Energy conservation in adaptive filtering

The study of the steady-state and transient performance of adaptive filters is a challenging task because of the nonlinear and stochastic nature of their update equations (e.g., References 1 to 4). The purpose of this chapter is to provide an overview of an energy-conservation approach to study the performance of adaptive filters in a unified manner. The approach is based on showing that certain a priori and a posteriori errors maintain an energy balance for all time instants. When examined under expectation, this energy balance leads to a variance relation that characterizes the dynamics of an adaptive filter. An advantage of the energy framework is that it allows us to push.