To approximate any time-invariant (nonlinear) system with fading memory, one can use a Volterra series. Volterra series describe the output of a nonlinear system as the sum of the responses of first, second, and higher order operators. It is important to minimize the number of parameters used. Several ways to do this have been employed in the literature. Here, the authors’ approach is to use a generalized orthonormal basis. The complexity reduction depends on the choice of basis or the poles that characterize it. A gradient-type algorithm may converge to a local minimum. Another approach in the literature, advocated by one of the authors, leads to an optimal solution for the Laguerre basis (one of the most frequently used in the literature for linear systems).

This paper extends the authors’ results obtained for the homogeneous case. They suggest expanding the linear and quadratic kernels of a second-order Volterra system on a generalized orthonormal basis. The generalized Fourier coefficients are estimated by orthogonal least squares. The authors also propose eliminating the least significant terms in the kernel expansion, in order to reduce the parametric complexity. An example shows the dependence of the error on the number of terms and the number of poles. It also shows an improved performance as compared to the Laguerre basis. The authors also demonstrate their pruning method.