  As previously shown, the direct extension of the impulse invariance principle
to Volterra kernels has to be modified in order to provide a condition for the
exact modeling of mixed-signal chains. At first sight this would seem to
seriously complicate the otherwise simple discrete-time realization of
separable kernels (among which bilinear kernels are of particular importance).
We show here, however, that this not the case. By defining a cascade operator,
the structure of a generalized impulse invariance can be unveiled, leading to a
realization without an inordinate increase in computational complexity.

Signal Processing