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Efficiency, accuracy, and stability issues in discrete-time simulations of single reed wind instruments

Summary: Efficiency, accuracy, and stability issues in discrete-time
simulations of single reed wind instruments
Federico Avanzinia)
Dipartimento di Elettronica e Informatica, Universita` di Padova, Via Gradenigo 6/A, 35131 Padova, Italy
Davide Rocchessob)
Dipartimento di Informatica, Universita` di Verona, Strada Le Grazie 15, 37134 Verona, Italy
Received 1 June 2000; accepted for publication 11 February 2002
A quantitative study of discrete-time simulations for a single reed physical model is presented. It is
shown that when the continuous-time model is discretized, a delay-free path is generated in the
computation. A general solution is proposed to this problem, that amounts to operating a geometrical
transformation on the equations. The transformed equations are discretized using four different
numerical methods. Stability properties of each method are assessed through analysis in the
frequency domain. By comparing the discrete and continuous frequency responses, it is studied how
the physical parameters are mapped by each method into the discrete-time domain. Time-domain
simulations are developed by coupling the four digital reeds to an idealized bore model. Quantitative
analysis of the simulations shows that the discrete-time systems produced by the four methods have
significantly different behaviors, even when high sampling rates are used. As a result of this study,
a general scheme for accurate and efficient time-domain simulations of the single reed model is
proposed. © 2002 Acoustical Society of America. DOI: 10.1121/1.1467674
PACS numbers: 43.75.Pq ADP


Source: Avanzini, Federico - Department of Information Engineering, Universitą degli Studi di Padova


Collections: Computer Technologies and Information Sciences