### 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

 (C.122)

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

 (C.123)

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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