Do-wnsampled Bunch-by-Bunch Feedback for PEP II*

_~ Figure 1: Conceptual diagram of bunch-by-bunch feedback. The phase-of each bunch is detected and a feedback signal particular to that bunch is produced by the filter and is applied via the kicker. _~ The phase is.. dejected, filtered, and the feedback correction signal is applied by the kicker. Since we are damping energy oscillations using measurements of phase, the required feedback signal must be proportional to the amplitude of the phase oscillations but phase shifted by 90 degrees. This signal must be calculated for each of the 1658 bunches, in parallel. In the original proposal, it was estimated that a farm of approximately 480 digital signal process.ors (DSPs) would be required to impJement the feedback system. However, using the technique of downsampling, this number can be reduced to about 50 DSPs. In what follows, we will briefly explain the basic idea of downsampling and its implementation.