A Novel approach to design Fractional Order Digital Differentiator using Power Function and Least-Square method

Abstract: In thi s p a p e r , we have proposed a t e c h n i q u e for designing of fractional order d i g i t a l differentiator by use of power f u n c t i o n and l e a s t -square method. The input signal is altered into a power function by using Taylor series expansion and its fractional derivativ e is calculated using the Grunwald-Letnikov explanation. Then, fractional order digital differentiator is demonstrated as a finite impulse response (FIR) system, which produces fractional order derivative of the Grunwald-Letnikov cat egory for a power function. The FIR system coefficients are achieved by using least square method . Two illustrations are used to demonstrate that the fractional derivative of the digital signals is calculated by using the suggested technique. The results of the second example divulges that the suggested method gives superior performance in comparison to existing filtering method.

Keywords: Digital differentiator, Fractional order differentiator (FOD), Finite impulse response (FIR), Fractional derivative, Least Square (LS) method, Grunwald-Letnikov definition.