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Summary of Wave Digital Elements

From Eq.$ \,$ (F.1), we have that the general reflectance of impedance $ R(s)$ with respect to the reference impedance $ R_0$ in the wave variable formulation is given by

$\displaystyle \fbox{$\displaystyle \hat{\rho}(s) \isdef \frac{R(s)-R_0}{R(s)+R_0}$} \protect$ (F.13)

In WDF construction, the free constant in the bilinear transform is taken to be $ c=1$ . Thus we obtain $ \hat{\rho}_d(z) = \hat{\rho}[(1-z^{-1})/(1+z^{-1})]$ . When $ R(s)$ is first order, it is possible to choose the reference impedance $ R_0$ so as to eliminate the delay-free path in the digital reflectance $ \hat{\rho}_d(z)$ , and so its value depends on the actual physical element being digitized.


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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