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Representations with poles and cuts for the time-domain simulation of fractional systems and irrational transfer functions

Abstract : Fractional differential systems are infinite-dimensional systems which are difficult to study and simulate: they can be represented with poles and cuts. This representation applies to a wider class of irrational transfer functions, and is most useful for signal processing purposes, such as frequency-domain and time-domain simulations: the approximations in low dimension which give the most striking numerical results are obtained through an optimization procedure, the parameters of which are meaningful from a signal point of view. Ten such systems of increasing complexity are thoroughly investigated.
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Thomas Hélie, Denis Matignon. Representations with poles and cuts for the time-domain simulation of fractional systems and irrational transfer functions. Signal Processing, Elsevier, 2006, vol. 86 (n° 10), pp. 2516-2528. ⟨10.1016/j.sigpro.2006.02.017⟩. ⟨hal-01373404⟩

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