We present the architecture and implementation overview of a proof-of-principle digital signal processing system developed to study control of Electron-Cloud and Transverse Mode Coupling Instabilities (TMCI) in the CERN SPS. This system is motivated by intensity increases planned as part of the High Luminosity LHC upgrade. It is based on a reconfigurable processing architecture which samples intra-bunch motion and applies correction signals at a 4GSa/s rate, allowing multiple samples across a single 3.2ns SPS bunch. This initial demonstration system is a rapidly developed prototype consisting of both commercial and custom designed hardware that implements feedback control on a single bunch. It contains a high speed ADC and DAC, capable of sampling at up to 4GSa/s, with a 16-tap FIR control filter for each bunch sample slice. Other system features include a timing subsystem to synchronize the sampling to the injection and the bunch 1 markers, the capability of generating arbitrary time domain signals to drive the bunch and diagnostic functions including a snapshot memory for ADC data. This paper describes the design, construction and operational experience of this system. Show Partial Abstract