We demonstrate a programmable microwave photonic bandpass filter with a rectan- gular frequency response and a reconfigurable spectral resolution. We achieved these features through dual-sidebands processing of a phase modulated signal using a network of four optical ring resonators in a low-loss silicon nitride (Si3N4) circuit. Furthermore, we integrate a pair of optical ring resonators in the same circuit to precisely control the amplitude and phase of the optical carrier to enhance the noise performance of the filter. We achieved filtering with a tunable bandwidth from 2 to 7 GHz with optical carrier suppression up to 6 dB, a maximum RF gain of -10 dB, and a minimum noise figure of 27 dB. These experiments are expected to provide a feasible design to approach fully integrated microwave photonic filters with improved link gain and reduced noise figure.