Authors: Qing Jiang Chen, Yu Ying Wang

Abstract: Wavelet analysis has become a popular subject in scientific research during the past twenty years. In this work, we introduce the notion of vector-valued multiresolution analysis and vector-valued multivariate wavelet packets associated with an integer-valued dilation matrix. A novel method for constructing multi-dimen-
-sional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas concerning the wavelet packets are established. Orthogonality decomposition relation formulas of the space are derived by constructing a series of subspaces of wavelet packets. Finally, one new orthonormal wavelet packet bases of are constructed from these wavelet packets.

896

Authors: Jin Cang Han, Yang Li

Abstract: The notion of matrix-valued multiresolution analysis. A procedure for designing orthogonal matrix-valued univariate wavelet packets is presented and their orthogonality properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Finally, one new orthonormal basis of are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

1147

Abstract: In this article, the notion of orthogonal nonseparable four-dimensional wavelet packets which is the generalizaion of orthogonal univariate wavelet packets is introduced. A new approach for constructing them is presented by iteration method. The orthogonality properties of five-dimensional wavelet packets are discussed. Three orthogonality formulas concerning these wavelet packets are estabished.

1377

Authors: Li Kun Xing, Long Wu, Ye Cai Guo

Abstract: Against the shortcomings of slow convergence and large residual error in norm decision feedback blind equalization, double error function decision feedback blind equalization algorithm based on orthogonal wavelet transform momentum (WT-DMCMA-DFE)was proposed. In the algorithm, the four combinations of two error functions, respectively, to make adjustments on the former right and the feedback right, and add momentum algorithm to the former right and the feedback right to accelerate the convergence rate, escape correlation by using the orthogonal wavelet transform and normalize the energy to further improve performance of the convergence. Underwater acoustic channel simulation results show that convergence performance and mean square error of WT-MCMA-DFE, WT-H-HMCMA-DFE, WT-H-CMCMA-DFE is different.

2097

Abstract: In this paper, we give a method for the construction of high dimension nonseparable and compactly supported orthogonal wavelet bases and the method to construct orthogonal wavelet bases are nonseparable . The orthogonal wavelets are associated with dilation 4.

1064