Steady-state superiority of lms over ls for time-varying line enhancer in noisy environment

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Abstract
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 used 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.

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