Minimally Supported Frequency Composite Dilation 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 wavelet is a collection of functions generating an orthonormal basis for L
2(ℝ
n
) under the actions of translations from a full rank lattice and dilations by products of elements of non-commuting groups A and B. A minimally supported frequency composite dilation wavelet has generating functions whose Fourier transforms are characteristic
functions of a lattice tiling set. In this paper, we study the case where A is the group of integer powers of some expanding matrix while B is a finite subgroup of the invertible n×n matrices. This paper establishes that with any finite group B together with almost any full rank lattice, one can generate a minimally supported frequency composite dilation wavelet system.
The paper proceeds by demonstrating the ability to find such minimally supported frequency composite dilation wavelets with
a single generator. |
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Keywords: | |
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