Design of efficient second and higher order FIR digital differentiators for low frequencies

Abstract

Digital differentiators of orders greater than unity are often required in processing various types of data in a number of practical applications. In many of these, the vital information in the signal is contained in the low frequency range. We propose, in this paper, a new and efficient design of FIR digital differentiators of second and higher orders for the low frequency range. Mathematical relations have been established between the weighting coefficients of the maximally linear (first order) FIR digital differentiators and those of the proposed (second and higher order) differentiators. Recursive as well as explicit formulas for the weighting coefficients of the second order differentiators have also been derived. Extremely high accuracies are obtainable from the proposed differentiators, for attractively low orders of the filters.