Feedback Delay Networks

Circulant and Elliptic Feedback Delay Networks for Artificial Reverberation

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 -branch DWN which is structurally
equivalent to the feedback loop of an -th order FDN. 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.

- Lossless Scattering
- Normalized Scattering
- Complexity
- Conditions for Losslessness
- Relation of DWNs to FDNs
- Finite-Wordlength Effects

Lossless Scattering

Feedback Delay Networks

Circulant and Elliptic Feedback Delay Networks for Artificial Reverberation

``Circulant and Elliptic Feedback Delay Networks for Artificial Reverberation'', by Davide Rocchesso and Julius O. Smith III, preprint of version in

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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