LeastSquares Frequency Analysis of Unequally Spaced Data
Abstract
The statistical properties of leastsquares frequency analysis of unequally spaced data are examined. It is shown that, in the leastsquares 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,f _{1} andf _{2}, which is equal to the mean height of the spectrum due to a sinusoidal signal of frequencyf _{1}, at the frequencyf _{2}. These correlations reduce the distortion in the spectrum of a signal affected by noise. Some numerical illustrations of the properties of leastsquares frequency spectra are also given.
 Publication:

Astrophysics and Space Science
 Pub Date:
 February 1976
 DOI:
 10.1007/BF00648343
 Bibcode:
 1976Ap&SS..39..447L
 Keywords:

 Astronomy;
 Data Reduction;
 Least Squares Method;
 Background Noise;
 Power Spectra;
 Sine Waves;
 Spectrum Analysis;
 Statistical Analysis;
 Variable Stars;
 Astronomy