Design of second order digital differentiator using Richardson extrapolation and fractional delay

In this paper, the design of second order differentiator is investigated. First, the backward difference formula in numerical differentiation is applied to derive the transfer function of second order differentiator. Then, the Richardson extrapolation is used to generate high-accuracy results while using low-order formulas. Next, conventional Lagrange FIR fractional delay filter is directly applied to implement the designed second order differentiator. Finally, several numerical examples are illustrated to demonstrate the effectiveness of this new design approach.