On-line powerspectra identification and whitening for the noise in interferometricgravitational wave detectors

Abstract

The knowledge of the noise power spectral density of aninterferometric detector of gravitational waves isfundamental for detection algorithms and for the analysis ofthe data. In this paper we address both the problem ofidentifying the noise power spectral density ofinterferometric detectors by parametric techniques and theproblem of the whitening procedure of the sequence of data.We will concentrate the study on a power spectral densitylike that of the Italian-French detector VIRGO and we showthat with a reasonable number of parameters we succeed inmodelling a spectrum like the theoretical one of VIRGO,reproducing all of its features.We alsopropose the use of adaptive techniques to identify and towhiten the data of interferometric detectors on-line. Weanalyse the behaviour of the adaptive techniques in the fieldof stochastic gradient and in the least-squares filters. As aresult, we find that the least-squares lattice filter is thebest among those we have analysed. It succeedsoptimally infollowing all the peaks of the noise power spectrum, and oneof its outputs is the whitened part of the spectrum. Besides,the fast convergence of this algorithm, it lets us follow theslow non-stationarity of the noise. These procedures could beused to whiten the overall power spectrum or only some regionof it. The advantage of the techniques we propose is that theydo not require a priori knowledge of the noise powerspectrum to be analysed. Moreover, the adaptive techniqueslet us identify and remove the spectral line, withoutbuilding any physical model of the source that producedit.