Next |
Prev |
Up |
Top
|
Index |
JOS Index |
JOS Pubs |
JOS Home |
Search
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/stress/pressure is scalar.) Equations (G.57),
(G.58), and (G.59) imply the following scattering
equations (a derivation is given in the next section for the more
general case of waveguides meeting at a junction):
where
|
(G.61) |
is called the th reflection coefficient. Since
, we have
. It can be shown that if
, then either or is negative, and this
implies an active (as opposed to passive) medium. Correspondingly,
lattice and ladder recursive digital filters are stable if and
only if all reflection coefficients are bounded by in magnitude
[275].
Figure G.17:
The Kelly-Lochbaum scattering
junction.
|
The scattering equations are illustrated in Figs. G.16b and
G.17. In linear predictive coding of speech [460], 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 [275].
Next |
Prev |
Up |
Top
|
Index |
JOS Index |
JOS Pubs |
JOS Home |
Search
[How to cite and copy this work]