Development of modern circular accelerators is nowadays focused on increasing energy and intensity of the beam. For high current operation, the electromagnetic fields self-generated by the beam can become sufficiently strong to cause beam instabilities. In this thesis, new concepts for the damping of coherent transverse instabilities in the heavy ion synchrotron SIS of the GSI at high intensities, e.g. with 2 · 10^11 Ne10+ ions and 4 · 10^10 U73+ are investigated. In particular, a new wide band transverse feedback system (TFS) has been designed, installed and tested. The new concept, based on digital-signal processing, which allows to integrate all required functions on a single chip, is presented. To implement a high-speed digital-signal processing system with variable parameters at a peak data processing rate of 800 MBytes/s, novel methods for data processing in real time are investigated. To cover all working modes, e.g. coasting beam during injection, bunched beam during acceleration and extraction, a programmable variable delay up to 10 µs is designed which includes novel methods for a delay step resolution of 1 ns. Thus, a theoretical description of a transverse feedback system taking into account the influence of its transfer function on a beam, as well as the design and installation of a 12 bits/100MHz automatic digital feedback system are presented.