Wave Digital Dashpot
Starting with a dashpot with coefficient , we have
![$\displaystyle R(s) = \mu
$](http://www.dsprelated.com/josimages_new/pasp/img4814.png)
![$\displaystyle \hat{\rho}_\mu(s) = \frac{\mu - R_0}{\mu + R_0}
$](http://www.dsprelated.com/josimages_new/pasp/img4815.png)
![$ R_0$](http://www.dsprelated.com/josimages_new/pasp/img141.png)
![$\displaystyle \hat{\rho}_\mu(s) = 0
$](http://www.dsprelated.com/josimages_new/pasp/img4816.png)
![$\displaystyle \fbox{$\displaystyle \hat{\tilde{\rho}}_\mu(z) = 0$}
$](http://www.dsprelated.com/josimages_new/pasp/img4817.png)
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
. While this may appear overly degenerate at first,
remember that the interface to the element is a port at impedance
. Thus, in this particular case only, the infinitesimal
waveguide interface is the element itself.
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Limiting Cases
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Wave Digital Spring