The Description and Characterization of Symmetric Frames and Gabor Frames and Applications in Material Engineering

Qing Jiang Chen; Xiao Ting Lei; Jian Feng Zhou

doi:10.4028/www.scientific.net/AMR.712-715.2458

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 712-715The Description and Characterization of Symmetric...

The Description and Characterization of Symmetric Frames and Gabor Frames and Applications in Material Engineering

Abstract:

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this paper, we discuss a new set of symmetric tight frame wave-lets with the associated filterbanks outputs downsampled by several generators. The frames consist of several generators obtained from the lowpass filter using spectral factorization, with lowpass fil-ter via a simple approach using Legendre polynomials. The filters are feasible to be designed and offer smooth scaling functions and frame wavelets. We shall give an example to demonstrste that so -me examples of symmetric tight wavelet frames with three compactly supported real-valued sym- metric generators will be presented to illustrate the results.

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Periodical:

Advanced Materials Research (Volumes 712-715)

Pages:

2458-2463

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.712-715.2458

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Online since:

June 2013

Authors:

Qing Jiang Chen, Xiao Ting Lei, Jian Feng Zhou

Keywords:

Affine Frames, Gabor Frames, Multiresolution Analysis, Sobolev Space, Symmetric Filterbanks, Symmetric Frames, Wavelet Frame Sub-Space

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