Fettweis [42] defines the *instantaneous pseudopower* absorbed by a port with port resistance (real) at time step in terms of the discrete input and output wave quantities as

which, when the transformation (2.14) is inverted, gives

This discrete power definition coincides with the standard definition of power in classical network theory from (2.2), aside from the factor of 4, which is of no consequence if definition (2.18) is applied consistently throughout a wave digital network.

For a real LTI -port, in an exponential state of complex frequency , the steady-state average pseudopower may be written in terms of the vectors
and
which contain the power-normalized complex amplitudes
and
, for
as

The steady-state reflectance is defined by

and gives

where is the identity matrix. For

is sometimes called a

where is the diagonal square root of the matrix containing the port resistances on its diagonal. We then have

for the voltage wave scattering matrix and thus we require

for passivity. For one-ports, the requirements (2.20) and (2.19) are the same.

Also note that we have, by applying the power wave variable definitions (2.16), and the discrete impedance relation (which is identical to the analog relation from (2.1), except that we now have ), that

If the -port is not LTI, then it is possible to apply a similar idea to the expression for the instantaneous pseudopower, from (2.18) in order to derive a passivity condition [46]; In this case, pseudopassivity has also been called *incremental pseudopassivity* [125].