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

Autor(en): Lemvig, Jakob
Stichwörter: Bandlimited wavelets; Dual wavelet frames; GENERATORS; Mathematics; Mathematics, Applied; Non-tight frames; Partition of unity; Real dilation matrix
Erscheinungsdatum: 2012
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
Volumen: 32
Ausgabe: 3
Startseite: 313
Seitenende: 328
Zusammenfassung: 
Given a real, expansive dilation matrix we prove that any bandlimited function Psi is an element of L-2(R-n), 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 Psi 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 Psi, and we exhibit a general class of function satisfying this condition. (C) 2011 Elsevier Inc. All rights reserved.
ISSN: 10635203
DOI: 10.1016/j.acha.2011.07.002

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