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FDNs as Digital Waveguide Networks

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.36 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 C.36: 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.
\includegraphics[scale=0.5]{eps/DWN}



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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2015-05-22 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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