Modified Constrained Notch Fourier Transform (MCNFT) for Sinusoidal Signals in Noise and Its Performance

Yegui XIAO; Takahiro MATSUO; Katsunori SHIDA

Modified Constrained Notch Fourier Transform (MCNFT) for Sinusoidal Signals in Noise and Its Performance

Yegui XIAO, Takahiro MATSUO, Katsunori SHIDA

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E85-A No.5 pp.1096-1103

Publication Date: 2002/05/01

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Type of Manuscript: PAPER

Category: Digital Signal Processing

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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 -