The research of a class of biorthogonal compactly supported vector-valued wavelets

Qingjiang Chen and Ailian Huo

Chaos, Solitons & Fractals, 2009, vol. 41, issue 2, 951-961

Abstract: In this paper, we introduce the biorthogonal vector-valued wavelets. We prove that, like in the scalar wavelet case, the existence of a pair of biorthogonal compactly supported vector-valued scaling functions guarantees the existence of a pair of biorthogonal compactly supported vector-valued wavelet functions. An algorithm for constructing a pair of biorthogonal compactly supported vector-valued wavelet functions is presented by means of vector-valued multiresolution analysis and matrix theory. The notion of biorthogonal vector-valued wavelet packets is introduced, and their properties are investigated by virtue of time–frequency analysis and algebra theory. Three biorthogonality formulas concerning the wavelet packets are established. Relation to some physical theories such as E-infinity Cantorian space–time theory is also discussed.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:41:y:2009:i:2:p:951-961

DOI: 10.1016/j.chaos.2008.04.025

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