• 대한수학회보
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• 제50권1호
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• pp.233-240
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• 2013

In this paper, we use the elementary method and the theory of complex functions to study the computational problem of the fourth power mean of the generalized two-term exponential sums, and give two exact identities for them.

• 한국통신학회논문지
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• 제26권12A호
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• pp.2043-2049
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• 2001

In this paper we study the convergence behavior of the least mean fourth(LMF) algorithm where the error raised to the power of four is minimized for a multiple sinusoidal input and Gaussian measurement noise. Here we newly obtain the convergence equation for the sum of the mean of the squared weight errors, which indicates that the transient behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant. It should be noted that no similar results can be expected from the previous analysis by Walach add Widrow.

• The Journal of the Acoustical Society of Korea
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• 제18권2E호
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• pp.3-9
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• 1999

In this paper we study the convergence behavior of the least mean fourth(LMF) algorithm where the error raised to the power of four is minimized for a multiple sinusoidal input and Gaussian measurement noise. Here we newly obtain the convergence equation for the sum of the mean of the squared weight errors, which indicates that the transient behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant. It should be noted that no similar results can be expected from the previous analysis by Walach and Widrow/sup [1]/.

• 한국소음진동공학회논문집
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• 제12권8호
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• pp.616-625
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• 2002

In this paper, we drove the filtered-x least mean fourth (FXLMF) algorithm where the error raised to the power of four is minimized and analyzed its convergence behavior for a multiple sinusoidal acoustic noise and Gaussian measurement noise. The application of the FXLMF adaptive filter to active noise control requires to estimate the transfer characteristics of the acoustic path between the output and the error signal of the adaptive controller. The results of the convergence analysis of the FXLMF algorithm indicate that the effects of the parameter estimation inaccuracy on the convergence behavior of the algorithm are characterized by two distinct components phase estimation error and estimated gain. In particular, the convergence is shown to be strongly affected by the accuracy of the phase response estimate. Also, we newly show that the convergence behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2001년도 제14회 신호처리 합동 학술대회 논문집
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• pp.915-918
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• 2001

In this paper we study a new convergence behavior of the least mean fourth (LMF) algorithm where the error raised to the power of four is minimized for a multiple sinusoidal input and Gaussian measurement noise. Here we newly obtain the convergence equation for the sum of the mean of the squared weight errors, which indicates that the transient behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant. It should be noted that no similar results can be expected from the previous analysis by Walach and Widrow.

• 한국음향학회지
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• 제14권1호
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• pp.22-30
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• 1995

본 논문은 입력 신호가 복수 정현파(multiple sinusoids) 신호로 구성되고 측정 잡음이 가우시안일 때 최소평균사승(least mean fourth : LMF) 알고리듬의 수렴 특성을 새로운 해석 기법을 적용하여 이론적으로 분석하였다. LMF알고리듬은 오차 신호의 4승을 비용 함수(cost function)로 하여 gradient-descent 방법으로 구한 적응 알고리듬인데 기존 Walach 와 Widrow의 수렴 특성 분석에서는 이루어지지 않았던 계수 추정 오차에 대한 2차 모멘트의 과도기 상태 수렴 특성을 본 논문에서 새로이 제시하였다. 결론적으로 가우시안 측정 잡음의 분산과 수렴 상수의 크기에 따라 서로 다른 수렴 특성을 나타냄을 알 수 있었다. 이러한 결과는 기존 Walach 와 Widrow의 분석 기법으로서는 알 수가 없었다.

• 한국통신학회논문지
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• 제26권12A호
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• pp.2050-2058
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• 2001

In this paper, we propose the filtered-x least mean fourth (LMF) algorithm where the error raised to the power of four is minimized and analyze its convergence behavior for a multiple sinusoidal acoustic noise and Gaussian measurement noise. Application of the filtered-x LMF adaptive filter to active noise cancellation (ANC) requires estimating of the transfer characteristic of the acoustic path between the output and error signal of the adaptive controller. The results of 7he convergence analysis of the filtered-x LMF algorithm indicates that the effects of the parameter estimation inaccuracy on the convergence behavior of the algorithm are characterized by two distinct components : Phase estimation error and estimated gain. In particular, the convergence is shown to be strongly affected by the accuracy of the phase response estimate. Also, we newly show that convergence behavior can differ depending on the relative sizes of the Gaussian measurement noise and convergence constant.

• The Journal of the Acoustical Society of Korea
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• 제15권3E호
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• pp.66-73
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• 1996

In this paper, we propose the filtered-x least mean fourth (LMF) algorithm where the error raised to the power of four is minimized and analyze its convergence behavior for a multiple sinusoidal acoustic noise and Gaussian measurement noise. Application of the filtered-x LMF adaptive filter to active noise control(ANC) requires estimating of the transfer characteristic of the acoustic path between the output and error signal of the adaptive controller. The results of the convergence analysis of the filtered-x LMF algorithm indicates that the effects of the parameter estimation inaccuracy on the convergence behavior of the algorithm are characterized by two distinct components : Phase estimation error and estimated gain. In particular, the convergence is shown to be strongly affected by the accuracy of the phase response estimate. Also, we newly show that convergence behavior can differ depending on the relative sizes of the Gaussian measurement noise and convergence constant.

• 전자공학회논문지B
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• 제32B권11호
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• pp.1506-1516
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• 1995

In this paper, we propose the filtered-x least mean fourth (FXLMF) algorithm where the error raised to the power of four is minimized and analyze its convergence behavior for a multiple sinusoidal acoustic noise and Gaussian measurement noise. Application of the FXLMF adaptive filter to active noise control requires to estimate the transfer characteristics of the acoustic path between the output and the error signal of the adaptive controller. The results of the convergence analysis of the FXLMF algorithm indicate that the effects of the parameter estimation inaccuracy on the convergence behavior of the algorithm are characterized by two distinct components : Phase estimation error and estimated gain. In particular, the convergence is shown to be strongly affected by the accuracy of the phase response estimate. Also, we newly show that the convergence behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant.

• 한국음향학회:학술대회논문집
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• 한국음향학회 1998년도 학술발표대회 논문집 제5권
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• pp.80-83
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• 1998

In this paper, we propose a new filtered-x least mean fouth (LMF) algorithm where the error raised to the power of four is minimized and analyze its convergence behavior or a multiple sinusoidal acoustic noise and Gaussian measurement noise. Application of the filtered-x LMF adaptive filter to active noise cancellation (ANC) requires estimating of the transfer characteristic of the acoustic path between the ouput and error signal of the adaptive canceller. The results of the convergence analysis of the filtered-x LMF algorithm indicates that the effects of the parameter estimation inaccuracy on the convergence behavior of the algorithm are characterized by two distinct component . Phase estimation error and estimated again. In particular , the convergence is shown to be strongly affected by the accuracy of the phase response estimate. Also, we newly show that convergence behavior can differ depending on the relative sizes of the Gaussian measurement noise and convergence constant.