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certain energy in the form of a sine wave is recorded. By using the mathematical

procedure ofFourier transform, the ‘time domain’ can be resolved into a ‘frequency

domain’. For a single-frequency sine wave, this procedure yields a single peak of fixed

amplitude. However, because the measured signal in NMR is the re-emission of energy

as the nuclei return from their high-energy into their low-energy states, the recorded

radiation will decay with time, as fewer and fewer nuclei will return to the ground

state. The signal measured is thus called thefree induction decay(FID). Figure 13.9b

shows the effect of the FID on the corresponding Fourier transform. The frequency

band broadens, but the peak position and the amplitude remain the same. The resolved

frequency peak represents the chemical shift of a nucleus resonating at this energy.

Amplitude

Frequency (Hz)

Amplitude

Frequency (Hz)

(a)

Amplitude

Time (s)

Fourier

transform

(b)

Amplitude

Time (s)

Fourier

transform

Amplitude

Frequency

Amplitude

(c)

Time

Fourier

transform

Fig. 13.9Diagrammatic representation of the Fourier transformation of (a) a single frequency sine wave,

(b) a single frequency FID, and (c) a three-sine-wave combination.

539 13.5 Nuclear magnetic resonance