Volterra series

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

Nonlinear dynamical system identification using reduced Volterra models with generalised orthonormal basis functions

Abstract: Volterra models can be used to describe a wide class of nonlinear systems. However their practical use is limited due to the huge number of coefficients that need to be estimated even for simple SISO systems. Orthonormal basis functions, like distorted sine functions and Laguerre functions, have been proposed as a means to reduce the number of parameters. In linear system identification generalized orthonormal basis functions have been widely used to reduce the number of parameters one needs to estimate with very promising results. In this paper, we extend the use of generalized orthonormal basis functions to cover the nonlinear system identification and discuss the merits of such use. Finally, we give two examples on which we implement the proposed method, a CSTR system (SISO case) and a model IV fluid catalytic cracking unit (MIMO case).

An efficient transient analysis algorithm for mildly nonlinear circuits

Abstract: This paper presents a new and efficient transient analysis method for mildly nonlinear circuits. The method is based on Volterra series representation of nonlinear circuits. It characterizes nonlinear circuits using a set of linear circuits called Volterra circuits. The input of the first-order Volterra circuit is identical to that of the nonlinear circuit, whereas that of higher order Volterra circuits is obtained from the response of lower order Volterra circuits. Fourier series interpolation is employed to approximate the input of higher order Volterra circuits. These circuits are analyzed using the sampled-data simulation of linear circuits for computational efficiency and the response of nonlinear circuits is obtained at equally spaced intervals of time. The accuracy of the method is. controlled by the order of Volterra and interpolating Fourier series. Various sources contributing to the error are analyzed. The method has been implemented in a computer program. Numerical results on example circuits demonstrate that the accuracy of the method is comparable to that of linear multistep predictor-corrector algorithms, but with greatly improved speed.

A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems

Abstract: To mitigate various physical impairments of long-haul dense wavelength division multiplexing (DWDM) systems and exploit their system capacity, there is a need to develop a two-dimensional (time and wavelength) discrete-time input-output model which can become the foundation of signal processing for optical communications. As the first step, this paper develops a model for single channel multipulse multispan systems based on the Volterra series transfer function (VSTF) method. This model is suitable for high-bit-rate time-division multiplexing (TDM) transmission in the pseudo-linear regime and is easily extendable to the multichannel case. We overcome the well-known triple integral problem and reduce it to a simple integral. This model takes into account fiber losses, frequency chirp and photodetection, which are ignored in the literature. Furthermore, with this model we introduce the intersymbol interference (ISI), self phase modulation (SPM), intrachannel cross phase modulation (IXPM) and intrachannel four wave mixing (IFWM) coefficients to characterize the impact of these effects on the system performance. The model is in excellent agreement with SSF (split-step Fourier) simulation. To illustrate its application, we develop a constrained coding scheme based on the system model to suppress the impact of various impairments.

Prediction of EMI effects in operational amplifiers by a two-input Volterra series model

Abstract: The authors present a new analytical model that describes the nonlinear behaviour of common CMOS operational amplifiers excited by radio-frequency interference (RFI) added to the input nominal signals. The new model is a valid support to analogue integrated circuit designers since it expresses a relationship between circuit parameters, parasitic elements and the amplitude of the RFI induced output offset voltage of a feedback CMOS operational amplifier. The validity of model prediction has been verified through a comparison with experimental and computer simulation results.