On the design of FIR digital differentiators which are maximally linear at the frequency p/p, p ∈ {positive integers}

Digital differentiators (DDs) which are maximally linear at the spot frequency ω=p/p, p ∈ {positive integers} are proposed for operation over a narrow band of frequencies. The suggested DDs, besides giving zero phase error over the entire band of frequencies (-π<ω<π), can achieve very high accuracy in the magnitude response, over a given frequency range, with attractively low order of structure. For example, for p=3, magnitude accuracy better than 99.999% can be achieved over the passband 0.26π<ω<0.41π with an order of structure of 21. Mathematical formulas for the weighting coefficients required in the design have also been given