Design of 1-D and 2-D Two-Channel Linear-Phase Filter Banks

• Main Authors: Ying-Ta Ho, 何英達
• Other Authors: Jong-Jy Shyu
• Format: Others
• Language: en_US
• Published: 1994
• Online Access: http://ndltd.ncl.edu.tw/handle/82123180805376848023

碩士 === 大同工學院 === 資訊工程研究所 === 82 === In this thesis, a new approach is presented for the design of 1-D and 2-D two-channel FIR filter banks employing linear-phase filters. For the design of perfect reconstruction (PR) system, we first design one of the analysis filter first using general least-squares approach, and formulate the design problem as a quadratic programing problem with linear constraints. Then the Lagrange multiplier approach is used to obtain the closed- form solution for the other of the analysis filter pair. Although this approach can find a PR filter banks which can yield high quality coding system at low bit rates, the filter bank's operation requires numerous multiplications and additions. Multiplicaton, in particular, is extremely time consuming. So, if a multiplication operation could be replaced by only a few additions or subtractions, then the complexity of the entire filter bank could be reduced quite dramatically, such that a fast real-time system becomes feasible. In this thesis, the Lagrange multiplier approach associating with a tree search algorithm is used iteratively. For each branch of the tree, the Lagrange multiplier approach is used to optimize the remaining unquantized coefficients of the designed filters. Examples including 1-D and 2-D design are presented to demonstrate the usefulness and effectiveness of the approach.