Volterra series

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

Non-linear multi-degree-of-freedom system random vibration by equivalent statistical quadratization

Abstract: The statistical linearization method is often inadequate for estimating spectral properties of random responses of non-linear systems. This is sometimes due to the fact that the power spectra of responses of linear systems span only the frequency range of the excitation spectrum, whereas significant responses outside this range are possible for non-linear systems. Recently, the concept of the statistical “quadratization” method was introduced to address this shortcoming of the linearization methods. The effectiveness of statistical quadratization was demonstrated on several single-degree-of-freedom systems. In this paper the method is generalized to multi-degree-of-freedom systems. The statistical quadratization solution procedure involves replacing the non-linear system by an “equivalent” system with polynomial non-linearities up to quadratic order. The non-linear equivalent system has a form whose solutions can be approximated by using the Volterra series method. The non-Gaussian joint response probability distribution is approximated by a third-order Gram-Charlicr expansion. The method is formulated for systems with general non-linearities and with non-linearities of a special form. To demonstrate the usefulness of the method, solutions are obtained for a specific system. The corresponding results compare well with Monte Carlo simulation data. Further, it is shown that the quadratization method is notably superior to the linearization method for the considered system.

A nonlinear dynamic S/H-ADC device model based on a modified Volterra series: identification procedure and commercial CAD tool implementation

Abstract: A nonlinear, dynamic empirical model, based on a Volterra-like approach, was previously proposed by the authors for the time-oriented characterization of sample/hold (S/H) and analog-to-digital conversion (ADC) devices. In this paper, the experimental procedure for model parameter measurement is presented, as well as techniques devoted to the implementation of the model in the framework of the main commercial CAD tools for circuit analysis and design. Examples of simulations, performed both in the time and frequency domain on the model obtained for a commercial device, are proposed, which show the model's capability of pointing out the dynamic nonlinear effects in the S/H-ADC response.

Bilinear system identification by Volterra kernels estimation

Abstract: This note considers the identification of bilinear discrete-time dynamic systems from sequences of input and noise corrupted output measurements. In contrast to other approaches, the proposed algorithm is simple and does not require knowledge of the noise statistics. It is also shown that the obtained estimates are unbiased and consistent, which is not shown in the previous papers.

A block LMS algorithm for third-order frequency-domain Volterra filters

Abstract: The objective of this paper is to present an adaptive algorithm to identify third-order frequency-domain Volterra filter coefficients, which correspond to the discrete Fourier transform (DFT) of the time-domain Volterra filter coefficients. The approach rests upon the block least mean square (LMS) algorithm based on the overlap-save method.

An efficient adaptive predistorter for nonlinear high power amplifier in satellite communication

Abstract: This paper presents an efficient adaptive predistortion technique for compensation of linear and nonlinear distortion caused by high-power amplifier with memory in satellite communication channels. The previous adaptive predistortion techniques, based on Volterra series modeling, are not suitable for real-time implementation due to high computational burden and slow convergence rate. In this paper, the memoryless HPA preceded by linear dynamic system is modeled by the Wiener system which is then precompensated by the proposed adaptive predistorter structured by the Hammerstein model. An adaptive algorithm for adjusting the parameters of the predistorter is derived using the stochastic gradient method. The validity of the proposed approach is confirmed via computer simulation by applying it to 16-QAM satellite communication channel where the HPA is preceded by a linear filter.