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Design and characterizations of a class of orthogonal multiple vector-valued wavelets with 4-scale

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  • Chen, Qingjiang
  • Cao, Huaixin
  • Shi, Zhi

Abstract

The notion of vector-valued multiresolution analysis of space L2(R,Cs×s) is introduced and the definition of orthogonal multiple vector-valued wavelets with 4-scale is given. First we obtain a necessary and sufficient condition on the existence of orthogonal multiple vector-valued wavelets by means of paraunitary vector filter bank theory. Second we propose an algorithm for constructing a class of compactly supported orthogonal multiple vector-valued wavelets. Finally, the notion of orthogonal multiple vector-valued wavelet packets is introduced. Their characterizations are presented by virtue of matrix theory, time–frequency analysis method and operator theory. In particular, orthonormal bases of space L2(R,Cs×s) are constructed from these wavelet packets. Relation to some physical theories such as E-infinity theory is also discussed.

Suggested Citation

  • Chen, Qingjiang & Cao, Huaixin & Shi, Zhi, 2009. "Design and characterizations of a class of orthogonal multiple vector-valued wavelets with 4-scale," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 91-102.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:91-102
    DOI: 10.1016/j.chaos.2007.11.014
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    References listed on IDEAS

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