Steady-state superiority of LMS over LS for time-varying line enhancer in noisy environment

Line enhancement uses linear prediction to recover a narrowband line embedded in noise. If the line has a frequency drift, an adaptive predictor can track it. The theoretical steady-state tracking performances of the LS and LMS updating algorithms have been analytically investigated in two previous papers. The condition of `slow adaptation´, which is assumed in the literature, is interpreted in this paper in a physical way. If the frequency drift is too large in comparison with the background noise, it is better to use the noisy input data sample than a prediction of the line. A comprehensive set of Monte-Carlo simulations is presented to support the mathematical assumptions to derive the theory. It is shown, both analytically and by simulation, that the LS algorithm has worse steady-state tracking performance than LMS for practical situations that are modelled by a chirp-like signal. This result does not violate the superiority of LS over LMS for transient situations