### One-Multiply Scattering Junctions

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

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

where

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