Peak and power

The estimation of power is problematic when the amplitudes in the discrete spectral component are random. An example of this is a mixed spectrum stationary Gaussian process with mean zero. In this regard, it is shown that the maximum likelihood estimator of the power from a random sample of peaks exceeding a relatively large threshold, the peak estimator is more efficient than the sample variance from a random sample of the same size of signal values. When evaluated from nonrandom samples, indications are that the peak estimator may still have a relatively small mean square error.