An Abstraction of Shannon's Sampling Theorem

Ikuji HONDA

An Abstraction of Shannon's Sampling Theorem

Ikuji HONDA

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E81-A No.6 pp.1187-1193

Publication Date: 1998/06/25

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Category: General Fundamentals and Boundaries

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Ikuji HONDA, "An Abstraction of Shannon's Sampling Theorem" in IEICE TRANSACTIONS on Fundamentals, vol. E81-A, no. 6, pp. 1187-1193, June 1998, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e81-a_6_1187/_p

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@ARTICLE{e81-a_6_1187,
author={Ikuji HONDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={An Abstraction of Shannon's Sampling Theorem},
year={1998},
volume={E81-A},
number={6},
pages={1187-1193},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - An Abstraction of Shannon's Sampling Theorem
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1187
EP - 1193
AU - Ikuji HONDA
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E81-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 1998
AB - 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.
ER -