Analysis of the dynamics of a digital gradient algorithm of adaptive signal filtering

The paper determines the stability condition and mean convergence rate of the transient change in the mean noise output power of an adaptive digital filter based on a gradient adaptation algorithm. It is assumed that the noise correlation matrix at the compensation inputs of the filter is diagonal and that the diagonal elements of the matrix are equal. The dynamic characteristics obtained are found to differ significantly from the usual characteristics, which correspond to the transient change in the mean value of the weight coefficients of the adaptation algorithm.