We demonstrate for the first time, to the best of our knowl- edge, an on-chip microwave photonic (MWP) notch filter with high stopband rejection and integrated optical car- rier suppression in a phase modulator-based system. The notch filter was achieved through phase modulation to intensity modulation (PM-to-IM) transformation and dual-sideband-processing using a network of three ring resonators (RRs) in a low-loss silicon nitride (Si3N4) plat- form. We show simultaneous PM-to-IM conversion and optical carrier processing for enhancing the filter per- formance using a single RR. We achieve filtering with a high stopband rejection of >55 dB, an optical carrier sup- pression up to 3 dB, a radio frequency link gain of 3 dB, a noise figure of 31 dB, and a spurious-free dynamic range of 100 dB · Hz2/3. These experiments point to the impor- tance of vectorial spectral shaping of an MWP spectrum for advanced functionalities.