

 Adaptive filters


Lms
remains the simplest and best algorithm when
slow convergence is not a serious issue (typically used)
$O(N)$

Nlms
simple extension of the LMS with much faster
convergence in many cases (very commonly used)
$O(N)$

Frequencydomain methods
offer computational savings
(
$O(\lg N)$ ) for long filters and usually offer faster
convergence, too (sometimes used; very commonly used whenthere are already FFTs in the system)

Lattice methods
are stable and converge quickly,
but cost substantially more than LMS and have higher residualEMSE than many methods (very occasionally used)
$O(N)$

Rls
algorithms that converge quickly and are
stable exist. However, they are considerably more expensivethan LMS. (almost never used)
$O(N)$

Block rls
(least squares) methods exist and can
be pretty efficient in some cases. (occasionally used)
$O(\lg N)$ ,
$O(N)$ ,
$O(N^{2})$

Iir
methods are difficult to implement
successfully and pose certain difficulties, but are sometimesused in some applications, for example noise cancellation of
low frequency noise (very occasionally used)

Cma
very useful when applicable (blind
equalization); CMA is
the method for
blind equalizer initialization (commonly used in a few specific equalization applications)
$O(N)$
In general, getting adaptive filters to work well in an
application is much more challenging than, say, FFTs or IIRfilters; they generally require lots of tweaking!
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Source:
OpenStax, Adaptive filters. OpenStax CNX. May 12, 2005 Download for free at http://cnx.org/content/col10280/1.1
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