In Fourier transform NMR spectroscopy and imaging, a pulse sequence describes a series of radio frequency pulses applied to the sample, such that the free induction decay is related to the characteristic frequencies of the desired signals. After applying a Fourier transform, the signal can be represented in the frequency domain as the NMR spectrum. In magnetic resonance imaging, additional gradient pulses are applied by switching magnetic fields that exhibit a space-dependent gradient which can be used to reconstruct spatially resolved images after applying Fourier transforms. The outcome of pulse sequences is often analyzed using the product operator formalism.