分割化區塊式頻率域適應性濾波器之步階增益範圍的探討

An Investigation on the Step-Size Bound of the Partitioned Frequency-Domain Block LMS (PFBLMS) Algorithm

陳耀華(Yao-Hua Chen)

指導教授 ： 李仲溪

元智大學/工程學院/電機工程學系/碩士(2005年)

摘要

在本論文中，我們針對「分割化區塊式頻率域適應性濾波器」（PFBLMS）提出其在收斂情況下之步階增益範圍的分析。頻率域適應性濾波器在需要使用大量係數的應用上非常引人注目，例如：聲學迴音消除。然而區塊式最小均方誤差（BLMS）演算法將由於其狹隘之步階增益範圍限制降低了其運用。由於PFBLMS演算法隸屬於BLMS演算法家族，因此亦有遭受狹隘之步階增益範圍的可能。雖然PFBLMS演算法之步階增益範圍已在最近被推導出來，但其結果卻不一致。所以我們將在本篇論文中對PFBLMS之步階增益範圍進行分析。我們推導發現PFBLMS之步階增益範圍為BLMS之N倍。其中N為PFBLMS演算法的子濾波器長度。這個發現將增加PFBLMS演算法在聲學迴音消除上之運用的可行性。我們用大量之實驗來驗證我們的分析。

關鍵字

適應性濾波器 ； 頻率域 ； 可行性 ； 演算法 ； 濾波器 ； 頻率域 ； 適應性 ； 步階增益

並列摘要

In this thesis, we present an analysis on the step-size bound that guarantees the stability of the partitioned frequency-domain block LMS (PFBLMS). Frequency domain adaptive filters are attractive in applications requiring a large number of coefficients such as acoustic echo cancellation (AEC). However, the very restrictive convergence bound for BLMS has limited its usefulness. Since PFBLMS belongs to the BLMS family, it may suffer the very restrictive step-size bound too. Derivations on step-size bounds for the PFBLMS have been reported recently, but are not consistent with each other. In this thesis, we analyze the step-size bound of PFBLMS, and derive a bound which is N times larger than that of the BLMS. This finding makes PFBLMS much more practical in the application of AEC. Extensive simulation results are provided to support our analysis.

並列關鍵字

adaptive filter ； LMS ； MDF ； GMDF ； PFBLMS ； family ； BLMS ； frewuency domain ； step-size

參考文獻

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[2] M. R. Asharif, and F. Amano, “Acoustic echo-canceler using the FBAF algorithm,” IEEE Transactions on Communications, Vol. 42, No. 12, pp. 3090-3094, Dec. 1994.

[4] N. Bershad, “Analysis of the normalized LMS algorithm with Gaussian inputs,” IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 34, No. 4, pp. 793-806, Aug. 1986.

[5] N. Bershad, “Behavior of the ε-normalized LMS algorithm with Gaussian inputs,” IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 35, No. 5, pp. 636–644, May 1987.

[6] K. S. Chan, and B. Farhang-Boroujeny, “Analysis of the partitioned frequency-domain block LMS (PFBLMS) algorithm,” IEEE Transactions on Signal Processing, Vol. 49, No. 9, pp. 1860-1874, Sep. 2001.