The Characteristics of a Pair of Dual Binary Canonical Frames Generated by Refinable Functions

Zhong Yin Chen; Jian Tang Zhao

doi:10.4028/www.scientific.net/AMR.461.864

Paper Titles

Evaluation of the City Integrated Emergency Response System Based on the Analytic Hierarchy Process
p.830

An Optimization Algorithm for Orthogonal Trivariate Wavelets with Short Support
p.835

Investigation of Low Energy Nitrogen Ion Implantation into Gold
p.840

Construction and Optimization of Plant Communities for Reducing Traffic Noise on Main Roads in Nanjing China
p.844

A Method of Restoring the Fog Degraded Image Based on the Monochromatic Atmospheric Scattering Model
p.849

State Modeling and Verification of Resistance Loss along the Long-Range Solid-Liquid Two-Phase Pipeline
p.854

Construction and Characteristics of Orthogonal Trivariate Multiwavelets with Finite Support
p.860

The Characteristics of a Pair of Dual Binary Canonical Frames Generated by Refinable Functions
p.864

The Traits of Nontensor Five-Variant Wavelet Packs and Applications in Management Science and Materials Science
p.868

HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 461The Characteristics of a Pair of Dual Binary...

The Characteristics of a Pair of Dual Binary Canonical Frames Generated by Refinable Functions

Abstract:

Materials science is an interdisciplinary field applyingthe properties of matter to various areas of science and engineering. Wavelet analysis has become a popular subject in researching into materials science during the past twenty years. Nowadays, it has been developed a mathematical br- anch. In this paper, we show that there exist binary wavelet frames generated by several compactly supported functions which have good dual binary wavelet frames, but for which the canonical dual binary wavelet frame does not consist of wavelets. That is to say, the canonical dual binary wavelet frame cannot be generated by the translations and dilations of a single binary function.

You might also be interested in these eBooks

Advanced Building Materials and Structural Engineering

View Preview

Info:

Periodical:

Advanced Materials Research (Volume 461)

Pages:

864-867

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.461.864

Citation:

Cite this paper

Online since:

February 2012

Authors:

Zhong Yin Chen, Jian Tang Zhao

Keywords:

Binary Harmonic Frames, Dual Tight Canonical Frames, General Wavelet Frame, Scaling Functions, Time-Frequency Analysis Method, Wavelet Frame

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] R.J. Duffin, and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., Vol. 72, pp.341-366, (1952).

DOI: 10.1090/s0002-9947-1952-0047179-6

Google Scholar

[2] I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., Vol 27, No. 5, pp.1271-1283.

DOI: 10.1063/1.527388

Google Scholar

[4] Q. Chen, Z. Shi. The characterization of a class of subspace pseudoframes with arbitrary real number translations. Chaos, Solitons & Fractals. Vol. 42(5), p.2696–2706, (2009).

DOI: 10.1016/j.chaos.2009.03.176

Google Scholar

[5] E. Weber. Orthogonal frames of translates, Appl. comput. Harmon. Anal., Vol. 17, pp.69-90, (2004).

Google Scholar

[6] Q. Chen, Z. Wei, J. Feng. A note on the standard dual frame of a wavelet frame with three-scale. Chaos, Solitons & Fractals. Vol. 42(2), pp.931-937, (2009).

DOI: 10.1016/j.chaos.2009.02.024

Google Scholar

[7] I. Daubechies, B． Han. The canonical dual. frame of a wavelet frame, Appl. comput. Harmon. Anal., Vol. 12, pp.269-285, (2002).

DOI: 10.1006/acha.2002.0381

Google Scholar

[8] O. Christensen, and Y C. Eldar, Oblique dual frames and shift-invariant spaces, Appl. comput. Harmon. Anal., Vol. 17, pp.48-68, (2004).

DOI: 10.1016/j.acha.2003.12.003

Google Scholar