Wave field synthesis operators for bent line arrays in a 3D space

Using the concept of Wave Field Synthesis (WFS) it is possible to generate acoustical wave fields which have an arbitrarily close resemblance to real wave fields. The acoustical principle of WFS lies in the Kirchhoff-Helmholt z theorem which states that any wave field can be generated by a distributi on of secondary point sources driven by a 3D operator. Since such configura tions are not suitable for practical use, WFS operators have been derived t o synthesize wave fields correctly in a certain (horizontal) plane in a 3D space using only horizontal(bent) line arrays. Two different simplification s can be made, yielding a 2D operator for 1D line arrays consisting of seco ndary point sources, and a 3D operator for 1D line arrays consisting of sec ondary line sources positioned perpendicularly to the array. These practica l and efficient operators form the basis of the WFS solution for many sound control problems. Much attention has been paid to the physical interpretat ion of the operators, which is very difficult or often impossible using oth er simplification methods.