On The Reconstruction of Irregularly Sampled Time Series

Roberto Vio, Thomas Strohmer, and Willem Wamsteker

We consider the question of numerical treatment of irregularly sampled time series. This problem is quite common in astronomy because of factors such as the day-night alternation, weather conditions, non-observability of the objects under study, etc. For this reason an extensive literature is available on this subject (Scargle 1982, 1989 and bibitems therein). Most of the proposed techniques, however, are based on heuristic arguments and their usefulness is essentially in the estimation of power spectra and/or autocovariance functions. Here we propose an approach, based on the reasonable assumption that many signal of astronomical interest are the realization of bandlimited processes, which can be used to fill up gaps in experimental time series. By using this approach we propose several reconstruction algorithms that, due to their regularization properties, yield reliable signal reconstructions even in case of noisy data and large gaps. A detailed description of these algorithms is provided, their theoretical implications are considered and their practical performances are tested via numerical experiments. MATLAB software implementing the methods described in this work is obtainable by request to the authors.

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