On the estimation of spectra from randomly sampled signals: a method of reducing variability

Abstract

Spectral estimates obtained from randomly sampled data arrays incur excess variability over and above that arising from the stochastic character of the signal. In previous papers estimators have been derived for both the direct transform and the correlation plane methods. Expressions for the excess variability showed its dependence on the magnitude of the mean square of the data. Here we show how improved estimates can be obtained by filtering out parts of the spectral energy so that the actual analysis for other parts of the spectrum can be performed on data of smaller mean square. The variability associated with this filtering operation limits the improvement in the stability of estimates that can be achieved. Analytical expressions for the bias and variability of these new estimates are compared with numerical experiments on simulated data arrays.