Novel Fractional-Order Difference Schemes Reducible to Standard Integer-Order Formulas
| Autor: | Milorad P. Paskas, Irini Reljin, Branimir Reljin |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Applied Mathematics
Mathematical analysis 020206 networking & telecommunications 02 engineering and technology Derivative Image segmentation Type (model theory) Transfer function Fractional calculus symbols.namesake Fourier transform Integer Signal Processing 0202 electrical engineering electronic engineering information engineering symbols Order (group theory) Applied mathematics 020201 artificial intelligence & image processing Electrical and Electronic Engineering Mathematics |
| Zdroj: | IEEE Signal Processing Letters. 24:912-916 |
| ISSN: | 1558-2361 1070-9908 |
| Popis: | In this letter, we advise numerical schemes for calculation of fractional derivatives of Grunwald–Letnikov type that reduce to standard integer-order derivative schemes. Since, in the literature, only forward differences have such a property, here, novel forms of backward differences and central differences based both on integer and half-integer mesh points are proposed. It enables the use of the proposed fractional differences interchangeably with standard difference formulas. The proposed schemes are qualitatively and quantitatively tested on 2-D signals for texture enhancement. The obtained results show that the proposed fractional differences provide better performances in comparison to traditional schemes. |
| Databáze: | OpenAIRE |
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