Here we describe the FADC modules for the 5184 channels of the forward tracking detector of the ZEUS experiment at HERA (DESY), which convert the incoming analogue signals on a 104 MHz clock and apply a hardware digital filtering and zero suppression procedure on the acquired data. A module works on 32 input channels, nine boards are grouped in a 9HU crate. On a given trigger, the data are sequentially transferred to an output buffer for final acquisition, passing a 30 MHz digital filter and zero suppression hardware. The module uses a 9 bit signed FIR filter with eight tabs, where the eight filter coefficients are freely programmable. Only signals with two successive filtered values above a certain threshold are stored for output. Due to the filter procedure the data reduction rate is greater than 95%. The system provides a processing power of 600 mops per board for the foreseen application. In addition to the data reduction the main benefit of the filtering process is the significantly improved separation of double signals.