Least-squares frequency analysis of unequally spaced data
- 1.5k Downloads
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 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,f1 andf2, which is equal to the mean height of the spectrum due to a sinusoidal signal of frequencyf1, at the frequencyf2. 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.
KeywordsGaussian Noise Frequency Spectrum Frequency Analysis Sinusoidal Signal Numerical Illustration
Unable to display preview. Download preview PDF.
- Abramowitz, M. and Stegun, I. A.: 1964,Handbook of mathematical functions, National Bureau of Standards, Washington, D.C.Google Scholar
- Barning, F. J. M.: 1963,Bull. Astron. Inst. Neth. 17, 22.Google Scholar
- Gray, D. F. and Desikachary, K.: 1973,Astrophys. J. 181, 523.Google Scholar
- Lomb, N. R.: 1975,Monthly Notices Roy. Astron. Soc., in press.Google Scholar
- Shobbrook, R. R., Lomb, N. R., and Herbison-Evans, D.: 1972,Monthly Notices Roy. Astron. Soc. 156, 165.Google Scholar
- Struve, O. and Ebbighausen, E.: 1934,Astrophys. J. 80, 365.Google Scholar
- Vaníček, P.: 1971,Astrophys. Space Sci. 12, 10.Google Scholar
- Wehlau, W. and Leung, K.-C.: 1964,Astrophys. J. 139, 843.Google Scholar