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| Received:June 15, 2011Revised:January 30, 2012 |
| 基金项目:This work was partly supported by the National Nature Science Foundation of China (Nos. 61175001, 60974102), partly by the National Basic Research Program of China (Nos. 2012CB821200, 2009CB320600), and partly by the Shandong Provincial Nature Science Foundation of China (No. ZR2010FQ016). This work has been appeared in the 30th Chinese Control Conference (CCC), held in Yantai, Shandong. |
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| Fast two-dimensional weighted least squares techniques for the design of two-dimensional finite impulse response filters |
| Ruijie ZHAO,Xiaoping LAI |
| (School of Mechanical, Electrical and Information Engineering, Shandong University at Weihai;Institute of Information and Control, Hangzhou Dianzi University) |
| Abstract: |
| This paper focuses on the design of two-dimensional (2D) quadrantally symmetric finite impulse response (FIR) filters, and presents three very efficient algorithms for the weighted least squares (WLS) design with a weight matrix that assigns four different weights to four different frequency bands. The first algorithm seeks for iterative solutions to the matrix equation describing the optimality condition of the design problem. The second algorithm aims at the limit solution of the solution sequence to the first algorithm, analytically obtained by using matrix diagonalization techniques. The third algorithm belongs to the category of iterative reweighting techniques. It uses the second algorithm as its iteration core, and aims at reducing the maximum magnitude error of the filter by iteratively adjusting the four entry values of the weight matrix. Design examples are provided to demonstrate the performance of the proposed algorithms. |
| Key words: 2D FIR filters Diagonalization Quadrantal symmetry WLS design |
