On the Realization of Impulse Invariant Bilinear Volterra Kernels

TL;DR

This paper presents a method to realize impulse invariant bilinear Volterra kernels efficiently, addressing previous complexities and enabling accurate modeling of mixed-signal chains with manageable computational effort.

Contribution

It introduces a cascade operator that simplifies the realization of impulse invariant bilinear Volterra kernels, making the process more practical and less computationally demanding.

Findings

Realization of bilinear Volterra kernels is feasible without high complexity.

A cascade operator enables generalized impulse invariance.

The method improves modeling accuracy for mixed-signal systems.

Abstract

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.