New approximation to design fractional order digital FIR differentiators

Abstract

In this paper an accurate and new digital approximation of the fractional-order differentiator (FOD) in the form of FIR filter is presented. This approach is based on power series expansion (PSE) of fractional order operators. First, an analog rational function approximation of the first order analog differentiator is given. The transformation of the analog domain to the discrete domain was made by using Bilinear transformation, which give us the digital version. Then, the digital FOD is obtained by taking fractional power of the ideal first order digital differentiator transfer function. Next, the PSE is applied to design fractional order digital FIR differentiator, with closed form formula. Finally, design examples are shown through the paper to illustrate the performance and the effectiveness of the proposed method.