### Digital Filter Models of Damped Strings

In an efficient digital simulation, lumped loss factors of the form
are approximated by a rational frequency response
. In general, the coefficients of the optimal rational
loss filter are obtained by minimizing
with respect to the filter coefficients or the poles
and zeros of the filter. To avoid introducing frequency-dependent
delay, the loss filter should be a *zero-phase,
finite-impulse-response* (FIR) filter [362].
Restriction to zero phase requires the impulse response
to
be finite in length (*i.e.*, an FIR filter) and it must be symmetric
about time zero, *i.e.*,
. In most implementations,
the zero-phase FIR filter can be converted into a causal, *linear
phase* filter by reducing an adjacent delay line by half of the
impulse-response duration.

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Well Posed PDEs for Modeling Damped Strings