A Computational Fractional Signal Derivative Method. Salinas, M., Salas, R., Mellado, D., Glaría, A., & Saavedra, C. Modelling and Simulation in Engineering, 2018:1–10, August, 2018.
A Computational Fractional Signal Derivative Method [link]Paper  doi  abstract   bibtex   
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.
@article{salinas_computational_2018,
	title = {A {Computational} {Fractional} {Signal} {Derivative} {Method}},
	volume = {2018},
	issn = {1687-5591, 1687-5605},
	url = {https://www.hindawi.com/journals/mse/2018/7280306/},
	doi = {10.1155/2018/7280306},
	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.},
	language = {en},
	urldate = {2018-08-06},
	journal = {Modelling and Simulation in Engineering},
	author = {Salinas, Matías and Salas, Rodrigo and Mellado, Diego and Glaría, Antonio and Saavedra, Carolina},
	month = aug,
	year = {2018},
	keywords = {mentions sympy},
	pages = {1--10},
}

Downloads: 0