A Computational Fractional Signal Derivative Method

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.