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: Nonlinear tomographic reconstruction algorithms are developed for inversion of data measured in scattering experiments in which the complex phase of the wavefields is modeled by an arbitrarily large number of terms in the Rytov series.
Abstract: Nonlinear tomographic reconstruction algorithms are developed for inversion of data measured in scattering experiments in which the complex phase of the wavefields is modeled by an arbitrarily large (possibly infinite) number of terms in the Rytov series. The algorithms attain the form of a Volterra series of nonlinear operators, with the usual filtered backpropagation algorithm of diffraction tomography as the leading linear term. A computer simulation study is included to illustrate the performance of the algorithms for the case of scattering objects with cylindrical symmetry.
42 citations
TL;DR: By showing that model reduction of kernels with different degrees can be decoupled in the problem formulation, the optimization problem is simplified into a mathematically more convenient form which can be solved with significantly less computational effort.
42 citations
TL;DR: In this paper, the authors investigated the convergence issue of the Volterra-series representations of the Duffing's oscillator subjected to harmonic inputs and proposed a simple criterion to determine the upper limit of the magnitude of the harmonic inputs.
42 citations
TL;DR: In this paper, the authors propose a nonlinear infinite moving average as an alternative to the standard state space policy function for solving nonlinear DSGE models and derive the third order approximation explicitly, examine the accuracy of the method using Euler equation tests and compare with state space approximations.
42 citations
TL;DR: This paper evaluates the performance of Volterra equalizers and maximum-likelihood sequence detection (MLSD) receivers for compensation of signal distortion in nonlinear band-limited satellite systems.
Abstract: This paper evaluates the performance of Volterra equalizers and maximum-likelihood sequence detection (MLSD) receivers for compensation of signal distortion in nonlinear band-limited satellite systems. In addition, the performance of a receiver with a fractionally-spaced equalizer followed by a Volterra equalizer is studied (FSE-Volterra equalizer). For the equalizers, adaptation of the equalizer weights is considered including a multiple-step LMS algorithm which improves the convergence characteristics. Two MLSD receiver structures are considered: the optimum receiver consisting of a matched-filter bank followed by a Viterbi (1967) detector and a suboptimum receiver consisting of a single receiver filter followed by a Viterbi detector. The performance of the MLSD receivers is then compared to that of the equalizers.
42 citations