Design of linear phase IIR digital diff-integrators

This paper presents a new kind of multi-purpose filter which acts 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. Thus, same filter can be used as a differentiator as well as an integrator in different frequency bands. The transfer functions of the proposed systems have infinite impulse response (IIR) and are derived using genetic algorithm optimization technique. The beauty of the proposed transfer functions is that these are only of second order and have almost linear phase response over the full Nyquist frequency range.