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A two-stage identification scheme is proposed for multivariable systems for applications including spectral estimation, and signal and system model estimation. The statistics of the signal and of the corrupting noise are taken as unknown, except that the signal is assumed to have a rational spectrum. First, a very high-order model is estimated and then a reduced-order model is derived from the higher-order model. An algorithm based on theory and heuristics is developed to select a set of frequencies where the signal-to-noise ratio is high. A reduced-order model is obtained from the best weighted least-squares fit at the selected frequencies.