Closed-Form Rational Approximations of Fractional, Analog and Digital Differentiators/Integrators

Author

Maione, Guido

Author_Institution

Diparitmento di Ing. Elettr. e dell´Inf., Politec. di Bari, Bari, Italy

Volume

3

Issue

3

fYear

2013

fDate

Sept. 2013

Firstpage

322

Lastpage

329

Abstract

This paper provides closed-form formulas for coefficients of convergents of some popular continued fraction expansions (CFEs) approximating s^ν, with , and (2/T)^ν((z-1)/(z+1))^ν. The expressions of the coefficients are given in terms of ν and of the degree n of the polynomials defining the convergents. The formulas greatly reduce the effort for approximating fractional operators and show the equivalence between two well-known CFEs in a given condition.

Keywords

analogue integrated circuits; convergence; digital integrated circuits; function approximation; polynomial approximation; CFE; analog differentiators-integrators; approximating fractional operators; closed-form rational approximations; continued fraction expansions; convergent coefficients; digital differentiators-integrators; fractional differentiators-integrators; Analog and discrete fractional-order operators; approximation; continued fractions; fractional-order controllers; realization of noninteger order circuits and systems;

fLanguage

English

Journal_Title

Emerging and Selected Topics in Circuits and Systems, IEEE Journal on

Publisher

ieee

ISSN

2156-3357

Type

jour

DOI

10.1109/JETCAS.2013.2268949

Filename

6547753