An Energy Interpretation of the Kirchhoff-Helmholtz Boundary Integral Equation and its Application to Sound Field Synthesis
An Energy Interpretation of the Kirchhoff-Helmholtz Boundary Integral Equation and its Application to Sound Field Synthesis
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DOI：
10.3813/aaa.918770
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发表时间：
2014-09-01
影响因子：
--
通讯作者：
Lam, Yiu W.
中科院分区：
文献类型：
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作者：
Hargreaves, Jonathan A.;Lam, Yiu W.
大多数空间音频再现系统具有所有扬声器必须与收听者等距的约束，这是在真实的房间中难以实现的属性。在传统的高保真度立体声响复制中，这是因为用于对空间声场进行编码的球谐函数在球体上是正交的，并且因为扬声器接近度没有被完全解决。最近，通过声场合成理论已经取得了重大进展，以解除这一限制，该理论在基于单层势的数学框架中形式化了各种空间音频系统。这种方法已经显示出许多好处，但将音频渲染视为声音软散射问题的理论可能会出现一步远离物理现实，并且还具有解决方案不唯一的频率。在时域边界元法中，解决这种非唯一性的方法相当于测试声能流动而不是单独考虑压力的陈述。本文将这一概念应用于空间音频渲染，通过重新审视Kirchhoff-Helmholtz积分方程作为波匹配度量，并提出了一个物理解释，其内核在波之间的共同声功率通量密度。它表明，球面基函数（球面调和乘以球面贝塞尔或汉克尔函数）是正交的任何表面上关于这个度量。最后讨论了其他应用，包括高阶麦克风阵列的设计和虚拟声学模型的可听化硬件的耦合。
Most spatial audio reproduction systems have the constraint that all loudspeakers must be equidistant from the listener, a property which is difficult to achieve in real rooms. In traditional Ambisonics this arises because the spherical harmonic functions, which are used to encode the spatial sound-field, are orthonormal over a sphere and because loudspeaker proximity is not fully addressed. Recently, significant progress to lift this restriction has been made through the theory of sound field synthesis, which formalizes various spatial audio systems in a mathematical framework based on the single layer potential. This approach has shown many benefits but the theory, which treats audio rendering as a sound-soft scattering problem, can appear one step removed from the physical reality and also possesses frequencies where the solution is non-unique. In the time-domain Boundary Element Method approaches to address such non-uniqueness amount to statements which test the flow of acoustic energy rather than considering pressure alone. This paper applies that notion to spatial audio rendering by re-examining the Kirchhoff-Helmholtz integral equation as a wave-matching metric, and suggests a physical interpretation of its kernel in terms of common acoustic power flux density between waves. It is shown that the spherical basis functions (spherical harmonics multiplied by spherical Bessel or Hankel functions) are orthogonal over any arbitrary surface with respect to this metric. Finally other applications are discussed, including design of high-order microphone arrays and the coupling of virtual acoustic models to auralization hardware.