The preceding derivation generalizes immediately to
frequency-dependent losses. First imagine each
in Fig.C.7
to be replaced by
, where for passivity we require
In the time domain, we interpret
where
denotes convolution (in the time dimension only).
Define filtered node variables by
Then the frequency-dependent FDTD scheme is simply
We see that generalizing the FDTD scheme to frequency-dependent losses requires a simple filtering of each node variable
The frequency-dependent generalization of the FDTD scheme described in this section extends readily to the digital waveguide mesh. See §C.14.5 for the outline of the derivation.