Parseval frame wavelets with -dilations |
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Authors: | Damir Baki , Ilya Krishtal,Edward N. Wilson |
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Affiliation: | aDepartment of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia;bDepartment of Mathematics, Washington University, Box 1146, St. Louis, MO 63130-4899, USA |
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Abstract: | We study Parseval frame wavelets in with matrix dilations of the form , where A is an arbitrary expanding n×n matrix with integer coefficients, such that |detA|=2. We show that each A-MRA admits either Parseval frame wavelets, or Parseval frame bi-wavelets. The minimal number of generators for a Parseval frame associated with an A-MRA (i.e. 1 or 2) is determined in terms of a scaling function. All Parseval frame (bi)wavelets associated with A-MRA's are described. We then introduce new classes of filter induced wavelets and bi-wavelets. It is proved that these new classes strictly contain the classes of all A-MRA Parseval frame wavelets and bi-wavelets, respectively. Finally, we demonstrate a method of constructing all filter induced Parseval frame (bi)wavelets from generalized low-pass filters. |
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Keywords: | Parseval frame Wavelet Multiresolution analysis Filter Multiplier |
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