The Application of the Linear Prediction Principle to NMR Spectroscopy

  • H. Gesmar
  • J. J. Led
Part of the NATO ASI Series book series (NSSA, volume 225)


The deviations of the discrete Fourier transform from the theoretical spectrum are shortly reviewed based on the exact analytical expression of the discrete Fourier transform of an exponentially decaying FID. They are aliasing, truncation errors, non-linear phase distortions, and pseudo baseline levels. These discrepancies can be reduced significanly by linear prediction extrapolation of the FID prior to the Fourier transformation. Frequencies, relaxation rates, intensities and phases can also be estimated directly from the FID.


Unit Circle Discrete Fourier Transform Truncation Error Linear Prediction Free Induction Decay 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. R. Ernst, Adv. Magn. Reson. 2, 7 (1966).Google Scholar
  2. 2.
    H. Gesmar, J. J. Led, and F. Abildgaard, Prog. NMR Spectrosc. 22, 255 (1990).CrossRefGoogle Scholar
  3. 3.
    G. Otting, H. Widmer, G. Wagner, and K. Wütrich, J. Magn. Reson. 66, 187 (1986).Google Scholar
  4. 4.
    P. Plateau, C. Dumas, and M. Guéron, J. Magn. Reson. 54, 46 (1983).Google Scholar
  5. 5.
    D. I. Hoult and R. E. Richards, Proc. R. Soc. London, Ser. A 344, 311 (1975).CrossRefGoogle Scholar
  6. 6.
    E. O. Brigham, The Fast Fourier Transform, Chap 6, Prentice-Hall Inc., Englewood Cliffs, NJ (1974).Google Scholar
  7. 7.
    D. S. Stephenson, Prog. NMR Spectrosc. 20, 515 (1988).CrossRefGoogle Scholar
  8. 8.
    H. Barkhuijsen, R. de Beer, W. M. M. J. Bovée, and D. van Ormondt, J. Magn. Reson. 61, 465 (1985).Google Scholar
  9. 9.
    J. Tang, C. P. Lin, M. K. Bowman, and J. R. Norris, J. Magn. Reson. 62, 167 (1985).Google Scholar
  10. 10.
    H. Gesmar and J. J. Led, J. Magn. Reson. 76, 183 (1988).Google Scholar
  11. 11.
    C. F. Tirendi and J. F. Martin, J. Magn. Reson. 81, 577 (1989).Google Scholar
  12. 12.
    D. Marion and A. Bax, J. Magn. Reson. 83, 205 (1989).Google Scholar
  13. 13.
    S. M. Kay and S. L. Marple, Proc. IEEE 69, 1380 (1981).CrossRefGoogle Scholar
  14. 14.
    R. Kumaresan, IEEE Trans. ASSP-31, 217 (1983).Google Scholar
  15. 15.
    G. R. B. Prony, J. de L’Ecole Polytechnique, Paris 1, 24 (1795).Google Scholar
  16. 16.
    R. Kumaresan and D. W. Tufts, IEEE Trans. ASSP-30, 833 (1982).Google Scholar
  17. 17.
    H. Gesmar and J. J. Led, J. Magn. Reson. 76, 575 (1988).Google Scholar
  18. 18.
    H. Gesmar and J. J. Led, J. Magn. Reson. 83, 53 (1989).Google Scholar
  19. 19.
    A. G. Redfield and S. D. Kunz, J. Magn. Reson. 19, 250 (1975).Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • H. Gesmar
    • 1
  • J. J. Led
    • 1
  1. 1.Department of Chemistry, The H.C. Ørsted InstituteUniversity of CopenhagenCopenhagen ØDenmark

Personalised recommendations