Constructing pairs of dual bandlimited frame wavelets in L^2(R^n)

Publication: Research - peer-reviewJournal article – Annual report year: 2011

Documents

DOI

View graph of relations

Given a real, expansive dilation matrix we prove that any bandlimited function ψ∈L2(Rn), for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for certain translation lattices. Moreover, there exists a dual wavelet frame generated by a finite linear combination of dilations of ψ with explicitly given coefficients. The result allows a simple construction procedure for pairs of dual wavelet frames whose generators have compact support in the Fourier domain and desired time localization. The construction relies on a technical condition on ψ, and we exhibit a general class of function satisfying this condition.
Original languageEnglish
JournalApplied and Computational Harmonic Analysis
Volume32
Issue number3
Pages (from-to)313-328
ISSN1063-5203
DOIs
StatePublished - 2012
Peer-reviewedYes
CitationsWeb of Science® Times Cited: 0

Keywords

  • Dual wavelet frames, Bandlimited wavelets, Real dilation matrix, Partition of unity, Non-tight frames
Download as:
Download as PDF
Select render style:
APAAuthorCBE/CSEHarvardMLAStandardVancouverShortLong
PDF
Download as HTML
Select render style:
APAAuthorCBE/CSEHarvardMLAStandardVancouverShortLong
HTML
Download as Word
Select render style:
APAAuthorCBE/CSEHarvardMLAStandardVancouverShortLong
Word

Download statistics

No data available

ID: 6357125