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The focus of this paper is on interferometric systems that utilize spectral interferometry based on minimum-phase functions (MPFs) to fully characterize any fiber-Bragg-grating (FBG) spectra without exceptions. The approach presented involves sending a broadband light source (e.g., a short laser pulse) into the FBG of interest and using an optical spectrum analyzer (OSA) to record the spectrum of the interference between the reflected pulse from the grating and the time-delayed version(s) of the original short pulse. The square root of this measured spectrum, which yields the Fourier-transform (FT) magnitude of the input-pulse-sequence electric-field envelope, is then processed to uniquely recover both the phase and the amplitude of the FBG spectrum. The underlying principle for this unique recovery is that by construction, the input pulse sequence sent to the OSA is close to an MPF; thus, it is possible to recover its FT phase spectrum using only the measurement of its FT magnitude spectrum. This is an important result since, by merely measuring the FT magnitude, the entire complex spectrum of the grating can be recovered. Furthermore, this technique can conveniently be used to simultaneously characterize more than one FBG, using a single FT magnitude measurement. This technique has important advantages over existing techniques: a higher resolution and the ability to use longer duration laser pulses.