A Study of Vector-Valued Binary Scaling Functions and Parseval Frames with Integer Dilation Constant

2013 ◽  
Vol 321-324 ◽  
pp. 980-983
Author(s):  
Bing Qing Lv ◽  
Jing Huang
Keyword(s):  
Materials Science ◽  
Analysis Method ◽  
Time Frequency ◽  
Finite Group Theory ◽  
Parseval Frames ◽  
Design Production ◽  
Novel Method ◽  
Analysis Design ◽  
Production And Operation ◽  
Vector Valued

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. It is the branch of engineering that involves the production and usage of heat and mechanical power for the design, production, and operation of machines and tools. It is one of the oldest and broadest engineering disciplines. The notion of orthogonal vector-valued binary wavelet packs is introduced. Their traits is investigated by virtue of time-frequency analysis method and finite group theory. Orthogonality formulas are established. Orthonormal wavelet pack bases are obtained. A novel method for constructing a kind of orthogonal shortly supported vector-valued wavelets is presented.

A Study of Orthogonal Vector-Valued Binary Wavelets and Wavelet Packs with Integer Dilation Constant

2011 ◽  
Vol 204-210 ◽  
pp. 1763-1766
Author(s):  
Yan Hui Lv ◽  
Qing Jiang Chen
Keyword(s):  
Finite Group ◽  
Group Theory ◽  
Frequency Analysis ◽  
Analysis Method ◽  
Orthonormal Wavelet ◽  
Time Frequency ◽  
Orthogonal Vector ◽  
Finite Group Theory ◽  
Novel Method ◽  
Vector Valued

The notion of orthogonal vector-valued binary wavelet packs is introduced. Their traits is investigated by virtue of time-frequency analysis method and finite group theory. Orthogonality formulas are established. Orthonormal wavelet pack bases are obtained. A novel method for constructing a kind of orthogonal shortly supported vector-valued wavelets is presented.

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 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.

The Optimality Characters of Vector-Valued Binary Small-Wave Wraps with a Constant Dilation Factor

2011 ◽  
Vol 58-60 ◽  
pp. 1460-1465
Author(s):  
Ming Pu Guo
Keyword(s):  
Matrix Theory ◽  
Wavelet Packet ◽  
Analysis Method ◽  
Time Frequency ◽  
Decomposition Scheme ◽  
Finite Group Theory ◽  
Small Wave ◽  
Dilation Factor ◽  
Active Research ◽  
Vector Valued

Frame theory has been the focus of active research for twenty years, both in theory and applications. In this work, the notion of orthogonal vector-valued binary small-wave wraps, which is a generalization of uni-wavelet packets, is introduced. A procedure for constructing them is presented. Their orthogonality traits are investigated by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas concerning these binary small-wave wraps are established. Orthonormal wavelet packet bases are obtained. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided.

Construction and Characteristics of Orthogonal Trivariate Multiwavelets with Finite Support

2012 ◽  
Vol 461 ◽  
pp. 860-863
Author(s):  
De Lin Hua ◽  
Ruo Hui Liu
Keyword(s):  
Filter Bank ◽  
Materials Science ◽  
Matrix Theory ◽  
New Method ◽  
Analysis Method ◽  
Time Frequency ◽  
Orthogonal Vector ◽  
Fundamental Properties ◽  
Necessary And Sufficient ◽  
Vector Valued

Materials science also deals with fundamental properties and characteristics of materi- als.In this paper, the notion of orthogonal vector-valued wavelets is introduced. A new method for constructing associated multiwavelets from multi-scaling functions is presented which is simple for computation. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is presented by using paraunitary vector filter bank theory, time-frequency analysis method and matrix theory. A new method for constructing a class of orthogonal finitectly supported vector-valued wavelets is presented.

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.

The Traits of Two-Directional Orthogonal Multivariate Small-Wave Packages with Finite Support

2012 ◽  
Vol 430-432 ◽  
pp. 543-546
Author(s):  
Zhong Yin Chen
Keyword(s):  
Operator Theory ◽  
Matrix Theory ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Small Wave ◽  
Novel Method ◽  
Vector Valued

In this paper, we introduce the notion of vector-valued multiresolution analysis and two-directional vector-valued multivariate wavelet packages associated with an integer-valued dilation matrix. A novel method for constructing multi-dimensional 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 establ- lished. Orthogonality decomposition relation formulas of the space are derived by constru- cting a series of subspaces of wavelet packets.

The Nice Feature of Orthogonal Vector-Valued Bivariate Wavelet Packets with Arbitrary Integer Dilation Factor

2010 ◽  
Vol 439-440 ◽  
pp. 1184-1189
Author(s):  
Jian Tang Zhao ◽  
Jie Li
Keyword(s):  
Matrix Theory ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Analysis Method ◽  
Arbitrary Integer ◽  
Time Frequency ◽  
Orthogonal Vector ◽  
Finite Group Theory ◽  
Dilation Factor ◽  
Vector Valued

In this paper, the notion of orthogonal vector-valued bivariate wavelet packets, which is a generalization of uni-wavelet packets, is introduced. A procedure for constructing them is presented. Their characteristics is investigated by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas are established. Orthonormal wavelet packet bases are obtained.

The Presentation of the Quarternary Super-Wavelet Wraps and Applications in Material Science

2013 ◽  
Vol 684 ◽  
pp. 469-472
Author(s):  
Jian Guo Shen
Keyword(s):  
Material Science ◽  
Materials Science ◽  
Dimensional Space ◽  
Tight Frame ◽  
Analysis Method ◽  
Necessary And Sufficient Condition ◽  
Time Frequency ◽  
Decomposition Scheme ◽  
Necessary And Sufficient ◽  
Vector Valued

Our goal is to obtain a character -ization of normalized tight frame super-wavelets The basis of materials science involves relating the desired properties and relative performance of a material in a certain application to the structure of the atoms and phases in that material through characterization. An approach for designing a sort of biorthogonal vector-valued wavelet wraps in four-dimensional space is presented and their biorthogonality traits are characterized by virtue of iteration method and time-frequency analysis method. The biorthogonality formulas concerning these wavelet wraps are established. A necessary and sufficient condition for the existence of the pyramid decomposition scheme of space is presented.

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.

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