### One-Multiply Scattering Junctions

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

where

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