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A general and practical approach for designing ultra-fast all-optical (all-fiber) signal processing devices based on chirped fiber Bragg gratings (C-FBGs) working in transmission is presented. The approach can be used to design any minimum-phase linear optical device, e.g., first and high-order all-optical time differentiators and integrators and a large variety of optical pulse shapers, significantly overcoming the bandwidth limitations of previous FBG-based designs. Processing speeds in the THz range, corresponding to sub-picosecond time features, can be achieved using readily feasible grating apodization profiles. The approach is successfully proved through the design of two relevant functionalities, namely a THz-bandwidth optical differentiator and a 1-ps flat-top optical pulse shaper.