Tolerance of Spectral Estimation

A statistical expression for the mean square error of a spectrum estimation has been derived in terms of the variances and covariances of the amplitude and phase errors of a complex data sequence. No restrictions need be imposed on the magnitude of these variances and covariances. Numerical results have been systematically presented in graphs which illustrate the dependence of the spectrum error on the standard deviation and correlation distance of the amplitude and phase errors. It is shown that large phase error tends to dominate the spectrum error, and that large correlation distances worsen the spectrum error and sharpen its dependency on the frequency index. An expression to estimate the variance of frequency error has also been derived under the assumption of small phase errors. Numerical results are given, which demonstrate the linear dependency of the frequency error on the phase error and shows that a large correlation distance worsens the frequency error while a large number of samples reduces it.