Design of digital differentiators satisfying prescribed specifications using optimization techniques

Two methods for the design of nonrecursive digital differentiators based on standard optimization methods are described. The methods are used in conjunction with the prediction technique for the differentiator order described by A. Antoniou and C. Charalambous (Proc. IEE, vol.128, pt.E, no.5, p.190-6, Sept. 1981) to design several differentiators, assuming first a prescribed bandwidth and various prescribed maximum in-band errors and then a prescribed maximum in-band error and various prescribed bandwidths. The methods are also used to design a wideband differentiator. The designs obtained satisfy the prescribed specifications in all cases. The results show that the even-order digital differentiators require lower order for the same prescribed specifications and that the error function with weighting yields better results in terms of relative error, as expected