Volterra series

About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.

Edge extraction by a class of second-order nonlinear filters

Abstract: The application of a class of nonlinear 2-D digital filters, based on the discrete Volterra series, as edge detectors is considered Independence on edge orientation is achieved by the use of symmetry conditions on the coefficients Two examples are presented

Lattice algorithms for recursive least squares adaptive second-order Volterra filtering

Abstract: This paper presents two computationally efficient recursive least-squares (RLS) lattice algorithms for adaptive nonlinear filtering based on a truncated second-order Volterra system model. The lattice formulation transforms the nonlinear filtering problem into an equivalent multichannel, linear filtering problem and then generalizes the lattice solution to the nonlinear filtering problem. One of the algorithms is a direct extension of the conventional RLS lattice adaptive linear filtering algorithm to the nonlinear case. The other algorithm is based on the QR decomposition of the prediction error covariance matrices using orthogonal transformations. Several experiments demonstrating and comparing the properties of the two algorithms in finite and "infinite" precision environments are included in the paper. The results indicate that both the algorithms retain the fast convergence behavior of the RLS Volterra filters and are numerically stable. >

QR-decomposition based algorithms for adaptive Volterra filtering

Abstract: A QR-recursive-least squares (RLS) adaptive algorithm for non-linear filtering is presented. The algorithm is based solely on Givens rotation. Hence the algorithm is numerically stable and highly amenable to parallel implementations. The computational complexity of the algorithm is comparable to that of the fast transversal Volterra filters. The algorithm is based on a truncated second-order Volterra series model; however, it can be easily extended to other types of polynomial nonlinearities. The algorithm is derived by transforming the nonlinear filtering problem into an equivalent multichannel linear filtering problem with a different number of coefficients in each channel. The derivation of the algorithm is based on a channel-decomposition strategy which involves processing the channels in a sequential fashion during each iteration. This avoids matrix processing and leads to a scalar implementation. Results of extensive experimental studies demonstrating the properties of the algorithm in finite and 'infinite' precision environments are also presented. The results indicate that the algorithm retains the fast convergence behavior of the RLS Volterra filters and is numerically stable. >

Identification of nonlinear dynamic systems classical methods versus radial basis function networks

Abstract: This paper compares radial basis function networks for identification of nonlinear dynamic systems with classical methods derived from the Volterra series. The performance of these different approaches, such as Hammerstein, Wiener and NDE models, is analysed. Since the centres and variances of the Gaussian radial basis functions will be fixed before learning and only the weights are learned, a linear optimization problem arises. Therefore training the network and parameter estimation becomes comparable in computational effort. It is shown that the classical methods can compete or even perform better than the neural network, if the assumptions for the structure are valid. However, in practical applications when the structure is not known the radial basis function network performs much better than the classical methods.