This paper introduces a novel sub-class of linear-in-the-parameters nonlinear filters, the Legendre nonlinear filters. Their basis functions are polynomials, specifically, products of Legendre polynomial expansions of the input signal samples. Legendre nonlinear filters share many of the properties of the recently introduced classes of Fourier nonlinear filters and even mirror Fourier nonlinear filters, which are based on trigonometric basis functions. In fact, Legendre nonlinear filters are universal approximators for causal, time invariant, finite-memory, continuous, nonlinear systems and their basis functions are mutually orthogonal for white uniform input signals. In adaptive applications, gradient descent algorithms with fast convergence speed and efficient nonlinear system identification algorithms can be devised. Experimental results, showing the potentialities of Legendre nonlinear filters in comparison with other linear-in-the-parameters nonlinear filters, are presented and commented.

In this paper we consider the identification of a class of linear-in-the parameters nonlinear filters that has been recently introduced, the so-called even mirror Fourier nonlinear filters. We show that perfect periodic sequences can be derived for these filters. A periodic sequence is perfect for a nonlinear filter if all cross-correlations between two different basis functions, estimated over a period, are zero. By applying perfect periodic sequences as input signals to even mirror Fourier nonlinear filters, it is possible to model unknown nonlinear systems exploiting the cross-correlation method. Then, the most relevant basis functions, i.e., those that guarantee the most compact representation of the nonlinear system according to some information criterion, can be easily estimated. Experimental results on the identification of a real nonlinear system illustrate the effectiveness of the proposed approach.

In this paper, we introduce a novel class of nonlinear filters characterized by two interesting properties: (i) according to the Stone-Weierstrass approximation theorem, the proposed nonlinear filters are able to arbitrarily well approximate any discrete-time, time-invariant, causal, infinite-memory, continuous, nonlinear system; (ii) the filters are always stable according to the bounded-input-bounded-output criterion. This novel class includes as a subclass the finite-memory even mirror Fourier nonlinear filters, which have been recently introduced as an useful tool for modeling strong saturation nonlinearities.

In this study, the unconstrained linear combination of the outputs of even mirror Fourier non‐linear filters is considered. These filters are new members of the class of causal, shift‐invariant, finite‐memory and linear‐in‐the parameters non‐linear filters. Their name derives from the even symmetry of their trigonometric basis functions. Even mirror Fourier non‐linear filters are universal approximators for causal, time invariant, finite‐memory and continuous non‐linear systems. Moreover, their basis functions are mutually orthogonal for white uniform input signals in the interval [−1, +1]. The authors show in this study how to exploit these characteristics, in the framework of the unconstrained linear combination of non‐linear filters, for modelling unknown non‐linear systems. In particular, they show that the filters whose outputs are combined can be adapted avoiding the choice of the step sizes, by using a simple algorithm presented in this study. The analysis of the proposed structures is accompanied by a set of simulation results that confirm the good performance obtained in different situations.

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.

This paper deals with methods for multiple position room response equalization. Differently from a well-known technique working in the time domain and based on fuzzyc-means clustering, in the proposed approach most of the operations are performed in the frequency domain and, in particular, the fuzzyc-means clustering is applied to the room magnitude responses at different positions. It is shown that working in the frequency domain allows us to obtain equalization performances at least similar to those of the time domain approach with a strongly reduced computational complexity. In addition, different techniques that can replace the fuzzyc-means clustering algorithm in the derivation of the prototype room response equalizer, with additional reduction of the number of operations, are discussed. Finally, the results of three sets of experiments are used to illustrate the performance, the robustness and the quality of the proposed room response equalization method using alternative prototype design strategies applied to different environments.

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.

The paper discusses computationally efficient NLMS and RLS algorithms for a broad class of nonlinear filters using periodic input sequences. The class comprises all nonlinear filters whose output depends linearly on the filter coefficients. The algorithms presented in the paper are exact, suitable for identification and tracking of every nonlinear system in the class, and require a real-time computational effort of a single multiplication, an addition, and a subtraction per input sample. The transient and steady-state behavior of the algorithms are discussed and the effect of a model mismatch between the unknown system and the adaptive filter is also analyzed. The low computational complexity, good performance, and applicability of the algorithm to a large class of nonlinear systems make the approach of this paper a valuable alternative to the current techniques for nonlinear system identification.

