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Volume 113, Issue 1, January 2003
- MUSIC AND MUSICAL INSTRUMENTS 
113(2003); http://dx.doi.org/10.1121/1.1515776View Description Hide Description
A method for simulation of acoustical bores, useful in the context of sound synthesis by physical modeling of woodwind instruments, is presented. As with previously developed methods, such as digital waveguidemodeling (DWM) [Smith, Comput. Music J. 16, 74–91 (1992)] and the multi convolution algorithm (MCA) [Martı́nez et al., J. Acoust. Soc. Am. 84, 1620–1627 (1988)], the approach is based on a one-dimensional model of wave propagation in the bore. Both the DWM method and the MCA explicitly compute the transmission and reflection of wave variables that represent actual traveling pressure waves. The method presented in this report, the wave digital modeling (WDM) method, avoids the typical limitations associated with these methods by using a more general definition of the wave variables. An efficient and spatially modular discrete-time model is constructed from the digital representations of elemental bore units such as cylindrical sections, conical sections, and toneholes. Frequency-dependent phenomena, such as boundary losses, are approximated with digital filters. The stability of a simulation of a complete acoustic bore is investigated empirically. Results of the simulation of a full clarinet show that a very good concordance with classic transmission-line theory is obtained.