A unified approach to the steady-state and tracking analyses of adaptive filters

Most adaptive filters are inherently nonlinear and time-variant systems. The nonlinearities in the update equations tend to lead to difficulties in the study of their steady-state performance as a limiting case of their transient performance. This paper develops a unified approach to the steady-state and tracking analyses of adaptive algorithms that bypasses many of these difficulties. The approach is based on the study of the energy flow through each iteration of an adaptive filter, and it relies on a fundamental error variance relation.