Energy Conservation in Adaptive Filtering

Adaptive filters are systems that respond to variations in their environment by adapting their internal structure in order to guarantee certain performance specifications. Such systems are widely used in communications, biomedical applications, signal processing, and control.

The performance of an adaptive filter is evaluated in terms of its transient behavior and its steady-state behavior. The former provides information about how fast a filter learns, while the latter provides information about how well a filter learns. Such performance analysis are often challenging since adaptive filters are, by design, time-variant nonlinear stochastic systems. For this reason, it is common to study different adaptive schemes separately due to the differences that exist in their update equations.

This talk provides an overview of an energy-based approach to the performance analysis of adaptive filters. The framework is based on studying the energy flow through each iteration of an adaptive filter and establishing a fundamental energy conservation relation. By specializing the relation to the cases of steady-state operation, tracking, and transient operation, and by formulating state-space models in terms of moment variables, steady-state results as well as stability and robustness results can be pursued uniformly across algorithms.