Multitaper
From Wikipedia, the free encyclopedia
The multitaper method is a technique developed by David J. Thomson to estimate the power spectrum 
of a stationary ergodic finite-variance random process X, given a finite contiguous realization of X as data. In the multitaper approach, the data 
is premultiplied by each element of a set of K pairwise orthonormal tapers (or window functions) prior to taking magnitude-squared Fourier transforms. In the most basic formulation, the arithmetic average of the resulting K direct spectrum estimates yields the estimate, although different averaging schemes exist.
Generally, the tapers are chosen to be discrete prolate spheroidal sequences (also known in the literature as DPS sequences or Slepian sequences, after David Slepian). The lowest-order DPS sequence is known to minimize the effects of broad-band spectral leakage, while the higher-order DPS sequences exhibit the same property, with the added constraint that all tapers be pairwise orthonormal. It should be noted that the DPS sequences depend first on N, the length of the realization, and, more importantly, on a half-bandwidth parameter W which controls a bias-variance tradeoff. It can be shown that if W is chosen appropriately (the choice depending on local features of ), then the multitaper estimate is approximately unbiased.
[edit] References
Percival, D. B., and A. T. Walden. Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques. Cambridge: Cambridge University Press, 1993.
Slepian, D. "Prolate spheroidal wave functions, Fourier analysis, and uncertainty - V: The discrete case." Bell System Technical Journal, Volume 57 (1978), 1371-430.
Thomson, D. J. "Spectrum estimation and harmonic analysis." In Proceedings of the IEEE, Volume 70 (1982), 1055-1096.
