Semi-orthogonal frame wavelets and Parseval frame wavelets associated with GMRA

Zhanwei Liu, Guoen Hu, Guochang Wu and Bin Jiang

Chaos, Solitons & Fractals, 2008, vol. 38, issue 5, 1449-1456

Abstract: In this paper, we study semi-orthogonal frame wavelets and Parseval frame wavelets (PFWs) in L2(Rd) with matrix dilations of form (Df)(x)=2f(Ax), where A is an arbitrary expanding d×d matrix with integer coefficients, such that |detA|=2. Firstly, we obtain a necessary and sufficient condition for a frame wavelet to be a semi-orthogonal frame wavelet. Secondly, we present a necessary condition for the semi-orthogonal frame wavelets. When the frame wavelets are the PFWs, we prove that all PFWs associated with generalized multiresolution analysis (GMRA) are equivalent to a closed subspace W0 for which {Tkψ:k∈Zd} is a Parseval frame (PF). Finally, by showing the relation between principal shift invariant spaces and their bracket function, we discover a property of the PFWs associated with GMRA by the PFWs’ minimal vector-filter. In each section, we construct concrete examples.

Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077908001665
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:38:y:2008:i:5:p:1449-1456

DOI: 10.1016/j.chaos.2008.04.005

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().