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,...

Abstract A new numerical method based on Haar wavelet is proposed for two-dimensional nonlinear Fredholm, Volterra and Volterra-Fredholm integral equations of first and second kind. The proposed method is an extension of the Haar wavelet method [1–3] from one-dimensional nonlinear integral equations (Fredholm and Volterra) to twodimensional nonlinear integral equations (Fredholm, Volterra and V...

Subharmonic images are becoming interestingly in medical ultrasound, as the improvement of contrastto-tissue ratio (CTR). However, an important part for image enhancement is processing techniques. In this study, frequency response functions (FRFs) of multiple-input-multiple-output (MIMO) Volterra systems were used to investigate potentially possible in separating subharmonic frequency for the q...

Integrability and linearizability of the Lotka–Volterra systems are studied. We prove sufficient conditions for integrable but not linearizable systems for any rational resonance ratio. We give new sufficient conditions for linearizable Lotka–Volterra systems. Sufficient conditions for integrable Lotka–Volterra systems with 3 : q resonance are given. In the particular cases of 3 : 5 and 3 : 4 r...

This paper presents a lattice structure for adaptive Volterra systems. The stucture is applicable to arbitrary planes of support of the Volterra kernels. A fast least squares lattice and a fast QR-lattice adaptive nonlinear filtering algorithms based on the lattice structure are also presented. These algorithms share the fast convergence property of fast least squares transversal Volterra filte...

Multirate architectures have been used for realizing linear FIR digital filters with reduced computational complexity. The Volterra kernel can be represented as a generalized convolution. It would thus be expected that multirate architectures could be used to advantage in realizing Volterra kernels as well. The quadratic Volterra kernel may be realized in the form of an “LDL structure.” The LDL...

With this paper we want to present a black-box model, that can be applied to a vast number of RF electron devices (e.g. FET). We will show that an analytical Volterra series approximation of the nonlinear behavior time-dependent model of an electron device can be built using a neural network and its parameters, once the proper training data are given. Key-Words: black-box model, nonlinearity, V...

Volterra integral equations arise in many problems pertaining to mathematical physics like heat conduction problems. Several numerical methods for approximating the solution of Volterra integral equations are known [1-10]. This paper is focused on the solution of Volterra integral equations of the second kind with weakly singular kernel via Haar function by taking advantage of the nice properti...

In this paper, two methods of distortion analysis are described. The Volterra series is usually used to determine nonlinear behaviour. The direct method is an extension of the Volterra series method to circuits with multiple inputs. The Volterra series method of distortion analysis is presented in the analysis of a common emitter circuit. Next the direct method is used to analyze a mixer circui...

This work builds on the Volterra series formalism presented in [D. W. Dreisigmeyer and P. M. Young, J. Phys. A 36, 8297, (2003)] to model nonconservative systems. Here we treat Lagrangians and actions as ‘time dependent’ Volterra series. We present a new family of kernels to be used in these Volterra series that allow us to derive a single retarded equation of motion using a variational princip...