Open Access

Audio Effects Based on Biorthogonal Time-Varying Frequency Warping

EURASIP Journal on Advances in Signal Processing20012001:289319

DOI: 10.1155/S1110865701000130

Received: 31 March 2000

Published: 1 March 2001

Abstract

We illustrate the mathematical background and musical use of a class of audio effects based on frequency warping. These effects alter the frequency content of a signal via spectral mapping. They can be implemented in dispersive tapped delay lines based on a chain of all-pass filters. In a homogeneous line with first-order all-pass sections, the signal formed by the output samples at a given time is related to the input via the Laguerre transform. However, most musical signals require a time-varying frequency modification in order to be properly processed. Vibrato in musical instruments or voice intonation in the case of vocal sounds may be modeled as small and slow pitch variations. Simulation of these effects requires techniques for time-varying pitch and/or brightness modification that are very useful for sound processing. The basis for time-varying frequency warping is a time-varying version of the Laguerre transformation. The corresponding implementation structure is obtained as a dispersive tapped delay line, where each of the frequency dependent delay element has its own phase response. Thus, time-varying warping results in a space-varying, inhomogeneous, propagation structure. We show that time-varying frequency warping is associated to an expansion over biorthogonal sets generalizing the discrete Laguerre basis. Slow time-varying characteristics lead to slowly varying parameter sequences. The corresponding sound transformation does not suffer from discontinuities typical of delay lines based on unit delays.

Keywords

signal transformations frequency warping Laguerre transform Kautz functions

Authors’ Affiliations

(1)
École Polytechnique Fédérale de Lausanne
(2)
Department of Physical Sciences, University of Naples

Copyright

© Evangelista and Cavaliere 2001