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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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Proceedings ArticleDOI
01 May 1982
TL;DR: This paper deals with a class of nonlinear, time-invariant systems with memory based on the truncation of discrete-time Volterra series expansions of input-output relationships, which can be implemented by a finite-length transversal filter, a finite number of multipliers, and a summing bus.
Abstract: This paper deals with a class of nonlinear, time-invariant systems with memory - called discrete Volterra processors - based on the truncation of discrete-time Volterra series expansions of input-output relationships. These systems can be implemented by a finite-length transversal filter, a finite number of multipliers, and a summing bus, and share the interesting property of being described by a linear combination of suitable nonlinear functions of the input samples. Two examples of application are considered in some detail: (i) The design of minimum mean-square error predictors of discrete-time random processes, and (ii) The identification of discrete nonlinear systems with memory.

36 citations

Journal ArticleDOI
TL;DR: In this article, a method to solve weakly non-linear partial differential equations with Volterra series is presented in the context of single-input systems, where the solution x(z,t) is represented as the output of a z-parameterized VOLTERRA system, where z denotes the space variable but z could also have a different meaning or be a vector.
Abstract: A method to solve weakly non-linear partial differential equations with Volterra series is presented in the context of single-input systems. The solution x(z,t) is represented as the output of a z-parameterized Volterra system, where z denotes the space variable, but z could also have a different meaning or be a vector. In place of deriving the kernels from purely algebraic equations as for the standard case of ordinary differential systems, the problem turns into solving linear differential equations. This paper introduces the method on an example: a dissipative Burgers'equation which models the acoustic propagation and accounts for the dominant effects involved in brass musical instruments. The kernels are computed analytically in the Laplace domain. As a new result, writing the Volterra expansion for periodic inputs leads to the analytic resolution of the harmonic balance method which is frequently used in acoustics. Furthermore, the ability of the Volterra system to treat other signals constitutes an improvement for the sound synthesis. It allows the simulation for any regime, including attacks and transients. Numerical simulations are presented and their validity are discussed.

36 citations

Proceedings ArticleDOI
04 Sep 2019
TL;DR: This paper establishes connections between the deep learning and the system identification communities and explores the explicit relationships between the recently proposed temporal convolutional network (TCN) and two classic system identification model structures; Volterra series and block-oriented models.
Abstract: Recent developments within deep learning are relevant for nonlinear system identification problems. In this paper, we establish connections between the deep learning and the system identification communities. It has recently been shown that convolutional architectures are at least as capable as recurrent architectures when it comes to sequence modeling tasks. Inspired by these results we explore the explicit relationships between the recently proposed temporal convolutional network (TCN) and two classic system identification model structures; Volterra series and block-oriented models. We end the paper with an experimental study where we provide results on two real-world problems, the well-known Silverbox dataset and a newer dataset originating from ground vibration experiments on an F-16 fighter aircraft.

36 citations

Journal ArticleDOI
TL;DR: In this paper, the authors extended the time-domain criterion to the frequency domain to accommodate the analysis of nonlinear oscillators subject to harmonic excitation, and used the new frequency domain criterion to predict the onset point of the jump.

36 citations

Journal ArticleDOI
TL;DR: In this paper, the authors established the link between the sensitivity functions and the Volterra kernel functions, which are an expansion of nonlinear impulse response functions and can be extracted directly from the sample estimates of the statistical moments obtained from the time series data.

36 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202315
202246
202146
202057
201983
201881