Abstract
Several properties of the filtered-error (filtered-E or adjoint) least mean square (LMS) algorithm, such as the stability condition, the upper limit of the step size and the variance of the error signal are quantitatively evaluated and compared with the those of the filtered-X LMS algorithm. For this purpose, the averaged system and the ordinary differential equation (ODE) method are applied to the frequency domain expression of both algorithms. From the averaged system, it is demonstrated that the stability condition and the upper limit of the step size of the filtered-E LMS algorithm are same with those of the filtered-X LMS algorithm. On the other hand, from the ODE analysis, it is shown that the excess mean square error of the filtered-E LMS algorithm is two thirds of that of the filtered-X LMS algorithm.
