Astrophysics and Space Science

, Volume 39, Issue 2, pp 447–462

Least-squares frequency analysis of unequally spaced data


  • N. R. Lomb
    • School of PhysicsUniversity of Sydney

DOI: 10.1007/BF00648343

Cite this article as:
Lomb, N.R. Astrophys Space Sci (1976) 39: 447. doi:10.1007/BF00648343


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 aX22 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 andf2, which is equal to the mean height of the spectrum due to a sinusoidal signal of frequencyf1, at the frequencyf2. 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 also given.

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© D. Reidel Publishing Company 1976