Journal of Mathematical Chemistry

, Volume 20, Issue 1, pp 47–65 | Cite as

A system theoretic formulation of NMR experiments

  • Raimund J. Ober
  • E. Sally Ward


A detailed system theoretic description is given of NMR experiments including relaxation effects. The approach is based on an exact and analytical solution to the master equation. It is shown that NMR experiments can be described in the framework of bilinear time-invariant systems. This description is used to derive closed-form expressions for the spectrum of one- and two-dimensional experiments. The simulations show that the approach accounts for the frequency dependence of a pulse, distinguishes between soft and hard pulses and also explains artifacts such as axial peaks.


Physical Chemistry Frequency Dependence Master Equation Theoretic Description Relaxation Effect 
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  1. [1]
    T. Kailath,Linear Systems (Prentice Hall, 1980).Google Scholar
  2. [2]
    M. Aoki,State Space Modelling of Time Series (Springer, 1987).Google Scholar
  3. [3]
    L. Ljung, System Identification (Prentice Hall, 1987).Google Scholar
  4. [4]
    R.R. Ernst, G. Bodenhausen and A. Wokaun,Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, 1987).Google Scholar
  5. [5]
    D.R. Brillinger and R. Kaiser, Fourier and likelihood analysis in NMR spectroscopy, Report No. 287, Department of Statistics, University of California (1981).Google Scholar
  6. [6]
    D.R. Brillinger, Some statistical aspects of NMR spectroscopy, Actas Del 2 Congreso Latinoamericano De Probabilidad Y Estadistica Matematica (1985).Google Scholar
  7. [7]
    R.A. Horn and C.R. Johnson,Topics in Matrix Analysis (Cambridge University Press, 1991).Google Scholar
  8. [8]
    W.J. Rugh,Nonlinear System Theory (The Johns Hopkins University Press, 1981).Google Scholar
  9. [9]
    R.K. Miller and A.N. Michel,Ordinary Differential Equations (Academic Press, 1982).Google Scholar
  10. [10]
    C.P. Slichter,Principles of Magnetic Resonance, 3rd ed. (Springer, 1992).Google Scholar
  11. [11]
    F.R.Gantmacher,The Theory of Matrices (Chelsea,1959).Google Scholar

Copyright information

© J. C. Baltzer AG, Science Publishers 1996

Authors and Affiliations

  • Raimund J. Ober
    • 1
  • E. Sally Ward
    • 2
  1. 1.Center for Engineering Mathematics EC35University of Texas at DallasRichardsonUSA
  2. 2.Cancer Immunobiology Center and Department of MicrobiologyUniversity of Texas Southwestern Medical CenterDallasUSA

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