Giovanni L. Sicuranza

A Generalized FLANN Filter for Nonlinear Active Noise Control

In this paper, we propose an extension of the well-known FLANN filter using trigonometric expansions to include suitable cross-terms, i.e., products of input samples with different time shifts. It is shown that in some applications of nonlinear active noise control, the generalized FLANN filter can offer performance as good as that of high-order Volterra filters with a reduced complexity.

Adaptive nonlinear digital filters using distributed arithmetic

A nonlinear adaptive filter structure, based upon the theory of the truncated discrete Volterra series, is presented. A memory-oriented implementation exploiting distributed arithmetic is considered, and the conventional LMS adaptation algorithms are suitably modified. Memory-size reduction methods are developed to obtain simpler actual realizations. Computer simulation results are presented.

Filtered-X affine projection algorithm for multichannel active noise control using second-order Volterra filters

A multichannel controller based on Volterra filters is described. A filtered-X affine projection algorithm is derived in detail for homogeneous quadratic filters. The proposed algorithm can be also extended to higher-order Volterra kernels and includes linear controllers as a particular case.

Fourier nonlinear filters

In this paper, two new sub-classes of linear-in-the-parameters nonlinear discrete-time filters, derived from the truncation of multidimensional generalized Fourier series, are presented. The filters, called Fourier nonlinear filters and even mirror Fourier nonlinear filters, are universal approximators for causal, time-invariant, finite-memory, continuous nonlinear systems, according to the Stone-Weierstrass approximation theorem. Their properties and limitations are discussed in detail. In particular, we show, by means of appropriate simulation examples, that an orthogonality property they satisfy for white uniform input signals is useful for improving the identification of nonlinear systems.

Quadratic digital filters for image processing

A class of nonlinear two-dimensional filters is presented. A matrix description is developed for such operators, and some symmetry conditions are imposed which simplify and render more effective the filter structure. A strategy for the design of filters capable of enhancing images having reduced contrast and degraded by noise is proposed. >

On the BIBO Stability Condition of Adaptive Recursive FLANN Filters With Application to Nonlinear Active Noise Control

In this paper, a bounded-input bounded-output (BIBO) stability condition for the recursive functional link artificial neural network (FLANN) filter, based on trigonometric expansions, is derived. This filter is considered as a member of the class of causal shift-invariant recursive nonlinear filters whose output depends linearly on the filter coefficients. As for all recursive filters, its stability should be granted or, at least, tested. The relevant conclusion we derive from the stability condition is that the recursive FLANN filter is not affected by instabilities whenever the recursive linear part of the filter is stable. This fact is in contrast with the case of recursive polynomial filters where, in general, specific limitations on the input range are required. The recursive FLANN filter is then studied in the framework of a feedforward scheme for nonlinear active noise control. The novelty of our study is due to the simultaneous consideration of a nonlinear secondary path and an acoustical feedback between the loudspeaker and the reference microphone. An output error nonlinearly Filtered-U normalized LMS adaptation algorithm, derived for the elements of the above-mentioned class of nonlinear filters, is then applied to the recursive FLANN filter. Computer simulations show that the recursive FLANN filter, in contrast to other filters, is able to simultaneously deal with the acoustical feedback and the nonlinearity in the secondary path.

Accuracy and Performance Evaluation in the Genetic Optimization of Nonlinear Systems for Active Noise Control

This paper investigates the performance of genetic optimization in a nonlinear system for active noise control based on Volterra filters. While standard Filtered-X algorithms may converge to local minima, genetic algorithms (GAs) may handle this problem efficiently. In addition, this class of algorithms does not require the identification of the secondary paths. This is a key advantage of the proposed approach. Computer simulations show that a simple GA is able to find satisfactory solutions even in the presence of nonlinearities in the secondary path. The results are more accurate than using the linear techniques and the nonlinear systems based on classical LMS algorithms.

Adaptive echo cancellation with nonlinear digital filters

This paper deals with the description of a class of nonlinear digital filters by means of the discrete Volterra series. The related hardware realizations are based on combinatorial networks obtained by using the distributed arithmetic. Such realizations can be applied for compensating, in multilevel data transmission channels, the most typical nonlinearities which affect an adaptive echo canceller.

Nonlinear digital filter realization by distributed arithmetic

It is assumed that a nonlinear shift-invariant digital filter is represented by a truncated discrete Volterra series. A matrix notation, based on the properties of the Kronecker product of matrices, is derived for the nonlinear operator of order K in the Volterra expansion. The matrix notation shows how the well-known distributed arithmetic, originally proposed for linear digital filters, can be adopted for the realization of nonlinear operators. The characteristics of combinatorial and memory-oriented structures are compared, and the problem of complexity reduction is discussed.

Transient and steady-state analysis of filtered-x affine projection algorithms

This paper provides an analysis based on energy conservation arguments of the transient and steady-state behaviors of two filtered-x affine projection algorithms in presence of an imperfect estimation of the secondary paths of an active noise control system. Very mild assumptions are posed on the system model, which is only required to have a linear dependence of the output from the filter coefficients.