Carlos E. D'Attellis

Detection of epileptic events in electroencephalograms using wavelet analysis

This study deals with the problem of identification of epileptic events in electroencephalograms using multiresolution wavelet analysis. The following problems are analyzed: time localization and characterization of epileptiform events, and computational efficiency of the method. The algorithm presented is based on a polynomial spline wavelet transform. The multiresolution representation obtained from this wavelet transform and the corresponding digital filters derived allows time localization of epileptiform activity. The proposed detector is based on the multiresolution energy function. Electroencephalogram records from epileptic patients were analyzed, and results obtained are shown. Some comparisons with other methods are given.

Estimation of fractal signals using wavelets and filter banks

A filter bank design based on orthonormal wavelets and equipped with a multiscale Wiener filter was recently proposed for signal restoration and for signal smoothing of 1/f family of fractal signals corrupted by external noise. The conclusions obtained in these papers are based on the following simplificative hypotheses: (1) The wavelet transformation is a whitening filter, and (2) the approximation term of the wavelet expansion can be avoided when the number of octaves in the multiresolution analysis is large enough. In this paper, we show that the estimation of 1/f processes in noise can be improved avoiding these two hypotheses. Explicit expressions of the mean-square error are given, and numerical comparisons with previous results are shown.

Estimation of fractional Brownian motion with multiresolution Kalman filter banks

A filter bank design based on orthonormal wavelets and equipped with a multiscale Kalman filter was proposed for deconvolution of fractal signals. We use the same scheme for estimating fractional Brownian motion in noise considering (1) the effect of correlation in the sequence of wavelet coefficients; (2) the approximation term in the wavelet expansion; (3) aliasing effects; (4) the optimal number of scales in the filter bank. Considerations on the minimum number of filters in the bank are made, and comparisons between Wiener and Kalman filters are given. Explicit expressions of the mean-square error are given, and comparisons between theoretical and simulation results are shown.

On the convergence of the LMS algorithm in adaptive filtering

An independence assumption on the input vectors is commonly used when stating the convergence of the least mean square algorithm is adaptive filtering. From this hypothesis a range in which the convergence factor must be chosen is determined. In this paper the independence assumption, unrealistic in the case of adaptive filtering, is avoided. From stability theory of discrete-time systems, a new range for the convergence factor is obtained.

On the optimal number of scales in estimation of fractal signals using wavelets and filters banks

Abstract In this paper we deal with the problem of finding the optimal number of scales used in a multiscale Wiener filter for obtaining the minimum mean-square estimation error of fractional Brownian motion (fBm) in noise. Several simulations are presented avoiding simplificative hypotheses previously used and considering also the effects of aliasing. Furthermore, it is shown that the mean-square error does not a strictly decreasing function with respect to the number of scales J . In all the analyzed cases, the optimal number of scales is J ⩽ 6.

Analysis of the BSB Model Dynamics Using Control Theory

A novel method to analyze the dynamics of the BSB (Brain State in a Box) model is presented. The method is able to determine if a proposed interconnection matrix generated with the CMM rule can achieve the desired behavior, and what are the parameters that should be changed in case of obtaining an incorrect final rest point. By means of an application of the techniques used in control system theory it is possible to evaluate the evolution of each of the training points individually and also to establish what are the points of the training set that are competing between them. So, this kind of analysis can be useful not only as a medium to modify the learning rule to obtain a better performance, but also as a tool to understand the limitations that the initial learning rule has. As an example of the application of this tool some simulated experiments were carried out in order to show the effectiveness of the proposed method.

Identification structures using rational wavelets: examples of application

In this paper we present three examples that show the applications of a black-box identification structure already defined. This structure can be described as a concatenation of a mapping from observed data to a finite set of linear filters realized using rational wavelets, and a nonlinear mapping from the output of the linear dynamic part to the system output represented by a hidden layer perceptron neural network, or a basis (that might be orthonormal) of high level canonical piecewise linear functions. The wavelets used for identifying the linear dynamic part are selected taking into account the linear dynamics of the system and consequently they can be considered as semiphysical regressors. Also, this structure allows to approximate the dynamic evolution of any nonlinear, causal, time-invariant system with fading memory.

Automatic detection of epileptic events in scalp EEG

In this work we present a technique base don wavelet analysis for EEGs processing of epileptic patients explored with scalp electrodes. Our aim is to provide a contribution to the automatic treatment of EEGs in the following areas of clinical applications: detection of transients, data reduction in long-term records and tracking of crisis propagation. We show the results obtained with the prosed method applied to several EEGs records.