The Fourier transform
We may compare the NMR spectroscopy and the optic one.
In the optical spectroscopy, the prism allows the monochromatic analysis of a polychromatic source interacting with the mater. In the NMR spectroscopy, the impulsion yield a broad frequency spectrum and the Fourier transform allows a "monochromatic" analysis of the interaction beam/nucleus.
The technique is to treat the signal M(t) according to the following relationship:
Since the pulse sequence last generally less than a second, we may achieve a great number of accumulations of data before to proceed to the Fourier transform. The signal to noise ratio thus improves (This ratio is proportional to where S = number of scans.)