Filtering of discrete time series by symmetric least-squares operators

  • S. H. Chan
  • L. S. Leong


Least-squares operators with real and symmetric coefficients are shown to be equivalent to low-pass digital filters. By viewing these operators as digital filters one gains considerable insight into their properties. This in turn leads to a better understanding of their usefulness and limitations in data smoothing. It is shown that complete removal of noise from a given input time series is possible with the use of least-squares operators if spectral overlapping between signal and noise does not exist. Power-spectral analysis which provides information about the frequency composition of the input data is essential for successful application of least-squares operators.

Key words

filtering least squares power-spectrum analysis smoothing time series geophysics 


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Copyright information

© Plenum Publishing Corporation 1974

Authors and Affiliations

  • S. H. Chan
    • 1
  • L. S. Leong
    • 2
  1. 1.Department of GeologyUniversity of MalayaMalaysia
  2. 2.School of Physics and MathematicsScience University MalaysiaMalaysia

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