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 mean-square and tracking performance of adaptive filters by relying on energy conservation arguments. Some of the key results in the chapters are reproduced here for ease of reference.
SUMMARY OF MAIN RESULTS
Stationary Environments
- Consider adaptive filters that are described by stochastic difference equations of the form
where g[·] is some function of e(i) = d(i) – uiwi–1. The mean-square error (MSE) of any such filter is defined as the limiting value of E |e(i)|2,
- When the data {d(i), ui} satisfy the stationary model (15.16), then the MSE is also given by
where
and 
. The limiting variance of the a priori error ea(i) is called the excess mean-square error (EMSE) of the filter,
- For any such adaptive filter, and for any data {d(i), ui}, the following energy conservation relation holds for all
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