In NMR, the sample both absorbs and shifts the phase of the components of the exciting pulse. The re-radiated energy contains information on both the absorbance and phase response, and these are usually recorded in the time domain as complex data.

Unfortunately, because of practical hardware limitations the sampling process mixes the real and imaginary parts of the signal. Usually one is interested only in the sample absorbance; but in any case, one certainly needs to have the absorbance and phase information properly sorted. This is a nontrivial task. Existing algorithms, even the best of them, are prone to failure in the presence of noise. We have recently developed a rephasing algorithm that is relatively free from data set quality considerations.

Figures 1 and 2 show the properly phased noisy NMR absorbance and phase spectra of a sample, superimposed on the same data from which the noise has been removed prior to the rephasing. The phasing results are essentially the same for the noisy data as for the smoothed data. The displacement and rotation angles through which the complex signal vector must be rotated to obtain complete separation are the same within two degrees for the linear phase, and within 1 degree for the constant phase.

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