Possibilities for transverse feedback phase adjustment by means of digital filters

In transverse feedback systems a phase adjustment is generally required to convert a beam position signal from a pick-up into a momentum correction signal used by a transverse kicker. In this paper we outline several possibilities for phase adjustments using only single pickups or the vector combination of two pick-ups. Analytical expressions are given as a function of the fractional tune and the betatron phase advance between the pick-up location and the kicker. The shortest possible digital filter is formulated, including a notch for closed orbit suppression and a free parameter to adjust for betatron phase. We introduce a novel, fully parametrized digital filter with the feature to be insensitive to variations in fractional tune. Examples are given for the SPS transverse feedback system and compared with measurements.