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

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.