Showing papers on "Volterra series published in 1971"
01 Dec 1971
TL;DR: Results, both old and new, which will aid the reader in applying Volterra-series-type analyses to systems driven by sine waves or Gaussian noise are presented.
Abstract: Troublesome distortions often occur in communication systems. For a wide class of systems such distortions can be computed with the help of Volterra series. Results, both old and new, which will aid the reader in applying Volterra-series-type analyses to systems driven by sine waves or Gaussian noise are presented. The n-fold Fourier transform G n of the nth Volterra kernel plays an important role in the analysis. Methods of computing G n from the system equations are described and several special systems are considered. When the G n are known, items of interest regarding the output can be obtained by substituting the G n in general formulas derived from the Volterra series representation. These items include expressions for the output harmonics, when the input is the sum of two or three sine waves, and the power spectrum and various moments, when the input is Gaussian. Special attention is paid to the case in which the Volterra series consists of only the linear and quadratic terms.
479 citations
TL;DR: In this article, a new technique for the association of variables is proposed which overcomes the limitations of the earlier methods, and the variables are then associated to reduce the multidimensional transforms to the usual 1-dimensional situation.
Abstract: Multidimensional Laplace transforms are used to transform the functional series of Volterra into the multidimensional frequency domain. The variables are then associated to reduce the multidimensional transforms to the usual 1-dimensional situation. A new technique for the association of variables is now proposed which overcomes the limitations of the earlier methods.
15 citations
TL;DR: In this article, the sign of the non-linearity of a system is taken into account to find the contraction region of the system and the bounds on the slope of nonlinearity can be expanded to reach the slopes of the boundary lines of the Hurwitz sector.
Abstract: Previous methods of finding the contraction region of a system do not take into account the sign of the non-linearity. This paper presents a method which expands the contraction region for a class of systems by providing a term for comparison with the slope of the non-linearity. It is shown how this leads to a unique convergent Volterra series over the region for a class of systems and how the bounds on the slope of the non-linearity can be expanded to reach the slopes of the boundary lines of the Hurwitz sector.
2 citations
TL;DR: In this paper, Nonzero initial conditions are included in the Volterra series solution of a class of nonlinear sampled-data systems that is described by ordinary difference equations with constant coefficients.
Abstract: Nonzero initial conditions are included in the Volterra series solution of a class of nonlinear sampled-data systems that is described by ordinary difference equations with constant coefficients. Also, it is shown how one can find an upper bound on the intersampling response of the system under consideration. These developments are made through the use of the Banach fixed-point theorem.
1 citations