FDNs as Digital Waveguide Networks

Householder FDN

$$\mathbf{A}_N = \mathbf{I}_N - \frac{2}{N}\underline{u}\underline{u}^T$$

is equivalent to a network of $N$ digital waveguides intersecting at a single scattering junction:

• Single scattering junction indicated by open circle
• Far end of each waveguide branch is terminated by an ideal reflection (filled circle).
• Wave impedance if $i$ th waveguide = $\underline{u}[i]$
• $\underline{u}^T=[1,1,\dots,1]$ means all waveguides have same impedance (``isotrophic junction'')