In an ideal case, each transition in an NMR spectrum will be represented by a Lorentzian lineshape. That is because Lorentzian functions are related to decaying sine and cosine waves, that which we experimentally detect.

Below, you can watch how the oscillation frequency of a detected signal translates into a frequency shift in the corresponding Lorentzian. In addition, notice how it is the decay rate of the detected signal that relates to the width of the Lorentzian.

Above, the decaying oscillation would be one of many similar oscillations simultaneously detected in a pulsed NMR experiment. This collection of oscillations is called a Free Induction Decay (FID) and represents the spectrum in the time domain. More useful is the spectrum in the Frequency domain, where each.

The conversion between the (time domain) FID and (frequency domain) spectrum is typically performed using a Fourier transform. using our oscillating decay

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