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Wave Digital Dashpot

Starting with a dashpot with coefficient $ \mu $, we have

$\displaystyle R(s) = \mu
$

and reflectance

$\displaystyle S_\mu(s) = \frac{\mu - R_0}{\mu + R_0}
$

This time, choosing $ R_0$ equal to the element value gives

$\displaystyle S_\mu(s) = 0
$

Conformally mapping the zero function yields the zero function so that

$\displaystyle \fbox{$\displaystyle \tilde{S}_\mu(z) = 0$}
$

as well. Thus, the WDF of a dashpot is a ``wave sink,'' as diagrammed in Fig. N.4.

Figure N.4: Wave flow diagram for the Wave Digital Dashpot.
\includegraphics{eps/lWaveDigitalDashpot}

In the context of waveguide theory, a zero reflectance corresponds to a matched impedance, i.e., the terminating transmission-line impedance equals the characteristic impedance of the line.

The difference equation for the wave digital dashpot is simply $ f^{{-}}(n)=0$. While this may appear overly degenerate at first, remember that the interface to the element is a port at impedance $ R_0=\mu$. Thus, in this particular case only, the infinitesimal waveguide interface is the element itself.


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[How to cite and copy this work] 
``Physical Audio Signal Processing for Virtual Musical Instruments and Digital Audio Effects'', by Julius O. Smith III, (December 2005 Edition).
Copyright © 2006-07-01 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA  [Automatic-links disclaimer]