Behavior of the Adaptive Line Enhancer During Initial Adaptation.

摘要

The behavior of the Adaptive Line Enhancer (ALE) during initial adaptation is analyzed analytically via the direct solution of the Widrow-Hoff least-mean-square (LMS) algorithm. The result shows that the initial transient response of the weight vector is approximately equal to 2mu/T times the cross correlation vector of the input, i.e., W sub l(t) = 2mu/T Integral from tau = delta + lT to tau = t of (x(tau) x(tau-delta-lT)d tau), where mu is the adaptation constant, delta is the bulk delay of the filter, l is the weight index and T is the sampling period or an element delay. (Author)