Natural Interpolation and Consistent Extrapolation of Time Series arising from Dense Multi-Mode Spectra

Details Natural Interpolation and Consistent Extrapolation of Time Series arising from Dense Multi-Mode Spectra Natural Interpolation and Consistent Extrapolation of Time Series arising from Dense Multi-Mode Spectra

May 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003spd....34.0810l&link_type=abstract

American Astronomical Society, SPD meeting #34, #08.10; Bulletin of the American Astronomical Society, Vol. 35, p.823

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The study of the temporal variation of phenomenon is often hampered by the incompleteness of our observations. This is particularly disruptive for highly periodic signals that are interrupted by periodic gaps, which introduce sidelobes that are difficult - if not impossible - to remove by deconvolution techniques if the spectral peaks are dense compared to the sidelobe separation. This is the case for the study of many classes of variable stars, including the Sun, where once per day interuptions are the norm. However, for signals with coherence times longer than the interuptions, there is little ambiguity as to the unobserved behaviour of the signal - that is the frequency, phase, and amplitude of a mode can not change significantly during a time small compared with the mode lifetime - and the missing data can be replaced with high fidelity, by an iterative procedure. The interpolated data is consistent with the observed time series, and can also be used to extrapolate the time series for times comparable with the coherence times of the constituent modes. The method works well for spectra of unknown content, and a priori information, e.g. the approximate frequenices of modes, can be simply incorporated to accelerate convergence. Applications to helio- and astereo-seismic time series will be presented.

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