Spectral contents of astronomical unequally spaced time-series: contribution of time-frequency and time-scale analyses

We analyze how time-scale and time-frequency methods can be suited to study unequally spaced astronomical time-series, in terms of recovering precise spectral contents of a pulsating star. In many situations in astronomy, nonuniform sampling proves to be the natural way in which the signal is available for investigation and the spectral information of interest is lost. We propose to study two kinds of methods which enables us to treat this type of signal: first, an approach with global wavelet spectra leading to a wavelet scale that can be compared to the Fourier period. Second, a time-frequency analysis (matching pursuit) providing a progressive constructive process allowing us to identify the fine structure of the driven frequencies and to control the error propagation. We apply, compare and discuss these methods for simulations and for luminosity observations of variable stars. This allows us to conclude that the matching pursuit is the more efficient method, in particular independent of the quality of sampling.