... (19.2)whereW(n)=[w0(n)w1(n)···wL−1(n)]Tisthecoefficientvector,X(n)=[x(n)x(n−1)···x(n−L+1)]Tistheinputsignalvector,d(n)isthedesiredsignal,e(n)istheerrorsignal,andµ(n)isthestepsize.TherearethreemainreasonswhytheLMSadaptivefilterissopopular.First,itisrelativelyeasytoimplementinsoftwareandhardwareduetoitscomputationalsimplicityandefficientuseofmemory.Second,itperformsrobustlyinthepresenceofnumericalerrorscausedbyfinite-precisionarithmetic.Third,itsbehaviorhasbeenanalyticallycharacterizedtothepointwhereausercaneasilysetupthesystemtoobtainadequateperformancewithonlylimitedknowledgeabouttheinputanddesiredresponsesignals.c1999byCRCPressLLC[22] Farden,D.C., Tracking properties of adaptivesignal processingalgorithms,IEEETrans.Acoust.,Speech, Signal Processing, ASSP-29(3), ... algorithms,IEEE Trans. Signal Processing, 41(9), 2811–2825, Sept. 1993.[25] Douglas, S.C. and Meng, T.H Y., Normalized data nonlinearities for LMS adaptation,IEEETrans. Signal Processing, 42(6), ... Contr. Signal Processing, 4(3), 219–216, May-June 1990.[28] Harris, R.W., Chabries, D.M., and Bishop, F.A., A variable step (VS) adaptive filter algorithm,IEEE Trans. Acoust., Speech, Signal Processing, ASSP-34(2),...