Topic
Volterra series
About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.
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01 Apr 1998
TL;DR: In this article, a recursive least-squares adaptive nonlinear equaliser based on Volterra series expansion is presented. But the main approach is to transform the non-linear equalization problem into an equivalent multichannel, but linear, equalisation problem.
Abstract: The authors present a new recursive least-squares adaptive nonlinear equaliser based on Volterra series expansion. The main approach is to transform the nonlinear equalisation problem into an equivalent multichannel, but linear, equalisation problem. Then the multichannel input signal is completely orthogonalised using sequential processing multichannel lattice stages. With the complete orthogonalisation of the input signal, only scalar operations are required, instability problems owing to matrix inversion are avoided, and good numerical properties are achieved. Avoidance of matrix inversion and vector operations reduce the complexity considerably, and make the filter highly modular and suitable for VLSI implementation. Several experiments demonstrating the performance under different channel distortion and channel noise conditions are also included in the paper.
16 citations
TL;DR: In this article, an analytical expression about the bispectrum calculation for nonlinear systems subjected to zero mean Gaussian excitation was derived, and based on the expression, an explicit relationship was established as a polynomial function between the nonlinear characteristic parameters, which greatly facilitates the analysis of how the former affects the latter.
16 citations
TL;DR: A modification to the standard cross-correlation method is proposed which improves the estimation of the diagonal elements of the kernels of Volterra and Wiener nonlinear functional series.
Abstract: Cross-correlation techniques have been used for years to identify the kernels of Volterra and Wiener nonlinear functional series. This note proposes a modification to the standard cross-correlation method which improves the estimation of the diagonal elements of the kernels. The mathematical derivation is given and simulations are presented, which show that modification improves the kernel estimates with very little increase in computational cost.
16 citations
TL;DR: The conclusion is drawn that the so-called Direct Method, which only uses the eigenstructure to characterise the signal subspace, offers the best performance.
16 citations
TL;DR: In this article, necessary and sufficient conditions for a stationary finite Volterra series to have a linear (in the controls) analytic realization, which at the same time has a Hamiltonian structure are given.
Abstract: In this paper we give necessary and sufficient conditions for a stationary finite Volterra series to have a linear (in the controls) analytic realization, which at the same time has a Hamiltonian structure. The result generalizes that for linear systems, where the condition is that the impulse response should be an odd function, and is expressed as a particular symmetry condition on the Volterra kernals. The relation between this problem and that of the inverse problem in Newtonian mechanics is explored. The finiteness of the Volterra series implies a nilpotence condition on a certain Lie algebra defined by the realization. The additional requirement that the system be Hamiltonian adds further structure to the classical representation of a nilpotent Lie algebra by lower triangular matrices.
16 citations