Showing papers on "Volterra series published in 1980"

The Volterra and Wiener Theories of Nonlinear Systems

Abstract: This text presents a complete and detailed development of the analysis, design and characterization of non-linear systems using the Volterra and Wiener theories, as well as gate functions, thus yielding new insights and a better comprehension of the subject. The Volterra and Wiener theories are useful in the study of systems in biological, mechanical, and electrical fields.

Intermodulation Distortion Analysis of MESFET Amplifiers Using the Volterra Series Representation

Abstract: Third-order intermodulation distortion generated in a MESFET amplifer is analyzed by means of the Volterra series representation. A transistor model is used which enables direct analytical determination of the nonlinear elements from small-signal measurements. The four nonlinearities considered are the gate capacitance, transconductance, drain feedback capacitance, and output conductance. Volterra transfer functions are derived for a simplified model and closed-form expressions for the third-order intermodulation ratio and intercept point are determined. The equations show the dependence of distortion on frequency, terminating impedances, and transistor parameters. Principal sources of distortion are identified and the influence of device parameters and network terminations is investigated. Experimental verification on specific MESFET amplifiers, with 2-mu m and 1-mu m gate devices, comparing predicted and measured intermodulation products for various load conditions is presented.

A best approximation framework and implementation for simulation of large-scale nonlinear systems

Abstract: A conceptual and mathematical framework is presented for optimally approximating a large-scale continuous-time-parameter nonlinear dynamical system S_C by a continuous-time-parameter model \hat{S}_C as well as a discrete-time-parameter model \hat{S}_D , which can be readily simulated respectively on an analog and on a digital computer. A reproducing kernel Hilbert space approach in appropriate weighted Fock spaces is used in the problem formulation and solution. Assuming that the input-output map of the system S_C can be represented by a Volterra functional series V_t , belonging to a Fock space F_{\underline{\rho}}(E) , the input-output maps for the simulators \hat{S}_C and \hat{S}_D are obtained as "best approximations" in F_{\underline{\rho}}(E) for the entire (untruncated) series V_t . Each of these models has the following features: (a) It is adaptive because it is based on a set of test input-output pairs which can be incorporated in the system by on-line multiplexing, (b) it is optimal in the sense of being a projection in a Hilbert space of nonlinear operators, (c) it is easily implementable by means of a set of interconnected linear dynamical systems and zero-memory nonlinear functions of single variables, and (d) unlike polynomic (truncated Volterra series) approximations, it constitutes a global approximation and thus is valid under both small- and large-signal operating conditions.

A shift operator approach to bilinear system theory

Abstract: Using a transform representation, we present a bilinear realization theory for a Volterra series input–output map. The approach involves the definition of appropriate shift operators on linear spaces associated with the transforms of the kernals in the Volterra series. This approach yields in a very simple manner a theory of minimality and connections with the concepts of span reachability and observability. It also leads to a characterization of finite dimensional realizability in terms of rationality properties of the transforms.

A note on volterra series expansions for nonlinear differential systems

Abstract: By using known results on noncummutative formal power series, we derive the Volterra series expansions for forced nonlinear differential systems in closed form.

Equivalent Low-Pass Representations for Bandpass Volterra Systems

Abstract: Relationships are derived for finding equivalent low-pass representations of the Volterra kernels corresponding to a widely used model for a nonlinear communication channel. The results are a logical extension of the usual complex envelope representation for bandpass signals. The equivalent low-pass representations are useful for simplifying calculations in cases where the input and output signals of the system are bandpass.

Dynamical realizations of finite Volterra series

Abstract: In this paper we investigate the structure of minimal realizations of finite volterra series, within the class of nonlinear, analytic systems. The structure of Nilmanifolds described by A. Malcev is used to show that the natural state space of these realizations is a vector space. Additionally it is shown that minimal realizations of finite Volterra series can be viewed as cascades of linear subsystems with polynomic link maps. The dimensions of these subsystems do not depend on the minimal realization, and an algorithm is given to compute them from the kernels.

