Mathematics – Logic
Scientific paper
Dec 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007o%26t....67...12h&link_type=abstract
Observations & Travaux, vol. 67, p. 12-16
Mathematics
Logic
Scientific paper
Fourier analysis allows to identify periodical components in a time series of measurements under the form of a spectrum of the periodical components mathematically included in the series. The reading of a spectrum is often delicate and contradictory interpretations can be presented in some cases as for the luminosity of Seyfert galaxy NGC 4151 despite the very large number of observations since 1968. The present study identifies the causes of these difficulties thanks to an experimental approach based on analysis of synthetic series with one periodic component only. The total duration of the campaign must be long as compared to the periods to be identified: this ratio governs the separation capability of the spectral analysis. A large number of observations is obviously favourable but the intervals between measurements are not critical : the analysis can accommodate intervals significantly longer than the periods to be identified. But interruptions along the campaign, with separate sessions of observations, make the physical understanding of the analysis difficult and sometimes impossible. An analysis performed on an imperfect series shows peaks which are not significant of the signal itself but of the chronological distribution of the measurements. These chronological peaks are becoming numerous and important when there are vacancy periods in the campaign. A method for authentication of a peak as a peak of the signal is to cut the chronological series in pieces with the same length than the period to identify and to superpose all these pieces. The present study shows that some chronological peaks can exhibit superposition graphics almost as clear as those for the signal peaks. Practically, the search for periodical components necessitates to organise the campaign specifically with a neutral chronological distribution of measurements without vacancies and the authentication of a peak as a peak of the signal requires a dominating amplitude or a graphic of periodical superposition significantly clearer than for any peak with a comparable or bigger amplitude.
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