Novel class of digital integrators and differentiators

A novel class of digital integrators and differentiators is presented. These first-order filters are very convenient for real-time applications. Every integrator is expressed as a weighted sum of the classical rectangular and trapezoidal integrators, with the additional constraint of a minimum phase. The corresponding differentiator is obtained by inverting the transfer function of the integrator. The filter class depends on a parameter. Properties of the filters are derived and the filter parameter is determined according to different chosen criteria. The capability of these filters to approximate the ideal linear phase integrator and differentiator with good accuracy and over a large frequency band is shown.