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Statistical analysis of linear NMR spectrum measurements

Authors
Journal
Journal of Magnetic Resonance (1969)
0022-2364
Publisher
Elsevier
Publication Date
Volume
11
Issue
2
Identifiers
DOI: 10.1016/0022-2364(73)90001-2
Disciplines
  • Mathematics

Abstract

Abstract High resolution nuclear magnetic resonance spectrometry is analysed in the framework of the statistical theory for the interpretation of measurements. The small-signal spectrum is represented by parameters of the transfer function of a linear system, and a spectrometer model is developed for the measurement of these parameters in the presence of additive, signal-independent noise. The measurement is performed by a Bayesian receiver, which converts a prior into a posterior probability density by means of a signal transmitted through the linearized spin system and by a decision unit operating with the maximum likelihood strategy. The measurement process can be divided into two steps: a coarse measurement is based on a channel structure corresponding to orthogonal spectral elements and yields decision information, and a fine measurement gives increased accuracy and resolution. Uncertainty relations for accuracy and resolution are discussed, and the operating characteristics of the measurement system are described by means of the signal/noise ratio. Results for spectral line frequency and intensity measurements are illustrated with two simple pulsed Fourier transform experiments.

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