A New Technique for the Detection of Periodic Signals in “coloured” Power Spectra

The light curves from a variety of celestial objects display aperiodic variations, often giving rise to red–noise components in their power spectra. Searching for a narrow power spectrum peak resulting from a periodic modulation over the frequency range in which these “coloured” noise components are dominant has proven a very complex task. Commonly used methods rely upon spectral smoothing or incoherent summation of sample spectra in order to decrease the variance of the power estimates. The consequent reduction in frequency resolution causes also a reduction of sensitivity to periodic signals. We develop here a technique aimed at detecting periodicities in the presence of “coloured” power spectrum components, while mantaining the highest Fourier frequency resolution. First we introduce a simple approximation to the statistical properties of the “coloured” power spectra from celestial objects, based on a few examples and the theory of linear processes. We then estimate the continuum components in the power spectrum through an ad hoc smoothing technique. This involves averaging the spectral estimates adjacent to each frequency over a suitably chosen interval, in order to follow steep red–noise features and produce estimates that are locally unaffected by the possible presence of a sharp peak. By dividing the sample spectrum by the smoothed one, a white–noise like spectrum is obtained, Affiliated to the International Center for Relativistic Astrophysics Now at the Astronomical Observatory of Rome, Via dell’Osservatorio 2, I–00040, Monteporzio Catone (Roma), Italy