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We experimentally demonstrate an arbitrary-order bandwidth-tunable differentiator using a programmable optical pulse shaper, which is based on spatial diffraction and liquid crystal modulation. The impact of bandwidth of optical pulse shaper on output power and pulsewidth of differentiation is theoretically analyzed. In the experiment, all first-order, second-order, and third-order differentiators with bandwidths of 80, 160, and 320 GHz are obtained with average deviations of less than 4.2%. The differentiation of pseudorandom nonreturn-to-zero (NRZ) signals at 10 and 20 Gbit/s is also discussed.