Theoretical and numerical modeling of wind instruments: virtual lutherie and time-domain simulations

Abstract

The present research work deals with the synthesis of the sound produced by a wind instrument through the direct physical modeling. Specifically the purpose is the development theoretical physical models and numerical solution procedures aimed at the time–domain simulations. The attention is mainly focused on two fundamental topics: the identification of the acoustic response of the resonator as well as the environment in which the performance takes place, and the characterization of the interaction between the resonator and the musician, with particular emphasis to the connection between the mathematical parameters governing the physics of the phenomenon and the properties of the resulting sound. The acoustical characterization of the resonators and the surroundings is addressed with a prime–principles based approach. The simulation of the acoustic field produced by the instruments alone and in a realistic performing environment is achieved using an integral representation in the frequency–domain. A particular attention is paid to the identification of the transfer functions aimed at the auralized signal propagation. A simplified model of valve is used to represent the exciter behaviour. The attention has been especially focused on the analysis of a brass instrument during the performance, since the link between the acousto–elastic coupled system and the performed note is crucial. The transfer functions have been analytically approximated as rational functions in the frequency–domain in order to obtain a block diagram representation of the dynamical system suitable for real–time application. The algorithm has demonstrated to be accurate and efficient in offline calculation, and the observed performance discloses the possibility to implement real–time applications compatible with the consumer devices currently available on the market.