ABSTRACT
A unified approach to mean-square
analysis of adaptive filters
Adaptive
filters are systems that respond to variations
in their environment by adapting their internal
structure in order to meet certain performance
specifications. Such systems are widely
used in communications, signal processing,
and control. Many adaptive algorithms have
been suggested in literature. To choose
one for a given application, the designer
must evaluate its performance in terms of
its transient behavior and steady-state
response. It is common to study different
adaptive filters separately due to the differences
that exist in their update equations. These
differences in turn call for distinct assumptions
and analysis methods, which obscures commonalities
that might exist among them.
In this talk, we present
a unified approach to the analysis of adaptive
filters that employ general data or error
nonlinearities. The approach is based on
energy conservation arguments
to derive closed form expressions for the
transient and steady-state performance and
conditions for stability. In addition
to deriving earlier results in a unified
manner, the approach also leads to new stability
and performance results without imposing
restrictions on the color or statistics
of the input sequence.