In this paper, a recursive nonlinear filter exploiting trigonometric expansions of the past output samples is introduced. Its peculiarity is, in general, the ability to model real nonlinear systems with a reduced number of coefficients in comparison to finite-memory filters, as IIR filters often do in the linear case. However, the main drawback of recursive models is the need to guarantee, or at least verify, their bounded-input-bounded-output stability. In this paper, a sufficient stability condition is presented, showing that our recursive nonlinear filter is not affected by instabilities when the input signal has finite amplitude and the recursive linear part of the filter is stable. The filter has an interesting application in nonlinear feedforward active noise control since it is able to take into account the acoustic feed back between the loudspeaker, that generates the canceling sound, and the reference microphone, that senses the noise to be canceled, in presence of nonlinear effects. In the paper, a suitable nonlinear adaptation algorithm is derived in such a framework and then applied with good results to a realistic scenario.

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.

The paper provides an analysis of transient and steady-state behavior of a multichannel filtered-x set-membership affine projection algorithm, suitable for multichannel active noise control. The analysis relies on energy conservation arguments and it does not apply the independence theory nor it imposes any restriction to the signal distributions. The analysis results show that the filtered-x set-membership affine projection algorithm can reduce the computational complexity without trading residual mean-square-error and convergence speed

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

The paper provides an analysis of the steady-state and transient behavior of two filtered-x affine projection algorithms suitable for multichannel active noise control. The analysis relies on energy conservation arguments, it does not apply the independence theory nor does it impose any restriction to the signal distributions. The paper also shows that filtered-x affine projection algorithms always provide a biased estimate of the minimum-mean-square solution of the active noise control problem.

We consider in this paper a model for nonlinear multichannel active noise controllers based on truncated Volterra filters. A previously proposed approximate affine projection (AP) adaptation algorithm is revisited with the aim of reducing its implementation complexity by applying suitable partial update strategies. The experimental results confirm that remarkable computational reductions are achieved with limited degradations of the convergence behavior.

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.

A dedicated hardware system is developed for a recent class of nonlinear hybrid filters called Order Statistics-Rational Hybrid Filters (OSRHF). The performance of these filters is also studied and compared against three effective nonlinear filters from the literature. The application at hand is noise filtering in grey level images. The proposed hardware system uses a residue number system (RNS) to compute the numerator and the denominator of the rational filter. The resulting structure is suitable for direct implementation on FPGAs.

Thee Median-Rational Hybrid Filter (MRHF) has been recently introduced as a new class of nonlinear filters and successfully applied to image filtering problems. The main characteristics of the MRHF are the good noise attenuation property in smooth areas and the preservation of edges end details. In fact, in changing areas the noise attenuation is traded for a good response to the change. Moreover, the median filters effectively remove the impulsive noise while the rational filter performs well in relatively high SNR Gaussian contaminated environments. Another relevant characteristic is that MRHF's usually act on small windows and thus require a reduced number of operations, resulting in simple and fast filtering structures. In this paper we present a programmable hardware implementation for the MRHF's. Exploiting the features of the dynamic logic families it is possible to achieve high speed and compactness, while keeping the power dissipation very low.

This letter presents some theorems for the exact and pth-order equalization of nonlinear systems described by recursive polynomial input-output relationships. It is shown that the nonlinear equalizers derived on the basis of this theory have simple and computationally efficient structures. Furthermore, the pth-order equalizers can be shown to operate in a stable manner for a finite range of values of the input amplitude when the linear component of the nonlinear system being equalized has minimum phase properties.

This paper addresses the issue of testing and quality assessment of motion rendition in digital video coding. Motion estimation and compensation are critical modules in video coders, as they are the most demanding resources and largely account for the visual quality of the resulting compressed stream. The testing of such modules is thus very important. A computational metric, based on a spatiotemporal model of the human visual system and of human motion sensing, is proposed and used to evaluate MPEG-2 compressed video. The metric is able to assess the quality of motion rendition and exhibits a good correlation with subjective data.

This paper presents a theory for the exact and the pth order equalization or linearization of nonlinear systems with known recursive or nonrecursive polynomial input-output relationships. The equalizing and linearizing filters have simple and computationally efficient structures. An experimental result that illustrates the good properties of the technique we propose is also included in this paper.

