The Direct Solution of Nonconvex Nonlinear FIR Filter Design Problems by a SIP Method

Abstract

FIR filter design problems in the frequency domain are nonlinear (semi-infinite) optimization problems. In practice, however, these almost always have not been approached directly, but been solved in a simplified form and/or only under restricting assumptions. In this paper, quite general mathematical formulations of the four main design approximation problems in the frequency domain are presented, which enable the derivation of theoretical results (collected here from R. Reemtsen, 2000b, 2000c) and the application of general-purpose optimization procedures to their direct solution. For the actual solution, a nonlinear semi-infinite programming method from the thesis (S. Gorner, Ph.D. Thesis, Technische Universitat Berlin, Berlin, 1997) of the first author is discussed and applied to several specific design problems. In some cases, the computed solution of the nonlinear problem is compared with that of a convex approximation of the problem.