The cross-talk cancellation problem is in a sense the ultimate sound reproduction problem since an efficient cross-talk canceller gives one complete control over the sound field at a number of "target" positions. 

The objective of a cross-talk canceller is to reproduce a desired signal at a single target position while cancelling out the sound perfectly at all remaining target positions. The basic principle of cross-talk cancellation using only two loudspeakers and two target positions has been known for more than 30 years. In 1966, Atal and Schroeder used physical reasoning to determine how a cross-talk canceller comprising only two loudspeakers placed symmetrically in front of a single listener could work. In order to reproduce a short pulse at the left ear only, the left loudspeaker first emits a positive pulse. This pulse must be cancelled at the right ear by a slightly weaker negative pulse emitted by the right loudspeaker. This negative pulse must then be cancelled at the left ear by another even weaker positive pulse emitted by the left loudspeaker, and so on. Atal and Schroeder's model assumes free-field conditions; the influence of the listener's torso, head and outer ears on the incoming sound waves are ignored.

The graphic demonstrates the cross-talk cancellation principle under free-field conditions when the two loudspeakers span 60 degrees as seen by the listener (this corresponds to the loudspeaker setup recommended for listening to conventional stereo material such as pop music). Note that the "zone of cross-talk cancellation" is very small.