A beamforming system that can be used for both receive and transmit beamforming is provided. The system receives samples of a number of signals, each sample containing a band of frequencies and routes all sampled signals associated with the same beamformed frequency band to a predetermined processing block. A predetermined number of the routed sampled signals are selected sequentially according to predetermined criteria, weighted and accumulated to form a composite signal. Individual signals are then selected from the composite signal and routed to an appropriate output. The system uses a much smaller number of weighting functions than conventionally required, with processing for a single frequency being performed in the same processing block. This reduces the complexity of beamforming processing substantially and simplifies frequency reuse. In addition a single DSP design that works for both transmit and receive beamforming can be implemented.