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Chirped radio-frequency (RF) pulse generation based on optical spectral shaping and nonlinear wavelength-to-time mapping in a nonlinearly chirped fiber Bragg grating (NLCFBG) is investigated. In the proposed approach, the spectrum of a femtosecond pulse generated by a mode-locked fiber laser is shaped by an optical filter that has a sinusoidal frequency response. The spectrum-shaped optical pulse is sent to the NLCFBG, to implement nonlinear wavelength-to-time mapping. A chirped electrical pulse with the central frequency and chirp rate determined respectively by the first- and second-order dispersions of the NLCFBG is then obtained at the output of a high-speed photodetector. An approximate model that describes the chirped RF pulse generation is derived, which is verified by numerical simulations. Chirped pulse generation with a pulse compression ratio as high as 450 is demonstrated. The key device in the chirped RF pulse generation system is the NLCFBG, which is investigated in detail with an emphasis on the influence of its group delay ripples on the performance of the pulse generation system. Techniques to design and fabricate the NLCFBG are also discussed. The proposed approach provides a potential solution for the generation of chirped RF pulse with a high central frequency and large chirp rate for applications in pulse compression radar systems.