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

$$\fbox{$\displaystyle \hat{\rho}(s) \isdef \frac{R(s)-R_0}{R(s)+R_0}$} \protect$$ (F.10)

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.