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

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

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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
Publication date2012
Volume32
Issue3
Pages313-328
ISSN1063-5203
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 0

Keywords

  • Dual wavelet frames, Bandlimited wavelets, Real dilation matrix, Partition of unity, Non-tight frames
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