A frequency-domain beamformer is used with arrays comprising M rings with a maximum of N elements per ring, the positions of the elements having rotational symmetry. An element need not be present at each position. The outputs of each of the M rings of arrays are connected to the inputs of M sets of lowpass filters, each set comprising N filters. Each filter output is an input to a sample-and-hold circuit.A temporal discrete Fourier transform (DFT) is performed on the output signal from each sample-and-hold circuit. M demultiplexers, one for each of the M sets of DFT circuits, convert their parallel input signals into serial output signals.A memory, or function generator, is used for steering. A circular convolver convolves the outputs of the demultiplexers and the memories, the outputs of the convolvers being summed in an output summer.The beamformer is used with a 3-D array such that it has rotational symmetry, that is, if rotated at some angle, the situation is exactly the same as before the rotation.