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Wave-Field Synthesis
I started working on WFS in 2001, by means of a research project funded by my University to support young researchers. Since then, some people joint the team, and together we have achieved interesting results, including a lot of full functional prototypes developed entirely (software and hardware) by us. We are the pioneer of WFS in Spain and actually the most active research group in Spain both in WFS and in spatial sound. We have the biggest WFS array in the nation and one of the biggest in Europe. Now, we are working hard in this topic my means of other funded projects and many PhD students.
WFS fundamentals
In the late 80s, the Wave Field Synthesis (WFS) concept was introduced by the Technical University of Delft. The origin of this theory was in 1987 when Berkhout published the book "Applied Seismic Wave theory" and "A holographic approach to acoustic control" in 1988. Here, he suggested "acoustical holography", not yet called WFS, to be the ultimate tool for acoustical control systems in theatres. Berkhout introduced the physical basis of WFS by applying algorithms known from seismics to the field of acoustics. The basic work on WFS was continued in "Wave front synthesis: a new direction in electro-acoustics" and "Acoustic control by wave field synthesis".
The key point of WFS with respect to conventional techniques, is its capability of providing a realistic localization of virtual sources. To be concret, WFS is able to:
- Sinthesize virtual sources that are perceived on the same position throughout the entire listening area, both behind the loudspeaker (virtual source) and inside the listening area (focused source).
- Sinthesize plane waves that are perceived in the same direction throughout the entire listening area.
- Enhance the sense of presence and envelopment through a realistic reproduction of the amplitude distribution of a virtual source.
All these features are valid to a number of listeners inside the audition area. When a given listener is approaching the location of a virtual source the amplitude increases in a realistic way. Accordingly, the amplitude of a plane wave changes least on different listener positions since they come from an infinite position.
As a consequence, each listener experiences the sound scene created by WFS while moving around within the listening area. Moreover, it has been shown that the enhanced resolution of the localization compared with stereophony enables the listener to easily distinguish between different virtual sources, which makes the sound scene significantly more transparent.
However, the theoretical continuous source distribution is discretized in practice, which causes a limited spatial resolution. As a consequence, the wave field is correctly synthesized up to a limiting frequency, known as aliasing frequency. Moreover, when a loudspeaker array, which has a limited lenght, is used to reproduce a WFS scene, another drawback arises. These two are the main constraints in the practical implementation of WFS.
1. Spatial aliasing.
The discretization of the integral that describes the a theoretical continuous line of sources results in spatial aliasing due to spatial sampling. The cut-off frequency is given by where theta_max denotes the maximum angle of incidence of the synthesized wave field relative to the loudspeaker array. If a practical loudspeaker spacing is set to 18 cm, the minimum spatial aliasing frequency is about 1 kHz, which demonstrates that spatial aliasing seems to be a problem for practical WFS systems.
2. Truncation effects.
These effects are caused by wavefronts which propagate from the ends of the loudspeaker array. They can be understood as diffraction waves caused by the finite number of loudspeakers in practical implementations.
Prototypes
At this moment we have developed 4 prototypes: two prototypes using dynamic cone loudspeakers (32 & 96 elements), and two prototypes using DML panels (MAP’s) of two different panel sizes. The prototypes have been designed and build entirely by us, starting from the transducers and designing boxes, wiring, etc.Array of 96 loudspeakers
This array is made using conventional cone loudspeakers. A permanent installation (the 96 loudspeaker array) is set-up at the audio laboratory at iTeAM, used daily for research, experimental music production and different demos.
A PC is used to compute the excitation signals in real time. Four MOTU 24IO audio cards of 24 channels each one are used to generate the analog signals. Signals are amplified to excite the loudspeakers.
The array is composed of 12 panels of 8 loudspeakers each one, dx=18cm. This way, it can be adapted to different room shapes. This is the shape in our test room:
Arrays of Multiexcited DML Panels (MAP)
Built entirely by us in order to have flexibility to select materials, distances, clamps and other parameters. The panel used, presents an outer skin thermoplastic material to a polycarbonate inner honeycomb core. The panel bending stiffness is 16.4 and 16 Nm in the x and y directions and has a density of 0.89 Kg/m2.
We built too arrangements of 15 exciters each: one using big panels comprising 5 exciters per panel, and other of small panels with 3 exciters per panel, both with dx =18 cm.
