![]() The trivial case K=1 and p=1 is, again, the single-taperedįor typical length instrumental climate records, theĬhoice K=3, p=2 offers a good compromise between Tradeoff between spectral resolution and the stability or ``variance'' The choice of the bandwidth 2 pf n and number of tapers K thus represents the classical The first 2 p - 1 tapers provide usefully small spectral-leakage,Īnd thus the number of tapers used K shouldīe less than 2 p-1 in any application of MTM. The Rayleigh frequency, and p is an integer. The variational problem of minimizing leakage outside The tapers are the discrete set of eigenfunctions which solve Stable estimate - i.e., one with lower variance - than do single-taper ![]() ``eigentapers'' belong to a family of functions known asĭiscrete prolate spheroidal sequences (DPSS) which are defined as theĮigenvectors of a suitable Rayleigh-Ritz minimization problem.Īveraging over this (small) ensemble of spectra yields a better and more Pre-multiplying the data by orthogonal tapers which areĬonstructed to minimize the spectral leakage due Rather than the unique data taper or spectral window used byĪ set of independent estimates of the power spectrum is computed, by Model for the process generating the timeĪttempts to reduce the variance of spectral estimates by In that it does not prescribe an a priori (e.g., autoregressive) Offers the appeal of being nonparametric, MTM, like the method of Blackman and Tukey, To problems in geophysical signal analysis, includingĪnalyses of atmospheric and oceanic data, paleoclimate data, geochemical tracer data, and Of a time series which is believed to exhibit a spectrumĬontaining both continuous and singular components. Percival and Walden, 1993) and signal reconstruction Novel means for spectral estimation (Thomson, 1982 The MultiTaper method (MTM) of spectral analysis provides a
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