The Rectilinear 2D Mesh

Figure G.29: The 2D rectilinear digital waveguide mesh.

Figure G.29 shows the basic layout of the rectilinear 2D waveguide mesh. It can be thought of as simulating a plane using 1D digital waveguides in the same way that a tennis racket acts as a membrane composed of 1D strings.

At each node (string intersection), we have the following simple formula for the node velocity $v$ in terms of the four incoming traveling-wave components:

$$v = \frac{\mbox{in}_{1} + \mbox{in}_{2} + \mbox{in}_{3} + \mbox{in}_{4}}{2}$$

By continuity of velocity in a series connection (all string endpoints must move together at the node), the outgoing velocity-wave components must be given by

$$\hbox{out}_k = v -$$   in$$_{k}, \qquad k=1,2,3,4.$$