This paper derives sufficient time-varying bounds on the maximum variation of the coefficients of an exponentially stable, linear, time-varying and recursive filter. The stability bound is less conservative than all previously derived bounds for time-varying IIR systems. The bound is then applied to control the step size of output error adaptive IIR filters to achieve exponentially stable operation. Experimental results that demonstrate the good stability characteristics of the resulting algorithms are included in this paper.

We present some theorems for the exact inversion and the pth-order inversion of a wide class of causal, discrete-time, nonlinear systems. The nonlinear systems we consider are described by the input-output relationship y(n)=g[x(n)]h[x(n-1). y(n-1)]+f[x(n-1). y(n-1)], where g[/spl middot/], h[/spl middot/. /spl middot/], and f[/spl middot/. /spl middot/] are causal, discrete-time and nonlinear operators and the inverse function g/sup -1/[/spl middot/] exists. The exact inverse of such systems is given by z(n)=g/sup -1/[{u(n)-f[z(n-1). u(n-1)]}/h[z(n-1). u(n-1)]]. Similarly, when h[/spl middot/. /spl middot/]=1, the pth-order inverse is given by z(n)=g/sub p//sup -1/[u(n)-f[z(n-1), u(n-1)]] where g/sub p//sup -1/[/spl middot/] is the pth-order inverse of g[/spl middot/].

This article addresses duality assessment of motion rendition in digital video coding. Motion estimation and compensation are critical modules in video coders. A computational metric, based on a spatio-temporal model of the human visual system and of human motion sensing, is proposed and used to evaluate MPEG-2 compressed video. The metric is able to assess the quality of motion rendition and exhibits a good correlation with subjective data.

A novel method for image enhancement based on polynomial filters is presented. Its structure is similar to the one of the unsharp masking technique, but in the sharpening path a set of parallel branches are used; each is formed by the cascade of a linear operator and a nonlinear one, which act orthogonally with respect to each other. In this way, it is possible to sense the presence of correlated image details (which are enhanced) or noise (which is attenuated). Some experimental trials show that the proposed method can over-perform more classical techniques in the enhancement of blurred and noisy images; this is visually apparent but is also confirmed by a simple but effective figure of merit.>

Polynomial (or Volterra) filters are introduced, and the quadratic filters are presented as the simplest example of such filters. The principle aspects and properties of quadratic filters are derived in the framework of the discrete Volterra expansion. Fixed as well as adaptive filters are considered in one-dimensional and multidimensional environments. Such issues as design and efficient realizations are thoroughly addressed, and standard and advanced adaptation algorithms are presented. Several examples of signal processing applications requiring quadratic filters are discussed.>

A revision of the Ramstad hybrid structure which uses the B-spline function as analog resampler is presented. The effectiveness of the method is shown implementing a real-time conversion between the standard frequencies of digital audio using a single-chip solution. It is demonstrated that the B-spline functions give higher performances together with a reduced computational complexity. To achieve the required attenuation of 100 dB in the stop band, a B-spline of order six is used in place of a Lagrange polynomial of order nine, which needs about 50% of the multiplications and additions when the fast computation strategy suggested is used. The hybrid structure has been implemented on the Motorola 56001 digital signal processor (DSP).>

The problem considered is the effective compression of image data. Compared to the many methods which allow for high compression factors (mainly based on the DCT), the proposed neural approaches offer, after a suitable training, comparable performance both in terms of perceived image quality and measured SNR. Moreover, they are able to perform in the same step the two main required operations of transformation and selection of the most significant terms, with a correspondingly smaller computational effort.>

The performance of both intraframe and interframe quadratic Volterra predictors is considered and compared to that of classical linear operators. A design LMS optimization algorithm is described.

A class of M-D nonlinear digital filters based on the volterra series is presented. Both the theoretical and the implementation standpoints are considered, along with a performance example.

The structure of a nonlinear adaptive digital echo canceller is described. Distributed arithmetic is exploited by a memory-oriented realization. Various simulation tests are presented.

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.

This paper deals with the approximation of 2-D digital filters implemented with logarithmic number systems. Such systems guarantee accuracy and speed, then they are attractive for real-time digital processing of images. The limits on the maximum useful word length are discussed, and an optimization procedure for the base of the logarithmic number system is proposed. The possibility of designing efficient 2-D digital filters for logarithmic number systems is demonstrated with several examples.

A method for transposing large matrices stored on external storage devices allowing direct access is proposed. The method can be applied both to square and nonsquare matrices and it is particularly suitable when the number of rows and columns of the matrices are products of many factors.