Kelly-Lochbaum Scattering Junctions

Conservation of energy and mass dictate that, at the impedance
discontinuity, force and velocity variables must be *continuous*

where velocity is defined as positive to the right on both sides of the junction. Force (or stress or pressure) is a scalar while velocity is a vector with both a magnitude and direction (in this case only left or right). Equations (C.57), (C.58), and (C.59) imply the following

where

is called the th

The scattering equations are illustrated in Figs. C.19b and
C.20. In linear predictive coding of speech [485], this
structure is called the *Kelly-Lochbaum scattering junction*, and
it is one of several types of scattering junction used to implement
*lattice* and *ladder* digital filter structures
(§C.9.4,[299]).

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