Fourier Analysis of the Light Curves of Eclipsing Variables - XXV: Error Analysis in the Frequency-Domain
Abstract
The aim of the present paper has been two-fold. In the first part (Sections 1 2), closed algebraic formulae will be set up furnishing the momentsA μ of the light curves of arbitrary index μ, and, due to arbitrary type of eclipses, in terms of the coefficientsa π of Fourier cosine series obtained by least-squares fit to the given data; and the uncertainty of the momentsA μ deduced from that of thea π's. In the second part (Sections 3 4) we shall establish the explicit forms of the lincar functions δr 1,2, δ(cosi) and δL 1 for the variation of the respective elements expressible likewise in terms of the Fourier coefficientsa π. The probable errors of these elements can then be identified with those of the respective linear functions, and are obtainable from the same matrix of coefficients which furnished the most probable values of the elements.
- Publication:
-
Astrophysics and Space Science
- Pub Date:
- November 1979
- DOI:
- 10.1007/BF00648362
- Bibcode:
- 1979Ap&SS..66...91K
- Keywords:
-
- Eclipsing Binary Stars;
- Error Analysis;
- Fourier Analysis;
- Light Curve;
- Variable Stars;
- Fourier Transformation;
- Functions (Mathematics);
- Least Squares Method;
- Linear Transformations;
- Astrophysics