Volterra series

About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.

A Volterra Series Approach to the Approximation of Stochastic Nonlinear Dynamics

Abstract: A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system isapproximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this series. The parameters of the bilinear system are determined by minimizing, in a statistical sense,the difference between the original system and the bilinear system. Application to a piecewise linear modelof a beam with a nonlinear one-sided supportillustrates the effectiveness of this approach in approximatingtruly nonlinear, stochastic response phenomena in both the statistical momentsand the power spectral density of the response of this system in case ofa white noise excitation.

Adaptive Digital Predistortion for Wideband High Crest Factor Applications Based on the WACP Optimization Objective: A Conceptual Overview

Abstract: This paper proposes a method of digital predistortion suitable for wideband high crest factor applications such as those encountered in DAB, DVB-T and WCDMA transmitters. The proposed method is advantageous for four main reasons. Firstly, it utilizes a reliable frequency domain measure of transmitter output nonlinearity, specifically the Weighted Adjacent Channel Power (WACP), as the objective for predistortion filter parameter estimation. This is in direct contrast to traditional approaches which utilize a time domain measure obtained via a full feedback path and potentially corrupted by gain and phase compensation error as well as ADC distortion. Secondly, the method models predistortion filter parameter estimation as a generic nonlinear mathematical optimization problem. This model assumes a nonconvex objective function and therefore utilizes both global and local optimization algorithms to achieve true global convergence. This is once again in direct contrast to traditional approaches which model predistortion filter parameter estimation as a linear regression problem. Such a model incorrectly assumes a convex error surface and therefore restricts itself to inadequate local optimization algorithms which unfortunately cannot guarantee true global convergence. Thirdly, the method's predistortion filter is a pruned Volterra Series with memory which utilizes a hybrid pruning strategy in order to keep high order kernels to a practically manageable size, suitable for optimization parameter estimation. Predistortion filter memory ultimately makes the method highly suited to wideband applications. Finally, predistortion filter parameter estimation does not require known test signals to be injected into the transmitter and therefore the technique is on-air adaptive. This means any transmitter using this method of digital predistortion will be both on-air and optimally linearized for its entire operational life. Preliminary results obtained from actual hardware are presented.

Definition of Simplified Frequency-Domain Volterra Models With Quasi-Sinusoidal Input

Abstract: The Volterra approach to the modeling of nonlinear systems has been employed for a long time thanks to its conceptual simplicity and flexibility. Its main drawback lies in the number of coefficients, which rapidly grows with memory length and nonlinearity order. In some important cases, such as power system applications, the input signal is periodic and contains a fundamental component that is much larger with respect to the others. This peculiarity can be exploited in order to dramatically reduce the number of coefficients defining the frequency-domain Volterra model with slight drawbacks in terms of accuracy. A systematic procedure for the definition of simplified, frequency-domain models of arbitrary order is proposed. Thanks to the simplification, very high orders of nonlinearity can be managed. The proposed approach has been employed to model the behavior of two electrical devices with different amount of nonlinearity, and that of a power grid containing linear and nonlinear loads. Accuracy is discussed and compared with that obtained with a conventional Volterra model defined by a similar number of coefficients. Results show the effectiveness of the approach, which is particularly suitable to model and test voltage and current transducers as well as other ac power system devices.

Waveguide and Cavity Oscillations in the Presence of Nonlinear Media

Abstract: This paper deals with the problem of waves in metallic structures containing nonlinear media. Problems of this kind are encountered in the analysis of microwave devices operated at high power levels, or when the constitutive parameters of nonlinear materials are investigated by means of microwave measurements. The Volterra series are the functional analog of the well-known Taylor series for functions. This mathematical tool is adequate for a description of constitutive relations in dispersive nonlinear media. For practical purposes, we deal with weak nonlinearity, such that the series can be truncated. Weak nonlinearity also denotes the absence of shock waves, such that all spectral components of a wave are phase matched (i.e., propagate with the same phase velocity). The main effect of nonlinearity are the production of harmonics, and the dependence of the dispersion equation on the field amplitudes. These are incorporated into the present model. The development of the present model involves some heuristic assumptions which facilitate the derivation of an algebraic dispersion equation. Therefore, the range of validity of the present model will have to be determined by experimental results, when these are available. In waveguides, and cavities in particular, the question of the effect of the geometry and boundary conditions arises, too. It is shown here that nonlinearity induces harmonic modes in rectangular structures. In cylindrical and spherical structures, the geometry affects the budget of harmonics and produces mode coupling.

An extension of the m-sequence technique for the analysis of multi-input nonlinear systems

Abstract: White-noise analysis and related methods of nonlinear systems identification describe a physical system’s response to its input in terms of “kernels” of progressively higher orders. A popular analytic scheme in the laboratory uses a class of pseudorandom binary sequences, m-sequences, as a test signal. The m-sequence method has several advantages for investigating linear and nonlinear systems: ease of implementation, rapid calculation of system kernels, and a solid theoretical framework. One difficulty with this method for nonlinear analysis comes from the algebraic structure of m-sequences: linear and nonlinear terms can be confounded, especially in the analysis of systems with many inputs. We have developed a modification of the m-sequence method which allows control of these anomalies. This method is based on input signals consisting of a superposition of m-sequences whose lengths are relatively prime. The fast computational methods which facilitate kernel calculation for a single m-sequence input are readily extended to this new setting. We describe the theoretical foundation of this method and present an application to the study of ganglion cells of the macaque retina.