NMR Spectral Analysis and Modelling I. Basic Concepts and Fourier Transforms

Essentially all high‐resolution NMR experiments are now carried out with pulse excitation. Basic concepts, such as signal induction and sense of rotation, are discussed using a rotating magnetic needle as an analogy. The typical signal, recorded immediately after the r.f. pulse is a superposition of many single‐line free‐induction‐decay signals, each of which is described by the expression, Uo, j‐cos(2πvjt +Φj)·dj(t). The frequency, vj, carries structural information and the amplitude Uo, j is proportional to the molecular concentration. The function dj(t) accounts for the decay, and the phase Φj depends on instrumental parameters and the mode of observation. It is the purpose of spectral analysis to determine these parameters from the measured composite signal. Fourier analysis, the most prominent approach, is introduced in a graphical and analytical manner based on the concept of complex harmonic waves exp(i2πvt). To facilitate understanding, the reverse process, namely Fourier synthesis, as well as the number e and its complex powers eix, are introduced in an elementary way. Part I concludes with a discussion of: a) the relationship between the attainable spectral resolution and its time length of signal observation, and b) the difference between the actual and predicted time signals within and outside the observation‐time window.