Alberto Carini

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.

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.

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.

Optimal Variable Step-Size NLMS Algorithms With Auxiliary Noise Power Scheduling for Feedforward Active Noise Control

The paper introduces two improvements in the feedforward active noise control system with online secondary path modeling developed by Akhtar, Abe, and Kawamata: (1) optimal variable step-size parameters are derived for the adaptation algorithms of the secondary path modeling filter and of the control filter and (2) a self-tuning power scheduling for the auxiliary noise is introduced. The proposed power scheduling is chosen so that in every operating condition a specific ratio between the powers at the error microphone of the auxiliary noise and of the residual noise is achieved. It is shown that for the same auxiliary noise conditions the adaptation algorithms equipped with the optimal variable step-size parameters improve the convergence speed of the system and the estimation accuracy of the secondary path and of the optimal control filter. It is also shown that, compared with a fixed power auxiliary noise, the power scheduling of the auxiliary noise is capable to better meet the conflicting requirements of fast convergence speed of the secondary path modeling filter and of low residual noise in steady state conditions.

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.

On the Accuracy of Generalized Hammerstein Models for Nonlinear Active Noise Control

In this paper we extend a filtered-X affine projection (AP) algorithm for active noise control to controllers exploiting the recently proposed functional link artificial neural network (FLANN) based on trigonometric expansions. In fact, these structures belong to the class of filters characterized by a linear relationship between their output and the filter coefficients. Such a class includes linear filters as well as Volterra filters, for which filtered-X AP algorithms have already been derived. We show that the mentioned FLANN structures can be efficiently replaced by novel schemes using simple polynomial terms. These structures constitute a particular class of Volterra filters that we call generalized Hammerstein models

Even mirror Fourier nonlinear filters

In this paper, a novel sub-class of linear-in-the-parameters (LIP) nonlinear filters, formed by the so-called even mirror Fourier nonlinear (EMFN) filters, is presented. These filters are universal approximators for causal, time invariant, finite-memory, continuous nonlinear systems as the well-known Volterra filters. However, in contrast to Volterra filters, their basis functions are mutually orthogonal for white uniform input signals. Therefore, in adaptive applications, gradient descent algorithms with fast convergence speed and efficient nonlinear system identification algorithms can be devised. Preliminary results, showing the potentialities of EMFN filters in comparison with other LIP nonlinear filters, are presented and commented.

Piecewise-Linear Expansions for Nonlinear Active Noise Control

Functional link artificial neural networks exploiting orthogonal functional expansions have been recently proposed as efficient structures for nonlinear active noise control. In this paper it will be shown that simple piecewise-linear expansions can effectively replace trigonometric and orthogonal polynomial expansions. The controller is adapted using an extension of the affine projection algorithm we recently proposed and studied with reference to its transient and steady-state behavior

Low-complexity nonlinear adaptive filters for acoustic echo cancellation in GSM handset receivers

High-quality mobile services need to compensate for acoustic echoes that may affect modern cellular phone receivers. To this purpose, adaptive linear filters are generally used since their low complexity allows real-time implementations. However, they often have to identify an acoustic echo path that may contain significant nonlinearities. Therefore, in such cases, a nonlinear model is required. It is well known that Volterra filters are well suited for modeling a large class of nonlinear systems, but they often require too many computational resources for a real-time implementation. The purpose of this paper is twofold. First of all, we propose to use a simplified quadratic Volterra filter, derived taking into account the characteristics of the most important nonlinearities that affect cellular receivers. Second, an efficient adaptation algorithm is derived which extends the Affine Projection (AP) algorithm, proposed for linear filters, to quadratic Volterra filters. This adaptation algorithm offers better convergence and tracking capabilities with respect to the standard LMS and NLMS algorithms. The reduced complexity and the fast adaptation rate make the echo cancellers we are proposing attractive for real-time implementations. Copyright