Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2010-06-12
Astronomy and Astrophysics, 2010
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
10 pages, 11 figures, Astronomy and Astrophysics, in press
Scientific paper
The periodogram is a popular tool that tests whether a signal consists only of noise or if it also includes other components. The main issue of this method is to define a critical detection threshold that allows identification of a component other than noise, when a peak in the periodogram exceeds it. In the case of signals sampled on a regular time grid, determination of such a threshold is relatively simple. When the sampling is uneven, however, things are more complicated. The most popular solution in this case is to use the "Lomb-Scargle" periodogram, but this method can be used only when the noise is the realization of a zero-mean, white (i.e. flat-spectrum) random process. In this paper, we present a general formalism based on matrix algebra, which permits analysis of the statistical properties of a periodogram independently of the characteristics of noise (e.g. colored and/or non-stationary), as well as the characteristics of sampling.
Andreani Paola
Biggs Andy
Vio Roberto
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