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Adaptive Filters
book

Adaptive Filters

by Ali H. Sayed
April 2008
Intermediate
832 pages
26h 2m
English
Wiley-IEEE Press
Content preview from Adaptive Filters

Summary and Notes

The chapters in this part describe several basic concepts of least-squares and recursive least-squares theory. The main ideas and results are the following.

SUMMARY OF MAIN RESULTS

Least-Squares

  1. The standard least-squares criterion seeks the vector c48_img01.jpg that is closest to a vector y in the column span of a matrix H. It does so by solving
    equation

    and by setting c48_img03.jpg, where c48_img04.jpg is any solution to the normal equations c48_img05.jpg.

  2. The normal equations are always consistent and they may even have infinitely many solutions. However, regardless of which solution c48_img06.jpg we pick, the projection c48_img07.jpg is unique.
  3. Least-squares solutions are characterized by a fundamental orthogonality principle, which states that c48_img06.jpg is ...
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Publisher Resources

ISBN: 9780470253885