The maximum beam particle intensity and minimum emittance that can be injected, accelerated and stored in high-brightness lepton as well as high-energy hadron accelerators is fundamentally limited by self-amplifying beam instabilities, intrinsic to unavoidable imperfections in accelerators. Traditionally, intra-bunch or head-tail particle motion has been measured using fast digitizers, with even using state-of-the-art technology being limited in their effective intra-bunch position resolution to few tens of um in the multi-GHz regime. To improve on the present signal processing, a multiband-instability-monitor (MIM) prototype system has been designed, constructed and tested at the CERN Super-Proton-Synchrotron (SPS) and Large Hadron Collider (LHC). The system splits the signal into multiple equallyspaced narrowfrequency bands that are processed and analysed in parallel. Working with narrow-band signals permits the use of much higher resolution analogue-to-digitalconverters that can be used to resolve nm-scale particlemotion already during the onset of instabilities.