### Loss Consolidation

In many applications, it is possible to realize vast computational savings
in digital waveguide models by *commuting* losses out of unobserved and
undriven sections of the medium and consolidating them at a minimum number
of points. Because the digital simulation is linear and time invariant
(given constant medium parameters
), and because linear,
time-invariant elements commute, the diagram in Fig.C.6 is
exactly equivalent (to within numerical precision) to the previous diagram
in Fig.C.5.

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Frequency-Dependent Losses

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Relation to the Finite Difference Recursion