Real-valued LMS Fourier analyzer for sinusoidal signals in additive noise

Xiao, Yegui; Tadokoro, Yoshiaki; Iwamoto, K.

doi:10.1016/s0165-1684(98)00095-4

Cited by 19 publications

(16 citation statements)

References 19 publications

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“…However, if the SNR is low or p :::: 5, the p-power algorithm loses its performance advantage over the LMS algorithm [13]. These two gradient algorithms were investigated in detail in [12] and [13]. They are effective for many real applications such as automatic music note transcription, dual-tone multiple frequencies (DTMF) signal estimation/detection, monitoring of electrical power and so forth.…”

Section: Conventional Adaptive Algorithmsmentioning

confidence: 99%

“…[e(n -l)xai (n -1)] (12) +CYifJi(n -1) one eventually reaches fJi(n) = �ifJi(n -1) (13) +TJie(n)X ai (n)e(n -l)xai (n -1) where �i (= 1 -TJiCYi) is a positive constant very close to unit, as CYi and TJi are all very small positive constants, and its function is very similar to the role the leakage factor plays in the leaky-LMS algorithm. It should be noted that there is another way to obtain the gradient \7 /Li J (n)…”

Section: A Variable Step-size Lms Algorithmmentioning

confidence: 99%

“…The LMS algorithm was applied in [2]- [4] to make the DFT adaptive and useful for non stationary signals. The same LMS algorithm was discussed and analyzed in [9] and [12] for real-valued signals with arbitrary frequencies. A set of gradient-based algorithms was proposed based on a p-power error criterion, and their statistical analysis was performed in 978-1-4799-0434-1/13/$31.00 ©20 13 IEEE detail in [13].…”

Section: Introductionmentioning

confidence: 99%

“…The above-mentioned gradient-based LMS and p-power algorithms are capable of providing reasonably good discrete Fourier coefficient (DFC) estimates and are quite efficient in terms of the number of multiplications required [2]- [4], [9], [12], [13]. However, their estimation and tracking performance may become inadequate for applications that fast convergence and low estimation error are simultaneously imposed.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Adaptive Fourier analysis using a variable step-size LMS algorithm

Xiao

Huang

Wei

2013

2013 9th International Conference on Information, Communications &Amp; Signal Processing

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Adaptive Fourier analysis has numerous applica tions in biomedical engineering, music signal processing, digital communications, power engineering etc. So far, a lot of adaptive algorithms and systems have been developed and applied. In this paper, a variable step-size LMS (VSS-LMS) algorithm is proposed for adaptive Fourier analysis of noisy sinusoidal signals. It significantly outperforms the conventional LMS and p-power algorithms in both stationary and nonstationary environments at the expense of very little increase in computational cost. Extensive simulations as well as application to real noise signals generated by large-scale factory rotating machines are conducted to confirm the improved performance and tracking capabilities of the proposed algorithm.

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Section: Conventional Adaptive Algorithmsmentioning

confidence: 99%

Section: A Variable Step-size Lms Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Adaptive Fourier analysis using a variable step-size LMS algorithm

Xiao

Huang

Wei

2013

2013 9th International Conference on Information, Communications &Amp; Signal Processing

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“…To solve this problem, the NFT (Notch Fourier Transform) [6] using a sliding algorithm to find the Fourier coefficients was proposed, and then modified as the CNFT (Constrained Notch Fourier Transform) [7] to improve noise tolerance. On the other hand, some adaptive algorithms have been proposed, such as using the LMS (Least Mean Square) method [8][9][10] and the Kalman filter [11]. In particular, the LMS method has been applied to a variety of problems in the real engineering field due to its low computational complexity.…”

Section: Introductionmentioning

confidence: 99%

Improvement of a Fourier coefficient estimation method using an adaptive algorithm and its performance analysis

Kudoh¹,

Tadokoro²

2004

Electrical Engineering Japan

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SUMMARYThere are many applications where it is necessary to estimate accurately the amplitude and phase of signals when the information regarding the frequencies is obtained in advance. This paper presents a new algorithm for estimating more accurately Fourier coefficients of a signal contaminated by additive noise where sinusoidal frequencies of interest are not distributed uniformly. In the proposed method, Fourier coefficients are adaptive parameters. It uses averaged gradient signals and has almost the same acquisition time as the conventional LMS algorithm with more accurate estimation. The performance analysis of the proposed method is presented and its validity and limits are verified under various conditions by computer simulations. It is shown that the proposed method has especially better performance than the LMS algorithm when both the number of frequencies and the step size parameter, µ, are large.

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Performance analysis of a Fourier coefficient estimation method using IIR‐BPFs and an LMS algorithm and improvement of its performance

Kudoh

Tadokoro

2002

Electron Comm Jpn Pt III

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SUMMARYIn many areas, it is extremely important to accurately estimate the amplitude and phase of a signal even if the frequency contained in the signal to be analyzed is known. For cases in which the signal frequencies to be analyzed are in a nonharmonic relation and white noise and interference are superposed on the signal, a method (BPLMS method) combining the IIR type BPF and the LMS algorithm has been proposed to derive the Fourier coefficients of the signal components accurately. In the present paper, in order to investigate a method of improving the BPLMS method, an approximate equation for the estimated accuracy is derived. Also, the validity of the approximate equation is confirmed by computer simulations under various conditions. As a result of the approximate analysis, it is shown that the normalized frequency difference between the signal and the interference can be increased by combining a downsampling process so that the estimation accuracy can be improved. Finally, by simulation, the proposed method and the BPLMS method are compared in terms of estimation accuracy. An example of application to the pitch estimation of musical sounds is given.

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Real-valued LMS Fourier analyzer for sinusoidal signals in additive noise

Cited by 19 publications

References 19 publications

Adaptive Fourier analysis using a variable step-size LMS algorithm

Adaptive Fourier analysis using a variable step-size LMS algorithm

Improvement of a Fourier coefficient estimation method using an adaptive algorithm and its performance analysis

Performance analysis of a Fourier coefficient estimation method using IIR‐BPFs and an LMS algorithm and improvement of its performance

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