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A novel approach to optically generating chirped millimeter-wave pulses with tunable chirp rate based on spectral shaping and nonlinear frequency-to-time mapping is proposed and experimentally demonstrated. In the proposed approach, the optical power spectrum of an ultrashort pulse from a femtosecond pulsed laser is shaped by a two-tap Sagnac loop filter that has a sinusoidal frequency response. The spectrum-shaped optical pulse is then sent to a nonlinearly chirped fiber Bragg grating (NL-CFBG) with a tunable nonlinear group delay to serve as a high-order dispersive device to perform the nonlinear frequency-to-time mapping. A chirped electrical pulse with a high central frequency and large chirp rate is then generated at the output of a high-speed photodetector. The NL-CFBG used in the proposed system is produced from a regular linearly chirped fiber Bragg grating based on strain-gradient beam tuning. A detailed theoretical analysis on the chirped pulse generation is developed, which is verified by numerical simulations and experiments. Millimeter-wave pulses with a central frequency of around 35 GHz and instantaneous frequency chirp rates of 0.053 and 0.074 GHz/ps are experimentally generated.