Physically Inspired Models for the Synthesis of Stiff Strings with Dispersive Waveguides

We review the derivation and design of digital waveguides from physical models of stiff systems, useful for the synthesis of sounds from strings, rods, and similar objects. A transform method approach is proposed to solve the classic fourth-order equations of stiff systems in order to reduce it to t...

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Bibliographic Details
Published in:EURASIP journal on advances in signal processing Vol. 2004; no. 7; p. 463747
Main Authors: Testa, I., Evangelista, G., Cavaliere, S.
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 2004
SpringerOpen
Subjects:
Algorithms
Delay lines
Dispersion curve analysis
dispersive waveguides
frequency warping
Mathematical models
physical models
Physical properties
Regularization
Resonant frequencies
Strings
Synthesis
TECHNOLOGY
TEKNIKVETENSKAP
Warping
Waveguides
physical models
frequency warping
dispersive waveguides
ISSN:1687-6180, 1687-6172, 1687-6180
Online Access:Get full text
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Summary:We review the derivation and design of digital waveguides from physical models of stiff systems, useful for the synthesis of sounds from strings, rods, and similar objects. A transform method approach is proposed to solve the classic fourth-order equations of stiff systems in order to reduce it to two second-order equations. By introducing scattering boundary matrices, the eigenfrequencies are determined and their dependency is discussed for the clamped, hinged, and intermediate cases. On the basis of the frequency-domain physical model, the numerical discretization is carried out, showing how the insertion of an all-pass delay line generalizes the Karplus-Strong algorithm for the synthesis of ideally flexible vibrating strings. Knowing the physical parameters, the synthesis can proceed using the generalized structure. Another point of view is offered by Laguerre expansions and frequency warping, which are introduced in order to show that a stiff system can be treated as a nonstiff one, provided that the solutions are warped. A method to compute the all-pass chain coefficients and the optimum warping curves from sound samples is discussed. Once the optimum warping characteristic is found, the length of the dispersive delay line to be employed in the simulation is simply determined from the requirement of matching the desired fundamental frequency. The regularization of the dispersion curves by means of optimum unwarping is experimentally evaluated.
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ISSN:1687-6180
1687-6172
1687-6180
DOI:10.1155/S1110865704402200