Simple Least-Squares Estimation of Intensities of Overlapping Signals in 2D NMR Spectra

It is described how a least-squares estimate of a two-dimensional NMR signal intensity can be calculated from two one-dimensional intensities, as estimated from a row and a column, respectively. The result is independent of artifacts associated with the Fourier transform, and it is unaffected by phase distortions and poor base plane definition in the spectrum. Cases of overlapping signals are discussed, and it is shown that because of the involved least-squares procedure, optimum results can be produced even when the overlap is substantial. Results of test calculations on simulated examples are presented, and it is shown that deviations of the calculated two-dimensional intensities from the correct values are small and in agreement with the standard deviations, also provided by the method. Finally, two-dimensional intensities calculated from experimental data are presented.