### Normalized Scattering

For ideal numerical scaling in the sense, we may choose to propagate
*normalized waves* which lead to normalized scattering junctions
analogous to those encountered in normalized ladder filters [297].
Normalized waves may be either normalized pressure
or normalized velocity
. Since the signal power associated with a traveling
wave is simply
,
they may also be called *root-power waves* [432].
Appendix C develops this topic in more detail.

The scattering matrix for normalized pressure waves is given by

The normalized scattering matrix can be expressed as a negative Householder reflection

where , and is the wave admittance in the th waveguide branch. To eliminate the sign inversion, the reflections at the far end of each waveguide can be chosen as -1 instead of 1. The geometric interpretation of (C.124) is that the incoming pressure waves are reflected about the vector . Unnormalized scattering junctions can be expressed in the form of an ``oblique'' Householder reflection , where and .

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Lossless Scattering