Astrophysics and Space Science

, Volume 12, Issue 1, pp 10–33

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

  • Petr Vaníček
Article

Abstract

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 analyzed time series is shown to transform the spectrum merely linearly. Examples of applications of the technique are presented.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berezin, I. S. and Zhidkov, N. P.: 1962,Metody Vychisleniy, Tom I, GIFML, Moscow.Google Scholar
  2. Blackman, R. B. and Tukey, J. W.: 1959,The Measurement of Power Spectra, Dover, New York.Google Scholar
  3. Faddeyev, D. K. and Faddeyeva, V. N.: 1964,Vychislitel'nye Metody Lineynoy Algebry (Czech. translation), SNTL, Prague.Google Scholar
  4. Handscomb, D. C.: 1965,Methods of Numerical Approximation, Pergamon Press.Google Scholar
  5. Hohn, F. E.: 1960,Elementary Matrix Algebra, MacMillan, New York.Google Scholar
  6. Lanczos, C.: 1957,Applied Analysis, Pitman, London.Google Scholar
  7. Munk, W. E. and Cartwright, D. E.: 1968,Tidal Spectroscopy, Philosophical Transactions of the Royal Society.Google Scholar
  8. Quraishee, G. S.: 1969, ‘Numerical Methods in Tidal Analysis and Prediction’, Ph.D. Thesis, The University of Liverpool.Google Scholar
  9. Quraishee, G. S. and Vaníček, P.: 1970, ‘A Search for Low Frequencies in Residual Tide and Mean Sea Level Observations by Means of the Least Squares Spectral Analysis’, Proceedings of the 1st International Symposium on Coastal Geodesy, Munich, in press.Google Scholar
  10. Thompson, E. H.: 1969,Introduction to the Algebra of Matrices with some Applications, The University of Toronto Press.Google Scholar
  11. Tidal Institute and Observatory, The University of Liverpool,Annual Report 1968–69, pp. 15–7.Google Scholar
  12. Vaníček, P.: 1967, ‘Anharmonic Analysis and Its Applications in Geophysics’, C.Sc., Thesis, Czechoslovak Academy of Sciences, Prague.Google Scholar
  13. Vaníček, P.: 1969a, ‘Approximate Spectral Analysis by the Least Squares Fit’,Astrophys. Space Sci. 4, 387–91.Google Scholar
  14. Vaníček, P.: 1969b, ‘New Analysis of the Earth Pole Wobble’,Studia Geophys. Geodaet. 13, 225–30.Google Scholar
  15. Vaníček, P.: 1969c, ‘An Analytical Technique to Minimize Noise in a Search for Lines in the Low Frequency Spectra’, Proceedings of the 6th International Symposium on Earth Tides, Strasbourg.Google Scholar
  16. Wilks, S. S.: 1962,Mathematical Statistics, J. Wiley and Sons, New York.Google Scholar

Copyright information

© D. Reidel Publishing Company 1971

Authors and Affiliations

  • Petr Vaníček
    • 1
  1. 1.Dept. of Energy, Mines and ResourcesSurveys and Mapping BranchOttawaCanada
  2. 2.Dept. of Surveying EngineeringUniversity of New BrunswickFrederictonCanada

Personalised recommendations