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Réalisation en guides d'ondes numériques stables d'un modèle acoustique réaliste pour la simulation en temps-réel d'instruments à vent

Abstract : This work deals with the physical modelling of acoustic tubes for digital simulation in real-time. The main application is the sound synthesis of wind instruments, with a realistic model, a modular method and a low-cost digital implementation. The acoustic model of "Webster-Lokshin", used in this work, is an unidimensional model which takes into account the "curvature" of the profile and the "visco-thermal losses" at the wall. With this acoustic model, we obtain a framework for simulation which is compatible with the "Waveguides" approach: a tube is then represented by a system with delays and closed loops, involving several sub-systems without internal delay. A difficulty is the presence of infinite-dimensional sub-systems which behave as infinite sums of first or second order systems. First, they are approximated by finite-dimensional systems, then their "state-space representation" in the discrete time domain is determined. Finally, using standard tools of automatic control, these representations facilitate the connection of acoustic elements and reduce the computational complexity of the digital simulation. In this work, an analysis of the stability and passivity of this approach is described. For some particular cases of tubes, a problem occurs: even if the input/output relations of the tube are stable, some sub-systems have an infinity of singularities which produce internal instabilities in the system. We present an explanation of this phenomenon and to solve this problem, a new decomposition into sub-systems is performed.
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https://pastel.archives-ouvertes.fr/tel-00456997
Contributor : Rémi Mignot <>
Submitted on : Tuesday, May 25, 2010 - 11:01:38 AM
Last modification on : Thursday, March 21, 2019 - 2:41:37 PM
Long-term archiving on: : Thursday, September 23, 2010 - 12:41:55 PM

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  • HAL Id : tel-00456997, version 2

Citation

Rémi Mignot. Réalisation en guides d'ondes numériques stables d'un modèle acoustique réaliste pour la simulation en temps-réel d'instruments à vent. Traitement du signal et de l'image [eess.SP]. Télécom ParisTech, 2009. Français. ⟨tel-00456997v2⟩

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