Design of digital differentiator using difference formula and Richardson extrapolation

The design of digital differentiators is investigated. First, the backward difference formula in numerical differentiation is applied to derive the transfer function of a digital differentiator. In this design, the Richardson extrapolation is used to generate high-accuracy results while using low-order formulas. Then, conventional Lagrange finite impulse response (FIR) and Thiran infinite impulse response (MR) allpass fractional delay filters are directly applied to implement the designed differentiator. Next, the proposed method is extended to design digital differentiators using central difference formula. Finally, several numerical examples are illustrated to demonstrate the effectiveness of this new design approach.