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Optimization Methods and Software Volume 28, 2013 - Issue 4: the 8th International Conference on Optimization: Techniques and Applications
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Original Articles

A fast algorithm for the optimal design of high accuracy windows in signal processing

K. F.C. Yiu Department of Applied Mathematics, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, People's Republic of ChinaCorrespondence[email protected]
,
M. J. Gao Department of Applied Mathematics, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, People's Republic of China
,
T. J. Shiu Department of Mathematics and National Center for Theoretical Sciences, National Cheng Kung University, Tainan, Taiwan, Republic of China
,
S. Y. Wu Department of Mathematics and National Center for Theoretical Sciences, National Cheng Kung University, Tainan, Taiwan, Republic of China
,
T. Tran Department of Telecommunications and Signal Processing, Blekinge Institute of Technology, Box 520, SE-372 25, Ronneby, Sweden
&
I. Claesson Department of Telecommunications and Signal Processing, Blekinge Institute of Technology, Box 520, SE-372 25, Ronneby, Sweden
Pages 900-916 | Received 29 Mar 2011, Accepted 28 Mar 2012, Published online: 11 Jun 2012
 
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Abstract

This paper presents a new optimal window design method with a general window design specification for the passband and stopband. The design problem is formulated as a semi-infinite linear programming problem. With suitable discretizations, an exchange algorithm is employed. The convergence of the proposed algorithm is established. In the formulation, since the stopband is minimized, the method can be employed for the design of very highly optimized windows.

Acknowledgements

The first author was supported by RGC Grant PolyU. (5365/09E), NSFC Grant (10901170), and the Research Committee of the Hong Kong Polytechnic University. The authors are grateful to the referees for a number of helpful suggestions and comments that greatly improved the paper.

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