Nonlinear systems usually have complicated output frequencies in the frequency domain. For the class of nonlinear Volterra systems, some interesting properties for system output frequencies are studied in this paper. These properties provide a novel insight into the output frequencies of Volterra systems, i.e., the periodicity of the output frequencies. They also demonstrate several novel frequ...

The paper proposes a nonlinear acoustic echo cancellation setup based on a decoupled scheme of the second-order adaptive Volterra filter. The acoustic distortions that take place in the Loudspeaker-Enclosure-Microphone setup are modeled using measured linear and quadratic Volterra kernels. The adaptation of the filter weights is achieved by exploiting the Normalized Least-Mean-Fourth algorithm....

Digital predistortion of nonlinear systems is an important topic in many practical applications. This paper considers direct predistortion of a Volterra system by connecting in tandem an adaptive Volterra predistorter. The coefficients of the predistorter can be recursively estimated using the nonlinear filtered-x least mean squares (NFxLMS) algorithm. In this paper, the prediction error method...

The present work addresses the identification of third-order Volterra models from input-output process data. Building on previous studies regarding input sequence design for third-order Volterra models (Soni and Parker, 2004), a new reduced-length sequence is designed to identify third-order sub-diagonal kernels. This input sequence leads to a 30% reduction in the data required to accurately es...

Nonlinearity in evoked hemodynamic responses often presents in event-related fMRI studies. Volterra series, a higher-order extension of linear convolution, has been used in the literature to construct a nonlinear characterization of hemodynamic responses. Estimation of the Volterra kernel coefficients in these models is usually challenging due to the large number of parameters. We propose a new...

here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...

in this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear volterra integral equations of the first-kind is proposed. this problem is transformedto a nonlinear two-dimensional volterra integral equation of the second-kind. the properties ofthe bivariate shifted legendre functions are presented. the operational matrices of integrationtogether with the produ...

In this paper, we introduce the Petrov-Galerkin method for solution of stochastic Volterra integral equations. Here, we use continues Lagrange-type k-0 elements, since these elements have simple structure and via them, the solution of stochastic Volterra integral equation is reduced to algebraic equations. Also the error analysis of this method is done. In Comparison with other methods, this me...

A diagonal coordinate representation for Volterra filters is developed and exploited to derive efficient Volterra filter implementations for processing carrier based input signals. In the diagonal coordinate representation the output is expressed as a sum of linear filters applied to modified input signals. Hence, linear filtering methods are employed to implement the nonlinear filter on a base...

Although the dynamical behavior of Lotka-Volterra systems has been studied thoroughly, there exist few results on control related aspects for these systems. We introduce controlled Lotka-Volterra systems and deal with their accessibility properties. Accessibility can be seen as a rst step towards controllability. In particular both a necessary condition and a suÆcient condition are proposed. Bo...