A New Look into the Discrete-Time Fractional Calculus: Transform and Linear Systems

Fernando José Almeida Vieira do Coito; Manuel Duarte Ortigueira

doi:10.3182/20130204-3-FR-4032.00078

A New Look into the Discrete-Time Fractional Calculus: Transform and Linear Systems

Fernando José Almeida Vieira do Coito, Manuel Duarte Ortigueira

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

9 Citations (Scopus)

Abstract

A derivative based discrete-time signal processing is presented. Both nabla (forward) and delta (backward) derivatives are studied and generalised including the fractional case. The corresponding exponentials are introduced as eigenfunctions of such derivatives. These lead to discrete-time Laplace transforms that are used to define and study the linear discrete-time derivatives.

Original language	Unknown
Title of host publication	Workshop on Fractional Differentiation and its Applications
Pages	635-640
DOIs	https://doi.org/10.3182/20130204-3-FR-4032.00078
Publication status	Published - 1 Jan 2013
Event	Fractional Differentiation and its Applications - Duration: 1 Jan 2013 → …

Conference

Conference	Fractional Differentiation and its Applications
Period	1/01/13 → …

Access to Document

10.3182/20130204-3-FR-4032.00078

Cite this

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title = "A New Look into the Discrete-Time Fractional Calculus: Transform and Linear Systems",

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AB - A derivative based discrete-time signal processing is presented. Both nabla (forward) and delta (backward) derivatives are studied and generalised including the fractional case. The corresponding exponentials are introduced as eigenfunctions of such derivatives. These lead to discrete-time Laplace transforms that are used to define and study the linear discrete-time derivatives.

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