## 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^{[1]}:

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.)