Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/16656
Title: Exponentials and Laplace transforms on nonuniform time scales
Author: Ortigueira, Manuel D.
Torres, Delfim F.M.
Trujillo, Juan J.
Keywords: Time-scale calculus
Exponentials
Generalised Laplace and Z transforms
Systems theory
Fractional derivatives
Issue Date: Oct-2016
Publisher: Elsevier
Abstract: We formulate a coherent approach to signals and systems theory on time scales. The two derivatives from the time-scale calculus are used, i.e., nabla (forward) and delta (backward), and the corresponding eigenfunctions, the so-called nabla and delta exponentials, computed. With these exponentials, two generalised discrete-time Laplace transforms are deduced and their properties studied. These transforms are compatible with the standard Laplace and Z transforms. They are used to study discrete-time linear systems defined by difference equations. These equations mimic the usual continuous-time equations that are uniformly approximated when the sampling interval becomes small. Impulse response and transfer function notions are introduced. This implies a unified mathematical framework that allows us to approximate the classic continuous-time case when the sampling rate is high or to obtain the standard discrete-time case, based on difference equations, when the time grid becomes uniform. © 2016 Elsevier B.V.
Peer review: yes
URI: http://hdl.handle.net/10773/16656
DOI: 10.1016/j.cnsns.2016.03.010
ISSN: 1007-5704
Appears in Collections:CIDMA - Artigos

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