An analysis of LMS adaptive two-sided transversal filters

Adaptive smoothing filters have been studied for the removal of narrow-band interference and for use in spectral estimation. The authors study the convergence of two LMS (least mean square) adaptive smoothers, one constrained to have symmetry, the other with each tap adapting independently. Since the behavior of the adaptive filters is dependent upon the characteristics of the signal on the filter taps, the authors explore differences in convergence among these two smoothing algorithms and the LMS predictor through this signal vector. By analyzing in detail this behavior for a sinusoid in white noise, they show that if the sinusoid is neither very low nor high in frequency then the constrained smoother has both better convergence and steady-state behavior than either the predictor or the unconstrained smoother while requiring one-half as many multiplications