We describe an interferometric technique for the demodulation of serial fibre Bragg grating sensor arrays, yielding absolute measurement of the individual grating mean wavelengths. The composite beam reflected from the array illuminates a scanning Michelson interferometer but, in contrast to spectral measurement by Fourier Transform Spectroscopy, our technique requires an OPD scan far shorter than the coherence length of the grating reflections. The technique is based on the high-resolution measurement of the phases of the complex analytic signals and of the relationship of these phases to interferometric delay. The analytic signals are derived via the Hilbert transform, allowing frequency domain filtering of individual signals within the signal processing. The technique has yielded a resolution of 0.007 nm for an OPD scan of 1.2 mm.