2010•Journal of Lanzhou University of TechnologyRequires access

Construction and properties of biorthogonal four-dimensional wavelets

Cao Gui-wen

Abstract

The matrix extension problem was discussed for constructing filters of biorthogonal four-dimensional wavelets from biorthogonal four-dimensional scaling functions.Explicit formulas for constructing filters of a class of biorthogonal four-dimensional wavelets were presented by means of interpolatory functions and polyphase matrix decomposition.The properties of biorthogonal four-dimensional wavelet packets were discussed,and three biorthogonality formulas concerning the wavelet packets were obtained.

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Key concepts: Biorthogonal system, Wavelet, Biorthogonal wavelet, Mathematics, Scaling, Pure mathematics, Matrix (chemical analysis), Polyphase system