The Autocorrelation Function and Doppler Spectral Moments: Geometric and Asymptotic Interpretations

Abstract

The relationships between the Doppler spectrum of velocities and the autocorrelation function can be studied via simple geometric and power series expansion relations. The asymptotic expansion of the autocorrelation function in terms of the central moments of the Doppler spectrum provides a new theoretical framework for time-domain spectral moment estimation and illustrates the trade-offs in optimal moment estimation. A number of new moment estimators are derived via this general approach and evaluations of three new spectral width estimators demonstrate that the implementation of a single spectral width estimator is generally not the best approach.