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The high resolution statistics of a periodogram-type spectral estimate for a periodic deterministic signal plus Gaussian noise are well understood. If, however, the signal plus noise is first passed through a nonlinear memoryless device (such as a hard limiter), the situation becomes much more complicated. The main result of this correspondence is the derivation of the high resolution limit of the joint statistics of the and components of a periodogram for a certain class of nonlinear devices with a deterministic periodic signal and Gaussian noise as input. This result permits the calculation of the asymptotic central moments of the spectral estimate formed from the foregoing periodogram. It then becomes possible to subject a device employing this technique for spectral estimation to a detailed performance analysis.