Astronomy and Astrophysics – Astrophysics
Scientific paper
Jan 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977ap%26ss..46...87k&link_type=abstract
Astrophysics and Space Science, vol. 46, Jan. 1977, p. 87-108.
Astronomy and Astrophysics
Astrophysics
16
Eclipsing Binary Stars, Fourier Analysis, Fourier Transformation, Light Curve, Stellar Spectra, Variable Stars, Autocorrelation, Moment Distribution, Power Spectra, Spectral Correlation
Scientific paper
A transition from terminating Fourier series to a continuous Fourier transform is accomplished for the light curves of eclipsing variables. It is proven that Fourier transforms of observed light curves can be expressed as functions of a continuous variable in terms of the odd 'light moments' of such curves. A systematic method is developed for expressing the odd moments in terms of even moments, and with them the corresponding Fourier transforms, to any desired degree of accuracy. Application of the results to a numerical example shows that almost all information about eclipses of spherical stars in the frequency domain appears to be contained in the low-frequency end of the Fourier spectra of the light curves. The Wiener-Khinchin theorem is used to introduce the concept of the autocorrelation function and power spectra of light curves of eclipsing variables as a means for specifying quadratic moments of the light curves in terms of their linear moments.
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