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Adaptive estimation of the linear coefficient vector in truncated expansions is considered for the purpose of modeling noisy, recurrent signals. The block LMS (BLMS) algorithm, being the solution of the steepest descent strategy for minimizing the mean square error in a complete signal occurrence, is shown to be steady-state unbiased and with a lower variance than the LMS algorithm. It is demonstrated that BLMS is equivalent to an exponential averager in the subspace spanned by the truncated set of basis functions. The performance of the BLMS algorithm is studied on an ECG signal and the results show that its performance is superior to that of the LMS algorithm.