Selection of generalized orthonormal bases for second-order Volterra filters

Volterra models are very useful for signal and system representation due to their general nonlinear structure and their property of linearity with respect to their parameters, the kernel coefficients. However, when using Volterra models we are confronted with a complexity problem that results from the very large number of parameters required by such models. Expanding the kernels on a generalized orthonormal basis allows to significantly reduce this parametric complexity. In the present paper, a new constructive procedure is described for selecting such a generalized orthonormal basis in the case of second-order Volterra systems. A pruning method is also proposed for eliminating the least significant terms in the kernel expansions.