Wave Digital Elements

In summary, our chosen digital element reflectances
(and their connecting wave impedances $R_0$ ) are

• ``Wave digital mass'' (interface impedance $R_0=mc$ )
  $$\fbox{$\displaystyle \tilde{S}_m(z) = - z^{-1}$} \quad\mbox{(mass reflectance)}$$

• ``Wave digital spring'' ($R_0=k/c$ )
  $$\fbox{$\displaystyle \tilde{S}_k(z) = z^{-1}$} \quad\mbox{(spring reflectance)}$$

• ``Wave digital dashpot'' ($R_0=\mu$ )
  $$\fbox{$\displaystyle \tilde{S}(z) = 0$} \quad\mbox{(dashpot [non-]reflectance)}$$
  (In this case, the interface is the element itself.)

These are the discrete-time reflectances of the basic circuit building-blocks as seen from their interface-waveguides

We still have the usual freedom in choosing our bilinear-transform frequency-scaling constant $c$