Examination of time series through randomly broken windows

The study of many astronomical problems involves a consideration of time series. The present investigation was prompted by a problem related to the determination of normal modes of oscillation of the sun. It is desirable to have an approach for obtaining an estimate of the accuracy with which oscillation modes may be determined when it appears possible to observe the sun over a long interval of time losing some blocks of time because of cloud cover. The present investigation has the objective to develop a model for addressing problems of this type. After presentation of a few general formulae, the problem is considerably simplified by supposing that observations are made over a large number N of equal time intervals, each of length t, so that the total time interval T is given by T = Nt. With certain additional simplifying assumptions, attention is given to the statistical properties of two functions which are representative of 'randomly broken' window functions.