The Properties of Multivariate Wavelet Packets Associated with Eight-Scaled Filter Bank Functions
Baoxian Lv, Xinxian Tian · 2010
In this paper, we introduce a sort of vector-valued wavelet packets with eight-scale dilation factor for vector-valued multivariate function space. A new procedure for designing a sort of biorthogonal vector-valued multivariate wavelet packets according to a pair of biorthogonal vector-valued scaling functions, is presented and their biorthogonality properties are characterized by virtue of matrix theory, time-frequency analysis method, and operator theory. Three biorthogonality formulas regarding these wavelet packets are obtained. Moreover, it is shown how to gain new Riesz bases of space L2(Rs,Cu) from these wavelet packets.