Article,
On the Reconstruction of Irregularly Sampled Time Series
Publications of the Astronomical Society of the Pacific, 112 (767): 74-90 (2000)
Abstract
ABSTRACT 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, nonobservability of the objects under study, etc. For this reason an extensive literature is available on this subject. 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 signals of astronomical interest are the realization of band‐limited processes, which can be used to fill gaps in experimental time series. By using this approach we propose several reconstruction algorithms that, because of 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 from the authors.
