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In this paper, a new gradient-based adaptive algorithm for the estimation of discrete Fourier coefficients (DFC) of a noisy sinusoidal signal is proposed based on a summed least mean squared error criterion. This algorithm requires exactly the same number of multiplications as the conventional LMS algorithm, and presents much improved performance in both white and colored noise environments at the expense of some additional memories and additions only. We first analyze the performance of the conventional LMS algorithm in colored additive noise, and point out when its performance deteriorates. Then, a summed least mean squared error criterion is proposed, which leads to the above-mentioned new gradient-based adaptive algorithm. The performance of the proposed algorithm is also analyzed for a single frequency case. Simulation results are provided to support the analytical findings and the superiority of the new algorithm.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.8 pp.1526-1535

- Publication Date
- 1999/08/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Digital Signal Processing)

- Category

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Yegui XIAO, Yoshihiro TAKESHITA, Katsunori SHIDA, "A New Gradient-Based Adaptive Algorithm Estimating Sinusoidal Signals in Arbitrary Additive Noise" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 8, pp. 1526-1535, August 1999, doi: .

Abstract: In this paper, a new gradient-based adaptive algorithm for the estimation of discrete Fourier coefficients (DFC) of a noisy sinusoidal signal is proposed based on a summed least mean squared error criterion. This algorithm requires exactly the same number of multiplications as the conventional LMS algorithm, and presents much improved performance in both white and colored noise environments at the expense of some additional memories and additions only. We first analyze the performance of the conventional LMS algorithm in colored additive noise, and point out when its performance deteriorates. Then, a summed least mean squared error criterion is proposed, which leads to the above-mentioned new gradient-based adaptive algorithm. The performance of the proposed algorithm is also analyzed for a single frequency case. Simulation results are provided to support the analytical findings and the superiority of the new algorithm.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_8_1526/_p

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@ARTICLE{e82-a_8_1526,

author={Yegui XIAO, Yoshihiro TAKESHITA, Katsunori SHIDA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={A New Gradient-Based Adaptive Algorithm Estimating Sinusoidal Signals in Arbitrary Additive Noise},

year={1999},

volume={E82-A},

number={8},

pages={1526-1535},

abstract={In this paper, a new gradient-based adaptive algorithm for the estimation of discrete Fourier coefficients (DFC) of a noisy sinusoidal signal is proposed based on a summed least mean squared error criterion. This algorithm requires exactly the same number of multiplications as the conventional LMS algorithm, and presents much improved performance in both white and colored noise environments at the expense of some additional memories and additions only. We first analyze the performance of the conventional LMS algorithm in colored additive noise, and point out when its performance deteriorates. Then, a summed least mean squared error criterion is proposed, which leads to the above-mentioned new gradient-based adaptive algorithm. The performance of the proposed algorithm is also analyzed for a single frequency case. Simulation results are provided to support the analytical findings and the superiority of the new algorithm.},

keywords={},

doi={},

ISSN={},

month={August},}

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TY - JOUR

TI - A New Gradient-Based Adaptive Algorithm Estimating Sinusoidal Signals in Arbitrary Additive Noise

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1526

EP - 1535

AU - Yegui XIAO

AU - Yoshihiro TAKESHITA

AU - Katsunori SHIDA

PY - 1999

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E82-A

IS - 8

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - August 1999

AB - In this paper, a new gradient-based adaptive algorithm for the estimation of discrete Fourier coefficients (DFC) of a noisy sinusoidal signal is proposed based on a summed least mean squared error criterion. This algorithm requires exactly the same number of multiplications as the conventional LMS algorithm, and presents much improved performance in both white and colored noise environments at the expense of some additional memories and additions only. We first analyze the performance of the conventional LMS algorithm in colored additive noise, and point out when its performance deteriorates. Then, a summed least mean squared error criterion is proposed, which leads to the above-mentioned new gradient-based adaptive algorithm. The performance of the proposed algorithm is also analyzed for a single frequency case. Simulation results are provided to support the analytical findings and the superiority of the new algorithm.

ER -