Direct inversion of acoustic scattering problems is nonlinear. One way to treat the inverse scattering problem is based on the reversion of the Born–Neumann series solution of the Lippmann–Schwinger equation. An important issue for this approach is the radius of convergence of the Born–Neumann series for the forward problem. However, this issue can be tackled by employing a renormalization tech...

The most robust treatment of the inverse acoustic scattering problem is based on the reversion of the Born-Neumann series solution of the Lippmann-Schwinger equation. An important issue for this approach to inversion is the radius of convergence of the Born-Neumann series for Fredholm integral kernels, and especially for acoustic scattering for which the interaction depends on the square of the...

In this paper, we continue our study that began in recent papers [2] and [3] concerning a simple yet effective Taylor series expansion method to approximate a solution of integral equations. The method is applied to Volterra integral equation of the second kind as well as to systems of Volterra equations. The results obtained in this paper improve significantly the results reported in recent pa...

This paper studies adaptive truncated Volterra filters employing parallel-cascade structures. Parallel-cascade realiza­ tions implement higher order Volterra systems as a parallel con­ nection of multiplicative combinations of lower order truncated Volterra systems. A normalized LMS adaptive filter is developed, and its performance capabilities are evaluated using a series of simulation experim...

Nonlinear intersymbol interferences (ISI) often arise in voiceThe major drawback of the Volterra approach is the enormous band communication channels at high transmission rates or in complexity. Even when the symmetry in the 3rd order Volterra satellite channels due to nonlinearities in the power amplifiers. Proposed equalizers for the cancellation of these nonlinear interferences are mainly ba...

A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter’s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identificatio...

This paper provides new solutions to the nonlinear system identification problem when the input to the system is a stationary non-Gaussian process. We propose the use of a model called the Hammerstein series, which leads to significant reductions in both the computational requirements and the mathematical tractability of the nonlinear system identification problem. We show that unlike the Volte...

We derive formulae for the calculation of Taylor coefficients of solutions to systems of Volterra integral equations, both linear and nonlinear, either without singularities or with singularities of Abel type and logarithmic type. We also obtain solutions to certain systems of Volterra equations of the first kind. In all cases except the case of logarithmic singularities, we obtain recursive fo...

The nonlinear speech signal decomposition based on Volterra-Wiener functional series is described. The nonlinear filter bank structure is proposed for phonemes recognition solving.

We propose a numerical approach for solving systems of nonautonomous ordinary differential equations under suitable assumptions. This approach is based on expansion of the solutions by Volterra series and allows to estimate the accuracy of the approximation. Also we can solve some ordinary differential equations for which the classical numerical methods fail.