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A new technique for the monitoring and multiplexing of fiber-Bragg-grating (FBG) sensors is described. The sensing elements - low-finesse Fabry-Perot interferometers formed with FBG pairs - are reflectively monitored with a linearly chirped Er:fiber laser. This reflected signal is convolved with a reference waveform which varies at a frequency proportional to the optical length of each sensor to 1) obtain a coarse measurement of FBG reflectance peak frequency and 2) refine this measurement using the phase of the convolved signal. Multiplexed sensors of different lengths are distinguished even though the reflectance spectra for the sensors may overlap or even coincide. A spectral resolution of 0.045 GHz (0.36 pm), corresponding to a temperature resolution of 0.035/spl deg/C, was achieved.