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A multichannel photonic temporal differentiator implemented based on a single multichannel fiber Bragg grating (FBG) for wavelength-division-multiplexed (WDM) signal processing is proposed for the first time to our knowledge. The multichannel FBG is designed using the discrete layer peeling (DLP) algorithm together with the spatial sampling technique. The DLP algorithm is used to design the spectral response of an individual channel, while the spatial sampling is employed to generate a multichannel response. The key feature of the proposed temporal differentiator is that WDM signals at multiple optical wavelengths can be simultaneously processed. Two sampling techniques, the phase-only and the amplitude-only sampling, are employed to design a 45-channel and a 3-channel first-order temporal differentiator, respectively. A proof-of-concept experiment is then carried out. A 3-channel first-order differentiator with a bandwidth of 33.75 GHz and a channel spacing of 100 GHz is fabricated. The use of the fabricated 3-channel FBG to perform first-order temporal differentiation of a 13.2-GHz Gaussian-like optical pulse with different optical carrier wavelength is demonstrated.