The Estimation of Spectral Moments

Book excerpt: The results of an investigation that considered the real time estimation of certain shape parameters of the power spectral density of a narrow band random process are presented. Systems are developed which directly estimate f sub a, the power mean frequency, and B, the standard deviation of the spectrum. The equivalence of these estimators to the classical estimators is demonstrated and simple implementations, due to the omission of the intermedicate computation of spectrum estimates, are presented. Statistical analyses are made for both estimators under the assumption of long time averaging and a gaussian input process. It is demonstrated that both estimators are asymptotically unbiased and that their mean square errors tend to zero, with order 1/T, as the averaging time goes to infinity. (Author).