Sign in

username:

password:



Not a member?

Search Online Books



Search tips

Free Online Books

Chapters

Chapter Contents:

Search Physical Audio Signal Processing

  

Book Index | Global Index


Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?

  

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.Q.4.

Figure Q.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.


Order a Hardcopy of Physical Audio Signal Processing

Previous: Wave Digital Spring
Next: Limiting Cases

written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


Comments


No comments yet for this page


Add a Comment
You need to login before you can post a comment (best way to prevent spam). ( Not a member? )