Design and properties of vector-valued wavelets associated with an orthogonal vector-valued scaling function

De-you Yuan, Shu-de Du and Zheng-xing Cheng

Chaos, Solitons & Fractals, 2009, vol. 41, issue 3, 1368-1376

Abstract: The notion of vector-valued wavelets associated with an orthogonal vector-valued scaling function with 3-scale is introduced. The existence of orthogonal vector-valued wavelets is discussed and a necessary and sufficient condition is presented by means of the theory of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a class of orthogonal vector-valued wavelets with compact support is proposed. The concept of vector-valued wavelet packets is introduced and their properties are characterized by virtue of operator theory, time–frequency analysis method. Moreover, it is shown how to construct various orthonormal bases of space L2(R,Cμ)(2⩽μ∈Z) from these wavelet packets. Relation to some physical theories such as fractal theory and E-infinity theory is also discussed.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:41:y:2009:i:3:p:1368-1376

DOI: 10.1016/j.chaos.2008.05.016

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