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We propose a novel approach to realizing all-optical microwave filtering using an array of fiber Bragg gratings with identical reflectivities. The filter tapping coefficients are determined by the spectrum profile of a broadband light source and the central wavelengths of the gratings. Since the fiber Bragg gratings have identical reflectivities, the characteristics of the gratings with high uniformity are possible, which simplifies the fiber Bragg grating fabrication and reduces the implementation error. In addition, the spectrum profile of the broadband light source can be controlled using an optical filter, which could be used to control the filter coefficients to suppress the filter sidelobes. A microwave filter using four fiber Bragg gratings is experimentally implemented.