The Orthogonality Character of Matrix Univariate Wavelet Packets Concerning an Integer Factor

Jin Cang Han; Yang Li

doi:10.4028/www.scientific.net/KEM.439-440.1147

Paper Titles

A Novel Approach for Constructing a Class of Orthogon Vector-Valued Wavelets with Finite Support
p.1123

The Research of Multiple Subspace Pseudoframes with Integer Translation
p.1129

The Characterization of a Pair of Canonical Frames Generated by Several Compactly Supported Functions
p.1135

Specific Properties of a King of Trivariable Wavelet Packets with Respect to an Integer-Valued Dilation Matrix
p.1141

The Orthogonality Character of Matrix Univariate Wavelet Packets Concerning an Integer Factor
p.1147

Statistical Properties of the Unsymmetrical P-Norm Distribution
p.1153

A Study on Characteristics of Biorthogonal Two-Dimensional Wavelet Packets
p.1159

A Study of Matrix-Valued Trivariate Wavelet Packets Associated with an Orthogonal Matrix-Valued Trivariate Scaling Function
p.1165

The Description of Two-Direction Biorthogonal Finitely Supported Wavelet Packets with Poly-Scale Dilation
p.1171

HomeKey Engineering MaterialsKey Engineering Materials Vols. 439-440The Orthogonality Character of Matrix Univariate...

The Orthogonality Character of Matrix Univariate Wavelet Packets Concerning an Integer Factor

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.

You might also be interested in these eBooks

View Preview

Info:

Periodical:

Key Engineering Materials (Volumes 439-440)

Pages:

1147-1152

DOI:

https://doi.org/10.4028/www.scientific.net/KEM.439-440.1147

Citation:

Cite this paper

Online since:

June 2010

Authors:

Jin Cang Han, Yang Li

Keywords:

Matrix Theory, Matrix Valued Wavelet Packet, Orthogonal, Orthogonality Formula, Time-Frequency Analysis Method

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] S. Yang, Z. Cheng, A-scale multiple orthogonal wavelet packets, MATHEMATICA APPLICATA, in Chinese, 2000, 13(1), pp.61-65.

Google Scholar

[2] Q. Chen, Z. Cheng, A study on compactly supported orthogonal vector-valued wavelets and wavelet packets, Chaos, Solitons & Fractals, 2007, 31(4), pp.1024-1034.

DOI: 10.1016/j.chaos.2006.03.097

Google Scholar

[3] Z. Shen, Nontensor product wavelet packets in L2(Rs), SIAM Math. Anal., 1995, 26(4), pp.1061-1074.

DOI: 10.1137/s0036141093243642

Google Scholar

[4] Q. Chen, Z. Shi, Construction and properties of orthogonal matrix-valued wavelets and wavelet packets, Chaos, Solitons & Fractals. 2008, 37(1), pp.75-86.

DOI: 10.1016/j.chaos.2007.08.006

Google Scholar

[5] Q. Chen, Z. Shi, Biorthogonal multiple vector-valued multivariate wavelet packets associated with a dilation matrix, Chaos, Solitons & Fractals, 2008, 35(3), pp.323-332.

DOI: 10.1016/j.chaos.2007.06.065

Google Scholar

[6] Q. Chen, H. Cao, Z. Shi, Construction and characterizations of orthogonal vector-valued multivariate wavelet packets, Chaos, Solitons & Fractals. doi: 10. 1016/j. chaos. 2007,. 09. 066, preprint.

DOI: 10.1016/j.chaos.2007.09.066

Google Scholar

[7] Z. Shen, Nontensor product wavelet packets in L2(Rs), SIAM Math. Anal., 1995, 26(4), pp.1061-1074.

DOI: 10.1137/s0036141093243642

Google Scholar