Time domain design of fractional differintegrators using least-squares

Authors:
Ramiro S. Barbosa;J. A. Tenreiro Machado;Manuel F. Silva
Affiliations:
Department of Electrotechnical Engineering, Institute of Engineering of Porto, Porto, Portugal;Department of Electrotechnical Engineering, Institute of Engineering of Porto, Porto, Portugal;Department of Electrotechnical Engineering, Institute of Engineering of Porto, Porto, Portugal
Venue:
Signal Processing - Fractional calculus applications in signals and systems
Year:
2006

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Abstract

In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type sα, α ∈ R. Adoption of the Padé, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.