Conclusions

Schroeder's diffusers proved to be very successful, and alternate designs as well as its original design have been applied to concert halls to evenly distribute the sound energy to the audience area [Cox and D'AntonioCox and D'Antonio2003]. In this paper, we have implemented a 2-D digital waveguide mesh with Schroeder's diffuser based on quadratic residue sequences, and have simulated its performance. We have shown that the diffusion occurs at the boundary in a mesh where Schroeder's diffuser is implemented, the sound energy is evenly dispersed everywhere after a while. On the other hand, a plain mesh shows more specular reflections, and the sound energy is more concentrated in some regions in a specific pattern. The computational efficiency of the 2-D digital waveguide mesh is largely preserved, since computations along the boundary of an $N\times N$ mesh are $\mathcal{O}(N)$, while the time-update for the entire mesh is $\mathcal{O}(N^2)$. This highly diffusing 2-D digital waveguide mesh may be extended to implement artificial reverberation, or to model a musical instrument's body.