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Digital Simulation of Stiff Strings
Allpass filters
implement a
frequency-dependent delay
For
stiff strings
, we must generalize
to
where
zero-stiffness
sampling interval
Thus, replace unit delay
by
Each delay element becomes an
allpass
filter
In general,
is
irrational
We approximate
in practice using some
finite-order
fractional delay
digital filter
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Download
WaveEquations.pdf
Download
WaveEquations_2up.pdf
Download
WaveEquations_4up.pdf
``
Distributed Modeling in Discrete Time
'', by
Julius O. Smith III
and
Nelson Lee
,
REALSIMPLE
Project — work supported by the
Wallenberg Global Learning Network
.
Released
2008-06-05
under the
Creative Commons License (Attribution 2.5)
, by
Julius O. Smith
III and Nelson Lee
Center for Computer Research in Music and Acoustics (CCRMA),
Stanford University