Further development and properties of the spectral analysis by least-squares

@article{Vanicek1971FurtherDA,
  title={Further development and properties of the spectral analysis by least-squares},
  author={Petr Vaníček},
  journal={Astrophysics and Space Science},
  year={1971},
  volume={12},
  pages={10-33}
}
  • P. Vaníček
  • Published 1 July 1971
  • Geology
  • Astrophysics and Space Science
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 necessity of knowing the magnitudes of the noise constituents. The technique can be used for irregularly spaced as well as equidistantly spaced data. The response to random noise is found to be constant in the frequency domain and its expected level is derived. Presence of random noise in the… 

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References

SHOWING 1-10 OF 10 REFERENCES

Approximate spectral analysis by least-squares fit

An approximate method of spectral analysis called ‘successive spectral analysis’ based upon the mean-quadratic approximation of an empirical function by generalised trigonometric polynomial with both

New analysis of the earth-pole wobble

RésuméPour témoigner l'efficacité de la nouvelle methode d'analyse spectrale employant l'approximation des moindres carrés, on a analysé le mouvement du pôle terrestre utilisant des observations