In almost all analyzes of the least mean-square (LMS)

finite impulse response (FIR) adaptive algorithm, it is assumed that

the length of the adaptive filter is equal to that of the unknown

system impulse response. However, in many practical situations,

a deficient length adaptive filter, whose length is less than that of

the unknown system, is employed, and analysis results for the sufficient

length LMS algorithm are not necessarily applicable to the

deficient length case.