A unified approach for the design of 2-D digital filters via semidefinite programming

作     者：Lu, WS 

作者机构：Univ Victoria Dept Elect & Comp Engn Victoria BC V8W 3P6 Canada 

出 版 物：《IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS》 (IEEE Trans Circuits Syst I Fundam Theor Appl)

年 卷 期：2002年第49卷第6期

页      面：814-826页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 

基　　金：Natural Sciences and Engineering Research Council of Canada  NSERC 

主　　题：constrained optimization digital filters semidefinite programming stability 

摘      要：This paper attempts to demonstrate that a modern optimization methodology known as semidefinite programming (SDP) can be served as the algorithmic core of a unified design tool for a variety of two-dimensional (2-D) digital filters. Representative SDP-based designs presented in the paper include minimax and weighted least-squares designs of FIR filters with continuous and discrete coefficients, and minimax design of stable separable-denominator HR filters. Our studies are motivated by the fact that SDP as a subclass of convex programming can be solved efficiently using recently developed interior-point methods and, more importantly, constraints on amplitude/phase responses in certain frequency regions and on stability (for UR filters), that are often encountered in many filter design problems, can be formulated in a natural way as linear matrix inequalities (LMI) which allow SDP to apply. Design examples for each class of filters are included to demonstrate that SDP-based methods can in many cases be useful in producing optimal or near-optimal 2-D filters with reduced computational complexity.