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A linear prediction based method is proposed for real harmonic sinusoidal frequency estimation. The estimator basically involves two steps. An initial fundamental frequency estimate is first obtained by solving a standard least-squares equation with exploitation of the harmonic structure of the sinusoidal signal or by using the MUSIC approach. Based on the initial estimate, an optimally weighted least squares cost function is then constructed from which the final estimate is acquired. Computer simulations show that the performance of the estimator approaches Crame´r-Rao lower bound for sufficiently high signal-to-noise ratios and/or data lengths.