Nonlinear Volterra Filters Research Articles

Improved EEG Segmentation Using Non-linear Volterra Model in Bayesian Method

ABSTRACTIn order to analyze non-stationary signals, like Electroencephalogram (EEG), it is sometimes easier to segment signals into pseudo-stationary segments. In this paper, the cascade of linear predictive coding (LPC) and non-linear Volterra filter is employed for modeling of noise in EEG signal and this methodology is applied to the procedure of change-point detection, for estimating the number of change-points and their exact location which is a powerful way to detect the change-points as precisely as possible. The earlier results are completed by constructing algorithms that use the cascade of LPC and non-linear Volterra filter for modeling the relation between noisy signal and noise in practical situations. In a Bayesian configuration, the posterior distribution of the change-point sequence is constructed and then Markov Chain Monte Carlo procedure is used for sampling this posterior distribution. The simulation results for segmentation of synthetic and real EEG data show that by applying our newly proposed methodology, the specificity and sensitivity of the segmentation are highly improved. In the case of synthetic data, the change-points are estimated completely precise (100% correct) in 70% of times and they are estimated with at least 98% accuracy in other times.

Nonlinear Adaptive Volterra Filter for Control of Distribution Static Compensator

This paper presents nonlinear adaptive Volterra filter for control of three-phase four wires Distribution Static Compensator under mixed type linear and nonlinear load. The proposed adaptive filter identifies and measures active and reactive weights of the fundamental components of load currents. These weights are used to generate the reference signals such that the currents drawn from a supply are close to balanced and sinusoidal. The performance of the proposed control algorithm is observed under nonlinear load in the laboratory environment. The test results are found satisfactory as total harmonic distortion in supply currents are within the 5% levels specified by the IEEE Standard 519-1992.

English

This paper propounds the adaptive polynomial filtering deploying the multifarious variable step-size least mean square (VSS-LMS) algorithms for the nonlinear Volterra multichannel system identification, and all are compared with a fixed step-size Volterra least mean square (VLMS) algorithm, under the various noise constraints comprising an individual signal-to-noise ratio (SNR). The VSS-LMS algorithm corroborates steady behaviour during convergence, and the step- size of the adaptive filter is altered in compliance with a gradient descent algorithm delineated to abate the squared estimation error in the course of each iteration, and it also revamps tracking rendition in the smoothly time-varying environments to the choice of the parameters and the boundaries of adaptive filter. In multitudinous practical implementations, the autocorrelation matrix of the input signal has the immense eigenvalue spread in the manifestation of nonlinear Volterra filter than in respect of the linear impulse response filter. In such circumstances, an adaptive step-size is a pertinent option to mitigate the unpropitious effects of eigenvalue spread on the convergence of VLMS adaptive algorithm. The simulation results are exhibited to reinforce the analysis, which compare the VSS-LMS algorithms with fixed step-size of the second-order Volterra filter, and also substantiate that the VSS-LMS algorithms are more robust than the fixed step-size algorithm when the input noise is logistic chaotic type. Index Terms-least mean square (LMS), minimum mean square error (MMSE), system identification, variable step-size least mean square (VSS-LMS), Volterra filter.

Adaptive Polynomial Filtering using Generalized Variable Step-Size Least Mean pth Power (LMP) Algorithm

This correspondence presents the adaptive polynomial filtering using the generalized variable step-size least mean $$p$$ p th power (GVSS-LMP) algorithm for the nonlinear Volterra system identification, under the $$\alpha $$ ? -stable impulsive noise environment. Due to the lack of finite second-order statistics of the impulse noise, we espouse the minimum error dispersion criterion as an appropriate metric for the estimation error, instead of the conventional minimum mean square error criterion. For the convergence of LMP algorithm, the adaptive weights are updated by adjusting $$p\ge 1$$ p ? 1 in the presence of impulsive noise characterized by $$1<\alpha <2$$ 1 < ? < 2 . In many practical applications, the autocorrelation matrix of input signal has the larger eigenvalue spread in the case of nonlinear Volterra filter than in the case of linear finite impulse response filter. In such cases, the time-varying step-size is an appropriate option to mitigate the adverse effects of eigenvalue spread on the convergence of LMP adaptive algorithm. In this paper, the GVSS updating criterion is proposed in combination with the LMP algorithm, to identify the slowly time-varying Volterra kernels, under the non-Gaussian $$\alpha $$ ? -stable impulsive noise scenario. The simulation results are presented to demonstrate that the proposed GVSS-LMP algorithm is more robust to the impulsive noise in comparison to the conventional techniques, when the input signal is correlated or uncorrelated Gaussian sequence, while keeping $$1<p<\alpha <2$$ 1 < p < ? < 2 . It also exhibits flexible design to tackle the slowly time-varying nonlinear system identification problem.

