Least-squares frequency analysis of unequally spaced data

The statistical properties of least-squares frequency analysis of unequally spaced data are examined. It is shown that, in the least-squares spectrum of gausian noise, the reduction in the sum of squares at a particular frequency is a chi22 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 and f2, which is equal to the mean height of the spectrum due to a sinusoidal signal of frequency f1, at the frequency f2. 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. (Auth.)