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 adaptative de Fourier des signaux sinusoïdaux dans le bruit revêt une importance essentielle dans de nombreux domaines d'ingénierie. Jusqu’à présent, de nombreux algorithmes adaptatifs ont été développés. En particulier, un algorithme basé sur un banc de filtres appelé transformation de Fourier à encoche contrainte (CNFT) est très attractif en termes de rentabilité et de performances facilement contrôlables. Cependant, ses performances deviennent médiocres lorsque les fréquences des signaux ne sont pas uniformément espacées (ou espacées à intervalles inégaux) dans le domaine fréquentiel. En effet, les estimations des coefficients de Fourier discrets (DFC) dans le CNFT sont inévitablement corrompues par des perturbations sinusoïdales dans un tel cas. Cet article propose, dans un premier temps, un CNFT modifié (MCNFT), pour compenser les performances du CNFT pour les signaux sinusoïdaux bruités avec des fréquences de signal connues et non uniformément espacées. Ensuite, l’analyse des performances du MCNFT est effectuée en détail. Une expression sous forme fermée pour l'erreur quadratique moyenne (MSE) en régime permanent de chaque estimation DFC est dérivée. Cette expression indique que le MSE est proportionnel à la variance du bruit additif et est une fonction complexe à la fois de la fréquence de chaque composante de fréquence et du rayon polaire du filtre passe-bande utilisé dans le banc de filtres. Des simulations approfondies sont présentées pour démontrer les performances améliorées du MCNFT et la validité des résultats analytiques.
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Yegui XIAO, Takahiro MATSUO, Katsunori SHIDA, "Modified Constrained Notch Fourier Transform (MCNFT) for Sinusoidal Signals in Noise and Its Performance" in IEICE TRANSACTIONS on Fundamentals,
vol. E85-A, no. 5, pp. 1096-1103, May 2002, doi: .
Abstract: Adaptive Fourier analysis of sinusoidal signals in noise is of essential importance in many engineering fields. So far, many adaptive algorithms have been developed. In particular, a filter bank based algorithm called constrained notch Fourier transform (CNFT) is very attractive in terms of its cost-efficiency and easily controllable performance. However, its performance becomes poor when the signal frequencies are non-uniformly spaced (or spaced with unequal intervals) in the frequency domain. This is because the estimates of the discrete Fourier coefficients (DFCs) in the CNFT are inevitably corrupted by sinusoidal disturbances in such a case. This paper proposes, at first, a modified CNFT (MCNFT), to compensate the performance of the CNFT for noisy sinusoidal signals with known and non-uniformly spaced signal frequencies. Next, performance analysis of the MCNFT is conducted in detail. Closed form expression for the steady-state mean square error (MSE) of every DFC estimate is derived. This expression indicates that the MSE is proportional to the variance of the additive noise and is a complex function of both the frequency of each frequency component and the pole radius of the bandpass filter used in the filter bank. Extensive simulations are presented to demonstrate the improved performance of the MCNFT and the validity of the analytical results.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e85-a_5_1096/_p
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@ARTICLE{e85-a_5_1096,
author={Yegui XIAO, Takahiro MATSUO, Katsunori SHIDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Modified Constrained Notch Fourier Transform (MCNFT) for Sinusoidal Signals in Noise and Its Performance},
year={2002},
volume={E85-A},
number={5},
pages={1096-1103},
abstract={Adaptive Fourier analysis of sinusoidal signals in noise is of essential importance in many engineering fields. So far, many adaptive algorithms have been developed. In particular, a filter bank based algorithm called constrained notch Fourier transform (CNFT) is very attractive in terms of its cost-efficiency and easily controllable performance. However, its performance becomes poor when the signal frequencies are non-uniformly spaced (or spaced with unequal intervals) in the frequency domain. This is because the estimates of the discrete Fourier coefficients (DFCs) in the CNFT are inevitably corrupted by sinusoidal disturbances in such a case. This paper proposes, at first, a modified CNFT (MCNFT), to compensate the performance of the CNFT for noisy sinusoidal signals with known and non-uniformly spaced signal frequencies. Next, performance analysis of the MCNFT is conducted in detail. Closed form expression for the steady-state mean square error (MSE) of every DFC estimate is derived. This expression indicates that the MSE is proportional to the variance of the additive noise and is a complex function of both the frequency of each frequency component and the pole radius of the bandpass filter used in the filter bank. Extensive simulations are presented to demonstrate the improved performance of the MCNFT and the validity of the analytical results.},
keywords={},
doi={},
ISSN={},
month={May},}
Copier
TY - JOUR
TI - Modified Constrained Notch Fourier Transform (MCNFT) for Sinusoidal Signals in Noise and Its Performance
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1096
EP - 1103
AU - Yegui XIAO
AU - Takahiro MATSUO
AU - Katsunori SHIDA
PY - 2002
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E85-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2002
AB - Adaptive Fourier analysis of sinusoidal signals in noise is of essential importance in many engineering fields. So far, many adaptive algorithms have been developed. In particular, a filter bank based algorithm called constrained notch Fourier transform (CNFT) is very attractive in terms of its cost-efficiency and easily controllable performance. However, its performance becomes poor when the signal frequencies are non-uniformly spaced (or spaced with unequal intervals) in the frequency domain. This is because the estimates of the discrete Fourier coefficients (DFCs) in the CNFT are inevitably corrupted by sinusoidal disturbances in such a case. This paper proposes, at first, a modified CNFT (MCNFT), to compensate the performance of the CNFT for noisy sinusoidal signals with known and non-uniformly spaced signal frequencies. Next, performance analysis of the MCNFT is conducted in detail. Closed form expression for the steady-state mean square error (MSE) of every DFC estimate is derived. This expression indicates that the MSE is proportional to the variance of the additive noise and is a complex function of both the frequency of each frequency component and the pole radius of the bandpass filter used in the filter bank. Extensive simulations are presented to demonstrate the improved performance of the MCNFT and the validity of the analytical results.
ER -