Deconvolution of high-resolution two-dimensional NMR signals by digital signal processing with linear predictive singular value decomposition

Abstract

NMR signals from high-resolution pulsed experiments can be adequately represented by sums of sinusoids (I). Normally these signals are transformed to the frequency domain by Fourier transformation and the chemical information inherent in the frequency, damping, intensity, or phase of the sinusoids is subsequently obtained by various deconvolutions, ranging from simple “peak-picking” for frequency to nonlinear least-squares fitting to obtain all the sinusoid properties (2) for an application see, e.g., Ref. (3). This deconvolution in the frequency domain is particularly complicated by the need to set initial parameters for the nonlinear least-squares analysis (4,5). The characteristics of the contributing sinusoids in the time domain are needed for recognition of patterns of signals (6) and correlation with expected properties (7). We show a new method of analyzing two-dimensional NMR spectra for this purpose. The technique of linear predictive singular value decomposition (LPSVD) (8), applied previously in NMR (9), permits the extraction of frequency information from a time-domain signal, While a Fourier transform of this signal produces another related signal, equivalent to the previous one but viewed in the frequency domain, this LPSVD technique presents the same information in a different and sometimes more useful manner. The algorithm presupposes that the signal is made up of a certain number of exponentially damped sinusoids of the form