Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Time-Scale and Time-Frequency Analyses of Irregularly Sampled Astronomical Time Series | EURASIP Journal on Applied Signal Processing 2005 15 2486-2499 2005 C. Thiebaut and S. Roques 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 S. Roques Laboratoire d Astrophysique de l Observatoire Midi-Pyrenees 14 avenue Edouard Belin 31400 Toulouse France Email 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 identity 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 Z-transform 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 .
