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

作     者：Goerner, Stephan Potchinkov, Alexander Reemtsen, Rembert 

作者机构：Univ Kaiserslautern Fachbereich Elektrotech D-67763 Kaiserslautern Germany Brandenburg Tech Univ Cottbus Inst Mathemat D-03044 Cottbus Germany 

出 版 物：《OPTIMIZATION AND ENGINEERING》 (最优化与工程学)

年 卷 期：2000年第1卷第2期

页      面：123-154页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 0701[理学-数学] 

主　　题：filter design FIR filters semi-infinite programming SQP methods 

摘      要：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.