FDNs as Digital Waveguide Networks

As discussed in §G.13, the FDN using a Householder-reflection feedback matrix $\mathbf{A}_N = \mathbf{I}_N - (2/N)\underline{u}\underline{u}^T$ is equivalent to a network of $N$ digital waveguides intersecting at a single scattering junction [435,436,359]. The wave impedance in the $i$th waveguide is simply $\underline{u}[i]$, the $i$th element of the axis-of-reflection vector $\underline{u}$. The choice $\underline{u}^T=[1,1,\dots,1]$ corresponds to all of the waveguides having the same impedance (the ``isotrophic junction'' case).