IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Regular Section
Invariance and Periodic Oversampling in Principal Shift-Invariant Spaces
Kil Hyun KWONDae Gwan LEE
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2014 Volume E97.A Issue 1 Pages 313-321

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Abstract

We first find simple characterizations of $\frac{1}{N} \mathbb{Z}$-invariance of arbitrary principal shift-invariant space $V(\phi)$. Then we find several equivalent conditions for $V(\phi)$ to admit periodic oversampling for a class of continuous frame generators $\phi$. In particular, when $\phi$ is band-limited and $\hat{\phi}$ is piecewise continuous, we find very simple and general sufficient conditions for $V(\phi)$ to admit periodic oversampling, which involve the extra invariance of $V(\phi)$, together with an illustrating example.

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© 2014 The Institute of Electronics, Information and Communication Engineers
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