Design of FIR first order digital differentiators of variable fractional sample delay using maximally flat error criterion

Optimum (in a maximally flat frequency response error sense) FIR digital differentiators of variable fractional sample delay are derived that calculate the derivative of an input uniformly sampled discrete-time signal with arbitrary centre frequency at an arbitrarily chosen instant of time within each sampling interval. The proposed class of differentiators includes maximally linear differentiators for low frequencies