#### Frequency-Dependent Losses

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

*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

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.

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