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An approach to generating chirped microwave pulse based on optical spectral shaping and nonlinear chromatic-dispersion-induced wavelength-to-time mapping using all-fiber components is proposed and demonstrated. In the proposed approach, the spectrum of a femtosecond pulse is shaped by a two-tap Sagnac-loop filter that has a sinusoidal spectrum response. The spectrum shaped pulse is then sent to a dispersive element that has first- and second-order chromatic dispersions. Thanks to the nonlinear wavelength-to-time mapping of the dispersive element, a temporal pulse that has a central frequency in the microwave band with a large chirp is generated, which provides the potential for applications in high-speed communications and radar systems. Numerical and proof-of-concept experimental results are presented.