Title

Characterizations Of Tight Over-Sampled Affine Frame Systems And Over-Sampling Rates

Abstract

Let M be a dilation matrix, Ψ a finite family of L2-functions, and P the collection of all nonsingular matrices P such that M, P, and P M P-1 have integer entries. The objective of this paper is two-fold. First, for each P in P, we characterize all tight affine frames X (Ψ, M) generated by Ψ such that the over-sampled affine systems XP (Ψ, M) relative to the "over-sampling rate" P remain to be tight frames. Second, we characterize all over-sampling rates P ∈ P, such that the over-sampled affine systems XP (Ψ, M) are tight frames whenever the affine system X (Ψ, M) is a tight frame. Our second result therefore provides a general and precise formulation of the second over-sampling theorem for tight affine frames. © 2006 Elsevier Inc. All rights reserved.

Publication Date

1-1-2007

Publication Title

Applied and Computational Harmonic Analysis

Volume

22

Issue

1

Number of Pages

1-15

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.acha.2006.04.009

Socpus ID

33751006993 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33751006993

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