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In this paper, a novel approach to optically generating chirped electrical pulses with tunable chirp rate using a tunable nonlinearly chirped fiber Bragg grating (NL-CFBG) is proposed and analyzed. In the approach, a femtosecond pulse is spectrally filtered by two tunable optical filters, with the two filtered pulses applied to the NL-CFBG, to introduce different dispersions. The chirped optical pulses are then applied to a high-speed photodetector (PD). The beating of the two optical pulses leads to the generation of a linearly chirped electrical pulse with a tunable chirp rate by tuning the center wavelength of one of the tunable optical filter. The NL-CFBG used in the proposed system is produced using a new technique based on strain-gradient beam tuning. A mathematical model to describe the chirped electrical pulse generation is developed, which is verified by numerical simulations.