Summary of Wave Digital Elements

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From Eq. $\,$ (Q.1), we have that the general reflectance of impedance with respect to the reference impedance in the wave variable formulation is given by

$\displaystyle \fbox{$\displaystyle S(s) \isdef \frac{R(s)-R_0}{R(s)+R_0}$} \protect$

(Q.13)

In WDF construction, the free constant in the bilinear transform is taken to be

. Thus we obtain $S_d(z) = S[(1-z^{-1})/(1+z^{-1})]$ . When

is first order, it is possible to choose the reference impedance

so as to eliminate the delay-free path in the digital reflectance

, and so its value depends on the actual physical element being digitized.

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.

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