Least-squares frequency analysis of unequally spaced data

@article{Lomb1976LeastsquaresFA,
  title={Least-squares frequency analysis of unequally spaced data},
  author={Nicholas R. Lomb},
  journal={Astrophysics and Space Science},
  year={1976},
  volume={39},
  pages={447-462}
}
  • N. Lomb
  • Published 1 February 1976
  • Geology
  • Astrophysics and Space Science
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… 

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References

SHOWING 1-10 OF 10 REFERENCES

Further development and properties of the spectral analysis by least-squares

The concept of spectral analysis using least-squares is further developed to remove any undesired influence on the spectrum. The influence of such a ‘systematic noise’ can be eliminated without the

A new approach to periodogram analyses

We present a method fof Fourier analyzing quasi-periodic light and radial velocity variations. The scheme gives a particularly clear interpetation to the periodogram, reduces the alias problem,

Handbook of Mathematical Functions.

The Multiple Periodicity of Delta Delphini.

Bull. Astron. Inst. Neth

  • Bull. Astron. Inst. Neth
  • 1963

Monthly Notices Roy. Astron. Soc

  • Monthly Notices Roy. Astron. Soc
  • 1972

Astrophys. J

  • Astrophys. J
  • 1964