Selective data acquisition in NMR. The quantification of anti-phase scalar couplings

Almost all time-domain NMR experiments employ ''linear sampling,'' in which the NMR response is digitized at equally spaced times, with uniform signal averaging. Here, the possibilities of nonlinear sampling are explored using anti-phase doublets in the indirectly detected dimensions of multidimensional COSY-type experiments as an example. The Cramer-Rao lower bounds are used to evaluate and optimize experiments in which the sampling points, or the extent of signal averaging at each point, or both, are varied. The optimal nonlinear sampling for the estimation of the coupling constant J, by model fitting, turns out to involve just a few key time points, for example, at the first node (t = 1/J) of the sin(pi Jt) modulation. Such sparse sampling patterns can be used to derive more practical strategies, in which the sampling or the signal averaging is distributed around the most significant time points. The improvements in the quantification of NMR parameters can be quite substantial especially when, as is often the case for indirectly detected dimensions, the total number of samples is limited by the time available. (C) 1996 Academic Press, Inc.