Filtering of discrete time series by symmetric least-squares operators

  • S. H. Chan
  • L. S. Leong
Article

Abstract

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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bendat, J. S., and Piersol, A. G., 1966, Measurement and analysis of random data: John Wiley & Sons, New York, 390 p.Google Scholar
  2. Blackman, R. B., and Tukey, J. W., 1958, The measurement of power spectra: Dover Publ., New York, 190 p.Google Scholar
  3. Bracewell, R., 1965, The Fourier transform and its application; McGraw-Hill Book Co., New York, 381 p.Google Scholar
  4. Chan, S. H., and Leong, L. S., 1972, Analysis of least-squares operators in the frequency domain: Geophys. Prospecting, v. 20, p. 892–900.Google Scholar
  5. Enochson, L. D., and Otnes, R. K., 1968, Programming and analysis for digital time series data: Shock & Vibration Information Center, U.S. Dept. of Defense, 277 p.Google Scholar
  6. Forsythe, G. E., 1957, Generation and use of orthogonal polynomials for data fitting with a digital computer: Jour. Soc. Indust. Appl. Math., v. 5, p. 74–87.Google Scholar
  7. Gold, B., and Rader, C. M., 1969, Digital processing of signal: McGraw-Hill Book Co., New York, 269 p.Google Scholar
  8. Grant, F. S., and West, G. F., 1965, Interpretation theory in applied geophysics: McGraw-Hill, Book Co., New York, 584 p.Google Scholar
  9. Holloway, J. L., Jr., 1958, Smoothing and filtering of time series and space fields,in Advances in geophysics, v. 4: Academic Press, New York, p. 351–389.Google Scholar
  10. Holtz, H., and Leonodes, C. T., 1966, The synthesis of digital filters: Jour. ACM, v. 13, p. 262–280.Google Scholar
  11. Ormsby, J., 1961, Design of numerical filters with application to missile data processing: Jour. ACM, v. 8, p. 440–466.Google Scholar
  12. Ralston, A., 1965, A first course in numerical analysis: McGraw-Hill, Book Co., New York, 578 p.Google Scholar
  13. Robinson, E. A., 1967, Statistical communication and detection: Charles Griffin & Co., London, 362 p.Google Scholar
  14. Schwarz, R. J., and Friedland, B., 1965, Linear system: McGraw-Hill Book Co., New York, 521 p.Google Scholar
  15. Shanks, J. L., 1967, Recursion filters for digital processing: Geophysics, v. 32, no. 1, p. 33–51.Google Scholar
  16. Wood, L. C., and Hockens, S. N., 1970, Least-squares smoothing operators: Geophysics, v. 35, no. 6, p. 1005–1019.Google Scholar

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

Personalised recommendations