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

1980 ◽  
Vol 102 (3) ◽  
pp. 163-167 ◽  
Author(s):  
G. A. Parker ◽  
E. L. Moore
Keyword(s):  
Cross Correlation ◽  
Volterra Series ◽  
Series Representation ◽  
Weighting Coefficient ◽  
Functional Series ◽  
Level Sequence ◽  
Input Signals ◽  
Volterra Functional Series ◽  
Special Case ◽  
Modified Functional

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.

Postsynaptic Dorsal Column and Cuneate Correlations in the Raccoon: A Re-evaluation by Parallel-Cascade Analysis

2002 ◽  
Vol 88 (6) ◽  
pp. 3372-3376
Author(s):  
Andrew S. French ◽  
Susan H. Dick ◽  
Douglas D. Rasmusson
Keyword(s):  
Cross Correlation ◽  
Volterra Series ◽  
Receptive Fields ◽  
Dorsal Column ◽  
Second Order ◽  
Input Signals ◽  
Cascade Analysis ◽  
Postsynaptic Dorsal Column ◽  
Positive Correlations ◽  
Cascade Method

In a previous study, we reported evidence for correlations between the firing of postsynaptic dorsal column (PSDC) neurons and cuneate neurons with overlapping receptive fields on the glabrous skin of the raccoon forepaw. The evidence was based on cross-correlation and frequency response analyses of spontaneously firing neurons. However, cross-correlation without white noise Gaussian analog inputs or Poisson distributed pulse train inputs is difficult to interpret because of the inherent convolution with the autocorrelation of the unknown input signals. While the data suggested positive correlations in the spinocuneate direction for most neuron pairs, we could not estimate the temporal characteristics of these putative connections. We have now re-analyzed these data using a parallel-cascade method to estimate the first- and second-order kernels of a Volterra series approximation to the spinocuneate system. This unbiased analysis suggests that a positive correlation occurs after about 5 ms, probably followed by a negative correlation at about 12 ms. Second-order kernels also had repeatable structure, indicating dual pathways with time separations of at least 10 ms.

Instantaneous Identification of Polynomial Nonlinearity Based on Volterra Series Representation

2005 ◽  
Vol 293-294 ◽  
pp. 703-710 ◽  
Author(s):  
Giacomo V. Demarie ◽  
Rosario Ceravolo ◽  
Alessandro de Stefano
Keyword(s):  
Structural Engineering ◽  
Volterra Series ◽  
Series Representation ◽  
Consistent Estimate ◽  
Short Time Fourier Transform ◽  
Dynamic Identification ◽  
Polynomial Nonlinearity ◽  
Definition Of ◽  
Short Time

In structural engineering applications a sufficient quantity of experimental data to be able to achieve a consistent estimate of nonlinear quantities is seldom available: this applies in particular when the structures are to be tested in situ. This report discusses the definition of instantaneous estimators to be used in the dynamic identification of invariant nonlinear systems on the basis of Short-Time Fourier Transform representation of excitation and system’s response and within the framework of a Volterra series representation of the input/output relationship. An estimation of the parameters of a dynamic system can be worked out from the evolution of such instantaneous estimators.

On Random Field Discretization in Stochastic Finite Elements

1998 ◽  
Vol 65 (2) ◽  
pp. 320-327 ◽  
Author(s):  
B. A. Zeldin ◽  
P. D. Spanos
Keyword(s):  
Random Field ◽  
Volterra Series ◽  
Interpolation Method ◽  
Series Representation ◽  
Stochastic Mechanics ◽  
Discretization Methods ◽  
Nonlinear Input ◽  
Midpoint Method ◽  
Stochastic Finite Elements ◽  
Theoretical Developments

Several traditional methods for discretizing random fields in stochastic mechanics applications are considered; they are the midpoint method, the interpolation method, and the local averaging method. A simple and computationally convenient criterion for estimating the accuracy of these discretization methods is developed. Also, the Volterra series representation of nonlinear input/output relationships is utilized to assess the effect of the random field discretization methods on the response variability of stochastic mechanics problems. The theoretical developments are elucidated by a numerical example involving a beam problem.

scholarly journals Identification of Nonlinear Systems: Volterra Series Simplification

10.14311/976 ◽  
2007 ◽  
Vol 47 (4-5) ◽  
Author(s):  
A. Novák
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Transfer Function ◽  
Linear System ◽  
Impulse Response ◽  
Volterra Series ◽  
Series Representation ◽  
Multimedia Systems ◽  
Audio Amplifier ◽  
Enormous Number

Traditional measurement of multimedia systems, e.g. linear impulse response and transfer function, are sufficient but not faultless. For these methods the pure linear system is considered and nonlinearities, which are usually included in real systems, are disregarded. One of the ways to describe and analyze a nonlinear system is by using Volterra Series representation. However, this representation uses an enormous number of coefficients. In this work a simplification of this method is proposed and an experiment with an audio amplifier is shown. 

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