Class of digital integrators and differentiators

A novel class of infinite impulse response digital integrators and differentiators is developed. A class of digital integrators is first derived from a class of numerical integration rules. A class of digital differentiators is then obtained by inverting the transfer functions of the obtained integrators and stabilising the resulting transfer functions together with magnitude compensation if necessary. Simulated annealing is applied to optimise some of the obtained integrators and differentiators.