On extensions of wavelet systems to dual pairs of frames
نویسندگان
چکیده
منابع مشابه
From Dual Pairs of Gabor Frames to Dual Pairs of Wavelet Frames and vice Versa Ole Christensen and Say
We discuss an elementary procedure that allows us to construct dual pairs of wavelet frames based on certain dual pairs of Gabor frames and vice versa. The construction preserves tightness of the involved frames. Starting with Gabor frames generated by characteristic functions the construction leads to a class of tight wavelet frames that include the Shannon (orthonormal) wavelet, and applying ...
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Starting from any two compactly supported refinable functions in L2(R) with dilation factor d, we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L2(R). Moreover, the number of vanishing moments of each of these wavelet frames is equal to the approximation order of the dual MRA; this is the highest...
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Recently, research on two distinct types of wavelet frames have emerged, each with its own characteristics. The dual-tree discrete wavelet transform (DWT) [1] is based on the concatenation of two wavelet bases, where the two wavelets are designed to form a Hilbert transform pair, Ãg(t) = HfÃh(t)g [4]. A second type of wavelet frame is based on a single scaling function and two distinct wavelets...
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15 صفحه اولOn Dual Wavelet Tight Frames
A characterization of multivariate dual wavelet tight frames for any general dilation matrix is presented in this paper. As an application, Lawton’s result on wavelet tight frames in L(IR) is generalized to the n-dimensional case. Two ways of constructing certain dual wavelet tight frames in L(IR) are suggested. Finally examples of smooth wavelet tight frames in L(IR) and H(IR) are provided. In...
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ژورنال
عنوان ژورنال: Advances in Computational Mathematics
سال: 2015
ISSN: 1019-7168,1572-9044
DOI: 10.1007/s10444-015-9432-1