Wave Digital Dashpot

Starting with a dashpot with coefficient , we have

and reflectance

This time, choosing equal to the element value gives

Conformally mapping the zero function yields the zero function so that

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

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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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.