Super-directional loudspeaker arrays can be used to achieve high directivity in a limited low-frequency range. As opposed to microphone arrays, the distance between the loudspeakers has to be relatively large, resulting in aliasing starting at relatively low frequencies. On the other hand, mounting a loudspeaker on a rigid baffle (e.g., a rigid cylinder or sphere) increases its directivity with frequency. Using super-directional array techniques at low frequencies and leveraging loudspeakers' increased directivity at high frequencies enables achieving high directivity both at low and high frequencies. The design of baffled circular loudspeaker arrays and an improved beamforming procedure for achieving high directivity in a broad frequency range is described.