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This paper reports on the application of a technique for high-resolution interrogation of a fiber Bragg grating array using an all-fiber Michelson interferometer where the method of scanning the interferometric delay is fiber stretching using a piezoelectric fiber stretcher. Compensation for the performance degrading effects associated with temporally scanned interferometers is achieved using Hilbert transform processing techniques. In contrast to measurement using Fourier transform spectroscopy, experimental data shows that a measurement accuracy of ??0.5 pm is attainable using the Hilbert transform technique from delay scans (~6 mm) which are shorter than the coherence length of the grating.