Performance of the linear models, widely used within the framework of adaptive line enhancement (ALE), deteriorates dramatically in the presence of non-Gaussian noises. On the other hand, adaptive implementation of nonlinear models, e.g. the Volterra filters, suffers from the severe problems of large number of parameters and slow convergence. Nonetheless, kernel methods are emerging solutions t...

This paper is concerned with a technique for solving Volterra integral equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series.An iterative method is given to obtain the approximate solution.The conver...

This paper is concerned with a technique for solving Volterra integro-dierential equationsin the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernelmethod, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series. An iterative method is given toobtain the...

• TOP OF ARTICLE • INPUT-OUTPUT SYSTEM REPRESENTATION • NONLINEAR DIFFERENTIAL ALGEBRAIC REPRESENTATION • VOLTERRA REPRESENTATION • STATE-SPACE REPRESENTATION • BILINEAR REPRESENTATION • NARMA REPRESENTATION • FUZZY-LOGIC NONLINEAR REPRESENTATION • NONLINEAR REPRESENTATION USING NEURAL NETWORKS • MODEL-FREE REPRESENTATION • FEATURES OF NONLINEAR REPRESENTATIONS • EXAMPLE • CONCLUDING REMARKS • ...

In this paper, stochastic Volterra equations driven by cylindrical and genuine Wiener process in Hilbert space are investigated. Sufficient conditions for existence of strong solutions are given. The key role is played by convergence of α-times resolvent families.

Sound production in musical instruments is the consequence of interactions and wave propagation that include nonlinear phenomena. Simulating these phenomena will enable sound synthesis softwares (such as Modalys, developed at IRCAM) to produce more realistic sounds. In order to do so, nonlinear physical models will be implemented in Modalys software using Green-Volterra kernels. Green-Volterra ...

Volterra and Wiener series are perhaps the best-understood nonlinear system representations in signal processing. Although both approaches have enjoyed a certain popularity in the past, their application has been limited to rather low-dimensional and weakly nonlinear systems due to the exponential growth of the number of terms that have to be estimated. We show that Volterra and Wiener series c...

The problem under consideration is the controllability of a wide class of convolution Volterra systems, namely the class of “diffusive” systems, for which there exists an input-output state realization whose state evolves in the so-called diffusive representation space. We first show that this universal state variable is approximately controllable, and then deduce that such Volterra systems alw...