The properties of orthogonal matrix-valued wavelet packets in higher dimensions

2006 ◽  
Vol 22 (3) ◽  
pp. 41-53 ◽  
Author(s):  
Qing-jiang Chen ◽  
Jin-shun Feng ◽  
Zheng-xing Cheng
Keyword(s):  
Higher Dimensions ◽  
Orthogonal Matrix ◽  
Wavelet Packets

The Biorthogonality Property of the Multidimensional Wavelet Packets with Multi-Scale Factor

2010 ◽  
Vol 439-440 ◽  
pp. 1093-1098
Author(s):  
Jian Feng Zhou ◽  
Ping An Wang
Keyword(s):  
Frequency Analysis ◽  
Operator Theory ◽  
Matrix Theory ◽  
Higher Dimensions ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency ◽  
Multi Scale ◽  
Vector Valued

In this article, we introduce a sort of vector-valued wavelet packets with multi-scale dilation of space , which are generalizations of multivariaale wavelet packets. A method for designing a sort of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality property is characterized by virtue of time-frequency analysis method, matrix theory, and operator theory. Three biorthogonality formulas regarding these wavelet packets are established. Furtherore, it is shown how to obtain new Riesz bases of space from these wavelet packets.

The Characteristics Concerning a Class of Orthogonal Multivariate Matrix-Valued Scaling Functions and Frame Packets

2013 ◽  
Vol 321-324 ◽  
pp. 1317-1320
Author(s):  
Hong Yun Liu ◽  
Jie Li
Keyword(s):  
Functional Analysis ◽  
Materials Science ◽  
Matrix Theory ◽  
Orthogonal Matrix ◽  
Wavelet Packets ◽  
Scaling Functions ◽  
Analysis Method ◽  
Orthonormal Wavelet ◽  
Time Frequency ◽  
Analysis Design

Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. In this work, the notion of matrix-valued multiresolution analysis of space is introduced. A method for constructing orthogonal matrix-valued ternary wavelet packs is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are provided. Finally, new orthonormal wavelet pack bases of space are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

A Study of Matrix-Valued Trivariate Wavelet Packets Associated with an Orthogonal Matrix-Valued Trivariate Scaling Function

2010 ◽  
Vol 439-440 ◽  
pp. 1165-1170
Author(s):  
Jian Zhang ◽  
Shui Wang Guo
Keyword(s):  
Functional Analysis ◽  
Frequency Analysis ◽  
Multiresolution Analysis ◽  
Matrix Theory ◽  
Scaling Function ◽  
Orthogonal Matrix ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency

Wavelet analysis has become a developing branch of mathematics for over twenty years. In this paper, the notion of matrix-valued multiresolution analysis of space is introduced. A method for constructing biorthogonal matrix–valued trivariate wavelet packets is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three biorthogonality formulas concerning these wavelet packets are provided. Finally, new Riesz bases of space is obtained by constructing a series of subspaces of biorthogonal matrix-valued wavelet packets.

Generation and Characteristics of a Class of Four-Dimensional Multiwavelet Packets with Six-Scale Dilation Factor

2011 ◽  
Vol 460-461 ◽  
pp. 317-322
Author(s):  
Qing Jiang Chen ◽  
Zong Tian Wei
Keyword(s):  
Frequency Analysis ◽  
Operator Theory ◽  
Matrix Theory ◽  
Higher Dimensions ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Factor ◽  
Vector Valued

In this paper, we introduce a class of vector-valued wavelet packets of space , which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions 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 derived. Moreover, it is shown how to gain new Riesz bases of space from these wavelet packets.

Construction and Characteristics of a Kind of Four-Dimensional Vector Wavelet Packets with Four-Scale Dilation

2010 ◽  
Vol 20-23 ◽  
pp. 1053-1059
Author(s):  
Xin Xian Tian ◽  
Ai Lian Huo
Keyword(s):  
Frequency Analysis ◽  
Operator Theory ◽  
Matrix Theory ◽  
Higher Dimensions ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Dimensional Vector ◽  
Analysis Method ◽  
Time Frequency ◽  
Vector Valued

In this paper, we introduce a class of vector-valued wavelet packets of space , which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions 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 derived. Moreover, it is shown how to gain new Riesz bases of space from these wavelet packets.

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