From 1D$+$ to 1D$\pm$

We have been modeling unidirectional traveling waves:

$$\begin{eqnarray*} \mbox{Attenuation per sample} &=& \vert H(e^{j\omega T})\vert\\ [10pt] \mbox{Phase-shift per sample} &=& \angle H(e^{j\omega T}) \end{eqnarray*}$$

Thanks to superposition, we can simulate both directions of propagation in a 1D medium separately and add them only when needed:

(Lossless, Non-Dispersive Case)