Free induction decay and Fourier transformation

One advantage of FT-NMR spectroscopy is the possibility of repeating the experiment many times and adding up all the FIDs. In this way, the signal adds up and electronic noise cancels out. The signal-to-noise ratio, S N, increases with the square root of the number of scans, Ms- 

The development of pulse techniques has not only boosted NMR spectroscopy by allowing accumulation of spectra the parallel gain in quantum-mechanical understanding of the action of r.f. pulses has also provided us with a detailed understanding of the experiments. Simplified versions (known as the product operator formalism) provide a toolbox using a comparatively low level of mathematical description. This allows the mechanisms of multi-pulse experiments (discussed in later sections) to be analyzed and understood and new experiments to be developed. This goes beyond the scope of this book, so the interested reader is referred to the literature. The principles and practice of Fourier transform NMR 

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