Astrophysics and Space Science

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

Least-squares frequency analysis of unequally spaced data

  • N. R. Lomb
Article

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 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.

Keywords

Gaussian Noise Frequency Spectrum Frequency Analysis Sinusoidal Signal Numerical Illustration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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