We have obtained relationships for frequency shifts resulting from the interference of spectral components for the magnitude mode Fourier transform. The approximation of a weak perturbation of well resolved peaks has been used. Both the low- and high-pressure limits for Fourier-transform ion cyclotron resonance (FTICR) operation have been considered. We have found that the shifts can be either negative or positive, depending on the initial phase and/or the choice of the time-domain interval. The magnitude of shifts generally does not exceed the peak width. In the approximation of small perturbations the shifts produced by multiple peaks are additive. We have compared theoretical results with experimental shifts for isotopic clusters of multiply charged insulin. Up to 1 ppm frequency variations were experimentally observed for the insulin 5+ charge state, consistent with theoretical estimates. The peak interference is of particular significance in the case of bio-molecular mass spectra having a large number of peaks and covering a considerable dynamic range (i.e., relative abundance). We conclude that the common mass measurement procedure based on the location of the magnitude mode maxima of well resolved peaks can result in systematic mass measurement errors. The relationships obtained provide corrections for the frequency shifts and thus improve the mass measurement accuracy.