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Thiele’s continued fractions in digital implementation of noninteger differintegrators

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Abstract

A rational approximation is the preliminary step of all the indirect methods for implementing digital fractional differintegrators s ν, with \({\nu \in \mathbb{R}, 0<|\nu| <1 }\) , and where \({s \in \mathbb{C}}\) . This paper employs the convergents of two Thiele’s continued fractions as rational approximations of s ν. 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.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, Technical University of Bari, Via E. Orabona, 4, 70125, Bari, Italy

    Guido Maione

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  1. Guido Maione
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Correspondence to Guido Maione.

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Maione, G. Thiele’s continued fractions in digital implementation of noninteger differintegrators. SIViP 6, 401–410 (2012). https://doi.org/10.1007/s11760-012-0319-z

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  • DOI: https://doi.org/10.1007/s11760-012-0319-z

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