Novel class of digital integrators and differentiators

A novel class of IIR (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 subsequently obtained by inverting the transfer functions of the obtained integrators and stabilizing the resulting transfer functions together with magnitude compensation if necessary. Simulated annealing is applied to optimize some of the obtained integrators and differentiators. [Notice to the Reader: It is recommended by the Editor-in-Chief that the following article not be used for citation after it was determined that it was substantially different from the reviewed and accepted version.]