2003 Prépublication d'Orsay numéro 2003-21 (07/11/2003)



A MODEL SELECTION APPROACH FOR ESTIMATING THE FREQUENCY OF A PERIODIC SIGNAL WITH UNKNOW SHAPE. APPLICATIONS IN LASER VIBROMETRY.

LAVIELLE, Marc - Modélisation Stochastique et Statistique, Université Paris-Sud, Bât. 425, 91405 Orsay cedex
LEVY-LEDUC, Céline - Modélisation Stochastique et Statistique, Université Paris-Sud, Bât. 425, 91405 Orsay cedex


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Abstract :
The commonly used methods for frequency estimation of particular signals such as sinusoids or trigonometric polynomials embedded in white noise do not work anymore when we have to deal with periodic signals whose spectra possesses a large number of harmonics.Using the cumulated periodogram of the observed signal, we propose a model selection procedure for estimating the fundamental frequency of the non observed signal.We also extend our technique for estimating the frequencies of a sum of periodic signals. We consider an application in laser vibrometry and compare the performances of our procedure with the socalled microdoppler procedure. We show that the cumulated periodogram procedure yields an accurate estimation at low signal to noise ratio.

Contact : Marc.Lavielle@math.u-psud.fr