The Solution to the General Problem of Spectral Analysis Illustrated with Examples from NMR
A general iterative method for locating the global minimum of an error functional ф = (s-ŝ.)T (s-ŝ) in the presence of a multitude of local minima is presented. It relies on the introduction of a square matrix W in data space whose off-diagonal elements can be exploited for inducing continuously adjustable correlation between the residuals by way of ф’ = (s-ŝ.)T W(s-ŝ). The general structure of W is derived from symmetry, boundary and continuity requirements. In spectroscopic applications the vector s in data space consists of n digitized signal intensities si and the theoretical model is expressed as a function ŝ = f (p, ω)) of a discrete vector p in parameter space and a continuous frequency variable ω. The solution has been fully worked out for NMR spectra (high-resolution isotropic; anisotropic; exchange-broadened), including practical aspects such as automated data acquisition, data format conversion, pretruncation, baseline flattening, smoothing and posttruncation, and will be illustrated by a variety of examples.
KeywordsData Space Bottom Trace Benzyl Acetate Middle Trace Baseline Flatten
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