The spectral resolving power of irregularly sampled time series

Abstract

A method is presented for investigating the periodic signal content of time series in which a number of signals is present, such as arising from the observation of multiperiodic oscillating stars in observational asteroseismology. Standard Fourier analysis tends only to be effective in cases when the data are perfectly regularly sampled. During normal telescope operation it is often the case that there are large, diurnal, gaps in the data, that data are missing, or that the data are not regularly sampled at all. For this reason it is advantageous to perform the analysis as much as possible in the time domain. Furthermore, for quantitative analyses of the frequency content and power of all real signals, it is of importance to have good estimates of the errors on these parameters. This is easiest to perform if one can use linear combinations of the measurements. Here such a linear method is described. The method is based in part on well-known techniques in radio technology used in every FM radio receiver, and in part on the SOLA inverse method