- The Laplace Transform of the valve displacement:
- The bilinear transform, defined by the substitution

where
yields
where
- The corresponding difference equation is
where
.
``MUS 206: Mechanical Vibration''
by Tamara Smyth,
Department of Music, University of California, San Diego (UCSD).
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Copyright © 2019-11-15 by Tamara Smyth.
Please email errata, comments, and suggestions to Tamara Smyth<trsmyth@ucsd.edu>