Astronomy and Astrophysics – Astronomy
Scientific paper
Feb 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976ap%26ss..39..447l&link_type=abstract
Astrophysics and Space Science, vol. 39, Feb. 1976, p. 447-462.
Astronomy and Astrophysics
Astronomy
903
Astronomy, Data Reduction, Least Squares Method, Background Noise, Power Spectra, Sine Waves, Spectrum Analysis, Statistical Analysis, Variable Stars
Scientific paper
The statistical properties of least-squares frequency analysis of unequally spaced data are examined. It is shown that, in the least-squares spectrum of gaussian noise, the reduction in the sum of squares at a particular frequency is a chi2-squared variable. The reductions at different frequencies are not independent, as there is a correlation between the height of the spectrum at any two frequencies, f1 and f2, which is equal to the mean height of the spectrum due to a sinusoidal signal of frequency f1, at the frequency f2. These correlations reduce the distortion in the spectrum of a signal affected by noise. Some numerical illustrations of the properties of least-squares frequency spectra are given.
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