# 0.1 Summary of adaptive filtering methods

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• ## 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) $O(N)$
• ## Frequency-domain 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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