Digital Waveguide Networks

A Digital Waveguide Network (DWN) consists of any number of digital waveguides interconnected by scattering junctions. For example, when two digital waveguides are connected together at their endpoints, we obtain a two-port scattering junction as shown in Fig.2.33. When three or more waveguides are connected at a point, we obtain a multiport scattering junction, as discussed in §C.12. In other words, a digital waveguide network is formed whenever digital waveguides having arbitrary wave impedances are interconnected. Since DWNs are lossless, they provide a systematic means of building a very large class of MIMO allpass filters.

Consider the following question:

Under what conditions may I feed a signal from one point inside a given allpass filter to some other point (adding them) without altering signal energy at any frequency?

The digital waveguide approach to allpass design [434] answers this question by maintaining a physical interpretation for all delay elements in the system. Allpass filters are made out of lossless digital waveguides arranged in closed, energy conserving networks. See Appendix C for further discussion.