次级通道模型误差下滤波X型最小均方差算法收敛性分析  

Convergence analysis of filtered-X LMS algorithm with secondary path modeling error

作　　者：孙旭[1] 陈端石[1] 

机构地区：[1]上海交通大学动力和能源工程学院,上海200030

出　　处：《声学学报》2002年第2期97-101,共5页Acta Acustica

摘　　要：给出了滤波Ｘ型ＬＭＳ（ＦＸＬＭＳ）算法收敛的一个充分条件，指出如果次级通道传递函数与其估计值在所有频带上满足正实条件，则ＦＸＬＭＳ算法对任意参考信号收敛。若上述正实条件仅在某些频带上满足，则ＦＸＬＭＳ算法的收敛将依赖于参考信号功率谱密度的分布。收敛步长取决于某特定相关矩阵特征值的分布。将上述结论应用于时延型ＬＭＳ（ＤＬＭＳ）算法，得出在时延估计存在误差时，ＤＬＭＳ算法收敛于若干离散的频带，而频带宽度完全取决于“对延估计误差频率”（时延估计误差倒数的１／４）。A more relaxed sufficient condition for the convergence of filtered-X LMS (FXLMS) algorithm is presented, which shown that if some positive real condition is satisfied within all the frequency range, FXLMS converges whatever the reference signal is. But if above positive real condition is satisfied only within some frequency range, the convergence of FXLMS algorithm is dependent on the spreading of power spectral density of the reference signal. Applying the conclusion above to the delayed LMS (DLMS) algorithm, it is shown that to guarantee the convergence of DLMS, the power of the reference signal should be dominant in some discrete frequency bands. The width of those bands is determined by the 'time-delay estimation error frequency' which is equal to one fourth of the inverse of the estimated error of the time delay.

关 键 词：滤波 X型 最小均方差算法 收敛性分析 次级通道模型误差 时延估计 噪声有源控制 信号处理 

分 类 号：TB535[理学—物理] TN911.7[理学—声学]