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We propose and demonstrate a simple and practical method for measuring the amplitude and the phase of an ultrahigh-speed train of uniform pulses. Apart from a specially designed fiber Bragg grating (FBG) filter, the method only requires equipment that is standard in a telecommunications laboratory. The measurement is performed in the spectral domain where the intensity is easily recorded, while the spectral phase is characterized on the basis of beating signals obtained by filtering the pulse train with the FBG filter, which is tuned in wavelength by mechanical means. The practical capabilities and limitations (e.g., achievable spectral and temporal resolutions) of the proposed method are discussed.