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Fourier transform ultrashort optical pulse shaping using a single linearly chirped fiber Bragg grating (LCFBG) is proposed and experimentally demonstrated in this letter. The LCFBG in the system performs three functions: temporally stretching the input ultrashort pulse, shaping the pulse spectrum, and temporally compressing the spectrum-shaped pulse. The impulse response of the entire pulse shaping system is equal to the Fourier transform of the square of the grating power reflectivity function. By appropriately designing the grating reflection response, a temporal optical waveform in the subpicosecond regime can be accurately synthesized. An example to show the synthesis of a triangular optical pulse with a full-width at half-maximum of 2 ps is demonstrated.