现有数据库中获得的测量。使用这些例子,我们提出了几个测试案例,以比较球形相关结果与数学和声学期望。应用了一系列可视化方法来分析测试用例,包括多维缩放,作为一种有效的数据简化和导航技术。本文是先前发表在[Carpentier and Einbond] .第16届法国声学大会(CFA),马赛,法国,2022年4月,第1-6页上的一项研究的扩展版本。https://openaccess.city.ac.uk/id/eprint/28202/]。
Spherical correlation as a similarity measure for 3-D radiation patterns of musical instruments
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/].
期刊介绍:
Acta Acustica, the Journal of the European Acoustics Association (EAA).
After the publication of its Journal Acta Acustica from 1993 to 1995, the EAA published Acta Acustica united with Acustica from 1996 to 2019. From 2020, the EAA decided to publish a journal in full Open Access. See Article Processing charges.
Acta Acustica reports on original scientific research in acoustics and on engineering applications. The journal considers review papers, scientific papers, technical and applied papers, short communications, letters to the editor. From time to time, special issues and review articles are also published. For book reviews or doctoral thesis abstracts, please contact the Editor in Chief.