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
A análise adaptativa de Fourier de sinais senoidais em ruído é de essencial importância em muitos campos da engenharia. Até agora, muitos algoritmos adaptativos foram desenvolvidos. Em particular, um algoritmo baseado em banco de filtros denominado transformada de Fourier de entalhe restrito (CNFT) é muito atraente em termos de custo-benefício e desempenho facilmente controlável. No entanto, seu desempenho torna-se ruim quando as frequências do sinal não são espaçadas uniformemente (ou espaçadas com intervalos desiguais) no domínio da frequência. Isso ocorre porque as estimativas dos coeficientes discretos de Fourier (DFCs) no CNFT são inevitavelmente corrompidas por distúrbios senoidais nesse caso. Este artigo propõe, a princípio, um CNFT modificado (MCNFT), para compensar o desempenho do CNFT para sinais senoidais ruidosos com frequências de sinal conhecidas e não uniformemente espaçadas. A seguir, a análise de desempenho do MCNFT é realizada detalhadamente. É derivada uma expressão de forma fechada para o erro quadrático médio (MSE) de estado estacionário de cada estimativa DFC. Esta expressão indica que o MSE é proporcional à variância do ruído aditivo e é uma função complexa tanto da frequência de cada componente de frequência quanto do raio do pólo do filtro passa-banda usado no banco de filtros. Extensas simulações são apresentadas para demonstrar o melhor desempenho do MCNFT e a validade dos resultados analíticos.
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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},}
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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 -