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We propose and analyze a new technique for optical pulse shaping that uses fiber Bragg gratings, which overcomes the depletion effects associated with long uniform gratings operating in the weak-grating limit (Born approximation). Our approach requires a simple linear reflection of the original input pulse to be shaped from a suitable apodized linearly chirped fiber Bragg grating and is based on the fact that, under certain conditions, the spectral and temporal reflection impulse responses of the grating are scaled versions of its corresponding apodization profile. Temporal waveforms in the picosecond/nanosecond regime can be accurately synthesized with this approach.