Digital differentiators for narrow band applications in the lower to midband range

Ripple designs of FIR digital differentiators are suitable for wideband applications, but cannot produce very high accuracies in narrow bands. In this paper, we present new simple designs for FIR digital differentiators, with very high accuracies in the narrow bands centered at arbitrary frequencies in the lower half of the frequency band. First, a new design with maximal linearity at the middle of the frequency band is presented, by imposing the maximal linearity constraints to the frequency response. This design is then combined with an existing design having maximal linearity at zero frequency, to obtain differentiators with very high accuracies at arbitrary frequencies in the lower half of the frequency band. Explicit formulas for the filter coefficients are derived, and design examples are presented to show their higher accuracies as compared to the existing designs.