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We demonstrate the first real-time implementation of linear spectrograms for the complete characterization of a train of optical pulses. The spectrogram is composed of the spectra of the train of pulses, measured with a fast scanning microelectromechanical Fabry-Pe´rot etalon, after gating with an electroabsorption modulator at various relative temporal delays programmed with a voltage-controlled phase shifter. The temporal intensity and phase of the train of pulses are retrieved using an iterative deconvolution algorithm with an update rate of 9 Hz allowing real-time optimization and feedback. This diagnostic is validated on 40-Gb/s pulses generated by a LiNbO3 Mach-Zehnder modulator.