Sampling and Reconstruction on a Diamond Grid and the Tetrahedral Digital Waveguide Mesh

It is shown that half of the points on the diamond grid are redundant for sampling and reconstructing a bandlimited 3-D signal. This redundancy is then exploited to show that the tetrahedral digital waveguide mesh requires four times more computational density and twice the memory storage for the same approximation as a finite difference scheme on the face-centered cubic lattice.