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Four-Channel Tight Wavelet Frames Design Using Bernstein Polynomial

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Abstract

The paper provides a novel technique for designing tight frame wavelet filters through the use of Bernstein polynomials. The perfect-reconstruction conditions of tight wavelet frame filters are established by using parameters of the Bernstein polynomials. The desired number of vanishing moments can be easily achieved by setting the appropriate parameters of the Bernstein polynomial to zero. The filters are obtained by the spectral factorization method and constructed by the appropriate parameters. The design technique is flexible in that it allows low-pass filters and high-pass filters with different characteristics to be designed easily.

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Acknowledgements

This work was supported in part by the China National Natural Science Foundation under Contract 60972089. The authors would like to express our deep thanks to Nick Kingsbury and the reviewers for their very helpful suggestions, which greatly improved the quality of this paper.

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Authors and Affiliations

  1. School of Science, Beijing Jiaotong University, Beijing, 100044, China

    Ping Zhao

  2. Faculty of Mathematics Science, Tianjin Normal University, Tianjin, 300074, China

    Chun Zhao

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  1. Ping Zhao
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  2. Chun Zhao
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Correspondence to Ping Zhao.

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Zhao, P., Zhao, C. Four-Channel Tight Wavelet Frames Design Using Bernstein Polynomial. Circuits Syst Signal Process 31, 1847–1861 (2012). https://doi.org/10.1007/s00034-012-9412-3

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