Numerical Computation of the Transfer Functions of an Axisymmetric Duct with the Extended Discrete Singular Convolution Method
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08.07.2014
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06 - Presentation
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France
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Abstract
This work takes part of the "cagima" project (supported by the ANR) which investigates the defects of
the tuning of reed musical instruments as well as their homogeneity of emission and timbre. The goal
consists in replacing the traditional approach adopted by instrument makers by a global and rational
approach in the design of new instruments /ab initio/ (called "logical instruments"), minimizing some
identi ed defects. In this context, an interactive virtual model, predictive and con gurable is proposed.
Several approaches are available in the literature but the main di culty is to design digital instruments
that are accurate (according to measurements) and that can be implemented in real-time. In this
paper, an approach based on the Extended Discrete Singular Convolution method (EDSC) is proposed.
The temporal operator (including the fractional derivative term for viscothermal losses) is implemented
according to the EDSC formalism. The method allows a fast, straightforward and accurate computation
of the transfer functions of an axisymmetric duct with an arbitrary pro le. The computation of the
case where the losses are dependent from the diameter causes no noticeable di culty. The results are
compared to measurements of a trombone bell.
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Musical acoustics
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International Symposium on Musical Acoustics
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English
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Published
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Taillard, P.-A., Hélie, T., & Bensoam, J. (2014, July 8). Numerical Computation of the Transfer Functions of an Axisymmetric Duct with the Extended Discrete Singular Convolution Method. International Symposium on Musical Acoustics. https://doi.org/10.26041/fhnw-200