A class of second-order integrators and low-pass differentiators

A novel class of stable, minimum phase, second-order, low-pass IIR digital differentiators is developed. It is obtained by inverting the transfer functions of a class of second-order integrators, stabilizing the resulting transfer functions, and compensating their magnitudes. The class of second-order integrators is obtained by interpolating the traditional Simpson and trapezoidal integrators. The resulting integrators have a perfect -90° phase over the Nyquist interval and could better approximate the ideal magnitude response than either of the two traditional integrators. In addition to the above two integrators, the Tick integrator is also a member of the class. The resulting integrators and differentiators extend the frequency range of operation beyond that possible by using either of the two traditional integrators. The low order and high accuracy of the filters make them attractive for real time applications