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Computationally lag-invariant recursive spectrum estimators

This paper is concerned with Fourier-based nonparametric 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 every data sample is independent of the number of the autocorrelation lags employed to produce this estimate. These estimators are termed lag invariant and form an important class due to their computational simplicity. Because of the lag-invariant property, resolution enhancement is achieved without additional cost in computations per frequency sample. The proposed class of recursive spectral estimators is based on specific selection of the lagged product windows used in the autocorrelation function estimation. In this paper, the conditions necessary to produce the lag-invariance property are delineated.