Design of fractional order differentiator using discrete fourier transform interpolation

In this paper, the design of digital fractional order differentiator is presented. First, the discrete Fourier transform (DFT) interpolation method is described. Then, the non-integer delay sample estimation of discrete-time signal is derived by using DFT interpolation method. Next, the Grünwald-Letnikov derivative and non-integer delay sample estimation are used to get the transfer function of digital fractional order differentiator. Finally, several numerical examples are shown to demonstrate the effectiveness of this new design approach.