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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

Problems and Computer Projects

PROBLEMS

Problem IX.1 (Initial conditions) Refer to the discussion in Sec. 37.3 on initial conditions and let П be as in (37.13).

  1. (a) Verify that in this case c60_img01.jpg
  2. (b) Conclude that
    equation

    along with c60_img03.jpg and

    equation

Problem IX.2 (Order- and time-update of conversion factor) Start from expression (38.22) for γM+I(i) in terms of γM (i– 1) and rewrite it as

equation
  1. (a) Since c60_img06.jpgdenotes the minimum cost of the regularized least-squares problem (38.19), it satisfies c60_img07.jpg(cf.Alg.30.2). Use this relation to show that the above expression for γM+I (i) leads to the equality
    equation
  2. (b) Likewise, show that
  3. (c) Use part (b) to show that and conclude from (38.12), and from the definition of νM+1 (i) in ...
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Publisher Resources

ISBN: 9780470253885