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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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Journal ArticleDOI
TL;DR: In this article, an original approach to the solution of the nonlinear Schrodinger equation (NLSE) following the regular perturbation (RP) method was pursued, and the authors showed that the order n RP solution coincides with the order 2n + 1 Volterra series solution proposed by Brandt-Pearce and co-workers.
Abstract: An original approach to the solution of the nonlinear Schrodinger equation (NLSE) is pursued in this paper, following the regular perturbation (RP) method. Such an iterative method provides a closed-form approximation of the received field and is thus appealing for devising nonlinear equalization/compensation techniques for optical transmission systems operating in the nonlinear regime. It is shown that, when the nonlinearity is due to the Kerr effect alone, the order n RP solution coincides with the order 2n + 1 Volterra series solution proposed by Brandt-Pearce and co-workers. The RP method thus provides a computationally efficient way of evaluating the Volterra kernels, with a complexity comparable to that of the split-step Fourier method (SSFM). Numerical results on 10 Gb/s single-channel terrestrial transmission systems employing common dispersion maps show that the simplest third-order Volterra series solution is applicable only in the weakly nonlinear propagation regime, for peak transmitted power well below 5 dBm. However, the insight in the nonlinear propagation phenomenon provided by the RP method suggests an enhanced regular perturbation (ERP) method, which allows the first order ERP solution to be fairly accurate for terrestrial dispersion mapped systems up to launched peak powers of 10 dBm.

132 citations

Journal ArticleDOI
TL;DR: This paper shows how a certain class of artificial neural networks are equivalent to Volterra series and gives the equation for the nth order VolterRA kernel in terms of the internal parameters of the network.
Abstract: The Volterra series is a well-known method of describing non-linear dynamic systems. A major limitation of this technique is the difficulty involved in the calculation of the kernels. More recently, artificial neural networks have been used to produce black box models of non-linear dynamic systems. In this paper we show how a certain class of artificial neural networks are equivalent to Volterra series and give the equation for the nth order Volterra kernel in terms of the internal parameters of the network. The technique is then illustrated using a specific non-linear system. The kernels obtained by the method described in the paper are compared with those obtained by a Toeplitz matrix inversion technique.

131 citations

Journal ArticleDOI
TL;DR: This paper investigates two scenarios in active noise control (ANC) that lead to performance degradation with conventional linear control techniques: the low-frequency noise itself and the actuator in an ANC system has been shown to be nonminimum phase.
Abstract: This paper investigates two scenarios in active noise control (ANC) that lead to performance degradation with conventional linear control techniques. The first scenario addresses the noise itself. The low-frequency noise, traveling as plane waves in a duct, is usually assumed to be broadband random or periodic tonal noise. Linear techniques applied to actively control this noise have been shown to be successful. However, in many practical applications, the noise often arises from dynamical systems, which cause the noise to be nonlinear and deterministic or stochastic, colored, and non-Gaussian. Linear techniques cannot fully exploit the coherence in the noise and, therefore, perform suboptimally. The other scenario is that the actuator in an ANC system has been shown to be nonminimum phase. One of the tasks of the controller, in ANC systems, is to model the inverse of the actuator. Obviously, a linear controller is not able to perform that task. To combat the problems, as mentioned above, a nonlinear controller has been implemented in the ANC system. It is shown in this paper that the nonlinear controller consists of two parts: a linear system identification part and a nonlinear prediction part. The standard filtered-x algorithms cannot be used with a nonlinear controller, and therefore, the control scheme was reconfigured. Computer simulations have been carried out and confirm the theoretical derivations for the combined nonlinear and linear controller.

130 citations

Journal ArticleDOI
J. Lee1, V.J. Mathews1
TL;DR: A fast, recursive least squares (RLS) adaptive nonlinear filter modeled using a second-order Volterra series expansion has a computational complexity of O(N/sup 3/) multiplications, and the steady-state behaviour predicted is in very good agreement with the experimental results.
Abstract: A fast, recursive least squares (RLS) adaptive nonlinear filter modeled using a second-order Volterra series expansion is presented. The structure uses the ideas of fast RLS multichannel filters, and has a computational complexity of O(N/sup 3/) multiplications, where N-1 represents the memory span in number of samples of the nonlinear system model. A theoretical performance analysis of its steady-state behaviour in both stationary and nonstationary environments is presented. The analysis shows that, when the input is zero mean and Gaussian distributed, and the adaptive filter is operating in a stationary environment, the steady-state excess mean-squared error due to the coefficient noise vector is independent of the statistics of the input signal. The results of several simulation experiments show that the filter performs well in a variety of situations. The steady-state behaviour predicted by the analysis is in very good agreement with the experimental results. >

130 citations

Proceedings ArticleDOI
Vladimir Aparin1, C. Persico1
13 Jun 1999
TL;DR: In this paper, the results of Volterra series analysis of the third-order intermodulation distortion in common-emitter circuits were presented, and the derived closed-form expression showed how out-of-band source and load impedances affect the distortion.
Abstract: This paper presents the results of Volterra series analysis of the third-order intermodulation distortion in common-emitter circuits. The derived closed-form expression shows how out-of-band source and load impedances affect the distortion. The expression was used to optimally tune the input matching network of a 2 GHz Si BJT LNA at the sub- and second-harmonic frequencies for a higher IIP/sub 3/. While the in-band noise figure, gain and input return loss were not affected, the peak IIP/sub 3/ increased by 14 dB.

130 citations


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