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The digital waveguide mesh models multidimensional wave propagation in discrete space and time. The finite difference wave equation used in the mesh is expressed in the space-time domain, which is not straightforward to reveal the analytical expression for the impulse response between a source and a receiver. This letter describes a procedure to derive an analytical impulse response expression between two nodes in a 2-D rectangular digital waveguide mesh based on the wave equation. The analytical expression can provide helpful insights and help verify simulation results for the digital waveguide mesh.