A system of spectroscopy using nuclear magnetic resonance (NMR) of at least one sample comprising at least one species to be characterized and a reference species taken from a solvent, with the content of the reference species in the sample being at least greater than twice the value of the at least one species to be characterized, with the system comprising at least one antenna so configured as to acquire one or more complex free induction decay (FID) signal(s) S(t) in the time domain, with each complex FID signal being generated by applying at least one field B0 to the at least one sample and comprising a real part and an imaginary part, characterized in that the system comprises processing means so configured as to calculate, for each complex FID signal, the module of each complex FID signal, and so configured as to perform, after the step of generating a FID module for each complex FID signal S(t) of the one or more complex FID signal(s) S(t), a summation of the FID modules to obtain a combined FID signal and preferably apply a Fourier transform to said combined FID signal.