A new microwave photonic signal processor that has the ability to realize a continuously tunable high-resolution notch filters response is presented. It is based on designing the filter impulse response to have a primary and secondary tap distribution. With a proper design on the tap amplitudes, the notch filters passband can be flattened. The filter notch frequency can be also continuously tuned by controlling the phase shift of the secondary taps via a diffraction-based Fourier-domain optical processor. The notch filters has a robust response and high signal-to-noise-ratio (SNR) performance. Experimental results demonstrate that the new microwave photonic notch filters can simultaneously realize a flat passband of only a 1-dB ripple, a large free spectral range of 4.7 GHz, and a notch depth of over 40 dB while tuning the notch frequency. © 2015 IEEE.