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International Conference on Intelligent and Interactive Systems and Applications

IISA 2017: Advances in Intelligent Systems and Interactive Applications pp 82–86Cite as

Gibbs Phenomenon for Bi-orthogonal Wavelets

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 686))

Abstract

In this paper, we consider that a Gibbs phenomenon exists for the biorthogonal wavelets expansions of a discontinuous function. Firstly, we study properties of the biorthogonal wavelets kernel. Based on these properties of the kernel, we discuss existence of this phenomenon for the biorthogonal wavelets expansions of a discontinuous function. Also, we present the necessary condition of this phenomenon existence for the biorthogonal wavelets expansions of a discontinuous function.

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Acknowledgments

This work is supported by Natural Science Basic Research Plan in Shaanxi Province of China (Program No, 2016, JM6065)

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, People’s Republic of China

    Jie Zhou & Hongchan Zheng

Authors
  1. Jie Zhou
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  2. Hongchan Zheng
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Corresponding author

Correspondence to Jie Zhou .

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Editors and Affiliations

  1. Technical University of Catalonia, Barcelona, Spain

    Fatos Xhafa

  2. Department of Computer Science and Engineering, Faculty of Engineering and Technology, SOA University, Bhubaneswar, Odisha, India

    Srikanta Patnaik

  3. School of Information Technologies, University of Sydney, Sydney, New South Wales, Australia

    Albert Y. Zomaya

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Zhou, J., Zheng, H. (2018). Gibbs Phenomenon for Bi-orthogonal Wavelets. In: Xhafa, F., Patnaik, S., Zomaya, A. (eds) Advances in Intelligent Systems and Interactive Applications. IISA 2017. Advances in Intelligent Systems and Computing, vol 686. Springer, Cham. https://doi.org/10.1007/978-3-319-69096-4_12

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  • DOI: https://doi.org/10.1007/978-3-319-69096-4_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-69095-7

  • Online ISBN: 978-3-319-69096-4

  • eBook Packages: EngineeringEngineering (R0)

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