April 2008
Intermediate
832 pages
26h 2m
English
Content preview from Adaptive Filters
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Summary and Notes
The chapters in this part describe a procedure for evaluating the transient behavior of adaptive filters by relying on energy conservation arguments.
SUMMARY OF MAIN RESULTS
- Consider adaptive filters that are described by data-normalized stochastic difference equations of the form
where g[.] is some positive-valued function of ui. The mean-square error (MSE) of any such filter is defined as the limiting value of E |e(i) |2,
Likewise, the mean-square deviation (MSD) of the filter is defined as the limiting value of
.
where
and w° is the unknown vector in the data model (22.1). - For any such adaptive filter, and for any data {d(i), ui) and Hermitian nonnegative-definite weighting matrix Σ, the following weighted energy-conservation relation holds for all i:
where
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