Bilbao Stefan, Ahrens Jens
Acoustics and Audio Group/Reid School of Music, University of Edinburgh, 12 Nicolson Square, Edinburgh, EH8 9DF, United Kingdom.
Audio Technology Group, Division of Applied Acoustics, Chalmers University of Technology, 412 96 Gothenburg, Sweden.
J Acoust Soc Am. 2020 Dec;148(6):3951. doi: 10.1121/10.0002956.
All acoustic sources are of finite spatial extent. In volumetric wave-based simulation approaches (including, e.g., the finite difference time domain method among many others), a direct approach is to represent such continuous source distributions in terms of a collection of point-like sources at grid locations. Such a representation requires interpolation over the grid and leads to common staircasing effects, particularly under rotation or translation of the distribution. In this article, a different representation is shown, based on a spherical harmonic representation of a given distribution. The source itself is decoupled from any particular arrangement of grid points, and is compactly represented as a series of filter responses used to drive a canonical set of source terms, each activating a given spherical harmonic directivity pattern. Such filter responses are derived for a variety of commonly encountered distributions. Simulation results are presented, illustrating various features of such a representation, including convergence, behaviour under rotation, the extension to the time varying case, and differences in computational cost relative to standard grid-based source representations.
所有声源都具有有限的空间范围。在基于体积波的模拟方法中（包括例如时域有限差分法以及许多其他方法），一种直接的方法是用网格位置处的一系列点状声源来表示这种连续的源分布。这种表示需要在网格上进行插值，并且会导致常见的阶梯效应，特别是在分布旋转或平移时。在本文中，展示了一种基于给定分布的球谐表示的不同表示方法。源本身与网格点的任何特定排列解耦，并紧凑地表示为一系列用于驱动一组标准源项的滤波器响应，每个源项激活给定的球谐指向性图案。针对各种常见分布推导了此类滤波器响应。给出了模拟结果，说明了这种表示的各种特征，包括收敛性、旋转下的行为、到时变情况的扩展以及相对于基于标准网格的源表示的计算成本差异。
