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.
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References
Berezin, I. S. and Zhidkov, N. P.: 1962,Metody Vychisleniy, Tom I, GIFML, Moscow.
Blackman, R. B. and Tukey, J. W.: 1959,The Measurement of Power Spectra, Dover, New York.
Faddeyev, D. K. and Faddeyeva, V. N.: 1964,Vychislitel'nye Metody Lineynoy Algebry (Czech. translation), SNTL, Prague.
Handscomb, D. C.: 1965,Methods of Numerical Approximation, Pergamon Press.
Hohn, F. E.: 1960,Elementary Matrix Algebra, MacMillan, New York.
Lanczos, C.: 1957,Applied Analysis, Pitman, London.
Munk, W. E. and Cartwright, D. E.: 1968,Tidal Spectroscopy, Philosophical Transactions of the Royal Society.
Quraishee, G. S.: 1969, ‘Numerical Methods in Tidal Analysis and Prediction’, Ph.D. Thesis, The University of Liverpool.
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.
Thompson, E. H.: 1969,Introduction to the Algebra of Matrices with some Applications, The University of Toronto Press.
Tidal Institute and Observatory, The University of Liverpool,Annual Report 1968–69, pp. 15–7.
Vaníček, P.: 1967, ‘Anharmonic Analysis and Its Applications in Geophysics’, C.Sc., Thesis, Czechoslovak Academy of Sciences, Prague.
Vaníček, P.: 1969a, ‘Approximate Spectral Analysis by the Least Squares Fit’,Astrophys. Space Sci. 4, 387–91.
Vaníček, P.: 1969b, ‘New Analysis of the Earth Pole Wobble’,Studia Geophys. Geodaet. 13, 225–30.
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.
Wilks, S. S.: 1962,Mathematical Statistics, J. Wiley and Sons, New York.
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Vaníček, P. Further development and properties of the spectral analysis by least-squares. Astrophys Space Sci 12, 10–33 (1971). https://doi.org/10.1007/BF00656134
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DOI: https://doi.org/10.1007/BF00656134