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A natural transfer function space for linear discrete time-invariant and scale-invariant systems

Daniel Alpay 1 Mamadou Mboup 2, 3
3 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
Abstract : In a previous work, we have defined the scale shift for a discrete-time signal and introduced a family of linear scale-invariant systems in connection with character-automorphic Hardy spaces. In this paper, we prove a Beurling-Lax theorem for such Hardy spaces of order 2. We also study an interpolation problem in these spaces, as a first step towards a finite dimensional implementation of a scale invariant system. Our approach uses a characterization of character-automorphic Hardy spaces of order 2 in terms of classical de Branges Rovnyak spaces.
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Submitted on : Wednesday, November 4, 2009 - 12:37:11 PM
Last modification on : Tuesday, November 24, 2020 - 2:18:20 PM
Long-term archiving on: : Tuesday, October 16, 2012 - 1:01:22 PM

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Daniel Alpay, Mamadou Mboup. A natural transfer function space for linear discrete time-invariant and scale-invariant systems. International Workshop on Multidimensional (nD) Systems, 2009- NDS 2009 (Invited session), Jun 2009, Thessaloniki, Greece. pp.1-4, ⟨10.1109/NDS.2009.5196173⟩. ⟨inria-00428994⟩

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