The functional form representation of input-output relationship through Volterra series provides a structured mathematical platform for the study of nonlinear systems. It employs multi-dimensional kernels, which upon convolution with the applied excitation forces, express system response in the form of a power series. Frequency domain transforms of these multi-dimensional kernels provide higher...

Block-based nonlinear structures as, e.g., the Wiener-Hammerstein model, are popular for analyzing a broad class of nonlinear distortions. On the other hand, these models can also be related to Volterra filters in diagonal coordinates which represent very general nonlinear filters with memory. In this work, we propose an approach for estimating the significant coefficients of the nonlinear Volt...

In this work, we present a numerical method for solving nonlinear Fredholmand Volterra integral equations of the second kind which is based on the useof Block Pulse functions(BPfs) and collocation method. Numerical examplesshow eciency of the method.

This paper presents a comparative analysis of various linear and nonlinear equalizers for a high density optical channel. Since the read-out process is nonlinear, a suitable model basedon the Volterra series has been adopted. In this work, we compare the performance and complexity of equalizers designed for linear and nonlinear channels. Specifically, Adaptive Minimum Mean Square Error (MSE), A...

A broad class of nonlinear systems can be modeled by the Volterra series representation. However, the practical use of such a representation is often limited due to the large number of parameters associated with the Volterra filter structure. This paper is concerned with the problem of identification of third-order Volterra systems. The SVD technique is used to represent the quadratic Volterra ...

In this paper, the successive overrelaxation iteration and the variation of parameters formula are used to discuss the stability of linear and nonlinear Volterra integrodifferential equations. Some sufficient conditions are obtained, such that the trivial solution of the Volterra integrodifferential equations is asymptotically stable; these stability conditions are given directly from the coeff...

A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.

Sub- and ultraharmonics generation by ultrasound contrast agents makes possible sub- and ultraharmonics imaging to enhance the contrast of ultrasound images and overcome the limitations of harmonic imaging. In order to separate different frequency components of ultrasound contrast agents signals, nonlinear models like single-input single-output (SISO) Volterra model are used. One important limi...

In this article, by means of considering an isospectral operator equation which corresponds to the Volterra lattice, and constructing opportune time evolution problems with negative powers of spectral parameter, and using discrete zero curvature representation, negative Volterra flows are proposed. We also propose the mixed Volterra flows, which come from positive and negative volterra flows. F...