Generalized sampling in shift-invariant spaces with multiple stable generators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:337

Article

Garcia, A. G.¹  Hernandez-Medina, M. A.²  Perez-Villalon, G.³ 

[1] Univ Carlos III Madrid, Dept Matemat, Madrid 28911, Spain

[2] UPM, ETSIT, Dept Matemat Aplicada, Madrid 28040, Spain

[3] UPM, EUITT, Dept Matemat Aplicada, Madrid 28031, Spain

关键词: shift-invariant spaces;    dual frames;    generalized sampling;   

DOI  :  10.1016/j.jmaa.2007.03.083

来源: Elsevier

【 摘 要 】

The aim of this paper is to derive stable generalized sampling in a shift-invariant space with l stable generators. This is done in the light of the theory of frames in the product Hilbert space L-l(2)(0, 1): = L-2(0, 1) x... x L-2(0, 1) (l times). The generalized samples are expressed as the frame coefficients of an appropriate function in L-l(2)(0, 1) with respect to some particular frame in L-l(2)(0, 1). Since any multiply stable generated shift-invariant space is the image of L-l(2)(0, 1) by means of a bounded invertible operator, the generalized sampling is obtained from some dual frame expansions in L-l(2)(0, 1). An example in the setting of the Hermite cubic splines is exhibited. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free