arXiv:2604.16970eess.AScs.SD2026-04

将声场建模为边界积分算子状态空间,实现多种声学模型统一表达。

A state-space representation of the boundary integral equation for room acoustic modelling

  • 用边界压力函数和积分算子构建声学状态空间模型
  • 可推导出反馈与并行结构的传递函数表示
  • 为声学建模提供统一框架,适合研究者拓展新方法

本文提出一种基于边界积分方程的状态空间建模新框架,用于房间声学模拟。传统线性时不变系统的状态空间由状态向量和四元组系统矩阵构成,而本工作引入的边界积分算子状态空间(BIOSS)模型,以边界压力分布作为状态函数,并包含四元组积分算子。每个积分算子均有明确的物理意义。由于向量与矩阵的数学运算可推广至函数与算子,BIOSS 框架可推导出具有反馈或并行前馈结构的传递函数表示,从而在时域、频域及连续/离散空间中获得多种等价的声学模型表达。文章还讨论了两个未来方向:一是揭示 BIOSS 与现有模型(如边界元法、延迟网络、几何模型)的等价关系,有助于建立模型间联系并发展新模型;二是探索状态空间理论中的可观测性、可控制性与状态实现等概念,可用于开发新的声学推理与控制方法。

原文摘要 · Abstract (English)

We introduce a new framework for room acoustics modelling based on a state-space model of the boundary integral equation representing the sound field in a room. Whereas state-space models of linear time-invariant systems are traditionally constructed by means of a state vector and a 4-tuple of system matrices, the state-space representation introduced in this work consists of a state function representing the pressure distribution at the room boundary, and a 4-tuple of integral operators. We refer to this representation as a boundary integral operator state-space (BIOSS) model and provide a physical interpretation for each of the integral operators. As many mathematical operations on vectors and matrices translate to functions and operators, the BIOSS representation can be manipulated to obtain two transfer function representations, having either a feedback or a parallel feedforward structure. Consequently, various equivalent representations for room acoustics are obtained in the BIOSS framework, in the time or frequency domain, and in continuous or discrete space. We discuss two future directions for how the proposed framework can be fertile for research on room acoustics modelling. Firstly, we identify equivalences between the BIOSS framework and various existing room acoustics models (boundary element models, delay networks, geometric models), which may be used to establish relations between existing models and to develop novel room acoustics models. Secondly, we postulate on how concepts from state-space theory, such as observability, controllability, and state realization, can be used for developing new inference and control methods for room acoustics.

声学建模状态空间积分方程

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