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We present a general quantitative description of the temporal and spectral responses of arrayed waveguide gratings pulse shapers to a single ultrashort optical pulse. Operation of the pulse shaper was described in terms of superposition of pulse replicas that are overlapping in the slab waveguide region of the device. We demonstrate that the analytical formulation requires only a combination of fast Fourier transform algorithm with waveguide-mode profile simulation to accurately describe the spectral and temporal responses of the pulse shaper. The proposed model was applied to pulse shapers based on digital amplitude and phase modulations. A supporting evidence of the effectiveness of the model described in this paper was obtained from the good agreement between simulations and experiments.