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.

中文翻译：

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在基于波的虚拟声学中建模连续源分布

所有声源都具有有限的空间范围。在基于体积波的仿真方法（包括例如时差有限时域方法）中，一种直接方法是根据网格位置处的点状源的集合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，并导致常见的阶梯效应，尤其是在分布的旋转或平移下。在本文中，基于给定分布的球谐表示，显示了一种不同的表示。源本身与任何特定的网格点排列解耦，并紧凑地表示为一系列滤波器响应，用于驱动一组标准的源项，每个项都激活给定的球谐方向性图。这样的滤波器响应是针对各种常见分布而得出的。给出了仿真结果，说明了这种表示的各种功能，包括收敛，旋转行为，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。