Spectral Representation of 2D NMR Spectra by Hypercomplex Numbers

This paper introduces a new spectral representation for phase-sensitive two-dimensional NMR experiments based on hypercomplex algebra. Some properties of this hypercomplex algebra are given. With this representation, it is shown that the Fourier transform and the phasing of phase-sensitive 2D NMR spectra can take simple expressions. Relationship of this representation with earlier proposed representation is considered. 0 1988 Academic press, Inc. Fourier transform nuclear ma.gnetic resonance spectroscopy exhibits a quite unique feature among all Fourier transform spectroscopies: the phase of the signal is pertinent and not trivial; furthermore, the signal acquired is usually in a complex representation. This implies that the power spectrum representation is not suitable for FT NMR, and the complex representation is usually chosen for the spectrum. The notion of “phasing” a spectrum has been introduced, which consists in multiplying the complex spectrum by a given phase factor exp(iO), in order to bring some interesting features of the signal in the real part of the spectrum. The introduction of phase-sensitive two-dimensional NMR (I-4) has raised th