自适应最小均方算法及其能量函数研究

根据递推随机理论，用李雅普诺夫法研究最小均方算法的微分方程，结论是，不管信号是平稳过程还是非平稳过程，该算法大范围渐近稳定。在均方意义下定义自适应时间常数为李雅普诺夫函数与其导数之比，由此建立时间常数、步长、信号特征值以及信号带宽之间的关系

Study of Adaptive LMS Algo rithm and Its Energy Function

Differential equation of the least mean squares algorithm is studied by method of Lyapunov based upon the recurisive stochastic algorithm. A conclusion comes that LMS algorithm converges asymptotically in the large area whether input signal is a stationary process or a nonstationary one. Adaptation time constants is defined, in the mean square sense, as the absolute of the ratio of the Lyapunov function to its differentiation. The paper establishes a new relationship among the time constants, the step size,the eigenvalue and the bandwidth of signal.