부대역 비선형 Volterra 적응필터의 응용과 성능분석

본 논문에서는 부대역 신호를 사용한 병렬 적응 비선형 Volterra 필터를 소개하고, 이 시스템의 성능을 분석하는 것을 주요 내용으로 한다. 연구 결과 제시한 부대역 신호를 사용한 적응 Volterra 필터는 수렴성이 우수함을 입력신호의 상관함수의 eigenvalue 분포를 사용하여 해석적으로 도출되었으며, 이러한 응용이 최근에 보고된 적응 반향 제거기에서 유용하게 사용될 수 있음을 이론적으로 밝혔다. 또한 각 부대역 에서의 최적필터를 이론적으로 유도하였고 컴퓨터 모의실험으로 이를 검증하였다. In this paper, the subband nonlinear adaptive Volterra filters are introduced and its analysis are presented. From the eigenvalue analysis of the input correlation matrix, we show that the proposed subband adaptive Volterra filter has superior convergence performance as compared to the conventional one, which shows that the it can be useful for the recently proposed subband nonlinear adaptive echo canceller. Also, the optimum filter in each subband are introduced and verified from the computer simulations.

A comparative study of adaptation algorithms for nonlinear system identification based on second order Volterra and bilinear polynomial filters

Nonlinear filtering techniques have recently become very popular in the field of signal processing. In this study we have considered the modeling of nonlinear systems using adaptive nonlinear Volterra filters and bilinear polynomial filters. The performance evaluation of these nonlinear filter models for the problem of nonlinear system identification has been carried out for several random input excitations and for measurement noise corrupted output signals. The coefficients of the two candidate filter models for are designed using several well known adaptive algorithms, such as least mean squares (LMS), recursive least squares (RLS), least mean p-norm (LMP), normalized LMP (NLMP), least mean absolute deviation (LMAD) and normalized LMAD (NLMAD) algorithms. Detailed simulation studies have been carried out for comparative analysis of Volterra model and bilinear polynomial filter, using these candidate adaptation algorithms, for system identification tasks and the superior solutions are determined.

Active Noise Cancellation Without Secondary Path Identification by Using an Adaptive Genetic Algorithm

This paper presents an adaptive genetic algorithm (AGA) for an active noise control (ANC) system. The conventional ANC system often implements the filtered extended least mean square (FXLMS) algorithm to update the coefficients of the linear finite-impulse response (FIR) and nonlinear Volterra filters, owing to its simplicity; meanwhile, the FXLMS algorithm may converge to local minima. In this paper, the FXLMS algorithm is replaced with an AGA to prevent the local minima problem. Additionally, the proposed AGA method does not require identifying the secondary path for the ANC, explaining why no plant measurement is necessary when designing an AGA-based ANC system. Simulation results demonstrate that the effectiveness of the proposed AGA method can suppress the nonlinear noise interference under several situations without clearly identifying the secondary path.

Employing Volterra filters in the ADPCM technique for speech coding: a comprehensive investigation

AbstractAlthough linear filters are useful in a various applications in the context of speech processing, there are several evidences for existence of nonlinearity in speech signals. Our main aim is to launch a comprehensive investigation into the exploitation of nonlinear Volterra filters in the context of the ADPCM‐based speech coding technique, using two methods of forward prediction, based on the LS criterion, and backward prediction, based on both LMS and RLS adaptation algorithms. In any case, after solving some innate problems, for example, ill‐conditioning and instability, schemes for optimum exploitation of nonlinear prediction are developed and simulation results are provided, tested with several performance criteria. With forward prediction a scheme is developed to detect and flag those frames for which, after stabilizing, including the quadratic predictor is beneficial. Scalar and vector quantisation methods are used for quantising the residual signal and the filter parameters, respectively. The results show that using this scheme a negligible improvement (up to 0.62 dB in the SNR) can be achieved, in spite of the increase in bit rate and complexity. With backward prediction two frame‐based schemes are developed in which for each frame, after examining a set of quadratic filters, the best filter in the sense of the best quality of the reconstructed speech is selected. The ultimate schemes result in an improvement of up to 1.5 dB in the overall SNR of the reconstructed speech at the cost of a slight increase in the bit‐rate, a short delay and a demanding increase in the complexity. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Local higher-order Volterra filter multi-step prediction model of chaotic time series

In general, the prediction modeling of chaotic time series is conducted by Volterra filters through constructing nonlinear fitting functions according to the methodology of pattern training. Since the proposed approach is consistent with the nonlinear characteristics of chaotic systems, the corresponding model turns to be more effective than conventional models. However, something abnormal is likely to occur, such as inadequate trainingor, over training, and the training data set size is not easy to choose, because the existing Volterra filters are trained point by point along the chaotic orbit. Based on the similarity of the evolving tendency of neighbor orbits in phase space, the chaotic time series multi-step-prediction model （MSP-HONFIR） employing the adaptive higher-order nonlinear Volterra filter （HONFIR） is constructed in this paper. A new method of choosing neighbor orbits in phase space is presented by considering the Euclidean distance and the evolving tendency. In addition, the criterion for the choice of the training data set size is discussed. Numerical experiments demonstrate that the performances of multi-step-prediction are improved compared to the original HONFIR method.

