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The normalized least mean square (NLMS) algorithm has the drawback that the convergence speed of adaptive filter coefficients decreases when the reference signal has high auto-correlation. A technique to improve the convergence speed is to apply the decorrelated reference signal to the calculation of the gradient defined in the NLMS algorithm. So far, only the effect of the improvement is experimentally examined. The convergence property of the adaptive algorithm to which the technique is applied is not analized yet enough. This paper first defines a cost function properly representing the criterion to estimate the coefficients of adaptive filter. The name given in this paper to the adaptive algorithm exploiting the decorrelated reference signal, 'normalized least mean *EE*' algorithm, exactly expresses the criterion. This adaptive algorithm estimates the coefficients so as to minimize the product of *E* and *E*' that are the differences between the responses of the unknown system and the adaptive filter to the original and the decorrelated reference signals, respectively. By using the cost function, this paper second specifies the convergence condition of the normalized least mean *EE*' algorithm and finally presents computer simulations, which are calculated using real speech signal, to demonstrate the validity of the convergence condition.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.4 pp.984-990

- Publication Date
- 2001/04/01

- Publicized

- Online ISSN

- DOI

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

- Category

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Kensaku FUJII, Mitsuji MUNEYASU, Takao HINAMOTO, Yoshinori TANAKA, "Normalized Least Mean EE' Algorithm and Its Convergence Condition" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 4, pp. 984-990, April 2001, doi: .

Abstract: The normalized least mean square (NLMS) algorithm has the drawback that the convergence speed of adaptive filter coefficients decreases when the reference signal has high auto-correlation. A technique to improve the convergence speed is to apply the decorrelated reference signal to the calculation of the gradient defined in the NLMS algorithm. So far, only the effect of the improvement is experimentally examined. The convergence property of the adaptive algorithm to which the technique is applied is not analized yet enough. This paper first defines a cost function properly representing the criterion to estimate the coefficients of adaptive filter. The name given in this paper to the adaptive algorithm exploiting the decorrelated reference signal, 'normalized least mean *EE*' algorithm, exactly expresses the criterion. This adaptive algorithm estimates the coefficients so as to minimize the product of *E* and *E*' that are the differences between the responses of the unknown system and the adaptive filter to the original and the decorrelated reference signals, respectively. By using the cost function, this paper second specifies the convergence condition of the normalized least mean *EE*' algorithm and finally presents computer simulations, which are calculated using real speech signal, to demonstrate the validity of the convergence condition.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_4_984/_p

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@ARTICLE{e84-a_4_984,

author={Kensaku FUJII, Mitsuji MUNEYASU, Takao HINAMOTO, Yoshinori TANAKA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Normalized Least Mean EE' Algorithm and Its Convergence Condition},

year={2001},

volume={E84-A},

number={4},

pages={984-990},

abstract={The normalized least mean square (NLMS) algorithm has the drawback that the convergence speed of adaptive filter coefficients decreases when the reference signal has high auto-correlation. A technique to improve the convergence speed is to apply the decorrelated reference signal to the calculation of the gradient defined in the NLMS algorithm. So far, only the effect of the improvement is experimentally examined. The convergence property of the adaptive algorithm to which the technique is applied is not analized yet enough. This paper first defines a cost function properly representing the criterion to estimate the coefficients of adaptive filter. The name given in this paper to the adaptive algorithm exploiting the decorrelated reference signal, 'normalized least mean *EE*' algorithm, exactly expresses the criterion. This adaptive algorithm estimates the coefficients so as to minimize the product of *E* and *E*' that are the differences between the responses of the unknown system and the adaptive filter to the original and the decorrelated reference signals, respectively. By using the cost function, this paper second specifies the convergence condition of the normalized least mean *EE*' algorithm and finally presents computer simulations, which are calculated using real speech signal, to demonstrate the validity of the convergence condition.},

keywords={},

doi={},

ISSN={},

month={April},}

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TY - JOUR

TI - Normalized Least Mean EE' Algorithm and Its Convergence Condition

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 984

EP - 990

AU - Kensaku FUJII

AU - Mitsuji MUNEYASU

AU - Takao HINAMOTO

AU - Yoshinori TANAKA

PY - 2001

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E84-A

IS - 4

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - April 2001

AB - The normalized least mean square (NLMS) algorithm has the drawback that the convergence speed of adaptive filter coefficients decreases when the reference signal has high auto-correlation. A technique to improve the convergence speed is to apply the decorrelated reference signal to the calculation of the gradient defined in the NLMS algorithm. So far, only the effect of the improvement is experimentally examined. The convergence property of the adaptive algorithm to which the technique is applied is not analized yet enough. This paper first defines a cost function properly representing the criterion to estimate the coefficients of adaptive filter. The name given in this paper to the adaptive algorithm exploiting the decorrelated reference signal, 'normalized least mean *EE*' algorithm, exactly expresses the criterion. This adaptive algorithm estimates the coefficients so as to minimize the product of *E* and *E*' that are the differences between the responses of the unknown system and the adaptive filter to the original and the decorrelated reference signals, respectively. By using the cost function, this paper second specifies the convergence condition of the normalized least mean *EE*' algorithm and finally presents computer simulations, which are calculated using real speech signal, to demonstrate the validity of the convergence condition.

ER -