FDNs as Digital Waveguide Networks

This section supplements §1.7 on Feedback Delay Networks in the context of digital waveguide theory. Specifically, we review the interpretation of an FDN as a special case of a digital waveguide network, summarizing [435,436,359].

Figure G.29 illustrates an $N$-branch DWN. It consists of a single scattering junction, indicated by a white circle, to which $N$ branches are connected. The far end of each branch is terminated by an ideal non-inverting reflection (black circle). The waves traveling into the junction are associated with the FDN delay line outputs $x_i(n-M_i)$, and the length of each waveguide is half the length of the corresponding FDN delay line $M_i$ (since a traveling wave must traverse the branch twice to complete a round trip from the junction to the termination and back). When $M_i$ is odd, we may replace the reflecting termination by a unit-sample delay.

Figure G.29: Waveguide network consisting of a single scattering junction, indicated by an open circle, to which $N$ branches are connected. The far end of each branch is terminated by an ideal, non-inverting reflection.