On the Equivalence between Integer-and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems

Manuel Duarte Ortigueira, Richard L. Magin

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9 Citations (Scopus)
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Abstract

The equivalence of continuous-/discrete-time autoregressive-moving average (ARMA) systems is considered in this paper. For the integer-order cases, the interrelations between systems defined by continuous-time (CT) differential and discrete-time (DT) difference equations are found, leading to formulae relating partial fractions of the continuous and discrete transfer functions. Simple transformations are presented to allow interconversions between both systems, recovering formulae obtained with the impulse invariant method. These transformations are also used to formulate a covariance equivalence. The spectral correspondence implied by the bilinear (Tustin) transformation is used to study the equivalence between the two types of systems. The general fractional CT/DT ARMA systems are also studied by considering two DT differential fractional autoregressive-moving average (FARMA) systems based on the nabla/delta and bilinear derivatives. The interrelations CT/DT are also considered, paying special attention to the systems defined by the bilinear derivatives.

Original languageEnglish
Article number242
Number of pages34
JournalFractal and Fractional
Volume6
Issue number5
DOIs
Publication statusPublished - 28 Apr 2022

Keywords

  • autoregressive-moving average
  • bilinear discrete-time systems
  • continuous-time ARMA
  • discrete-time ARMA
  • embedding
  • equivalence
  • FARMA
  • fractional ARMA
  • identification

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