Irregular Sampling on Shift Invariant Spaces

Kil Hyun KWON  Jaekyu LEE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A   No.6   pp.1163-1170
Publication Date: 2010/06/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.1163
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
shift invariant space,  irregular sampling,  frame,  Riesz basis,  

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Let V(φ) be a shift invariant subspace of L2(R) with a Riesz or frame generator φ(t). We take φ(t) suitably so that the regular sampling expansion : f(t) = f(n)S(t-n) holds on V(φ). We then find conditions on the generator φ(t) and various bounds of the perturbation {δ n }n∈Z under which an irregular sampling expansion: f(t) = f(n+ δn)Sn(t) holds on V(φ). Some illustrating examples are also provided.