Integrated microwave photonics has strongly emerged as a next-generation technology to address limitations of conventional RF electronics for wireless communications. High-resolution RF signal processing still remains a challenge due to limitations in technology that offer sub-GHz spectral resolution, in particular at high carrier frequencies. In this paper, we present an on-chip high-resolution RF signal processor, capable of providing high-suppression spectral filtering, large phase shifts and ns-scale time delays. This was achieved through tailoring of the Brillouin gain profiles using Stokes and anti-Stokes resonances combined with RF interferometry on a low-loss photonic chip with strong opto-acoustic interactions. Using an optical power of <40 mW, reconfigurable filters with a bandwidth of ~20 MHz and an extinction ratio in excess of 30 dB are synthesized. Through the concept of vector addition of RF signals we demonstrate, almost an order of magnitude amplification in the phase and delay compared to devices purely based upon the slow-light effect of Brillouin scattering. This concept allows for versatile and power-efficient manipulation of the amplitude and phase of RF signals on a photonic chip for applications in wireless communications including software defined radios and beam forming.