Bilbao Stefan, Ahrens Jens, Hamilton Brian
Acoustics and Audio Group/Reid School of Music, University of Edinburgh, Edinburgh, United Kingdom.
Audio Technology Group, Division of Applied Acoustics, Chalmers University of Technology, 412 96 Gothenburg, Sweden.
J Acoust Soc Am. 2019 Oct;146(4):2692. doi: 10.1121/1.5130194.
The modeling of source directivity is a problem of longstanding interest in virtual acoustics and auralisation. This remains the case for newer time domain volumetric wave-based approaches to simulation such as the finite difference time domain method. In this article, a spatio-temporal model of acoustic wave propagation, including a source term is presented. The source is modeled as a spatial Dirac delta function under the action of a series of differential operators associated with the spherical harmonic functions. Each term in the series gives rise to the directivity pattern of a given spherical harmonic, and is separately driven through a time domain filtering operation of an underlying source signal. Such a model is suitable for calibration against measured frequency-dependent directivity patterns and a procedure for arriving at time domain filters for each spherical harmonic channel is illustrated. It also yields a convenient framework for discretisation, and a simple strategy is presented, yielding a locally-defined operation over the spatial grid. Numerical results, illustrating various features of source directivity, including the comparison of measured and synthetic directivity patterns, are presented.
声源指向性建模是虚拟声学和听觉化领域长期以来备受关注的问题。对于诸如时域有限差分法等基于时域体波的新型模拟方法而言，情况依然如此。在本文中，提出了一种声波传播的时空模型，其中包括一个源项。源被建模为在与球谐函数相关的一系列微分算子作用下的空间狄拉克δ函数。该级数中的每一项都会产生给定球谐函数的指向性图案，并通过对基础源信号的时域滤波操作分别驱动。这样的模型适用于根据测量的频率相关指向性图案进行校准，并说明了为每个球谐通道确定时域滤波器的过程。它还为离散化提供了一个方便的框架，并提出了一种简单策略，在空间网格上产生局部定义的操作。给出了说明声源指向性各种特征的数值结果，包括测量和合成指向性图案的比较。
