Note on the convergence of linear predictive filters, adapted using the LMS algorithm

The convergence of an all-zero digital filter, adapted using the LMS algorithm, is shown to be stable for Gaussian input signals if the control parameter is less than a maximum value which depends on the order of the filter, the mean-square value of the input signal and the largest eigenvalue of the autocorrelation matrix. Experimental tests for predictive filters are described and the results show agreement with this stability criterion, which, in the cases investigated, differs significantly, from one reported previously.