Design of linear phase IIR digital differentiators and integrators for multipurpose applications

A new kind of multipurpose filters which act as a differentiator in lower half of the Nyquist frequency range and as an integrator in upper half of the Nyquist frequency range, and vice-versa, are presented. These filters have infinite impulse response (IIR) and are derived using Genetic algorithm optimization technique. The phase responses of the proposed designs are almost linear over the entire Nyquist frequency range. These designs are only of second order, and suitable for cost sensitive real time signal processing applications.