Kibangou, Alain Y.; Favier, Gérard; Hassani, Moha M. Selection of generalized orthonormal bases for second-order Volterra filters. (English) Zbl 1160.94338 Signal Process. 85, No. 12, 2371-2385 (2005). Summary: 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. Cited in 5 Documents MSC: 94A12 Signal theory (characterization, reconstruction, filtering, etc.) Keywords:quadratic Volterra filters; nonlinear systems; generalized orthonormal basis; basis selection; identification PDFBibTeX XMLCite \textit{A. Y. Kibangou} et al., Signal Process. 85, No. 12, 2371--2385 (2005; Zbl 1160.94338) Full Text: DOI