The Characteristics of Orthogonal Wavelet Frames and Canonical Frames and Applications in Material Science

Abstract:

Wavelet analysis has become a popular subject in scientific research during the past twenty years. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonical dual wavelet frame cannot be generated by the translations and dilations of a single function. Traits of tight wavelet frames are presented.

• Periodical: Advanced Materials Research (Volume 721)
• Pages: 741-744
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.721.741
• Online since: July 2013
• Authors: Yong Fan Xu
• Keywords: Banach Space, Canonical Frames, Dual Wavelet Frame, Frame Operator, Time-Frequency Analysis Method, Wavelet Frame

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