Article

Journal of Mathematical Chemistry

, Volume 20, Issue 1, pp 47-65

First online:

A system theoretic formulation of NMR experiments

  • Raimund J. OberAffiliated withCenter for Engineering Mathematics EC35, University of Texas at Dallas
  • , E. Sally WardAffiliated withCancer Immunobiology Center and Department of Microbiology, University of Texas Southwestern Medical Center

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Abstract

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.