Design of fractional order digital FIR differentiators using frequency response approximation

In this paper, we present a novel method for the design of fractional order FIR differentiators. Firstly, a fractional order differentiator (FOD) of power digital signal is defined in the frequency domain. Secondly, a FIR filter is chosen to approximate the ideal digital FOD under the weighting mean square error (MSE) sense of the frequency response. Finally, design example and fractional derivative simulation are given and the advantages of the proposed method are illustrated.