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A study of orthogonal, balanced and symmetric multi-wavelets on the interval

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Abstract

The construction and properties of interval multi-wavelets based on symmetric/anti-symmetric orthogonal multi-wavelets onL 2(R) with arbitrary supports and multiplicity 2 are introduced. The main contributions include that (1) we study the construction of general orthogonal interval multi-wavelets which preserve the polynomial-reproduction order, and obtain the parametric expressions of interval multi-wavelets; (2) we obtain the decomposition and reconstruction formulas of interval multi-wavelets; (3) we define the “balancing” concept of interval multi-wavelets for the first time and study the construction of orthogonal balancing multi-wavelets, which have been ignored in the past; (4) we study the necessary and sufficient conditions about the symmetry of interval multi-wavelets.

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Authors and Affiliations

  1. College of Information and Engineering, Xiangtan University, 411105, Xiangtan, China

    Gao Xieping & Zhou Siwang

  2. College of Computer and Communication, Hunan University, 410082, Changsha, China

    Zhou Siwang

Authors
  1. Gao Xieping
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  2. Zhou Siwang
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Correspondence to Gao Xieping.

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Gao, X., Zhou, S. A study of orthogonal, balanced and symmetric multi-wavelets on the interval. Sci China Ser F 48, 761–781 (2005). https://doi.org/10.1360/122004-137

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  • DOI: https://doi.org/10.1360/122004-137

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