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Digital Waveguide Networks

Digital waveguide networks provide a useful paradigm for sound synthesis based on physical modeling [29]. They have also been proposed for constructing arbitrarily complex digital reverberators [26] which are free of limit cycles and overflow oscillations if passive arithmetic is used [27]. In this section we explore the relationships between DWNs and FDNs.

Fig. Fig. 2 illustrates an $N$-branch DWN which is structurally equivalent to the feedback loop of an $N$-th order FDN. 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 $s_i(n)$, 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: 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.eps}



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``Circulant and Elliptic Feedback Delay Networks for Artificial Reverberation'', by Davide Rocchesso and Julius O. Smith III, preprint of version in IEEE Transactions on Speech and Audio, vol. 5, no. 1, pp. 51-60, Jan. 1996.

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Copyright © 2005-03-10 by Davide Rocchesso and Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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