4D Wave Field Synthesis

If you surround a listener with a great sphere of loudspeakers at a fixed distance, it should be trivial to produce a virtual source at any direction. What isn't trivial is producing a virtual source at an arbitrary distance, since the loudspeaker positions are fixed at a given distance from the listener. It could be said another way: it is not trivial even for this extravagant set of speakers to reproduce a complete acoustic space, and it does not represent the "ultimate virtual reality audio system." The ultimate audio reproduction system would be a fully 3-dimensional speaker array, where virtual sources could be channeled to discrete sources in a corresponding location.

So we are to emulate this "ultimate" system with what will now be properly seen as a reduced subset of the array: a mere 32 or 96 or perhaps 1024 speakers arranged in a line or plane.

Wave field synthesis is the formal name for the trick that allows us to raise the "order" of the array by one degree. (We exploit time to add an additional spatial dimension.) It is appropriate to say the loudspeaker array is a window into the virtual acoustic scene. A line array of loudspeakers can simulate a source on the plane of intersection with the listener; a plane array of loudspeakers can simulate any source in the space subtended by a cone extending from the listener through the loudspeaker array. This raises the interesting question, can we create a 4-dimensional sound field with a 3-dimensional speaker array, and what would that mean? ...

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