Second-order analysis of the output of a discrete-time Volterra system driven by white noise

Abstract: The second-order analysis of the output of a discrete-time nonlinear system described by a truncated Volterra series whose input consists of a sequence of independent random variables (white noise)is considered The main result consists of an explicit formula for the mean value of the output process in terms of the cumulants of the input and of Volterra kernels This formula, with suitable modifications, allows the calculation of the output correlation as well as of the continuous and discrete components of the spectral distribution Several applications are considered, and in particular the Gaussian white noise case is worked out in detail Finally, the computational aspects of the analysis are discussed with the aim of showing that in several situations closed-form results can be obtained

Formula for output autocorrelation and spectrum of a Volterra system with stationary Gaussian input

Abstract: It is shown how the output autocorrelation and spectrum of a time-invariant Volterra system with stationary Gaussian input can conveniently be found by converting the Volterra series into a Hermite functional series and then making use of the orthogonality property. The paper extends previous work by the author to derive the well-known formula of Bedrosian-Rice.

Nonlinearly loaded antennas

Abstract: Nonlinearly loaded antennas, e.g., wire, loop or spiral antennas connected to a nonlinear load, e.g., a diode, are considered. The nonlinear model of the load is analyzed, and it is then shown that, under suitable assumptions, computation of the voltage across the load is reduced to the solution of a Volterra-type nonlinear integral equation. The well known Volterra series solution is reviewed and, as a new contribution, convergence properties and truncation error are (heuristically) discussed. Furthermore, new and known numerical methods are presented, together with some computational examples .

Steady state response of a nonlinear system

Abstract: This paper presents a method of the determination of the steady state response for a class of nonlinear systems. The response of a nonlinear system to a given input is first obtained in the form of a series solution in the multi- dimensional frequency domain. Conditions are then determined for which this series solution will converge. The conversion from multidimensions to a single dimension is then made by the method of association of variables, and thus an equivalent linear model of the nonlinear system is obtained. The steady state response is then found by any technique employed with linear system.

Parametric modeling of linear and nonlinear systems.

Abstract: : The problem of obtaining parametric models for linear and nonlinear systems based on observations of the input and output of the system is one of wide ranging interest. For linear systems, moving average (MA) and autoregressive (AR) models have received considerable attention and, based on the Levinson algorithm, a number of very powerful methods involving lattice filter structures have been developed to obtain the model solutions. For nonlinear systems the Volterra series model which is a nonlinear extension of the moving average model is frequently used. The purpose of this research is to extend these techniques to more general linear and nonlinear models. Using the equation error formulation, lattice solution methods in batch processing and adaptive form are developed for both single and multichannel autoregressive moving average (ARMA) models for linear systems and Volterra series models for nonlinear systems. A nonlinear extension of the ARMA model is also considered and is shown in some cases to remedy problems encountered in Volterra modeling of nonlinear systems. Lattice methods are also developed for the nonlinear ARMA model and it is shown that the methods obtained for linear ARMA modeling follow as a special case of the nonlinear results.

Lumped Nonlinear System Analysis with Volterra Series.

Abstract: : This study investigates the application aspect of the Volterra series method to nonlinear system analysis, with special emphasis on nonlinear circuits. The contents are organized into five parts: (1) important aspects of Volterra series method; (2) characterization of multiple nonlinearity circuits (systems) using Volterra series; (3) response on nonlinear systems from Volterra series system characterization; (4) Computer-aided analysis of mildly nonlinear circuits using Volterra series; and (5) concrete examples from the application of Volterra series method to nonlinear circuit problems. Algorithms for adapting the Volterra series method for the computer-aided distortion and zero-state transient analysis of mildly nonlinear circuits are developed next. A symbolic approach is used which not only improves the computational efficiency but also provides a link to the earlier ideas on convergence, etc. An overview of the digital computer program PRANC, which uses the Volterra series method, is also given.

A Modified Volterra Series Representation for a Class of Single-Valued, Continuous Nonlinear Systems

Abstract: A modification is presented to the Volterra functional series representation of the response from a cascaded linear-nonlinear-linear system in which the nonlinear element is single-valued, separable, and continuous. The particular advantage of this approach is that the dynamic effects represented in the convolution terms are independent of the bias or mean level of the input signal to the system. The effects of bias and element gain are included in a weighting coefficient βi (m) to each term in the series, with the first term representing the small signal gain of the system. The special case of pseudo-random input signals to the nonlinear system model is also examined using the modified functional series. It is concluded that the three-level sequence is particularly useful in producing a truncation in the modified cross-correlation series representation of the system.

Shift operators and state-affine system theory

Abstract: Using a transform representation, a state-affine realization theory for a Volterra series input-output map is presented. The approach involves the definition of certain shift operators on linear spaces associated with the transforms of the kernals in the Volterra series. The result is a realization algorithm that is extremely easy to implement. The approach also yields a theory of minimality, span-reachability, and observability for infinite degree state-affine systems.