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 |
Files in This Item:
File | Description | Size | Format | |
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[343]CNSNS_Ortigueira_Torres_Trujillo.pdf | 597.89 kB | Adobe PDF |
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