A fast matrix iterative technique for the WLS design of 2-D quadrantally symmetic FIR filters
作者： Ruijie Zhao , Xiaoping Lai
DOI: 10.1007/S11045-010-0128-X
关键词: Finite impulse response 、 Mathematics 、 Optimal design 、 Algorithm 、 Linear phase 、 Rate of convergence 、 Filter (signal processing) 、 Computational complexity theory 、 Weighting 、 Iterative method 、 Mathematical optimization
摘要: High computational complexity is a major problem encountered in the optimal design of two-dimensional (2-D) finite impulse response (FIR) filters. In this paper, we present an iterative matrix solution with very low to weighted least square (WLS) 2-D quadrantally symmetric FIR filters two-valued weighting functions. Firstly, necessary and sufficient condition for WLS general nonnegative functions obtained. Then, based on optimality condition, novel algorithm derived function. Because filter parameters are arranged their natural form transition band not sampled, computation amount proposed reduced significantly, especially high-order The exponential convergence established, its estimated. Design examples demonstrating rate accuracy algorithm, as well relation between iteration number size transition-band width given.
springer.com
sci-hub.se 参考文章(16)
Wu-Sheng Lu, T. Hinamoto, A second-order cone programming approach for minimax design of 2-D FIR filters with low group delay international symposium on circuits and systems. pp. 4- ,(2006) , 10.1109/ISCAS.2006.1693136
Rabah W. Aldhaheri, Design of 2-D Linear Phase Digital Filters Using Schur Decomposition and Symmetries Multidimensional Systems and Signal Processing. ,vol. 15, pp. 65- 81 ,(2004) , 10.1023/B:MULT.0000003933.41677.03
Xiaoping Lai, Yun Cheng, A Sequential Constrained Least-Square Approach to Minimax Design of 2-D FIR Filters IEEE Transactions on Circuits and Systems Ii-express Briefs. ,vol. 54, pp. 994- 998 ,(2007) , 10.1109/TCSII.2007.903216
M.T. Hanna, Weighted least squares design of two-dimensional zero-phase FIR filters in the continuous frequency domain IEEE Transactions on Circuits and Systems Ii: Analog and Digital Signal Processing. ,vol. 43, pp. 534- 537 ,(1996) , 10.1109/82.508431
Hung-Ching Lu, Kuo-Hsien Yeh, Optimal design of 2-D FIR digital filters by scaling-free McClellan transformation using least-squares estimation Signal Processing. ,vol. 58, pp. 303- 308 ,(1997) , 10.1016/S0165-1684(97)00031-5
Chaur-Heh Hsieh, Chung-Ming Kuo, Yue-Dar Jou, Ying-Luan Han, Design of two-dimensional FIR digital filters by a two-dimensional WLS technique IEEE Transactions on Circuits and Systems Ii: Analog and Digital Signal Processing. ,vol. 44, pp. 348- 357 ,(1997) , 10.1109/82.580839
Wei-Ping Zhu, M. Omair Ahmad, M.N.S. Swamy, A least-square design approach for 2D FIR filters with arbitrary frequency response IEEE Transactions on Circuits and Systems Ii: Analog and Digital Signal Processing. ,vol. 46, pp. 1027- 1034 ,(1999) , 10.1109/82.782044
M.O. Ahmad, J.-D. Wang, An analytical least square solution to the design problem of two-dimensional FIR filters with quadrantally symmetric or antisymmetric frequency response IEEE Transactions on Circuits and Systems. ,vol. 36, pp. 968- 979 ,(1989) , 10.1109/31.31332
Wei-Ping Zhu, M.O. Ahmad, M.N.S. Swamy, A closed-form solution to the least-square design problem of 2-D linear-phase FIR filters IEEE Transactions on Circuits and Systems Ii: Analog and Digital Signal Processing. ,vol. 44, pp. 1032- 1039 ,(1997) , 10.1109/82.644586
C. Charalambous, The performance of an algorithm for minimax design of two-dimensional linear phase FIR digital filters IEEE Transactions on Circuits and Systems. ,vol. 32, pp. 1016- 1028 ,(1985) , 10.1109/TCS.1985.1085627