Adaptors for Wave Digital Elements

An adaptor is an -port memoryless interface which interconnects wave digital elements. Since each element's ``port'' is a connection to an infinitesimal waveguide section at some real wave impedance , and since the input/output signals are wave variables (traveling-waves within the waveguide), the adaptor must implement signal scattering appropriate for the connection of such waveguides. In other words, an -port adaptor in a wave digital filter performs exactly the same computation as an -port scattering junction in a digital waveguide network.^Q.2

This section first addresses the simpler two-port case, followed by a derivation of the general -port adaptor, for both parallel and series connections of wave digital elements.

As discussed in §L.2, a physical connection of two or more ports can either be in parallel (forces are equal and the velocities sum to zero) or in series (velocities equal and forces sum to zero). Combinations of parallel and series connections are also of course possible.

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Subsections

• Two-Port Parallel Adaptor for Force Waves
  • Compatible Port Connections
  
  
• General Parallel Adaptor for Force Waves
  • Alpha Parameters
  • Reflection Coefficient, Parallel Case
  • Physical Derivation of Reflection Coefficient
  • Reflection Free Port
  
  
• Two-Port Series Adaptor for Force Waves
• General Series Adaptor for Force Waves
  • Beta Parameters
  • Reflection Coefficient, Series Case
  • Physical Derivation of Series Reflection Coefficient
  • Series Reflection Free Port

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.