Nonstationary spectrum estimation and time-frequency concentration

This paper extends Thomson´s (1982) multitaper spectrum estimation method to nonstationary signals. The method uses a newly-derived set of basis functions which generalize the concentration properties of the prolate spheroidal waveforms to the time-frequency case. We solve for the basis which diagonalizes the nonstationary spectrum generating operator over a finite region of the time-frequency plane. These eigenfunctions are maximally concentrated to and orthogonal over the specified time-frequency region, and are thus doubly orthogonal. Individual spectrograms computed with these eigenfunctions form direct time-frequency spectrum estimates. We next present a multitaper time-frequency spectrum estimation procedure using these time-frequency eigenestimates. Bias and variance expressions are derived, allowing for a statistical characterization of the accuracy of the estimate. The time-frequency concentration property of the basis functions yields an estimator with excellent bias properties, while the variance of the estimate is reduced through the use of multiple orthogonal windows