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FDNs as Digital Waveguide Networks

As discussed in §C.15, 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 [463,464,385]. 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).

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