Maximally linear FIR digital differentiators for high frequencies

The frequency response of conventional FIR digital differentiators (DD), using only integral delays, is poor towards the high frequency end, and becomes identically zero at w=π. To overcome this problem, a half-sample delay, z^-1/2, is used in the minimax relative error DDs. However, the order of such DDs grows exponentially when accuracies better than 99.0% are desired. The authors propose maximally linear DDs, using one half-sample delay, which can achieve a frequency response accuracy better than 99.9%, with attractively low orders for 0.5π⩽w⩽π. Mathematical formulas have been derived for computing the coefficients for the design