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The Lossy 2D Mesh

Because the finite-difference form of the digital waveguide mesh is the more efficient computationally than explicitly computing scattering wave variables (too see this, count the multiplies required per node), it is of interest to consider the finite-difference form also in the case of frequency-dependent losses. The method of §C.5.5 extends also to the waveguide mesh, which can be shown by generalizing the results of §C.14.4 above using the technique of §C.5.5.

The basic idea is once again that wave propagation during one sampling interval (in time) is associated with linear filtering by $ G(z)$. That is, $ G(z)$ is regarded as the per-sample wave propagation filter.

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2D Mesh and the Wave Equation