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 . 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 . 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 .
General Conditions for Losslessness