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A negative tap photonic microwave filter based on a Mach-Zehnder modulator (MZM) and a tunable optical polarizer is proposed. In the proposed filter, the output light from the MZM, after experiencing a time delay difference between the two orthogonal modes in a polarization-maintaining fiber, is sent to the tunable optical polarizer. By adjusting the dc bias of the MZM and the polarization angle of the tunable polarizer with respect to the two orthogonal modes, two positive or one positive and one negative coefficient are generated. A theoretical analysis is presented which is verified by experiments. A two-tap microwave filter with two positive or one positive and one negative coefficient is demonstrated.