Implementation numerique du retard d’ordre fractionnaire

Abstract

In the recent years, the fractional order digital delay concept has been found to be useful in several practical problems in diffe rent fields of engineering. The transfer function of this ideal fractional order digital delay is given by: m z D(z) − = , with 0 < m < 1 Because of its representation by an irrational transfer function, the ideal fractional order digital delay cannot be exac tly implemented; only a lim ited implementation may be accomplished using approximation methods. In this thesis design methods of stable, causa l and minimum phase digital IIR filter, based on fractional order systems and operators, approximating the ideal fractional order digital delay z -m (0 < m <1) are presented. Illustrative exampl es and applications have been presented to demonstrate the effectiveness and the exactitude of the proposed fractional delay digital filter design methods. The simulation results obtained have been discussed and compared to the most recent implementation methods of the ideal fractional order dela y in the literature