The Solution to the General Problem of Spectral Analysis Illustrated with Examples from NMR

  • Gerhard Binsch
Part of the The IBM Research Symposia Series book series (IRSS)


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.


Data Space Bottom Trace Benzyl Acetate Middle Trace Baseline Flatten 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Gerhard Binsch
    • 1
  1. 1.Institute of Organic ChemistryUniversity of MunichMunich 2Germany

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