Inter-Extrapolation Formula in Sampling Theorem Convergent in the Sense of Distributions
Summary :
Sampling theorem for all bandlimited distributions which converges in the sense of distributions is presented. An inter-extrapolation formula with the most general sampling points on the negative time axis is provided and especially for equally-spaced sampling points an explicit formula is given, where it is proved that the Newton interpolating polynomial through the finite number of sample values converges with the Mittag-Leffler summation. These formulas are both proved to be convergent in the topology of distribution, hence a consistent theory is accomplished within the scope of distributions. As many linear operations on signals such as differentiation are continuous with respect to the distribution topology, the given formulas exhibit great facility when applied to signal analysis.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E72-E No.5 pp.578-583
- Publication Date
- 1989/05/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Analog Signal Processing
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Hirosi SUGIYAMA, "Inter-Extrapolation Formula in Sampling Theorem Convergent in the Sense of Distributions" in IEICE TRANSACTIONS on transactions,
vol. E72-E, no. 5, pp. 578-583, May 1989, doi: .
Abstract: Sampling theorem for all bandlimited distributions which converges in the sense of distributions is presented. An inter-extrapolation formula with the most general sampling points on the negative time axis is provided and especially for equally-spaced sampling points an explicit formula is given, where it is proved that the Newton interpolating polynomial through the finite number of sample values converges with the Mittag-Leffler summation. These formulas are both proved to be convergent in the topology of distribution, hence a consistent theory is accomplished within the scope of distributions. As many linear operations on signals such as differentiation are continuous with respect to the distribution topology, the given formulas exhibit great facility when applied to signal analysis.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e72-e_5_578/_p
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@ARTICLE{e72-e_5_578,
author={Hirosi SUGIYAMA, },
journal={IEICE TRANSACTIONS on transactions},
title={Inter-Extrapolation Formula in Sampling Theorem Convergent in the Sense of Distributions},
year={1989},
volume={E72-E},
number={5},
pages={578-583},
abstract={Sampling theorem for all bandlimited distributions which converges in the sense of distributions is presented. An inter-extrapolation formula with the most general sampling points on the negative time axis is provided and especially for equally-spaced sampling points an explicit formula is given, where it is proved that the Newton interpolating polynomial through the finite number of sample values converges with the Mittag-Leffler summation. These formulas are both proved to be convergent in the topology of distribution, hence a consistent theory is accomplished within the scope of distributions. As many linear operations on signals such as differentiation are continuous with respect to the distribution topology, the given formulas exhibit great facility when applied to signal analysis.},
keywords={},
doi={},
ISSN={},
month={May},}
Copy
TY - JOUR
TI - Inter-Extrapolation Formula in Sampling Theorem Convergent in the Sense of Distributions
T2 - IEICE TRANSACTIONS on transactions
SP - 578
EP - 583
AU - Hirosi SUGIYAMA
PY - 1989
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E72-E
IS - 5
JA - IEICE TRANSACTIONS on transactions
Y1 - May 1989
AB - Sampling theorem for all bandlimited distributions which converges in the sense of distributions is presented. An inter-extrapolation formula with the most general sampling points on the negative time axis is provided and especially for equally-spaced sampling points an explicit formula is given, where it is proved that the Newton interpolating polynomial through the finite number of sample values converges with the Mittag-Leffler summation. These formulas are both proved to be convergent in the topology of distribution, hence a consistent theory is accomplished within the scope of distributions. As many linear operations on signals such as differentiation are continuous with respect to the distribution topology, the given formulas exhibit great facility when applied to signal analysis.
ER -
English
