Showing papers on "Volterra series published in 1979"

Modeling and Performance Evaluation of Nonlinear Satellite Links-A Volterra Series Approach

Abstract: An analytical solution to the problem of modeling bandpass nonlinear channels and evaluating the performance of digital communication systems operating on them is presented. A method based on a Volterra series representation of the overall channel is first proposed, which allows one to extend to nonlinearities with memory the well-known concepts of complex envelope of bandpass signals and low-pass equivalent of bandpass linear systems. The general results previously mentioned are then applied to digital satellite communication systems operating over nonlinear channels. The effect of a nonlinear amplifier located in the satellite is considered, in combination with that of transmitting and receiving filters located in the Earth stations. In addition, both uplink and downlink noise are taken into account. Basic advantages of this approach are the generality it offers to the analysis and the fact that it allows accurate evaluation of the error probability in a short computer time.

Stochastic functional fourier series, Volterra series, and nonlinear systems analysis

Abstract: A functional Fourier series is developed with emphasis on applications to the nonlinear systems analysis. In analogy to Fourier coefficients, Fourier kernels are introduced and can be determined through a cross correlation between the output and the orthogonal basis function of the stochastic input. This applies for the class of strict-sense stationary white inputs, except for a singularity problem incurred with inputs distributed at quantized levels. The input may be correlated if it is zero-mean Gaussian. The Wiener expansion is treated as an example corresponding to the white Gaussian input and this modifies the Lee-Schetzen algorithm for Wiener kernel estimation conceptually and computationally. The Poisson-distributed white input is dealt with as another example. Possible links between the Fourier and Volterra series expansions are investigated. A mutual relationship between the Wiener and Volterra kernels is presented for a subclass of analytic nonlinear systems. Connections to the Cameron-Martin expansion are examined as well The analysis suggests precautions in the interpretation of Wiener kernel data from white-noise identification experiments.

Nonlinear systems analysis with non-Gaussian white stimuli; General basis functionals and kernels (Corresp.)

Abstract: The Wiener-Lee-Schetzen scheme of using Gaussian white noise to test a nonlinear dynamical system is extended in two ways 1) An arbitrary non-Ganssian white noise stationary signal can be used as the test stimulus 2) An arbitrary function of this stimulus can then be used as the analyzing function for cross correlating with the response to obtain the kernels characterizing the system Closed form expressions are given for the generalized orthogonal basis functions The generalized kernels are expanded in terms of Volterra kernels and Wiener kernels The expansion coefficients are closely related to the cumulants of the stimulus probability distribution These results are applied to the special case of a Gaussian stimulus and a three-level analysis function For this case a detailed analysis is Lade of the magnitude of the deviation of the kernels obtained with the ternary truncation as compared to the Wiener kernels obtained by cross correlating with the same Gaussian as was used for the stimulus The deviations are found to be quite small

A note on the identification of discrete-time polynomial systems

Abstract: Values of the kernels for a discrete-time system described by a finite Volterra series can be determined from the system responses to a set of inputs composed of unit pulses.

Optimal nonlinear estimation for a class of discrete-time stochastic systems

Abstract: Recursive estimation for nonlinear discrete-time stochastic systems with additive white Gaussian observation noise is investigated. It is proved that for certain classes of systems, described either by finite Volterra series expansions or by state-linear realizations under certain algebraic conditions, the optimal conditional mean estimator is recursive and of fixed finite dimension. An example is presented to illustrate the structure of the estimators.

A new cross correlation algorithm for Volterra kernel estimation of bilinear systems

Abstract: Correlation analysis is applied to estimate the first- and second-order kernels in a Volterra series expansion of bilinear systems. The kernels are estimated for a simulation model of a nuclear fission process. The method yields good estimates of the first-order kernel under noisy input-output measurements. However, the estimation of the second-order kernel is not satisfactory, due to the presence of higher order Volterra kernels. A new algorithm is developed to identify the parameter matrix B which characterizes the nonlinear part of a bilinear system. The estimation of the second-order kernel is significantly improved.

