Fourier Analysis of the Light Curves of Eclipsing Variables, X
Abstract
The aim of the present paper will be to develop methods for computation of the Fourier transforms of the light curves of eclipsing variables — due to any type of eclipses — as a function of a continuous frequency variablev. For light curves which are symmetrical with respect to the conjunctions (but only then) these transforms prove to be real functions ofv, and expressible as rapidly convergent expansions in terms of the momentsA _{2m+1} of the light curves of odd orders. The transforms are found to be strongly peaked in the lowfrequency domain (attaining a maximum forv=0), and become numerically insignificant forv>3. This is even more true of their power spectra. The odd momentsA _{2m+1} — not encountered so far in our previous papers — are shown in Section 3 of the present communication to be expressible as infinite series in terms of the even momentsA _{ 2m } well known to us from Papers I IV; and polynomial expressions are developed for approximating them to any desired degree of accuracy. The numerical efficiency of such expressions will be tested in Section 4, by application to a practical case, with satisfactory results. Lastly, in Section 5, an appeal to the WienerKhinchin theorem (relating the power spectra with autocorrelation function of the light curves) and Parseval's theorem on Fourier series will enable us to extend our previous methods for a specification of quadratic moments of the light curves in terms of the linear ones.
 Publication:

Astrophysics and Space Science
 Pub Date:
 January 1977
 DOI:
 10.1007/BF00643756
 Bibcode:
 1977Ap&SS..46...87K
 Keywords:

 Eclipsing Binary Stars;
 Fourier Analysis;
 Fourier Transformation;
 Light Curve;
 Stellar Spectra;
 Variable Stars;
 Autocorrelation;
 Moment Distribution;
 Power Spectra;
 Spectral Correlation;
 Astrophysics