Fermilab Booster has two transverse dampers which independently suppress beam instabilities in the horizontal and vertical planes. A suppression of the common mode signal is achieved by digital notch filter which is based on subtracting beam positions for two consecutive turns. Such system operates well if the orbit position changes sufficiently slow. Unfortunately it is not the case for FNAL Booster where the entire accelerating cycle consists of about 20000 turns, and successful transition crossing requires the orbit drifts up to about 10 [mu]m/turn, resulting in excessive power, power amplifier saturation and loss of stability. To suppress this effect we suggest an improvement of the digital filter which can take into account fast orbit changes by using bunch positions of a few previous turns. To take into account the orbit change up toN-th order polynomial in time the system requires (N + 3) turns of "prehistory". In the case of sufficiently small gain the damping rate and the optimal digital filter coefficients are obtained analytically. Numerical simulations verify analytical theory for the small gain and predict a system performance with gain increase.

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