Next |
Prev |
Up |
Top
|
Index |
JOS Index |
JOS Pubs |
JOS Home |
Search
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
as the impulse response
corresponding to
. We may now derive the frequency-dependent
counterpart of Eq.(C.31) as follows:
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
by the
per-sample propagation filter
. For computational efficiency,
two spatial lines should be stored in memory at time
:
and
, for all
. These state variables enable computation of
, after which each sample of
(
) is filtered
by
to produce
for the next iteration, and
is filtered by
to produce
for the next iteration.
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.
Next |
Prev |
Up |
Top
|
Index |
JOS Index |
JOS Pubs |
JOS Home |
Search
[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]