This section supplements §2.7 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 [465,466,388].
Figure C.38 illustrates an -branch DWN. It consists of a single scattering junction, indicated by a white circle, to which 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 , and the length of each waveguide is half the length of the corresponding FDN delay line (since a traveling wave must traverse the branch twice to complete a round trip from the junction to the termination and back). When is odd, we may replace the reflecting termination by a unit-sample delay.