A two-dimensional grid of intersecting vertical and horizontal digital waveguides is shown in Fig. 1. The junctions, labeled S, are 4-port scattering junctions. The double-arrow lines represent bi-directional unit delay elements.
A two-dimensional waveguide grid pattern.
We can view the grid of Fig. 1 as a lattice of interconnected vibrating strings, in which case the displacements or velocities at the four ports of each junction must be equal and the forces at each junction must sum to zero.
Alternately, we can view the grid of Fig. 1 as a lattice of interconnected acoustic elements, in which case the pressures at the four ports of each junction must be equal and the flows at each junction must sum to zero.