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Published online by Cambridge University Press: 03 August 2017
We present a set of spectrum analysis techniques described by Thomson (1982) in which the discrete Fourier transform (DFT) is windowed by an expanding set of prolate spheroidal wave functions. The homogeneous ILS polar motion series was chosen for the presentation because of its interesting spectrum. It contains lines at the annual and semi-annual frequencies, a band of uncertain width and structure around Chandler's frequency, and evidence for a 30-year periodicity. None has been measured with great certainty by traditional single-taper DFT spectrum analysis. Here, a multi-taper algorithm significantly improves the bias control and consistency of high-resolution DFT spectrum estimates. An analysis of variance is performed to locate significant harmonic lines, and jackknifed statistics are used as additional cross-checks on the stability of the results. In addition, multi-tapered coherence estimates confirm a previously noted correlation between a meteorological forcing function and a polar motion excitation derived from the ILS series.