Wave field synthesis

Wave field synthesis (WFS) is a spatial audio rendering technique, characterized by creation of virtual acoustic environments. It produces "artificial" wave fronts synthesized by a large number of individually driven speakers. Such wave fronts seem to originate from a virtual starting point, the virtual source or notional source. Contrary to traditional spatialization techniques such as stereo or surround sound, the localization of virtual sources in WFS does not depend on or change with the listener's position.

WFS is based on the Huygens–Fresnel principle, which states that any wave front can be regarded as a superposition of elementary spherical waves. Therefore, any wave front can be synthesized from such elementary waves. In practice, a computer controls a large array of individual loudspeakers and actuates each one at exactly the time when the desired virtual wave front would pass through it.

The basic procedure was developed in 1988 by Professor A.J. Berkhout at the Delft University of Technology. Its mathematical basis is the Kirchhoff-Helmholtz integral. It states that the sound pressure is completely determined within a volume free of sources, if sound pressure and velocity are determined in all points on its surface.

Therefore, any sound field can be reconstructed, if sound pressure and acoustic velocity are restored on all points of the surface of its volume. This approach is the underlying principle of holophony.

For reproduction, the entire surface of the volume would have to be covered with closely spaced monopole and dipole loudspeakers, each individually driven with its own signal. Moreover, the listening area would have to be anechoic, in order to comply with the source-free volume assumption. In practice, this is hardly feasible.

According to Rayleigh II the sound pressure is determined in each point of a half-space, if the sound pressure in each point of its dividing plane is known. Because our acoustic perception is most exact in the horizontal plane, practical approaches generally reduce the problem to a horizontal loudspeaker line, circle or rectangle around the listener.

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