Window based design of fractional order FIR digital differentiator using type- III discrete cosine transform

A method of designing a fractional order digital FIR differentiator using Type-III Discrete Cosine Transform is put forward in this paper. The Grünwald-Letnikov definition of Fractional calculus is implemented to calculate the filter coefficients of fractional order differentiator. Then, different windows are applied to modify the filter response that improve the accuracy of the linear phase FIR filter design. The frequency response of the designed filter is a very close approximation to the ideal response which clearly indicate the validity of our approach. Finally, the design examples compare the results with different windows and demonstrate that the design error with the proposed method are smaller than that with the conventional DCT technique. Extensive simulation results affirm that the proposed approach using DCT-III outperform its counter part DCT-II not only in terms of magnitude response but also in terms of phase response.