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A microwave photonic notch filter with a complex coefficient is proposed and demonstrated based on four wave mixing (FWM). FWM effect of two single-frequency laser beams occurs in a highly nonlinear fiber (HNLF), and multi-wavelength optical signals are generated and used to generate the multi-tap of microwave photonic filter (MPF). The complex coefficient is generated by using a Fourier-domain optical processor (FD-OP) to control the amplitude and phase of the optical carrier and phase modulation sidebands. The results show that this filter can be changed from bandpass filter to notch filter by controlling the FD-OP. The center frequency of the notch filter can be continuously tuned from 5.853 GHz to 29.311 GHz with free spectral range (FSR) of 11.729 GHz. The shape of the frequency response keeps unchanged when the phase is tuned.