Mathematical derivation of linear and nonlinear runoff kernels

Abstract: From a viewpoint of overall grasp of response characteristics of a basin to rainfall, an integral form of expression such as the unit hydrograph, the Volterra series, and the Wiener series is superior to differential equation type expressions. However, hitherto, response or runoff kernels have been derived from empirical data or at the most from numerical simulation data. In this paper the runoff is represented by the Wiener-Hermite orthogonal functional expansion. By application of the Galerkin technique a set of ordinary nonlinear differential equations for the expansion coefficients of kernel functions are derived from the basic equation of motion. The differential equations are solved by the Runge-Kutta-Gill scheme to obtain the runoff kernels. Various features of the theoretical linear and nonlinear runoff kernels thus derived compare well with the empirical ones.

Intermodulation Distortion in Microwave MESFET Amplifiers

Abstract: The third-order intermodulation distortion (IM/sub 3/) of a MESFET amplifier has been analysed using Volterra series representation. A model is described that takes into account the MESFET nonlinearities and their interaction with the surrounding microwave circuit. A theoretical and experimental study of the amplifier intermodulation products has been conducted. Their dependence on the input frequency and power-level of a two-tone test signal is investigated. For power inputs less than -10 dBm, the agreement obtained between measured and predicted IM/sub 3/ is within 3-dB over an amplifier bandwidth of 400 MHz.

A Volterra series approach to the solution of time varying linear differential equations

Abstract: A method of solving the response of linear dynamic systems with time varying parameters and arbitrary forcing functions is presented. The time varying parameters are regarded as additional system inputs and this non-linear problem is solved using the Volterra series approach. The time varying system's impulse response is obtained by constraining the forcing function to be impulsive, and this response can be used to define the convolution integral solution to arbitrary forcing functions. The method is illustrated by a single degree of freedom dynamic system with a time varying inertia.

A remark on the transfer functions and the realization of homogeneous continuous-time nonlinear systems

Abstract: We interpret some recent results on the transfer functions and the realization of homogeneous continuous-time nonlinear systems from the viewpoint of the relationship between Volterra series and noncommutative generating power series.

Non-gaussianity and non-linearity in electroencephalographic time series

Abstract: In this interdisciplinary contribution we discuss a number of problems related to stochastic models and statistical methods used in electroencephalography The main part of the paper is devoted to the assumption of a Gaussian process We present a variety of methods to check empirically such an assumption, together with examples The deviations from a Gaussian process which occur in EEG analysis are interpreted in terms of non-linear dynamics; the input-output-map is assumed to be well represented by a Volterra series

Addendum to "Volterra Systems with Random Inputs: A Formalized Approach"

Abstract: A newly derived expression for the higher order crosscorrelation function of two jointly stationary Gaussian random processes is used to determine the output autocorrelation function of a Volterra system driven by a Gaussian input and to simplify a previously published expression for the output power spectral density and its derivation.

A Volterra series-derived describing function for a motor/variable gearbox/load combination

Abstract: A solution to the speed variations of a load driven via a variable ratio gearbox from a non constant speed drive is obtained as a Volterra series. A particular solution is found when the gear ratio is varied sinusoidally. This leads to a simple transfer function, with coefficients varying with input amplitude, which is shown to adequately model the overall dynamics.

Intermodulation distortion in uhf transistors

Abstract: Intermodulation distortion in transistors operating between 1 and 2 GHz has been studied. Four sources of nonlinearity in the transistor were examined and characterized by polynomials which were expressed in terms of the voltages at the transistor junctions. By incorporating these nonlinearities into a linear model, a nonlinear UHF transistor model was derived. The nodal equations of this nonlinear model were successively solved by expressing each nodal voltage in terms of a Volterra series expansion of the input voltage. Based on this analysis, predictions of the intermodulation distortions in two types of transistor were made; these predictions compared favourably with meansurements.