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 detector of gravitational waves is fundamental for detection algorithms and for the analysis of the data. In this paper we address both the problem of identifying the noise power spectral density of interferometric detectors by parametric techniques and the problem of the whitening procedure of the sequence of data. We will concentrate the study on a power spectral density like that of the Italian-French detector VIRGO and we show that with a reasonable number of parameters we succeed in modelling a spectrum like the theoretical one of VIRGO, reproducing all of its features. We also propose the use of adaptive techniques to identify and to whiten the data of interferometric detectors on-line. We analyse the behaviour of the 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 following 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 algorithm, it lets us follow the slow non-stationarity of the noise. These procedures could be used to whiten the overall power spectrum or only some region of it. The advantage of the techniques we propose is that they do not require a priori knowledge of the noise power spectrum to be analysed. Moreover, the adaptive techniques let us identify and remove the spectral line, without building any physical model of the source that produced it.