Digital sound synthesis of string instruments with the functional transformation method

  • Authors:
  • Rudolf Rabenstein;Lutz Trautmann

  • Affiliations:
  • University of Erlangen-Nürnberg, Multimedia Communications and Signal Processing, Cauerstr. 7, D-91058 Erlangen, Germany;University of Erlangen-Nürnberg, Multimedia Communications and Signal Processing, Cauerstr. 7, D-91058 Erlangen, Germany

  • Venue:
  • Signal Processing - Special section: Hans Wilhelm Schüßler celebrates his 75th birthday
  • Year:
  • 2003

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Abstract

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.