Minimax Design of Digital Filters and Perfect-Reconstructioo Filter Banks

• Main Authors: Yang Shih-Ken, 楊世任
• Other Authors: Chieu Bin-Chang
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/40541120838292130400

博士 === 國立臺灣科技大學 === 電子工程技術研究所 === 86 === This dissertation presents several novel and efficient techniques for optimally designing one-dimensional (1-D) perfect-reconstruction (PR) filter banks, two-dimensional (2-D) FIR digital filters, and 2-D perfect- reconstruction and near-perfect-reconstruction parallelogram filter banks in the minimax senses. The proposed approaches are developed based on the affine and dual affine scaling variants of Karmarkar''s algorithm. As for the 1-D perfect-reconstruction digital filter banks, two novel techniques are proposed for designing PR filter banks with FIR analysis and synthesis filters having linear phase responses as well as low delay characteristics. The designed analysis and synthesis filters for both cases are optimal in the minimax sense subject to the perfect-reconstruction constraints. With regard to the design of 2-D digital filters, we propose design techniques for continuous and powers-of-two coefficients 2-D digital filters based on the minimax sense. The optimal continuous coefficient filters are first designed by an affine scaling variant of Karmarkar''s algorithm. Then a suboptimal powers-of-two coefficient filter is obtained by an efficient method from the optimal continuous filter coefficients. The design of 2-D parallelogram filter banks is also studied thoroughly. The linear-phase FIR analysis and synthesis optimal in minimax sense are considered. Two novel techniques for designing perfect-reconstruction and near-perfect-reconstruction 2-D parallelogram filter banks are presented. From the simulation examples demonstrated in each chapter of this dissertation, the effectiveness of the proposed design techniques for each considered design problem can be confirmed.