The Stability and Perturbation of Bivariate Gabor Frames and Applications in Material Engineering

De You Yuan

doi:10.4028/www.scientific.net/AMR.721.737

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HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 721The Stability and Perturbation of Bivariate Gabor...

The Stability and Perturbation of Bivariate Gabor Frames and Applications in Material Engineering

Abstract:

Material science broadly encompasses the fundamental study of solid matter with the goal of engineering new materials with superior properties, and ultimately enabling altogether new types of devices The window functions and bivariate Gabor frames are introduced. The existence of bivariate Gabor frames with compact support is discussed. Sufficient conditions for irregular bivariate Gabor system to be frames are presented by means of frame multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a sort of orthogonal bivariate vector-valued wavelets with compact support is proposed, and their properties are investigated. The pyramid decomposition scheme is derived based on a generalized multiresolution structure.

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Periodical:

Advanced Materials Research (Volume 721)

Pages:

737-740

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.721.737

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Online since:

July 2013

Authors:

De You Yuan

Keywords:

Banach Space, Bivariate Gabor Frames, Dual Gabor Frames, Filter Banks, Paraunitary Operator, Time-Frequency Analysis, Wavelet Transfer

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References

[1] Duffin R.J., and Schaeffer A.C.,"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] Daubechies I., Grossmann A., and Meyer Y.,"Painless nonorthogonal expansions", J.Math. Phys., Vol 27, No.5, pp.1271-1283,1992.

DOI: 10.1063/1.527388

Google Scholar

[3] Chen Q., Ailian Huo. The research of a class of biorthogonal compactly supported vector-valued wavelets. Chaos, Solitons & Fractals.Vol. 41, No.2,p.951–961, 2009.

DOI: 10.1016/j.chaos.2008.04.025

Google Scholar

[4] Daubechies I., and B. Han. "Pairs of dual wavelet frames from any two refinable functions"，J. Constr. Appro., Vol. 20, pp.325-352, 2004.

DOI: 10.1007/s00365-004-0567-4

Google Scholar

[5] Daubechies I., and Han B．，"The canonical dual. frame of a wavelet frame", J. Appl. comput. Harmon. Anal., Vol.12, pp.269-285, 2002.

DOI: 10.1006/acha.2002.0381

Google Scholar