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At the junction between the th and th tubes, the continuity relations (1.5), when multiplied together, imply that

This is simply a statement of *conservation of power* at the interface. Using the definitions of traveling wave variables from (1.6), we then have that

or, rearranging terms,

In other words, the sum of the squares of the *incident waves*, weighted by their respective tube admittances, is equal to the same weighted square sum of the *reflected* waves. Assuming that the are positive, then, a weighted measure of the signal variables (pressure waves) is preserved through the scattering operation. This reflects the inherent *losslessness* of the tube interface.
In terms of the power-normalized variables defined by (1.9), and scattered according to (1.10), we will have (due to the orthogonality of the scattering matrix),

Thus the norms of the incident and reflected vectors of power-normalized wave variables are the same.

** Next:** Discrete-time Vocal Tract Model
** Up:** Case Study: The Kelly-Lochbaum
** Previous:** Junctions Between Two Uniform
Stefan Bilbao
2002-01-22