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The mean-squared error (MSE) behaviour for Fourier linear combiner (FLC)-based filters is analyzed, using the independence assumption. The advantage of this analysis is its simplicity compared with previous results. The MSE transient behaviour for this kind of filters is also presented for the first time. Moreover, a time-varying sequence for the least mean square (LMS) algorithm step-size is proposed to provide fast convergence with small misadjustment error. It is shown that for this sequence, the MSE behaves better as the input signal-to-noise ratio (SNR) decreases, but increases with the number of harmonics. Lastly, the authors make a brief analysis on the nonstationary behaviour of these filters, and again they find simple expressions for the MSE behaviour.