Analysis Of Chaotic Signals Research Articles

A new algorithm for Largest Lyapunov Exponent determination for noisy chaotic signal studies with application to Electroencephalographic signals analysis for epilepsy and epileptic seizures detection

Electroencephalographic signals (EEG) are main examination of brain disease, because of their simple portability and their important temporal resolution of milliseconds or less. Nevertheless, the study of EEGs is confronted mainly with two problems: its complex behavior, which is considered in this paper due to its chaotic origin, and being contaminated by different types of noise from different sources. Our paper is thus carried out dealing with mentioned issues, we propose an algorithm for Largest Lyapunov Exponent (LLE) determination based on that of A. Wolf. In fact, LLE is an efficient tool for chaotic signal analysis. Our algorithm permits to study noisy chaotic signal. The proposed method was evaluated using a chaotic signal, obtained from the Logistic Map, for different values of the bifurcation parameter, we reach a low error rate in LLE determination using the proposed method (PLLE). Later, we use a noisy chaotic signal obtained from an additive noise to the previous signal, again PLLE leads to a perfect estimation of LLE, with a weak dependence on noise. The performance of the proposed PLLE, for LLE estimation, is also confirmed through other chaotic attractors, Hénon, Rössler and Lorenz. We then propose a supervised machine learning model for epilepsy and seizure detection based on PLLE, kernel tricks and features reduction using the benchmark EEG database provided by the University of Bonn. Comparisons with various state-of-the-art methods demonstrate the importance of our proposed method, which achieves 100% accuracy in different classification cases, runs fast and uses 4 features.

Improved wavelet packet denoising algorithm using fuzzy threshold and correlation analysis for chaotic signals

The research of an effective denoising algorithm for the actual obtained signals with chaotic characteristics is of great interest to all fields of the subject. To show the true chaotic state and analyze the dynamic characteristics of the chaotic system more accurately, an improved denoising algorithm using wavelet packet is proposed in this paper. Wavelet packet decomposition has an optimal sub-band tree structure, which can be used for local analysis of chaotic signals. Based on the correlation function value differences of wavelet packet coefficients, the algorithm determines the optimal decomposition layer, while the optimal wavelet packet basis is obtained with logarithmic energy entropy as the cost function. Furthermore, on the one hand, it makes efforts to divide wavelet packet coefficients into approximate parts, fuzzy parts and detail parts. On the other, it carries out singular spectrum analysis, the fuzzy threshold and the correlation analysis for the select of these three different types of coefficients in order to retain the dynamic performance of chaotic signals in the greatest extent. To verify the effectiveness of the algorithm, the Lorenz chaotic model is employed to analyzed. Simulation results verify the practicability of the improved denoising algorithm, which can also be well applied to various chaotic signals denoising with different noise levels.

Better Signals Are Processed Signals [Book/Software Reviews

This book provides in relatively few pages an extensive tour of practical signal processing. It covers a lot of ground and works through multiple matrix mathematics and transformations. The text, developed from courses taught by Prof. Yao, includes seven opening chapters that provide background and supporting mathematics. With five chapters devoted to applications, the book has a nice balance for a course. The final four chapters are on systolic arrays, which are interesting but not essential to a course. The chapter on chaotic signal analysis and processing is another area that many people will find intriguing and useful. The practical side of this book and the attention to historical development help balance out all of the mathematics and make of the signal processing more memorable. There is also space devoted to the history of mathematical transforms and arrayprocessing systems. This book covers three basic areas: mathematics background, applications, and systolic arrays. Of the 16 chapters, nine are devoted to the mathematical foundations of signal processing, with four chapters on systolic arrays, as noted previously, as well as three on applications. But applications are also part of the mathematical background chapters, so this text is useful in a number of ways. Of course, the book covers the basics of Fourier transforms, autoregressive and moving average models, windows, wavelet transforms, and time–frequency representations. and Kalman filters. This is a compact book with broad coverage and an enjoyable read, making it a nice addition to a rather crowded shelf of books in this field.

