Least-squares frequency analysis of unequally spaced data
@article{Lomb1976LeastsquaresFA,
title={Least-squares frequency analysis of unequally spaced data},
author={N. R. Lomb},
journal={Astrophysics and Space Science},
year={1976},
volume={39},
pages={447-462}
}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 14 REFERENCES
Further development and properties of the spectral analysis by least-squares
- Geology
- 1971
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
- Geology
- 1973
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,…
Astrophys. J
- Astrophys. J
- 1973
Monthly Notices Roy. Astron. Soc
- Monthly Notices Roy. Astron. Soc
- 1975
Astrophys. J
- Astrophys. J
- 1934