Digital differentiator design using fractional delay filter and limit computation

In this paper, the design of digital differentiator is investigated. First, the relation between fractional delay filter and first-order differentiator is established such that the differentiator can be obtained from fractional delay filter by using the computation of limit. Then, conventional finite-impulse response (FIR), allpass and Farrow-based fractional delay filters are directly applied to design first-order differentiator. Next, the proposed method is extended to design high-order differentiators. Finally, several design examples are illustrated to demonstrate the effectiveness of this new design approach.