Design of Fractional Order Digital Differentiator Using Radial Basis Function

In this paper, the design of fractional order digital differentiator is investigated. First, the radial basis function interpolation method is described. Then, the non-integer delay sample estimation of discrete-time sequence is derived by using the radial basis function interpolation approach. Next, the Grünwald-Letnikov derivative and non-integer delay sample estimation are applied to obtain the transfer function of fractional order digital differentiator. Finally, the applications in digital image sharpening and parameter estimation of fractional noise process are studied to demonstrate the usefulness of this new design approach.