Time-frequency spectrum estimation: an adaptive multitaper method

Abstract

This paper extends Thomson's (1982) adaptive multitaper spectrum estimation method to the nonstationary case. The general approach and the nonadaptive estimation procedure were first presented by Pitton (1998). The method uses time-frequency concentrated basis functions which generalize the properties of the prolate spheroidal waveforms. Individual spectrograms computed with these eigenfunctions form direct time-frequency spectrum estimates, and are combined to form the multitaper time-frequency spectrum estimate. We then develop a new adaptive procedure which reduces the bias of the individual eigenestimates using an estimate of their leakage characteristics. The revised multitaper estimator then has correspondingly improved bias properties. An expression for the variance of the adaptive estimator is also derived, providing a complete characterization of the statistical time-frequency estimator.