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Statistical-Mechanical Analysis of Adaptive Volterra Filter with the LMS Algorithm
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Summary :
The Volterra filter is one of the digital filters that can describe nonlinearity. In this paper, we analyze the dynamic behaviors of an adaptive signal-processing system including the Volterra filter by a statistical-mechanical method. On the basis of the self-averaging property that holds when the tapped delay line is assumed to be infinitely long, we derive simultaneous differential equations in a deterministic and closed form, which describe the behaviors of macroscopic variables. We obtain the exact solution by solving the equations analytically. In addition, the validity of the theory derived is confirmed by comparison with numerical simulations.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.12 pp.1665-1674
- Publication Date
- 2021/12/01
- Publicized
- 2021/06/01
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2021EAP1013
- Type of Manuscript
- PAPER
- Category
- Digital Signal Processing
Authors
Kimiko MOTONAKA
Kansai University
Tomoya KOSEKI
JB Toll System. Co. Ltd.
Yoshinobu KAJIKAWA
Kansai University
Seiji MIYOSHI
Kansai University
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Kimiko MOTONAKA, Tomoya KOSEKI, Yoshinobu KAJIKAWA, Seiji MIYOSHI, "Statistical-Mechanical Analysis of Adaptive Volterra Filter with the LMS Algorithm" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 12, pp. 1665-1674, December 2021, doi: 10.1587/transfun.2021EAP1013.
Abstract: The Volterra filter is one of the digital filters that can describe nonlinearity. In this paper, we analyze the dynamic behaviors of an adaptive signal-processing system including the Volterra filter by a statistical-mechanical method. On the basis of the self-averaging property that holds when the tapped delay line is assumed to be infinitely long, we derive simultaneous differential equations in a deterministic and closed form, which describe the behaviors of macroscopic variables. We obtain the exact solution by solving the equations analytically. In addition, the validity of the theory derived is confirmed by comparison with numerical simulations.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAP1013/_p
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@ARTICLE{e104-a_12_1665,
author={Kimiko MOTONAKA, Tomoya KOSEKI, Yoshinobu KAJIKAWA, Seiji MIYOSHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Statistical-Mechanical Analysis of Adaptive Volterra Filter with the LMS Algorithm},
year={2021},
volume={E104-A},
number={12},
pages={1665-1674},
abstract={The Volterra filter is one of the digital filters that can describe nonlinearity. In this paper, we analyze the dynamic behaviors of an adaptive signal-processing system including the Volterra filter by a statistical-mechanical method. On the basis of the self-averaging property that holds when the tapped delay line is assumed to be infinitely long, we derive simultaneous differential equations in a deterministic and closed form, which describe the behaviors of macroscopic variables. We obtain the exact solution by solving the equations analytically. In addition, the validity of the theory derived is confirmed by comparison with numerical simulations.},
keywords={},
doi={10.1587/transfun.2021EAP1013},
ISSN={1745-1337},
month={December},}
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TY - JOUR
TI - Statistical-Mechanical Analysis of Adaptive Volterra Filter with the LMS Algorithm
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1665
EP - 1674
AU - Kimiko MOTONAKA
AU - Tomoya KOSEKI
AU - Yoshinobu KAJIKAWA
AU - Seiji MIYOSHI
PY - 2021
DO - 10.1587/transfun.2021EAP1013
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2021
AB - The Volterra filter is one of the digital filters that can describe nonlinearity. In this paper, we analyze the dynamic behaviors of an adaptive signal-processing system including the Volterra filter by a statistical-mechanical method. On the basis of the self-averaging property that holds when the tapped delay line is assumed to be infinitely long, we derive simultaneous differential equations in a deterministic and closed form, which describe the behaviors of macroscopic variables. We obtain the exact solution by solving the equations analytically. In addition, the validity of the theory derived is confirmed by comparison with numerical simulations.
ER -
English
