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Title:
Least-squares frequency analysis of unequally spaced data
Authors:
Lomb, N. R.
Affiliation:
AA(Sydney, University, Sydney, Australia)
Publication:
Astrophysics and Space Science, vol. 39, Feb. 1976, p. 447-462. (Ap&SS Homepage)
Publication Date:
02/1976
Category:
Astronomy
Origin:
STI
NASA/STI Keywords:
Astronomy, Data Reduction, Least Squares Method, Background Noise, Power Spectra, Sine Waves, Spectrum Analysis, Statistical Analysis, Variable Stars
DOI:
10.1007/BF00648343
Bibliographic Code:
1976Ap&SS..39..447L

Abstract

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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