Discrete-time fractional signals and systems

Manuel D. Ortigueira, Jose Antonio Tenreiro Machado, Fernando J. V. Coito, Gabriel Bengochea

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


In this chapter, we formulate a coherent theory for discrete-time signals and systems taking two derivatives, namely the nabla (forward) and delta (backward), as basis. The eigenfunctions of such derivatives are the nabla and delta exponentials. With these eigenfunctions, two discrete-time Laplace transforms are introduced and their properties studied. These transforms are used to study the discrete-time linear systems defined by differential equations. The notions of impulse response and transfer function are introduced and discussed. Moreover, the Fourier transform and the frequency response are also considered. The framework is compatible with classic discrete-time signals and systems and allow for a uniform approximation of continuous systems when the sampling interval is reduced to zero.

Original languageEnglish
Title of host publicationApplications in Engineering, Life and Social Sciences, Part B
PublisherDe Gruyter
Number of pages30
ISBN (Electronic)9783110571929
ISBN (Print)9783110570922
Publication statusPublished - 1 Jan 2019


  • Delta laplace transform
  • Discrete-time
  • Fractional
  • Nabla laplace transform
  • Time scale


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