On the reconstruction of irregularly sampled time series

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 o bjects under study, etc. For this reason an extensive literature is availab le 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 approa ch, based on the reasonable assumption that many signals of astronomical in terest are the realization of band-limited processes, which can be used to fill gaps in experimental time series. By using this approach we propose se veral reconstruction algorithms that, because of their regularization prope rties, 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 a re tested via numerical experiments. MATLAB software implementing the metho ds described in this work is obtainable by request from the authors.