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Optics and Photonics SPIE Annual Meeting, San Diego, CA : États-Unis (2007)
Chains of chirplets for the detection of gravitational wave chirps
E. Chassande-Mottin1, A. Pai, O. Rabaste1
(20/09/2007)

A worldwide collaboration attempts to confirm the existence of gravitational waves predicted by Einstein's theory of General Relativity, through direct observation with a network of large-scale laser interferometric antennas. This paper is a contribution to the methodologies used to scrutinize the data in order to reveal the tiny signature of a gravitational wave from rare cataclysmic events of astrophysical origin. More specifically, we are interested in the detection of short frequency modulated transients or gravitational wave chirps. The amount of information about the frequency vs. time evolution is limited: we only know that it is smooth. The detection problem is thus non-parametric. We introduce a finite family of "template waveforms" which accurately samples the set of admissible chirps. The templates are constructed as a puzzle, by assembling elementary bricks (the chirplets) taken a dictionary. The detection amounts to testing the correlation between the data and the template family. With an adequate time-frequency mapping, we establish a connection between this correlation measurement and combinatorial optimization problems of graph theory, from which we obtain efficient algorithms to perform the calculation. We present two variants. A first one addresses the case of amplitude modulated chirps and the second allows the joint analysis of the data from several antennas. Those methods are not limited to the specific context for which they have been developed. We pay a particular attention to the aspects that can be source of inspiration for other applications.
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
APC - ADAMIS
Physique/Physique/Analyse de données, Statistiques et Probabilités