A digital transmit beamformer for an ultrasound system has a waveform sample memory which stores sequences of samples of different pulse transmit waveforms of differing pulse widths. The memory is shared by a plurality of transmit channels, each of which can access its own selected sample sequence, independent of the selections by other channels. Waveform sample readout by the channels occurs substantially simultaneously during a transmit event, producing a transmit beam from a transmit aperture with different pulse waveforms applied to different elements of the transmit aperture. Higher energy waveforms with wider pulse widths are applied to central elements of the aperture and lower energy waveforms with narrower pulse widths are applied to lateral elements of the aperture to produce an apodized transmit beam.