Interpretation of the Time-Domain KW Converter

As shown above, driving a single displacement sample $y_{n,m}$ in the FDTD corresponds to driving a velocity input at position $m$ on two alternating subgrids over time. Therefore, the filter $H(z)=1-z^{-2}$ acts as the filter $H(z)=1-z^{-1}$ on either subgrid alone--a first-order difference. Since displacement is being simulated, velocity inputs must be numerically integrated. The first-order difference can be seen as canceling this integration, thereby converting a velocity input to a displacement input, as in Eq.$\,$(O.23).