A Unified Quadratic Semi-Infinite Programming Approach To Optimal Least Square FIR Filter Design

• Main Authors: Xuan-Ling Cheng, 程宣菱
• Other Authors: Soon-Yi Wu
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/23704040003258836434

碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 97 === This paper is concerned with the design of linear-phase finite impulse response (FIR) digital filters which the weighted least square error is minimized, subject to maximum error constraints. The design problem is formulated as a quadratic semi-infinite optimization problem. We solve this problem by using relaxed cutting-plane scheme. The connection between the primal and the dual problems are established. When a cutting-plane method is applied to solve a quadratic semi-infinite programming problem, basically, it solves a sequence of finite-dimensional quadratic programs and shows that the corresponding solution sequence converges to the optimal solution of the original problem. Hence, the optimal solution to the original problem can be readily obtained and the convergence proof of our algorithm is given. Finally, examples are solved using the proposed computational procedure.