Sectionwise piecewise polynomial functions: Applications to the analysis and synthesis of nonlinear n- port networks

This paper presents a general technique for representing nonlinear multidimensional functions using a closed form analytical characterization. This technique is a generalization of sectionwise piecewise-linear (PL) representations and allows the degree of smoothness for the representation of a given function to be selected. The new sectionwise polynomial-wise functions are global representations and may be expressed in closed analytic form, allowing mathematical operations and manipulations to be carried out in theoretical studies. Potential applications of this new representation to the modeling, analysis and synthesis of nonlinear devices and circuits are considered in the text.