Suppose that you have a signal source, a set of point-transducers, and a handful of moderately powerful DSPs. Is it possible to construct an arrangement of the transducers such that the original signal propagates within a given region, but is absent or significantly attenuated outside of that region?
The obvious application would be sound systems that don't leak loud sound into neighboring rooms. But this would also be useful for limiting RF propagation to a physical space. In the audio example, you can shield the room with sound-absorbing materials. You could also build a faraday cage for the RF case, but either physical solution is likely to be prohibitively expensive. Now that powerful DSPs are cheap, can this be done entirely in the signal domain?