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 at least one of the following: determining a frequency shift error of an FID frame by performing spectral cross-correlation between the FID frame and a reference frame; adjusting a phase of an FID frame by a phase shift configured to reduce an extent of the post-processed MRS spectrum having a negative value; estimating a line width between two opposite walls of a water peak region of an FID frame of the series, comparing the estimated line width against a threshold value, and qualifying and including, or disqualifying and excluding, the FID frame from the set for further processing to provide the post-processed MRS spectrum based at least in part upon the comparison; associating first and second groups of FID frames within the set with first and second different relative phases, respectively, of a phase step cycle along the MRS acquisition series, processing the first and second groups separately, averaging the first and second groups separately to form first and second average interim spectra, and averaging the first and second average interim spectra; and generating a first baseline estimate using a rank order filter (ROF) on a range of interest of an interim MRS spectrum partially post-processed from the set, fitting a polynomial to at least a portion of the first baseline estimate to generate a baseline curve, and subtracting the baseline curve from the interim MRS spectrum to provide the post-processed MRS spectrum.