On-line power spectra identification and whitening for the noise in interferometric gravitational wave detectors

The knowledge of the noise power spectral density of an interferometric det ector of gravitational waves is fundamental for detection algorithms and fo r the analysis of the data. In this paper we address both the problem of id entifying the noise power spectral density of interferometric detectors by parametric techniques and the problem of the whitening procedure of the seq uence of data. We will concentrate the study on a power spectral density li ke that of the Italian-French detector VIRGO and we show that with a reason able number of parameters we succeed in modelling a spectrum like the theor etical one of VIRGO, reproducing all of its features. We also propose the use of adaptive techniques to identify and to whiten th e data of interferometric detectors on-line. We analyse the behaviour of th e adaptive techniques in the field of stochastic gradient and in the least- squares filters. As a result, we find that the least-squares lattice filter is the best among those we have analysed. It succeeds optimally in followi ng all the peaks of the noise power spectrum, and one of its outputs is the whitened part of the spectrum. Besides, the fast convergence of this algor ithm, it lets us follow the slow non-stationarity of the noise. These proce dures could be used to whiten the overall power spectrum or only some regio n of it. The advantage of the techniques we propose is that they do not req uire a priori knowledge of the noise power spectrum to be analysed. Moreove r, the adaptive techniques let us identify and remove the spectral line, wi thout building any physical model of the source that produced it.