Topic
Volterra series
About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.
Papers published on a yearly basis
Papers
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TL;DR: In this article, an adaptive second-order Volterra delay filter (ASOVDF) is proposed to model second-Order Volterras with a symmetric distribution, which is based on a stage-by-stage modeling process, where a dominant delay element is determined, the corresponding adaptive filter coefficient is incorporated to the adaptive filter coefficients from previous stages, and then these filter coefficients are adapted via the recursive least-squares algorithm.
Abstract: This paper proposes a simple technique for modeling second-order Volterra systems using an adaptive second-order Volterra delay filter (ASOVDF). The developed filter structure essentially extends an adaptive FIR delay filter to include linear and quadratic filter coefficients with an input assumed to be a zero-mean i.i.d. sequence with a symmetric distribution. The implementation of the ASOVDF is based on a stage-by-stage modeling process. At each stage, a dominant delay element is determined, the corresponding adaptive filter coefficient is incorporated to the adaptive filter coefficients from previous stages, and then these filter coefficients are adapted via the recursive least-squares algorithm. The ASOVDF requires few filter coefficients and has better performance and less computational complexity over the conventional adaptive second-order Volterra filter (ASOVF) in modeling second-order Volterra systems with sparse kernels.
18 citations
TL;DR: This paper addresses the issue of nonlinear model estimation for neural systems with arbitrary point-process inputs using a novel network that is composed of a pre-processing stage of a Laguerre filter bank followed by a single hidden layer with polynomial activation functions.
18 citations
TL;DR: This paper presents long-term nonlinear prediction based on second-order Volterra filters that can outperform conventional linear prediction techniques in terms of prediction gain and “whiter” residuals.
Abstract: Previous studies of nonlinear prediction of speech have been mostly focused on short-term prediction. This paper presents long-term nonlinear prediction based on second-order Volterra filters. It will be shown that the presented predictor can outperform conventional linear prediction techniques in terms of prediction gain and “whiter” residuals.
18 citations
01 Jun 2016
TL;DR: A stabilization scheme for nonlinear control systems whose vector fields satisfy Hormander's condition with the second-order Lie brackets is proposed, based on the use of trigonometric controls with bounded frequencies and a modification of Lyapunov's direct method.
Abstract: In this paper, we propose a stabilization scheme for nonlinear control systems whose vector fields satisfy Hormander's condition with the second-order Lie brackets. This scheme is based on the use of trigonometric controls with bounded frequencies. By using the Volterra series and a modification of Lyapunov's direct method, we reduce the stabilization problem to a system of cubic equations and prove its local solvability. Our approach ensures exponential stability of the equilibrium and gives explicit formulas for the coefficients of the control functions. The proposed methodology is illustrated by a rolling disc example.
18 citations