# Least-squares frequency analysis of unequally spaced data

- Received:

DOI: 10.1007/BF00648343

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

- 1.5k Citations
- 1.1k Views

## 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 a*X*_{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,*f*_{1} and*f*_{2}, which is equal to the mean height of the spectrum due to a sinusoidal signal of frequency*f*_{1}, at the frequency*f*_{2}. 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.