Representations with poles and cuts for the time-domain simulation of fractional systems and irrational transfer functions

Authors:
Thomas Hélie;Denis Matignon
Affiliations:
Laboratoire des Sciences et Technologie de la Musique et du Son, Equipe Analyse/Synthèse, Ircam, Centre Georges Pompidou, Paris, France;Laboratoire Traitement et Communication de l'Information, Département Traitement du Signal et des Images, Télécom Paris, Paris, France
Venue:
Signal Processing - Fractional calculus applications in signals and systems
Year:
2006

Citing 2
Cited 2

Identifiability of parametric models

Identifiability of parametric models
Brief Analysis of fractional delay systems of retarded and neutral type

Automatica (Journal of IFAC)

Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme

Computers & Mathematics with Applications
Digital waveguide modeling for wind instruments: building a state-space representation based on the Webster-Lokshin model

IEEE Transactions on Audio, Speech, and Language Processing - Special issue on virtual analog audio Effects and musical instruments

Quantified Score

Hi-index	0.00

Visualization

Abstract

Fractional differential systems are infinite-dimensional systems which are difficult to study and simulate: they can be represented with poles and cuts. This representation applies to a wider class of irrational transfer functions, and is most useful for signal processing purposes, such as frequency-domain and time-domain simulations: the approximations in low dimension which give the most striking numerical results are obtained through an optimization procedure, the parameters of which are meaningful from a signal point of view. Ten such systems of increasing complexity are thoroughly investigated.