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The Rectilinear 2D Mesh

Figure C.32: The 2D rectilinear digital waveguide mesh.
\includegraphics[width=4in]{eps/SchematicWaveguideMesh}

Figure C.32 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:

$\displaystyle 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

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

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