In this paper, we are to develop a second-order LMS-type adaptive equalizer to reduce distortions of data transmission over analog telephone channels due the channel impulse response and inter-symbol interference (ISI). A novel approach for updating the linear and quadratic coefficients vectors of a second-order Volterra filter is presented. The innovative features of this algorithm provide dis...

More than 20 years ago it was shown that adaptive Volterra filters can be used for telephone echo cancellation, but the inherent need for a large number of coefficients has inhibited their practical use. Recently, first attempts have been made to combat nonlinearities in the acoustic echo path of hands-free telephones, which are caused by low-cost audio components. As these attempts are based o...

An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations ...

The paper concerns studies the stochastic stability and stochastic asymptotic stability of the equilibrium solution of a nonlinear Volterra difference equation which is subject to stochastic state independent disturbances. It is shown that if the linearized deterministic equation has summable solutions, then the nonlinear stochastic equation will be stable or asymptotically stable, provided tha...

This paper proposes the use of a class of feedforward artificial neural networks with polynomial activation functions (distinct for each hidden unit) for practical modeling of high-order Volterra systems. Discrete-time Volterra models (DVMs) are often used in the study of nonlinear physical and physiological systems using stimulus-response data. However, their practical use has been hindered by...

T The nonlinear and linear Volterra-Fredholm ordinary integral equations arise from various physical and biological models. The essential features of these models are of wide applicable. These models provide an important tool for modeling a numerous problems in engineering and science [6, 7]. Modelling of certain physical phenomena and engineering problems [8, 9, 10, 11, 12] leads to two-dimens...

Volterra series expansions represent an important model for the representation, analysis and synthesis of nonlinear dynamical systems. However, a significant problem with this approach to system identification is that the number of terms required to be estimated grows exponentially with the order of the expansion. In practice, therefore, the Volterra series is typically truncated to consist of,...

The present paper involves the approximation of nonlinear systems using Wiener/Volterra models with Kautz orthonormal functions. It focuses on the problem of selecting the free complex pole which characterizes these functions. The problem is solved by minimizing an upper bound of the error arising from the truncated approximation of Volterra kernels using Kautz functions. An analytical solution...

In this work we want to present a novel application of Neural Networks as a Black-Box model, which allows representing the nonlinear behavior of a vast number of RF electronic devices with the Volterra series approximation. We propose a simple approach for the generation of the Volterra model for a device, even in the case of a nonlinearity that depends on more than one variable, which allows o...