Efficient frequency-wavenumber spectrum estimation using sliding time-division windows

A framework for quadratic estimators of the frequency-wavenumber spectrum is presented. Such estimators are nonparametric since they assume little of the observed process. Associated with quadratic estimators are the windows of classical spectrum estimators. The use of several windows provides spectral averaging and reduces estimator variance in exchange for decreased resolution. The use of several windows which are formed from circular shifts of a single window function is considered. These windows are selected to maximize a selectivity condition while satisfying an orthogonality constraint. It is shown how to use these windows to update estimates of the frequency-wavenumber spectrum efficiently as new data are acquired