Reduced multidimensional NMR experiments using a linear least-squares procedure

Linear least-squares procedures were found to be useful substitutes for the commonly used fast Fourier transform algorithm (1). They offer the advantage of much shorter experimental time, in particular for multidimensional NMR experiments. In this procedure (I), the amplitudes of the peak are determined together with the frequencies and the damping factors. However, in multidimensional experiments, the various linewidths and resonance frequencies can usually be determined prior to the multidimensional experiment, i.e., from the one-dimensional experiment; and the information can then be used to calculate the amplitudes in the multidimensional spectrum (2).
We suggest a mathematical procedure for such an evaluation whereby a system of linear equations is written for the amplitudes and is solved simply by matrix diagonalization. The procedure also permits easy determination of the accuracy of each calculated amplitude when the experimental S/N ratio is provided.