Improved design of IIR digital differentiator using Richardson extrapolation and fractional delay

In this paper, the improved designs of IIR digital Al-Alaoui and Tustin differentiators are presented. First, the fractional delay is used to reduce the errors of differentiators in the high frequency region. Then, the Richardson extrapolation is utilized to generate high-accuracy results while using low-order formulas. Next, conventional Lagrange FIR fractional delay filter is directly applied to implement the designed IIR differentiator. Finally, several numerical examples are illustrated to demonstrate the effectiveness of this improved design approach.