The digital waveguide was introduced in §2.4. A basic fact from acoustics is that traveling waves only happen in a uniform medium. For a medium to be uniform, its wave impedance3.17must be constant. When a traveling wave encounters a change in the wave impedance, it will reflect, at least partially. If the reflection is not total, it will also partially transmit into the new impedance. This is called scattering of the traveling wave.
Let denote the constant impedance in some waveguide, such as a stretched steel string or acoustic bore. Then signal scattering is caused by a change in wave impedance from to . We can depict the partial reflection and transmission as shown in Fig.2.33.
That is, the coefficient of reflection for a traveling pressure wave leaving impedance and entering impedance is given by the impedance step over the impedance sum. The reflection coefficient fully characterizes the scattering junction.
Signal scattering is lossless, i.e., wave energy is neither created nor destroyed. An implication of this is that the transmission coefficient for a traveling pressure wave leaving impedance and entering impedance is given by
Digital Waveguide Networks
Gerzon Nested MIMO Allpass