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

Fuente: arXiv
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Main Authors: Ali, Randall, Dietzen, Thomas, Scerbo, Matteo, De Sena, Enzo, van Waterschoot, Toon
Format: Preprint
Published: 2026
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_version_ 1866911604215382016
author Ali, Randall
Dietzen, Thomas
Scerbo, Matteo
De Sena, Enzo
van Waterschoot, Toon
author_facet Ali, Randall
Dietzen, Thomas
Scerbo, Matteo
De Sena, Enzo
van Waterschoot, Toon
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_16970
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A state-space representation of the boundary integral equation for room acoustic modelling
Ali, Randall
Dietzen, Thomas
Scerbo, Matteo
De Sena, Enzo
van Waterschoot, Toon
Audio and Speech Processing
Sound
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.
title A state-space representation of the boundary integral equation for room acoustic modelling
topic Audio and Speech Processing
Sound
url https://arxiv.org/abs/2604.16970