MAXACC FIR digital differentiators of higher degrees

Digital differentiators of higher degrees are generally realized by cascading multiple first-degree differentiators, which makes them computationally inefficient. In our previous work, we have presented closed form designs of first-degree maximally linear digital differentiators based on the Taylor series. In this paper, we extend that work and present new designs of maximally accurate digital differentiators of arbitrary degrees. Explicit formulas and recursive relationships between tap-coefficients are given, which make their computation very simple.