Invariance and Periodic Oversampling in Principal Shift-Invariant Spaces

Kil Hyun KWON  Dae Gwan LEE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.1   pp.313-321
Publication Date: 2014/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.313
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
principal shift-invariant space,  oversampling,  frame,  invariance,  

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We first find simple characterizations of $ rac{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.