Minimally Supported Frequency Composite Dilation Parseval Frame Wavelets |
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Authors: | Jeffrey D Blanchard |
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Institution: | (1) Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA |
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Abstract: | A composite dilation Parseval frame wavelet is a collection of functions generating a Parseval frame for L
2(ℝ
n
) under the actions of translations from a full rank lattice and dilations by products of elements of groups A and B. A minimally supported frequency composite dilation Parseval frame wavelet has generating functions whose Fourier transforms
are characteristic functions of sets contained in a lattice tiling set. Constructive proofs are used to establish the existence
of minimally supported frequency composite dilation Parseval frame wavelets in arbitrary dimension using any finite group
B, any full rank lattice, and an expanding matrix generating the group A and normalizing the group B. Moreover, every such system is derived from a Parseval frame multiresolution analysis. Multiple examples are provided including
examples that capture directional information.
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Keywords: | Affine systems Composite dilation wavelets Coxeter groups Minimally supported frequency Parseval frames Wavelet frames Wavelet sets Wavelets |
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