The Direct Solution of Nonconvex Nonlinear Fir Filter Design Problems by a Sip Method

FIR lter design problems in the frequency domain are nonlinear (semi-innnite) optimization problems. In practice these almost always have been solved in a simpliied form and/or only under restricting assumptions. In this paper, the four main design approximation problems in the frequency domain are stated in general forms, which allow the inclusion of constraints and the choice of an arbitrary L P-resp. l p-norm, 1 p 1; for the approximation. The careful mathematical formulation of these problems enables the derivation of several theoretical results (given in another paper), and it empowers the application of optimization procedures to their direct solution. Then, for the actual solution of these problems, a novel method for nonlinear semi-innnite programming is introduced and applied to several speciic design problems. For some examples, the computed solution of the nonlinear problem is compared with a solution obtained from a convex approximation of the problem. 1. Introduction Given a set of design frequency intervals and a lter length, the lter designer has to prescribe his requirements on the frequency domain characteristics of the requested lter and some norm as a measure of evaluation for each interval. Especially for each passband, he has to specify whether he requests best approximation or approximation only within given bounds (fullllment of a tolerance scheme) of