The Properties of Multivariate Wavelet Packets Associated with Eight-Scaled Filter Bank Functions

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(R^s,C^u) from these wavelet packets.