A New Technique for the Detection of Periodic Signals in ``Colored'' Power Spectra
Abstract
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 "colored" noise components are dominant has proved 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 also causes a reduction of sensitivity to periodic signals.
We develop here a technique aimed at detecting periodicities in the presence of "colored" power spectrum components, while maintaining the highest Fourier frequency resolution. First, we introduce a simple approximation to the statistical properties of the "colored" 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 noiselike spectrum is obtained, the approximate probability distribution of which is derived. A search for coherent pulsations is then carried out by looking for peaks in the divided spectrum, the chance probability of which is below a given detection threshold. If no significant peaks are found, an upper limit to the amplitude of a sinusoidal modulation is worked out for each searched frequency.
The technique is tested and its range of applicability determined through extensive numerical simulations. We present also an application to the Xray light curves of V0332+53, a highly variable accreting Xray pulsar, and GX 13+1, a bright and variable accreting source in the Galactic bulge.
 Publication:

The Astrophysical Journal
 Pub Date:
 September 1996
 DOI:
 10.1086/177697
 arXiv:
 arXiv:astroph/9603038
 Bibcode:
 1996ApJ...468..369I
 Keywords:

 METHODS: NUMERICAL;
 METHODS: STATISTICAL;
 STARS: OSCILLATIONS;
 XRAYS: STARS;
 Astrophysics
 EPrint:
 20 pages plus 10 postscript figures, uuencoded zipped file, PostScript. Accepted for publication in the Astrophysical Journal