Astrophysics and Space Science

, Volume 39, Issue 2, pp 447–462 | Cite as

Least-squares frequency analysis of unequally spaced data

  • N. R. Lomb


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 aX 2 2 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.


Gaussian Noise Frequency Spectrum Frequency Analysis Sinusoidal Signal Numerical Illustration 
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Copyright information

© D. Reidel Publishing Company 1976

Authors and Affiliations

  • N. R. Lomb
    • 1
  1. 1.School of PhysicsUniversity of SydneyAustralia

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