A rational approximation is the preliminary step of all the indirect methods for implementing digital fractional differintegrators s^nu, with nu in R, 0 < |nu| < 1, and where s in C. This paper employs the convergents of two Thiele’s continued fractions as rational approximations of s^nu. In a second step, it uses known s-to-z transformation rules to obtain a rational, stable, and minimum-phase z-transfer function,with zeros interlacing poles. The paper concludes with a comparative analysis of the quality of the proposed approximations in dependence of the used s-to-z transformations and of the sampling period.

Thiele’s continued fractions in digital implementation of noninteger differintegrators / Maione, Guido. - In: SIGNAL, IMAGE AND VIDEO PROCESSING. - ISSN 1863-1703. - 6:3(2012), pp. 401-410. [10.1007/s11760-012-0319-z]

Thiele’s continued fractions in digital implementation of noninteger differintegrators

MAIONE, Guido
2012-01-01

Abstract

A rational approximation is the preliminary step of all the indirect methods for implementing digital fractional differintegrators s^nu, with nu in R, 0 < |nu| < 1, and where s in C. This paper employs the convergents of two Thiele’s continued fractions as rational approximations of s^nu. In a second step, it uses known s-to-z transformation rules to obtain a rational, stable, and minimum-phase z-transfer function,with zeros interlacing poles. The paper concludes with a comparative analysis of the quality of the proposed approximations in dependence of the used s-to-z transformations and of the sampling period.
2012
Thiele’s continued fractions in digital implementation of noninteger differintegrators / Maione, Guido. - In: SIGNAL, IMAGE AND VIDEO PROCESSING. - ISSN 1863-1703. - 6:3(2012), pp. 401-410. [10.1007/s11760-012-0319-z]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/8448
Citazioni
  • Scopus 22
  • ???jsp.display-item.citation.isi??? 17
social impact