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An algorithm for constructing orthogonal armlet multi-wavelets with multiplicity r and dilation factor a

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Journal of Electronics (China)

Abstract

The purpose of this paper is to construct an orthogonal Armlet multi-wavelets with multiplicity r and dilation factor a. Firstly, the definition of Armlets with dilation factor a is proposed in this paper. Based on the Two-scale Similar Transform (TST), the notion of the Para-unitary A-scale Similar Transform (PAST) is introduced, and we also give the transform on the all two-scale matrix symbols of the multi-wavelets with dilation a. Then we show that the PAST and the transform on the matrix symbols of the multi-wavelets keep the orthogonality of the multi-wavelets system. We discuss the condition ndition that a − 1 multi-wavelets corresponding to the multi-scaling functions are all Armlets. After performing the PAST and the transform on the matrix symbols of the multi-wavelets, the multi-scaling function can be balanced and the corresponding multi-wavelets can be Armlets at the same time. The construction of Armlets with high order is also discussed. At last, by a given example, we can conclude that the algorithm is feasible and efficient.

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Authors and Affiliations

  1. School of Mathematics Science, Xinjiang Normal University, Urumqi, 830054, China

    Xiaohui Zhou, Gang Wang & Baoqin Wang

Authors
  1. Xiaohui Zhou
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  2. Gang Wang
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  3. Baoqin Wang
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Corresponding author

Correspondence to Baoqin Wang.

Additional information

Supported by the Development Program for Young Teacher in the Science Researcher Project for Colleges and Universities of Xinjiang Province of China (No. XJEDU-2009S67).

Commuication author: Wang Baoqin, born in 1937, male, Professor.

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Zhou, X., Wang, G. & Wang, B. An algorithm for constructing orthogonal armlet multi-wavelets with multiplicity r and dilation factor a . J. Electron.(China) 28, 643–651 (2011). https://doi.org/10.1007/s11767-012-0736-8

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  • DOI: https://doi.org/10.1007/s11767-012-0736-8

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