Reflectively Terminated Waveguide Filters

A reflecting termination occurs when the wave impedance of the next section is either zero or infinity (§C.8.1). Since Fig.C.24 is labeled for force waves, an infinite terminating impedance on the right results in

$$f^{{-}}_{i+1}(t+T) \eqsp f^{{+}}_{i+1}(t-T).$$

Similarly, a zero terminating impedance on the right gives

$$f^{{-}}_{i+1}(t+T) \eqsp -f^{{+}}_{i+1}(t-T).$$

For velocity waves, the signs are interchanged. Thus, a reflectively terminated ladder digital waveguide corresponds to a final feedback with gain $\pm 1$ at the end of the ladder. Such a termination will be used below to derive conventional ladder/lattice filters.