Efficient Computation of Bilinear Approximations and Volterra Models of Nonlinear Systems

Bilinear and Volterra models are important when dealing with nonlinear systems which arise in several signal processing applications. The former can approximate a large class of systems affine in the input with relatively low parametric complexity. Such an approximate bilinear model can be derived by means of Carleman bilinearization (CB). Then, a Volterra model can be computed from it, having the advantage of being linear in the parameters, but often involving a large number of them. In this paper, we develop efficient routines for CB and for computing the Volterra kernels of a bilinear system. We argue that they are useful for studying a class of systems for which a reference physical model is known. In particular, the so-derived kernels allow assessing the suitability of a Volterra filter and of other alternatives for modeling the system of interest. Techniques exploiting sparsity and low rank of involved matrices are proposed for alleviating computing cost. Several examples are given along the paper to illustrate their use, based on existing physical models of loudspeakers.