A technique for multiple criterion approximation of FIR filters in magnitude and group delay

In spite of the attention received by nonlinear phase (NLP) FIR filter design, the ''best'' way to solve this problem is still open to debate. The formulation of nonlinear phase FIR filter design in terms of simultaneous magnitude and group-delay approximation addresses the two parameters of ultimate interest for applications. The simultaneous minimization of these two functions (one of which, the group delay, rational) is approached on the basis of an original extension of the differential correction algorithm. The proposed design tool enjoys interesting theoretical properties and works very effectively. The filters obtained according to the multiple criterion optimization (MCO) formulation are compared against filters that are optimal in the complex Chebychev norm. Then, the flexibility characteristic of MCO formulations of trading off between magnitude and group-delay performance is exemplified.