Stability of the fast recursive least square algorithms with perfectly predictable signals

In this paper, we present a detailed study of the perfectly predictable signals in the case of pure sinusoids, in order to determine the cause of instability of the fast recursive least squares (FRLS) algorithms with speech signal. To avoid instability of the FRLS algorithm, an assigned choice of the sampling rate compared to the frequency of the sinusoid is proposed. Tests were carried out on pure sinusoids in the very long term without any tendency to divergence.