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Design of Sparse Filters by a Discrete Filled Function Technique

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Abstract

In this paper, we consider the sparse filter design problem where some of the coefficients can be reduced to zeroes in order to lower implementation complexity. The objective is to choose the fewest number of nonzero filter coefficients to meet a given performance requirement. We formulate a discrete optimization problem to minimize the number of nonzero terms and develop a discrete search method to find the minimal nonzero terms. In each step, we need to consider a subproblem to design the filter coefficients with a given set of nonzero terms. We formulate this subproblem as a linear programming problem and apply an exchange algorithm to find the optimal coefficients. For illustration, we compare the proposed algorithm with existing methods and show that the proposed method gives better results in all our test cases.

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Acknowledgements

This work is supported by RGC Grant PolyU. (152200/14E) and PolyU Grant 4-ZZGS. The first author is also supported by the National Natural Science Foundation of China (No. 61673078), the Grant of Chongqing Science and Technology Commission (No. cstc2017jcyjAX0161) and the Grant of Chongqing Normal University (No. 17XLB010).

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong, People’s Republic of China

    Zhi Guo Feng

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, People’s Republic of China

    Ka Fai Cedric Yiu

  3. Department of Mathematics and National Center for Theoretical Sciences, National Cheng Kung University, Tainan, Taiwan

    Soon Yi Wu

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  1. Zhi Guo Feng
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  2. Ka Fai Cedric Yiu
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  3. Soon Yi Wu
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Correspondence to Ka Fai Cedric Yiu.

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Feng, Z.G., Yiu, K.F.C. & Wu, S.Y. Design of Sparse Filters by a Discrete Filled Function Technique. Circuits Syst Signal Process 37, 4279–4294 (2018). https://doi.org/10.1007/s00034-018-0758-z

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  • DOI: https://doi.org/10.1007/s00034-018-0758-z

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