A Computational Fractional Signal Derivative Method. (1st August 2018)

• Record Type: Journal Article
• Authors: Salinas, Matías; Salas, Rodrigo; Mellado, Diego; Glaría, Antonio; Saavedra, Carolina
• Other Names: Hong Jing-song Academic Editor.
• Is Part Of: Modelling and simulation in engineering. Volume 2018(2018)
• Publication Date: 2018-08-01
• Subjects: Engineering -- Simulation methods -- Periodicals; Engineering -- Mathematical models -- Periodicals; 620.004
• DOI: 10.1155/2018/7280306
• Languages: English
• ISSNs: 1687-5591

Abstract

Abstract : We propose an efficient computational method to obtain the fractional derivative of a digital signal. The proposal consists of a new interpretation of the Grünwald–Letnikov differintegral operator where we have introduced a finite Cauchy convolution with the Grünwald–Letnikov dynamic kernel. The method can be applied to any signal without knowing its analytical form. In the experiments, we have compared the proposed Grünwald–Letnikov computational fractional derivative method with the Riemman–Louville fractional derivative approach for two well-known functions. The simulations exhibit similar results for both methods; however, the Grünwald–Letnikov method outperforms the other approach in execution time. Finally, we show an application of how our proposal can be useful to find the fractional relationship between two well-known biomedical signals.