This paper presents an approach to characterizing evoked hemodynamic responses in fMRI based on nonlinear system identification, in particular the use of Volterra series. The approach employed enables one to estimate Volterra kernels that describe the relationship between stimulus presentation and the hemodynamic responses that ensue. Volterra series are essentially high-order extensions of lin...

Taking the standard zero curvature approach we derive an infinite set of inte-grable equations, which taken together form the negative Volterra hierarchy. The resulting equations turn out to be nonlocal, which is usual for the negative flows. However, in some cases the nonlocality can be eliminated. Studying the combined action of both positive (classical) and negative Volterra flows, i.e. cons...

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...

We present a qualitative analysis of the Lotka-Volterra differential equation within rectangles that are transverse with respect to the flow. In similar way to existing works on affine systems (and positively invariant rectangles), we consider here nonlinear Lotka-Volterra n-dimensional equation, in rectangles with any kind of tranverse patterns. We give necessary and sufficient conditions for ...

In this paper, we propose a new class of Volterra series based filters for image enhancement and restoration. Generally the linear filters reduce the noise and cause blurring at the edges. Some nonlinear filters based on median operator or rank operator deal with only impulse noise and fail to cancel the most common Gaussian distributed noise. A class of second order Volterra filters is propose...

This work is concerned with the optimization of Laguerre bases for the orthonormal series expansion of discrete-time Volterra models. The aim is to minimize the number of Laguerre functions associated with a given series truncation error, thus reducing the complexity of the resulting finite dimensional representation. Fu and Dumont [14] indirectly approached this problem in the context of linea...

The paper proposes a novel updating concept for adaptive Volterra kernels that relies on a robust statistics approach. The optimization of a certain cost function leads to the update equations for the linear and quadratic kernels with respect to an optimum error threshold, set according to the relative local noise power. Thereby, for absolute error samples larger than the threshold, which occur...

In this paper, the Volterra series decomposition of a class of quadratic, time invariant single-input finite dimensional systems is analyzed. The kernels are given by a recursive sequence of linear PDE’s in the time domain, and an equivalent algebraic recursion in the Laplace domain. This is used to prove the convergence of the Volterra series to a (possibly weak) trajectory of the system, to p...

The present paper involves the approximation of nonlinear systems using Wiener/Volterra models with Kautz orthonormal functions. It focuses on the problem of selecting the free complex pole which characterizes these functions. The problem is solved by minimizing an upper bound of the error arising from the truncated approximation of Volterra kernels using Kautz functions. An analytical solution...