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Biometrika 1995 82(1):201-214; doi:10.1093/biomet/82.1.201
© 1995 by Biometrika Trust
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The effective bandwidth of a multitaper spectral estimator

A. T. WALDEN1, E. J. McCOY1 and D. B. PERCIVAL2

1Department of Mathematics, Imperial College of Science, Technology and Medicine 180 Queens Gate, London SW7 2BZ, U. K.
2Applied Physics Laboratory, University of Washington HN-10 Seattle, Washington 98195, U.S.A.

The bandwidth of a spectral estimator is a measure of the minimum separation in frequency between approximately uncorrelated spectral estimates. We determine an effective bandwidth measure for multitaper spectral estimators, a relatively new and very powerful class of spectral estimators proving to be very valuable whenever the spectrum of interest is detailed and/ or varies rapidly with a large dynamic range. The multitaper spectral estimator is the average of several direct spectral estimators, each of which uses one of a set of orthogonal tapers. We show that the equivalent width of the autocorrelation of the overall spectral window is a suitable measure of the effective bandwidth of a multi-taper spectral estimator and illustrate its use in the case of both Slepian and sinusoidal orthogonal tapers. This measure allows a unified treatment of bandwidth for the class of quadratic spectral estimators. Hence, for example, it is now possible properly to compare multitaper spectral estimators with traditional lag window spectral estimators, by assigning a fixed and equal effective bandwidth to both methods. An application is given to the spectral analysis of ocean wave data.

Key Words: Bandwidth • Lag window • Multitapering • Quadratic estimator • Sinusoidal taper • Slepian taper • Spectral estimation • Tapering


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