From (5), we have, using (13),

and we have

Thus, the wave impedance is the factor of proportionality between pressure and velocity in a traveling wave. In the cases governed by the ideal wave equation (7), is diagonal if and only if the mass matrix is diagonal (since is assumed diagonal). The minus sign for the left-going wave accounts for the fact that velocities must move to the left to generate pressure to the left. The

A linear propagation medium in the discrete-time case is completely
determined by its *wave impedance*
which, in a
generalized formulation, is frequency dependent and spatially
varying. Examples of such general cases will be given in the sections
that follow. A *waveguide* is defined for purposes of this
paper as a length of medium in which the wave impedance is either
constant with respect to spatial position
, or else it varies
smoothly with
in such a way that there is no scattering (as in
the conical acoustic tube^{}). For simplicity, we will suppress the possible
spatial dependence and write only
, which is intended to be an
function of the complex variable , analytic for .

The generalized version of (20) is

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