Silicon micro-ring resonators (MRRs) are compact and versatile devices whose periodic frequency response can be exploited for a wide range of applications. In this paper, we review our recent work on linear alloptical signal processing applications using silicon MRRs as passive filters. We focus on applications such as modulation format conversion, differential phase-shift keying (DPSK) demodulation, modulation speed enhancement of directly modulated lasers (DMLs), and monocycle pulse generation. The possibility to implement polarization diversity circuits, which reduce the polarization dependence of standard silicon MRRs, is illustrated on the particular example of DPSK demodulation.