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Title: A new least-squares approach to differintegration modeling
Author: Ortigueira, M.D.
Serralheiro, António J.
Keywords: Discrete-time fractional differintegrator
Pseudo-fractional ARMA
Gru¨ nwald–Letnikov derivative
Tustin bilinear transformation
Issue Date: Oct-2006
Publisher: Elsevier B.V.
Abstract: In this paper a new least-squares (LS) approach is used to model the discrete-time fractional differintegrator. This approach is based on a mismatch error between the required response and the one obtained by the difference equation defining the auto-regressive, moving-average (ARMA) model. In minimizing the error power we obtain a set of suitable normal equations that allow us to obtain the ARMA parameters. This new LS is then applied to the same examples as in [R.S. Barbosa, J.A. Tenreiro Machado, I.M. Ferreira, Least-squares design of digital fractional-order operators, FDA’2004 First IFAC Workshop on Fractional Differentiation and Its Applications, Bordeaux, France, July 19–21, 2004, P. Ostalczyk, Fundamental properties of the fractional-order discrete-time integrator, Signal Processing 83 (2003) 2367–2376] so performance comparisons can be drawn. Simulation results show that both magnitude frequency responses are essentially identical. Concerning the modeling stability, both algorithms present similar limitations, although for different ARMA model orders.
Description: Signal Processing, Vol. 86, nº 10
ISSN: 0165-1684
Appears in Collections:FCT: DEE - Artigos em revista internacional com arbitragem científica

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