A study on compactly supported orthogonal vector-valued wavelets and wavelet packets. (English) Zbl 1142.42014

Chen, Qingjiang; Cheng, Zhengxing

Chaos Solitons Fractals 31, No. 4, 1024-1034 (2007).

This paper studies orthogonal vector-valued wavelets and vector-valued wavelet packets derived from vector-valued multiresolution analysis. In Theorem 2, the orthogonal wavelet is derived from a refinable vector-valued scaling function whose mask has \(3\) coefficients. Some properties of the associated orthogonal wavelet packets are presented in Section 5.
Reviewer’s remark: The so-called vector-valued scaling functions and wavelets proposed by X.G. Xia and B.W. Suter [Vector-valued wavelets and vector filter banks. IEEE Trans. Signal Process. 44, No. 3, 508–518 (1996)] are square matrices of functions in \(L^2\). However, the scaling functions considered in this paper are column vectors of functions in \(L^2\), which are also known as refinable function vectors in the literature. Therefore, the wavelets considered in this paper are essentially the traditional orthogonal multiwavelets derived from orthogonal refinable function vectors, instead of the vector-valued wavelets proposed in [loc. cit.].

Reviewer: Bin Han (Edmonton)

MSC:

42C40

Nontrigonometric harmonic analysis involving wavelets and other special systems

Keywords:

refinable function vectors; multiwavelets

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