An ultrafast 4GSa/s transverse feedback processor has been developed for proof-of-concept studies of feedback control of e-cloud driven and transverse mode coupled intra-bunch instabilities in the CERN SPS. This system consists of a high-speed ADC on the front end and equally fast DAC on the back end. All control and signal processing is implemented in FPGA logic. This system is capable of taking up to 16 sample slices across a single SPS bunch and processing each slice individually within a reconfigurable signal processor. This demonstrator system is a rapidly developed prototype, consisting of both commercial and custom-design components. It can stabilize the motion of a single particle bunch using closed loop feedback. The system can also run open loop as a high-speed arbitrary waveform generator and contains diagnostic features including a special ADC snapshot capture memory. This paper describes the overall system, the feedback processor and focuses on the hardware architecture, design and implementation. Show Partial Abstract