Lag-invariant adaptive spectrum estimation

This paper is concerned with Fourier-based non-parametric spectral estimation methods for time-varying environments. It presents a class of interactive spectrum estimators in which the number of computations required to update the estimate at each sample is independent of the number of the autocorrelation lags employed to produce the estimate. These estimators are termed lag invariant and form an important class due to their computational simplicity. (Memory requirements, however, do increase as greater autocorrelation lags are employed.) The estimators are based on the use of lagged-product windows specifically selected to form autocorrelation estimates which are then Fourier transformed to produce adaptive spectral estimators having the desired lag-invariant property. It is shown that the special requirements which lead to lag invariance are not always satisfied when the estimation process is based on the use of a data weighting window. In this paper, these requirements are formulated using a generalized lagged-product window approach and the conditions necessary to produce the lag invariance property are delineated.