1. A method for processing a set of multiple serially acquired magnetic resonance spectroscopy (MRS) free induction decay (FID) frames from a multi-frame MRS acquisition series from a region of interest (ROI) in a subject, and for providing a post-processed MRS spectrum, comprising: receiving the multi-frame MRS acquisition series comprising the set of FID frames; forming a reference spectrum by averaging multiple FID frames from the acquisition series; determining a frequency shift error of an FID frame by performing spectral cross-correlation between the FID frame and the reference spectrum; shifting the FID frame based on the frequency shift error so as to increase coherence of the FID frame with the reference spectrum; and combining multiple FID frames by coherent averaging to produce the post-processed MRS spectrum.