Most Magnetic Resonance Spectroscopy (MRS) localization methods can generate gradient vibrations at acoustic frequencies and/or magnetic field oscillation, which can cause a time-varying magnetic field superimposed onto the static one. This effect can produce frequency modulations of the spectral resonances. When localized MRS data are acquired without water suppression, the associated frequency modulations are manifested as a manifold of spurious peaks, called sidebands, which occur symmetrically around the water resonance. These sidebands can be larger than the small metabolite resonances and can present a problem for the quantitation of the spectra, especially at short echo times. Furthermore, the resonance lineshapes may be distorted if any low frequency modulations are present. A simple solution is presented which consists of selecting the modulus of the acquired Free Induction Decay (FID) signal. Since the frequency modulations affect only the phase of the FID signal, the obtained real spectrum of the modulus is free from the spurious peaks where quantitative results may be directly obtained. Using this method, the distortions caused by the sidebands are removed. This is demonstrated by processing proton MRS spectra acquired without water suppression collected from a phantom containing metabolites at concentrations comparable to those in human brain and from a human subject using two different localization methods (PRESS and Chemical Shift Imaging PRESS-(CSI)). The results obtained illustrate the ability of this approach to remove the spurious peaks. The corrected spectra can then be fit accurately. This is confirmed by the results obtained from both the relative and the absolute metabolites concentrations in phantoms and in vivo.