Publication IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer SciencesVol.E81-ANo.6pp.1187-1193 Publication Date: 1998/06/25 Online ISSN: DOI: Print ISSN: 0916-8508 Type of Manuscript: PAPER Category: General Fundamentals and Boundaries Keyword: sampling theorem, nonband-limited signal, Riesz basis, frame, multiresolution analysis,

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Summary: This paper proves a general sampling theorem, which is an extension of Shannon's classical theorem. Let _{o} be a closed subspace of square integrable functions and call _{o} a signal space. The main aim of this paper is giving a necessary and sufficient condition for unique existence of the sampling basis {S_{n}}_{o} without band-limited assumption. Using the general sampling theorem we rigorously discuss a frequency domain treatment and a general signal space spanned by translations of a single function. Many known sampling theorems in signal spaces, which have applications for multiresolution analysis in wavelets theory are corollaries of the general sampling theorem.