Rabenstein R, Trautmann L (2003)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2003
Publisher: Elsevier
Book Volume: 83
Pages Range: 1673-1688
Journal Issue: 8
DOI: 10.1016/S0165-1684(03)00083-5
The theory of multidimensional continuous and discrete systems is applied to derive a parametric description of musical sounds from a physical model of real or virtual string instruments. The mathematical representation of this model is given by a partial differential equation for a vibrating string. Suitable functional transformations with respect to time and space turn this partial differential equation into a multidimensional transfer function. It is the starting point for the derivation of a discrete-time system by classical analog to discrete transformations. The coefficients of this discrete model depend explicitly on the geometric properties and material constants of the underlying physical model. This ensures a meaningful behaviour of the discrete system under varying conditions and allows for an intuitive control by the user. Furthermore, the performance of real-time implementations is discussed. Finally, several extensions of this synthesis method for computer music applications are presented. © 2003 Elsevier Science B.V. All rights reserved.
APA:
Rabenstein, R., & Trautmann, L. (2003). Digital sound synthesis of string instruments with the functional transformation method. Signal Processing, 83(8), 1673-1688. https://dx.doi.org/10.1016/S0165-1684(03)00083-5
MLA:
Rabenstein, Rudolf, and Lutz Trautmann. "Digital sound synthesis of string instruments with the functional transformation method." Signal Processing 83.8 (2003): 1673-1688.
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