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A microwave bandpass differentiator implemented based on a finite impulse response (FIR) photonic microwave delay-line filter with nonuniformly-spaced taps is proposed and experimentally demonstrated. To implement a microwave bandpass differentiator, the coefficients of the photonic microwave delay-line filter should have both positive and negative coefficients. In the proposed approach, the negative coefficients are equivalently achieved by introducing an additional time delay to each of the taps, leading to a π phase shift to the tap. Compared with a uniformly-spaced photonic microwave delay-line filter with true negative coefficients, the proposed differentiator features a greatly simplified implementation. A microwave bandpass differentiator based on a six-tap nonuniformly-spaced photonic microwave delay-line filter is designed, simulated, and experimentally demonstrated. The reconfigurability of the microwave bandpass differentiator is experimentally investigated. The employment of the differentiator to perform differentiation of a bandpass microwave signal is also experimentally demonstrated.