A Linear Phase Condition for Volterra Filters

In linear finite-impulse-response filter design, it is desirable that the filter frequency response has linear phase (LP). In this brief, we investigate the LP concept for nonlinear Volterra filters. The LP condition of Volterra filters is defined in terms of its output spectrum in which the phase term introduced by the Volterra kernels is linear. It is shown that under certain symmetry conditions, the LP condition is satisfied by Volterra filters. Moreover, the LP condition for Volterra filters can be considered as an extension to the linear filter case.

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

This paper provides an analysis of transient and steady-state behavior of different filtered-x affine projection algorithms. Algorithms suitable for single-channel and for multichannel active noise controllers are treated within a unified framework. Very mild assumptions are posed on the active noise control system model, which is only required to have a linear dependence of the output from the filter coefficients. Therefore, the analysis applies not only to the linear finite impulse response models but also to nonlinear Volterra filters, i.e., polynomial filters, and other nonlinear filter structures. The convergence analysis presented in this paper relies on energy conservation arguments and does not apply the independence theory, nor does it impose any restriction to the signal distributions. It is shown in the paper that filtered-x affine projection algorithms always provide a biased estimate of the minimum mean square solution. Nevertheless, in many cases, the bias is small and therefore these algorithms can be profitably applied to active noise control.

Nonlinear adaptive bilinear filters for active noise control systems

The reference and error channels of active noise control (ANC) systems may be saturated in real-world applications if the noise level exceeds the dynamic range of the electronic devices. This nonlinear saturation degrades the performance of ANC systems that use linear adaptive filters with the filtered-X least-mean-square (FXLMS) algorithm. This paper derives a bilinear FXLMS algorithm for nonlinear adaptive filters to solve the problems of signal saturation and other nonlinear distortions that occur in ANC systems used for practical applications. The performance of this bilinear adaptive filter is evaluated in terms of convergence speed, residual noise in steady state, and the computational complexity for different filter lengths. Computer simulations verify that the nonlinear adaptive filter with the associated bilinear FXLMS algorithm is more effective in reducing saturation effects in ANC systems than a linear filter and a nonlinear Volterra filter with the FXLMS algorithm.

Reduced complexity Retinex algorithm via the variational approach

Retinex theory addresses the problem of separating the illumination from the reflectance in a given image, and thereby compensating for non-uniform lighting. In a previous paper ( Kimmel et al., 2003), a variational model for the Retinex problem was introduced. This model was shown to unify previous methods, leading to a new illumination estimation algorithm. The main drawback with the above approach is its numerical implementation. The computational complexity of the illumination reconstruction algorithm is relatively high, since in the obtained Quadratic Programming (QP) problem, the whole image is the unknown. In addition, the process requirements for obtaining the optimal solution are not chosen a priori based on hardware/software constraints. In this paper we propose a way to compromise between the full fledged solution of the theoretical model, and a variety of efficient yet limited computational methods for which we develop optimal solutions. For computational methods parameterized linearly by a small set of free parameters, it is shown that a reduced size QP problem is obtained with a unique solution. Several special cases of this general solution are presented and analyzed: a Look-Up-Table (LUT), linear or nonlinear Volterra filters, and expansion using a truncated set of basis functions. The proposed solutions are sub-optimal compared to the original Retinex algorithm, yet their numerical implementations are much more efficient. Results indicate that the proposed methodology can enhance images for a reduced computational effort.

Layered Polynomial Filter Structures

It is shown that nonlinear Volterra, polynomial autoregressive, and bilinear filters have the same layered implementation procedure. Using the layered structure, the order of nonlinearity can be increased by adding more layers to the structure. The structure is modular and consists of the simple moving average (MA) or autoregressive (AR) filters which can be added to the structure to achieve a desired degree of complexity. In addition, the modular layered structures admit very large scale integration (VLSI) implementation of the polynomial nonlinear filters.

A computational method for the design of 2-D nonlinear Volterra filters

A class of nonlinear 2-D filters based on the truncated discrete Volterra series is considered, together with a suited matrix notation. An optimization method is developed for the design of the filters according to the required input/output relation. The performance of different optimization algorithms is studied, specifically, the method of steepest descent, Powell's conjugate directions algorithm, and simulated annealing. It is found that the Powell technique is the most suited to the problem. A design example, together with the results obtained after processing a test image by the proposed filters and other standard techniques, is used to compare the performance of the three methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>