The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
L'analyse de Fourier des signaux sinusoïdaux et/ou quasi-périodiques dans le bruit additif a été utilisée dans divers domaines. Jusqu’à présent, de nombreux algorithmes d’analyse, dont le célèbre DFT, ont été développés. En particulier, de nombreux algorithmes adaptatifs ont été proposés pour gérer des signaux non stationnaires dont les coefficients de Fourier discrets (DFC) varient dans le temps. Transformée de Fourier Notch (NFT) et transformée de Fourier Notch contrainte (CNFT) proposées par Tadokoro et al. et Kilani et al., respectivement, en sont deux, qui sont implémentés par des bancs de filtres et estiment les DFC via de simples algorithmes glissants qui leur sont propres. Cet article présente, pour la première fois, des analyses statistiques des performances du NFT et du CNFT. Les biais d'estimation et les erreurs quadratiques moyennes (MSE) de leurs algorithmes glissants seront dérivés sous forme fermée. En conséquence, il est révélé que les deux algorithmes sont impartiaux et que leurs MSE d’estimation sont liés aux fréquences des signaux, à la variance additive du bruit et aux ordres des filtres en peigne utilisés dans leurs bancs de filtres. Des simulations approfondies sont effectuées pour confirmer les résultats analytiques.
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Yegui XIAO, Takahiro MATSUO, Katsunori SHIDA, "Performance Analyses of Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform (CNFT)" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 9, pp. 1739-1747, September 2000, doi: .
Abstract: Fourier analysis of sinusoidal and/or quasi-periodic signals in additive noise has been used in various fields. So far, many analysis algorithms including the well-known DFT have been developed. In particular, many adaptive algorithms have been proposed to handle non-stationary signals whose discrete Fourier coefficients (DFCs) are time-varying. Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform(CNFT) proposed by Tadokoro et al. and Kilani et al., respectively, are two of them, which are implemented by filter banks and estimate the DFCs via simple sliding algorithms of their own. This paper presents, for the first time, statistical performance analyses of the NFT and the CNFT. Estimation biases and mean square errors (MSEs) of their sliding algorithms will be derived in closed form. As a result, it is revealed that both algorithms are unbiased, and their estimation MSEs are related to the signal frequencies, the additive noise variance and orders of comb filters used in their filter banks. Extensive simulations are performed to confirm the analytical findings.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_9_1739/_p
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@ARTICLE{e83-a_9_1739,
author={Yegui XIAO, Takahiro MATSUO, Katsunori SHIDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Performance Analyses of Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform (CNFT)},
year={2000},
volume={E83-A},
number={9},
pages={1739-1747},
abstract={Fourier analysis of sinusoidal and/or quasi-periodic signals in additive noise has been used in various fields. So far, many analysis algorithms including the well-known DFT have been developed. In particular, many adaptive algorithms have been proposed to handle non-stationary signals whose discrete Fourier coefficients (DFCs) are time-varying. Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform(CNFT) proposed by Tadokoro et al. and Kilani et al., respectively, are two of them, which are implemented by filter banks and estimate the DFCs via simple sliding algorithms of their own. This paper presents, for the first time, statistical performance analyses of the NFT and the CNFT. Estimation biases and mean square errors (MSEs) of their sliding algorithms will be derived in closed form. As a result, it is revealed that both algorithms are unbiased, and their estimation MSEs are related to the signal frequencies, the additive noise variance and orders of comb filters used in their filter banks. Extensive simulations are performed to confirm the analytical findings.},
keywords={},
doi={},
ISSN={},
month={September},}
Copier
TY - JOUR
TI - Performance Analyses of Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform (CNFT)
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1739
EP - 1747
AU - Yegui XIAO
AU - Takahiro MATSUO
AU - Katsunori SHIDA
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E83-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2000
AB - Fourier analysis of sinusoidal and/or quasi-periodic signals in additive noise has been used in various fields. So far, many analysis algorithms including the well-known DFT have been developed. In particular, many adaptive algorithms have been proposed to handle non-stationary signals whose discrete Fourier coefficients (DFCs) are time-varying. Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform(CNFT) proposed by Tadokoro et al. and Kilani et al., respectively, are two of them, which are implemented by filter banks and estimate the DFCs via simple sliding algorithms of their own. This paper presents, for the first time, statistical performance analyses of the NFT and the CNFT. Estimation biases and mean square errors (MSEs) of their sliding algorithms will be derived in closed form. As a result, it is revealed that both algorithms are unbiased, and their estimation MSEs are related to the signal frequencies, the additive noise variance and orders of comb filters used in their filter banks. Extensive simulations are performed to confirm the analytical findings.
ER -