Time-Scale and Time-Frequency Analyses of Irregularly Sampled Astronomical Time Series
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Time-Scale and Time-Frequency Analyses of Irregularly Sampled Astronomical Time Series C. Thiebaut Centre d’Etude Spatiale des Rayonnements, 9 avenue du Colonel Roche - Boite postale 4346, 31028 Toulouse Cedex 4, France Email: [email protected]
S. Roques Laboratoire d’Astrophysique de l’Observatoire Midi-Pyr´en´ees, 14 avenue Edouard Belin, 31400 Toulouse, France Email: [email protected] Received 27 May 2004; Revised 21 January 2005 We evaluate the quality of spectral restoration in the case of irregular sampled signals in astronomy. We study in details a timescale method leading to a global wavelet spectrum comparable to the Fourier period, and a time-frequency matching pursuit allowing us to identify the frequencies and to control the error propagation. In both cases, the signals are first resampled with a linear interpolation. Both results are compared with those obtained using Lomb’s periodogram and using the weighted wavelet Ztransform developed in astronomy for unevenly sampled variable stars observations. These approaches are applied to simulations and to light variations of four variable stars. This leads to the conclusion that the matching pursuit is more efficient for recovering the spectral contents of a pulsating star, even with a preliminary resampling. In particular, the results are almost independent of the quality of the initial irregular sampling. Keywords and phrases: astronomical time series, irregular sampling, time-scale methods, time-frequency methods, wavelets, matching pursuit.
1.
INTRODUCTION
Nonuniform sampling problems arise in many astronomical fields [3, 22], particularly in Stellar physics when one observes the light curves of variable stars (asteroseismology) or spectroscopic variabilities. The frequencies deduced from the light variations of such stars represent an important source of information. In particular, they can help constrain stellar evolution models, because the structure of the vibration modes and their frequency separations may yield physical parameters of the star, such as the rotation period or the composition of its layers [1, 16]. Another field of application concerns the development of automatic classifiers for variable stars, where the period is a very discriminating parameter [27]. Of course, observations have to cover a long enough time span for the best possible resolution of the power density spectra. The difficulty in obtaining such complete observations is well known: the lack of information is essentially due to diurnal cuts, poor weather conditions, or equipment malfunctions. Generally, such astronomical data This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
are of two types. First, evenly spaced time series separated by wide gaps [9] (typically day/night alternation for observations of short-period stars taken over several days). In that case, many different methods have been propose
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