NDLI: Minimally Supported Frequency Composite Dilation Parseval Frame Wavelets

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Minimally Supported Frequency Composite Dilation Parseval Frame Wavelets

Content Provider	Semantic Scholar
Author	Blanchard, Jeffrey D.
Copyright Year	2009
Abstract	A composite dilation Parseval frame wavelet is a collection of functions generating a Parseval frame for L2(ℝn) 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.
Starting Page	19
Ending Page	35
Page Count	17
File Format	PDF HTM / HTML
DOI	10.1007/s12220-008-9049-4
Volume Number	19
Alternate Webpage(s)	http://www.math.grinnell.edu/~blanchaj/Research/MSFCDPFW.pdf
Alternate Webpage(s)	http://www.math.grin.edu/~blanchaj/Research/MSFCDPFW.pdf
Alternate Webpage(s)	https://doi.org/10.1007/s12220-008-9049-4
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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