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

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.

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.712-715.2487 ◽

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

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.1093 ◽

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.

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The Properties of Multidimensional Semi-Orthogonal Frame Wavelet Packets

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.896 ◽

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

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.460-461.317 ◽

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.

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.430-432.543 ◽

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.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.20-23.1053 ◽

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

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.1184 ◽

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.

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

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.932 ◽

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.

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Characterization of the Quarternary Wavelet Wraps with Multi-Scale Factor and Applications in Physics

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.461.656 ◽

2012 ◽

Vol 461 ◽

pp. 656-660

Author(s):

Hai Lin Gao

Keyword(s):

Frequency Analysis ◽

Operator Theory ◽

Matrix Theory ◽

Wavelet Packets ◽

Riesz Bases ◽

Analysis Method ◽

Time Frequency ◽

Multi Scale ◽

Vector Valued

In t In this article, we introduce a sort of vector-valued wavelet wraps with multi-scale dilation of space L 2(Rn, Cv) , which are generaliza-tions of multivariaale wavelet wraps. A method for designing a sort of biorthogonal vector-valued wavelet wraps 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 L 2(Rn, Cv) from these wavelet wraps.

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