Energy Conservation and State-Space Characterization of Adaptive Filter Performance

This article provides an overview of an energy-based approach to the study of the steady-state and transient performances of adaptive filters. The analysis employs energy-conservation arguments and is based on studying the energy flow through each iteration of an adaptive filter. Among other results, the approach characterizes the transient behavior of adaptive filters in terms of a linear time-invariant state-space model. The stability and steady-state behavior of the model then translate into stability and mean-square performance results for the adaptive filter. In addition to deriving earlier results in a unified manner, the approach does not restrict the regression data to being Gaussian or white