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The power spectrum Of a zero-mean stationary Gaussian random process is assumed to be known except for one or more parameters which are to be estimated from an observation of the process during a finite time interval. The approximation is introduced that the coefficients of the Fourier series expansion of a realization of long-time duration are uncorrelated. Based on this approximation maximum likelihood estimates are derived and lundamental limits on the variances attainable are found by evaluation of the Cramér-Rao lower bound. Parameters specifically considered are amplitude, center frequency, and frequency scale factor. Also considered is ripple frequency which refers to the cosine factor in the spectrum produced by the addition of a delayed replica of the random process. The dual problem of estimating parameters of the time-varying power level of a nonstationary baud-limited white noise process is examined.