An ultrasound beamformer that processes the signals of an array transducer includes a plurality of processing channels, one for each element of the active transducer array. Each channel includes a digitizing element for converting the received signal into digital samples and a delay element for delaying the digitized signal. The delays are chosen so that when the signals from the individual channels are combined, a beam forms in a particular direction. The invention implements sub-sampling period delays in the individual channels with low-complexity digital filters having superior delay characteristics with respect to frequency, but having undesirable attenuation characteristics with respect to frequency. The invention corrects for the undesirable attenuation characteristics via a single digital filter after the signals from the individual channels have been combined.