Skip to main content

Dispersion versus Absorption (DISPA): Hilbert Transforms in Spectral Line Shape Analysis

  • Chapter

Abstract

Chapter 1 describes the origin and shape of a hypothetical spectral absorption signal arising from a single driven oscillator with a single natural frequency and a single relaxation time. Experimental spectra, on the other hand, often exhibit signals composed of a sum of two or more peaks of different natural frequencies and/or line widths. Most generally, one can distinguish between a superposition of lines of different position (Fig. 1a) and a superposition of lines of different width (Fig. 1b).

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Marshall, A. G. 1981, in “Physical Methods of Modern Analytical Chemistry,” Vol. 3., ed. Kuwana, T., Academic Press, N. Y., in press.

    Google Scholar 

  2. Bartholdi, E., and Ernst, R. R. 1973, J. Magn. Reson. 11, 9.

    CAS  Google Scholar 

  3. Herring, F. G., Marshall, A. G., Phillips, P. S., and Roe, D. C. 1980, J. Magn. Reson. 37, 293–303.

    CAS  Google Scholar 

  4. Marshall, A. G., and Roe, D. C. 1978, Anal. Chem. 50, 756–763.

    Article  CAS  Google Scholar 

  5. Cole, K. S., and Cole, R. H. 1941, J. Chem. Phys. 9, 341.

    Article  CAS  Google Scholar 

  6. Marshall, A. G. 1978, Biophysical Chemistry: Principles, Techniques, and Applications, Wiley, N. Y., Chapters 13-14.

    Google Scholar 

  7. Salefran, J. L., and Bottreau, A. M. 1977, J. Chem. Phys 67, 1909–1917.

    Article  CAS  Google Scholar 

  8. Colonomos, P., and Gordon, R. G. 1979, J. Chem. Phys. 71 1159–1166.

    Article  CAS  Google Scholar 

  9. Marshall, A. G. 1979, J. Phys. Chem. 83, 521–524.

    Article  CAS  Google Scholar 

  10. Marshall, A. G., and Roe, D. C. 1979, ”J. Magn. Reson. 33, 551–557.

    CAS  Google Scholar 

  11. Marshall, A. G., and Bruce, R. E. 1980, J. Magn. Reson. 39, 47–54.

    CAS  Google Scholar 

  12. Slichter, C. P. 1978, “Principles of Magnetic Resonance,” 2nd ed., Springer-Verlag, Berlin, pp. 47–50.

    Book  Google Scholar 

  13. Champeney, D. C. 1973, “Fourier Transforms and their Physical Applications,” Academic Press, London, pp. 244–246.

    Google Scholar 

  14. Bracewell, R. 1965, “The Fourier Transform and Its Applications,” McGraw-Hill, New York, pp. 267–272.

    Google Scholar 

  15. Cooley, J. W., and Tukey, J. W. 1965, Math. Comp. 19, 297.

    Article  Google Scholar 

  16. Squire, W. 1976, Int. J. Numeric. Methods Eng. 10, 478.

    Article  Google Scholar 

  17. Bruce, R. E., and Marshall, A. G. 1980, J. Phys. Chem. 84, 1372–1375.

    Article  CAS  Google Scholar 

  18. Cole, R. H. 1955, J. Chem. Phys. 23, 493–499.

    Article  CAS  Google Scholar 

  19. Roe, D. C, Marshall, A. G., and Smallcombe, S. H. 1978, Anal. Chem. 50, 764–767.

    Article  CAS  Google Scholar 

  20. Allerhand, A., and Gutowsky, H. S. 1964, J. Chem. Phys. 41 2115.

    Article  CAS  Google Scholar 

  21. Tritton, T. R. 1980, FEBS Lett. 120, 141–144.

    Article  CAS  Google Scholar 

  22. Hagen, D. S., Weiner, J. H., and Sykes, B. D. 1979, Biochemistry 18, 2007.

    Article  CAS  Google Scholar 

  23. Poole, C. P., Jr. 1967, “Electron Spin Resonance,” InterScience, New York, Chapter 10.

    Google Scholar 

  24. Herring, F. G. 1981, private communication.

    Google Scholar 

  25. Werbelow, L. G., and Marshall, A. G. 1981, submitted for publication.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer Science+Business Media New York

About this chapter

Cite this chapter

Marshall, A.G. (1982). Dispersion versus Absorption (DISPA): Hilbert Transforms in Spectral Line Shape Analysis. In: Marshall, A.G. (eds) Fourier, Hadamard, and Hilbert Transforms in Chemistry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0336-5_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-0336-5_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-0338-9

  • Online ISBN: 978-1-4899-0336-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics