IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Regular Section
Irregular Sampling on Shift Invariant Spaces
Kil Hyun KWONJaekyu LEE
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2010 Volume E93.A Issue 6 Pages 1163-1170

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Abstract

Let V(φ) be a shift invariant subspace of $L^{2}(\mathbb{R})$ with a Riesz or frame generator φ(t). We take φ(t) suitably so that the regular sampling expansion : $f(t) = \sum _{n\in \mathbb{Z}}f(n)S(t-n)$ holds on V(φ). We then find conditions on the generator φ(t) and various bounds of the perturbation $\{ \delta _n \}_{n \in \mathbb{Z}}$ under which an irregular sampling expansion: ƒ(t) = $\sum_{n \in \mathbb{Z}} f(n+ \delta_n)S_n(t)$ holds on V(φ). Some illustrating examples are also provided.

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© 2010 The Institute of Electronics, Information and Communication Engineers
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