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A new spectral estimator is developed from the high-order Yule-Walker equations and pseudoinverse solutions to the equations. The approach circumvents the usual difficulties associated with inverting ill-conditioned matrices and allows the choice of high model order. It also provides high resolution spectral estimates as substantiated by simulation results. A byproduct of this spectral estimator is a constant false alarm rate detector for a single sinusoid in noise. The detector's receiver operating characteristics curves are constructed from histograms, based on 1000 runs, of the detection statistics.