caa a22 4500 606205004 CHVBK 20210128101005.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00034-014-9928-9 doi (NATIONALLICENCE)springer-10.1007/s00034-014-9928-9 Improved Digital Rational Approximation of the Operator $$S^{\alpha }$$ S α Using Second-Order s-to-z Transform and Signal Modeling [Elektronische Daten] [Fouzia Leulmi, Youcef Ferdi] In this paper, an improved stable digital rational approximation of the fractional-order operator $$s^\alpha ,\alpha \in \,R$$ s α , α ∈ R is developed. First, a novel efficient second-order digital differentiator is derived from the transfer function of the digital integrator proposed by Tseng. Then, the fractional power of the new s-to-z transform is expanded using power series expansion (PSE)-signal-modeling technique to obtain stable rational approximation of $$s^\alpha $$ s α . Simulation results show that the proposed rational approximation has better frequency characteristics in almost the whole frequency range than that of existing first-order s-to-z transforms based approximations for different values of the fractional-order $$\alpha $$ α . This paper also shows the benefit of using PSE-signal-modeling approach with first- or second-order mapping functions over PSE-truncation approach that is used in recent works for rational approximation of the operator $$s^\alpha $$ s α , and highlights the major disadvantage of the latter approach that leads to undesirable rational models with complex conjugate poles and zeros. Springer Science+Business Media New York, 2014 s-to-z transform nationallicence Power series expansion nationallicence Deterministic signal modeling nationallicence Fractional-order differentiator nationallicence Fractional-order integrator nationallicence Al-Alaoui's operator nationallicence Leulmi Fouzia LRES Laboratory, Electrical Engineering Department, Skikda University, BP. 26, Route d'El-Hadaîek, 21000, Skikda, Algeria aut Ferdi Youcef LRES Laboratory, Electrical Engineering Department, Skikda University, BP. 26, Route d'El-Hadaîek, 21000, Skikda, Algeria aut Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/6(2015-06-01), 1869-1891 0278-081X 34:6<1869 2015 34 34 https://doi.org/10.1007/s00034-014-9928-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00034-014-9928-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Leulmi Fouzia LRES Laboratory, Electrical Engineering Department, Skikda University, BP. 26, Route d'El-Hadaîek, 21000, Skikda, Algeria aut NATIONALLICENCE 700 1- Ferdi Youcef LRES Laboratory, Electrical Engineering Department, Skikda University, BP. 26, Route d'El-Hadaîek, 21000, Skikda, Algeria aut NATIONALLICENCE 773 0- Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/6(2015-06-01), 1869-1891 0278-081X 34:6<1869 2015 34 34