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.