In this paper, a reliable iterative approach, for solving a wide range of linear and nonlinear Volterra-Fredholm integral equations is established. First the approach considers a discretized form of the integral terms where considering some conditions on the kernel of the integral equation it is proved that solution of the discretized form converges to the exact solution of the problem. Then th...

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 ...

Absfrucf -Volterra filters are a particular class of nonlinear filters defined by an extension of the concept of impulse response to the nonlinear case. Linear-quadratic filters are a special example of Volterra filters limited to the second order. In the first part of this paper it is shown that all the results recently published, valid in the linear-quadratic case, can be extended with the ap...

| This paper studies approximations for a class of nonlinear lters known as Volterra lters. Although the Volterra lter provides a relatively simple and general representation for nonlinear ltering, often it is highly over-parameterized. Due to the large number of parameters, the utility of the Volterra lter is limited. The over-parameterization problem is addressed in this paper using a tensor ...

In this study, a fractional nonlinear mixed integro-differential equation (Fr-NMIDE) is presented and has general discontinuous kernel based on position time space. Conditions of the existence uniqueness solution provided through principal form integral equation, Banach fixed point theorem. After applying properties integral, Fr-NMIDE conformed to Volterra–Hammerstein (V-HIE) second kind, with ...

Since Lotka and Volterra’s seminal and pioneering works (see [10]) many decades ago, modeling of interacting, competing species have received considerable attention in the fields of biology, ecology, mathematics (for example, see [3, 9]). In their remarkably simple deterministic model, Lotka and Volterra considered two coupled nonlinear differential equations that mimic the temporal evolution o...

We demonstrate the capabilities of nonlinear Volterra models to simulate the behavior of an audio system and compare them to linear filters. In this paper a nonlinear model of an audio system based on Volterra series is presented and Normalized Least Mean Square algorithm is used to determine the Volterra series to third order. Training data for the models were collected measuring a physical sp...

This paper presents an innovative Non-Linear Receiver (NLR) for the high density optical channel. This receiver is based on the combination of Maximum Likelihood Sequence Estimation (MLSE) and nonlinear Inter-Symbol Interference (ISI) cancellation. For the nonlinear channel description a suitable model based on the Volterra series has been adopted. Simulation results show that the proposed NLR ...

This paper presents an original approach for nonlinear Volterra and NARMAX filter identification. We propose here to use a non persistent excitation of input sequence to excite few terms of the Volterra and NARMAX filter, which must satisfy a set of physical constraints. Expressions have been developped to evaluate the accurate number of excited terms of the Volterra and NARMAX filter.

Volterra series have been in the engineering literature for some time now, and yet there have been few attempts to measure Volterra kernels. This paper discusses techniques for measuring the Volterra kernels of weakly nonlinear systems. We introduce a new quick method for measuring the second Volterra kernel which is analogous to pseudo-noise testing of a linear device. To illustrate the discus...