| Summary: | In this paper we develop rational discrete-time approximations (IIR filters) to continuous fractional-order integrators and differentiators of type sα, α ∈ ℜ. For that, it is proposed the adoption of the techniques of Padé, Prony and Shanks usually applied in the signal modelling 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 this approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, through several examples.
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