Piecewise Volterra filters based on the threshold decomposition operator

We report our results concerning the study of multivariate functions of threshold-decomposed signals. In particular we show that multilinear tensor forms of the decomposed signal yield a class of filters that we propose to call piecewise Volterra filters (PWV). A filter can be viewed as a transformation of ℛ^N→ℛ, where N is the number of filter taps. PWV filters partition ℛ^N using a hyper-rectangular lattice, and assign a Volterra filter to each of the partition regions. At the partition boundaries continuity between the multivariate polynomials is preserved resulting in class 𝒞⁰ piecewise polynomials. PWV filters constitute an efficient alternative for describing some systems rich in hard nonlinear structures, especially since parameter estimation remains a linear problem for PWVs