### One-Multiply Scattering Junctions

By factoring out in each equation of (C.60), we can write

 (C.62)

where

 (C.63)

Thus, only one multiplication is actually necessary to compute the transmitted and reflected waves from the incoming waves in the Kelly-Lochbaum junction. This computation is shown in Fig.C.21, and it is known as the one-multiply scattering junction [297].

Another one-multiply form is obtained by organizing (C.60) as

 (C.64)

where
 (C.65)

As in the previous case, only one multiplication and three additions are required per junction. This one-multiply form generalizes more readily to junctions of more than two waveguides, as we'll see in a later section.

A scattering junction well known in the LPC speech literature but not described here is the so-called two-multiply junction [297] (requiring also two additions). This omission is because the two-multiply junction is not valid as a general, local, physical modeling building block. Its derivation is tied to the reflectively terminated, cascade waveguide chain. In cases where it applies, however, it can be the implementation of choice; for example, in DSP chips having a fast multiply-add instruction, it may be possible to implement the inner loop of the two-multiply, two-add scattering junction using only two instructions.

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Normalized Scattering Junctions
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Kelly-Lochbaum Scattering Junctions