Designing digital IIR low-pass differentiators with multi-objective optimization

In this paper we examine the possibility of designing IIR low-pass differentiators by approaching it as a weighted multi-objective optimization problem and solving it with an unbiased metaheuristic search algorithm. By collecting several solutions with different sets of weights we are able to make a thorough comparison of different design strategies. We present possible designs that are realizable with (1) cascading classical IIR low-pass filters with appropriate operators, and (2) non-cascaded general IIR differentiator designs. Elliptical filters are found to be the most magnitude-optimal among the first type. However, the non-cascaded approach found more optimal IIR differentiators at the expense of a more complicated search. Finally, we present some non-cascaded general designs that compare favorably with the available designs given in literature, and which we reason are nearly optimal.