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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TL;DR: A new approach to causal functionals is presented, which parallels the algebraic approach with formal power series in noncommutative variables developed by Fliess, Lamnabhi and LamNabhi-Lagarrigue, and makes use of certain combinatorial objects called weighted increasing trees, weighted paths and histories.
14 citations
01 Jan 2018
TL;DR: The nonlinear modeling approach using a truncated Volterra series with regularization, provides a quantitative way of investigating the sensorimotor system, offering insight into the underlying physiology.
Abstract: Joint manipulation elicits a response from the sensors in the periphery which, via the spinal cord, arrives in the cortex. The average evoked cortical response recorded using electroencephalography was shown to be highly nonlinear; a linear model can only explain 10% of the variance of the evoked response, and over 80% of the response is generated by nonlinear behavior. The goal of this paper is to obtain a nonparametric nonlinear dynamic model, which can consistently explain the recorded cortical response requiring little a priori assumptions about model structure. Wrist joint manipulation was applied in ten healthy participants during which their cortical activity was recorded and modeled using a truncated Volterra series. The obtained models could explain 46% of the variance of the evoked cortical response, thereby demonstrating the relevance of nonlinear modeling. The high similarity of the obtained models across participants indicates that the models reveal common characteristics of the underlying system. The models show predominantly high-pass behavior, which suggests that velocity-related information originating from the muscle spindles governs the cortical response. In conclusion, the nonlinear modeling approach using a truncated Volterra series with regularization, provides a quantitative way of investigating the sensorimotor system, offering insight into the underlying physiology.
14 citations
TL;DR: In this paper, a numerically stable linear estimation algorithm is used to determine a third order Volterra model for a free gas bubble with a resting radius r 0 = 1 μ m.
14 citations
TL;DR: The discrete Volterra kernels associated with the input-output map of a non-linear analytic discrete-lime system, initialized at an equilibrium point, are shown to possess a separability property.
Abstract: It is shown that a separability property of a given finite family of stationary kernels turns out to be necessary and sufficient for the realization of the associated functional by means of a polynomial affine system (i.e. a system that is polynomial in the input and affine in the state). Moreover, the discrete Volterra kernels associated with the input-output map of a non-linear analytic discrete-lime system, initialized at an equilibrium point, are shown to possess a separability property. On this basis, we state an approximation result for the given input-output map by considering the first kernels of the discrete Volterra series. Two explicit constructions of the approximating polynomial affine systems are proposed.
14 citations
TL;DR: A new algorithm for determining the output frequency range and the frequency components of Volterra models under multiple inputs is introduced for nonlinear system analysis.
Abstract: A new algorithm for determining the output frequency range and the frequency components of Volterra models under multiple inputs is introduced for nonlinear system analysis. For a given Volterra model, the output frequency components corresponding to a multi-tone input can easily be calculated using the new algorithm.
14 citations