Sound focalization by WFS
(Delft University of Technology, 90’s)
Array
Sensible parameters:
The front curvature is obtained by means of a gain-delay set ..
convex
focus
concave
100Hz 3000
Set the beam
width..
Spatial aliasing,
secondary lobes..
Gains
Delays
Common filter
r
13/02/2008
I would like to spend some word on the focalization technique by WFS. The array here represented may be the line one or a section of the disc, non differences since the plotted field is a vertical section od the 3D field.
The array cuses some concave wave fronts, which implode in a focus and then explodes in normal convex wave fronts centered on the focus. So from the point of view of listeners placed below the focus, the focus is a virtual sound source.
The front curvature is achieved with a set of gains and delays, in particular each speaker has an advance in time equal to the fly time which seaparate it from the focus, that is: each speaker signal get to the focus at the same time. This is the formula for the speaker signals, coming from the Rayleigh integral, (for line array)
Sensible parameters of such kind of applicaton are:
The ratio array width on wavelength, which mainly governs the beam and focus width: with wl comparable with the array length the focus will be very wide and the curvature of the fronts will be lost. For wl even greater, the array may loose completely is deirectivity.
The ratio speaker spacing to wl, which rules the phenomenon of spatial alising. Spatial aliasing arises at high frequencies, and in the particular case of focalization can leads to strong side lobes.. It is a good peculiarity of focalization to have the spacial aliasing effect far away from the focus. Hence the phenomenon is bad for the pourpose of spatially limiting the sound, but is not perceived by listeners staying beneath the array. Let’s see the phenomenon alittle it closer in a new slide...