Properties and Constructing of a Kind of Four-Dimensional Vector Wavelet Packets According to a Dilation Matrix

2010 ◽  
Vol 439-440 ◽  
pp. 920-925
Author(s):  
Yu Min Yu ◽  
Yu Qing Zhu
Keyword(s):  
Functional Analysis ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Sufficient Condition ◽  
Subdivision Scheme ◽  
Dimensional Vector ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Definition Of

In this paper, we introduce a sort of vector four-dimensional wavelet packets according to a dilation matrix, which are generalizations of univariate wavelet packets. The definition of biortho- gonal vector four-dimensional wavelet packets is provided and their biorthogonality quality is researched by means of time-frequency analysis method, vector subdivision scheme and functional analysis method. Three biorthogonality formulas regarding the wavelet packets are established. Finally, it is shown how to draw new Riesz bases of space from these wavelet packets. The sufficient condition for the existence of four-dimensional wavelet packets is established based on the multiresolution analysis method.

The Research of a Two-Directional Vector-Valued Quarternary Wavelet Packets and Applications in Material Engineering

2013 ◽  
Vol 712-715 ◽  
pp. 2487-2492
Author(s):  
Jian Feng Zhou
Keyword(s):  
Functional Analysis ◽  
Frequency Analysis ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Sufficient Condition ◽  
Subdivision Scheme ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Vector Valued

In this paper, we introduce a class of vector-valued four-dimensional wavelet packets according to a dilation matrix, which are generalizations of univariate wavelet packets. The defini -tion of biorthogonal vector four-dimensional wavelet packets is provided and their biorthogonality quality is researched by means of time-frequency analysis method, vector subdivision scheme and functional analysis method. Three biorthogonality formulas regarding the wavelet packets are established. Finally, it is shown how to draw new Riesz bases of space from these wavelet packets. The sufficient condition for the existence of four-dimensional wavelet packets is established based on the multiresolution analysis method.

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.

The Decription of a Sort of Two-Directional Biorthogonal Trivariate Wavelet Packets with Finite Support

2010 ◽  
Vol 439-440 ◽  
pp. 902-907
Author(s):  
Qing Jiang Chen ◽  
Lie Ya Yan
Keyword(s):  
Functional Analysis ◽  
Frequency Analysis ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Finite Support ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Algebra Theory

The advantages of wavelets and their promising features in various application have attracted a lot of interest and effort in recent years. In this article, the notion of two-directional biorthogonal finitely supported trivariate wavelet packets with multiscale is developed. Their properties is investigated by virtue of algebra theory, time-frequency analysis method and functional analysis method. In the final, new Riesz bases of space are constructed from these wavelet packets. Three biorthogonality formulas regarding these wavelet packets are established

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.

The Characterization of a Kind of Vector-Valued Multivariate Wavelet Packets with Composite Dilation Matrix

2010 ◽  
Vol 439-440 ◽  
pp. 932-937
Author(s):  
Yin Hong Xia ◽  
Hua Li
Keyword(s):  
Operator Theory ◽  
Matrix Theory ◽  
Higher Dimensions ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Vector Valued

In this article, the notion of a kind of multivariate vector-valued wavelet packets with composite dilation matrix is introduced. A new method for designing a kind of biorthogonal vector- valued wavelet packets in higher dimensions is developed and their biorthogonality property is inv- -estigated by virtue of matrix theory, time-frequency analysis method, and operator theory. Two biorthogonality formulas concerning these wavelet packets are presented. Moreover, it is shown how to gain new Riesz bases of space by constructing a series of subspace of wavelet packets.

Specific Properties of a King of Trivariable Wavelet Packets with Respect to an Integer-Valued Dilation Matrix

2010 ◽  
Vol 439-440 ◽  
pp. 1141-1146
Author(s):  
Jin Cang Han ◽  
Yang Li
Keyword(s):  
Finite Group ◽  
Group Theory ◽  
Frequency Analysis ◽  
Matrix Theory ◽  
Wavelet Packets ◽  
Analysis Method ◽  
Time Frequency ◽  
Finite Group Theory ◽  
Dilation Matrix ◽  
Vector Valued

In the work, the concept of orthogonal vector-valued trivariate wavelet packets, which is a generalization of uniwavelet packets, is introduced. A new method for constructing them is developed, and their characteristics is discussed by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas are established.

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 a Two-Directional Vector Multivariate Wavelet Wraps and Applications in Engineering Materials

2014 ◽  
Vol 889-890 ◽  
pp. 1270-1274
Author(s):  
Jin Shun Feng ◽  
Qing Jiang Chen
Keyword(s):  
Multiresolution Analysis ◽  
Riesz Bases ◽  
Scaling Functions ◽  
Sufficient Condition ◽  
Analysis Method ◽  
Compactly Supported ◽  
Dilation Matrix ◽  
Engineering Materials ◽  
Vector Valued

The existence of compactly supported orthogonal two-directional vector-valued wavelets associated with a pair of orthogonal shortly supported vector-valued scaling functions is researched. We introduce a class of two-directional vector-valued four-dimensional wavelet wraps according to a dilation matrix, which are generalizations of univariate wavelet wraps. Three orthogonality formulas regarding the wavelet wraps are established. Finally, it is shown how to draw new Riesz bases of space from these wavelet wraps. The sufficient condition for the existence of four-dimensional wavelet wraps is established based on the multiresolution analysis method.

The Properties of Multidimensional Semi-Orthogonal Frame Wavelet Packets

2010 ◽  
Vol 439-440 ◽  
pp. 896-901
Author(s):  
Qing Jiang Chen ◽  
Yu Ying Wang
Keyword(s):  
Matrix Theory ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Novel Method ◽  
Popular Subject ◽  
Vector Valued ◽  
Orthogonal Frame

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.

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