A Unified Approach to the Steady-state and Tracking Analyses of Adaptive Filtering Algorithms

Most adaptive filters are inherently nonlinear and time variant systems. The nonlinearities in the update equations of these filters usually lead to significant difficulties in the study of their performance. This paper develops a new feedback approach to the steady-state and tracking analyses of adaptive algorithms that bypasses many of the difficulties encountered in traditional approaches. In this new formulation, we not only re-derive several earlier results in the literature, but we often do so under weaker assumptions, in a considerably more compact way, and we also obtain new results.