Open loop synchronization of semiconductor lasers with periodical injection

In this paper, the influence of fluctuation amplitude and frequency of the injection field on the dynamics and synchronization of semiconductor lasers are studied numerically. The fluctuation amplitude and frequency of the injection field are controlled by external modulation of the master laser. In the simulation, we use a modified correlation coefficient named similarity index to evaluate the synchronization performance. The results show that frequency and fluctuation amplitude of the injection field play important roles on the dynamics and synchronization quality of the system. Large fluctuation amplitude and moderate fluctuation frequency of the injection field will contribute to the synchronization of the two lasers. The results can also be extended to the analysis of chaotic signals.

Nonlinear speech analysis using models for chaotic systems

In this paper, we use concepts and methods from chaotic systems to model and analyze nonlinear dynamics in speech signals. The modeling is done not on the scalar speech signal, but on its reconstructed multidimensional attractor by embedding the scalar signal into a phase space. We have analyzed and compared a variety of nonlinear models for approximating the dynamics of complex systems using a small record of their observed output. These models include approximations based on global or local polynomials as well as approximations inspired from machine learning such as radial basis function networks, fuzzy-logic systems and support vector machines. Our focus has been on facilitating the application of the methods of chaotic signal analysis even when only a short time series is available, like phonemes in speech utterances. This introduced an increased degree of difficulty that was dealt with by resorting to sophisticated function approximation models that are appropriate for short data sets. Using these models enabled us to compute for short time series of speech sounds useful features like Lyapunov exponents that are used to assist in the characterization of chaotic systems. Several experimental insights are reported on the possible applications of such nonlinear models and features.

Horseshoe templates with global torsion in a driven laser

We perform a topological analysis of chaotic signals from a Nd-doped fiber laser with pump modulation at different values of the modulation frequency. In this experiment, the system displays chaotic behavior in three regions ${\mathrm{C}}_{1\mathrm{/}4}$, ${\mathrm{C}}_{1\mathrm{/}3}$, and ${\mathrm{C}}_{1\mathrm{/}2}$ of parameter space, located around the subharmonics ${\mathrm{\ensuremath{\omega}}}_{\mathrm{r}}$/4, ${\mathrm{\ensuremath{\omega}}}_{\mathrm{r}}$/3, and ${\mathrm{\ensuremath{\omega}}}_{\mathrm{r}}$/2 of the relaxation frequency ${\mathrm{\ensuremath{\omega}}}_{\mathrm{r}}$. We observe that the topological structures of the chaotic regimes inside a given region ${\mathrm{C}}_{1\mathrm{/}\mathrm{n}}$ are described by the same template. However, templates corresponding to different regions display different global torsions ${\mathrm{\ensuremath{\theta}}}_{\mathrm{g}}$, which we find to be related to the order of the subharmonics by ${\mathrm{\ensuremath{\theta}}}_{\mathrm{g}}$(${\mathrm{C}}_{1\mathrm{/}\mathrm{n}}$)=n-1.

Symbolic Analysis of Chaotic Signals and Turbulent Fluctuations

The symbolic analysis introduced in this paper allows quantitative description of dynamical coupling between different time signals. In order to demonstrate how this method works we applied it to the explicit examples of chaotic signals. Our results appear to be quite robust when external noise is added.

Application of methods based on higher-order statistics for chaotic time series analysis

The aim of this paper is to illustrate some applications of HOS within the context of chaotic time series analysis. After reviewing briefly some of the most popular methods and approaches used in chaotic signal analysis, we show how HOS may lead to some significant improvement. First, an HOS expansion of the mutual information is shown to provide an easy way to estimate the reconstruction delay that must be used in the embedding reconstruction method. Then, a fourth-order extension of the local intrinsic dimension analysis (LID) is proposed. The ability of this HOS extension to separate between chaotic and stochastic behaviour is illustrated by examples on simulated data and experimental time series.

Parallel implementation of a general purpose functional predictor for chaotic time series

A general purpose predictor for complex and chaotic deterministic dynamics is proposed. This consists of a functional reconstructor whose base functions are the polynomials orthonormal to the invariant measure associated to the time series, and of a preprocessing unit providing the necessary reconstruction parameters (the optimal time delay and the reconstructed phase space dimension). The proposed criterion for the estimation of these parameters is independent of the reconstruction method and is grounded on the results of chaotic signal analysis. A parallel implementation of reconstruction is discussed on the basis of a VME architecture. The applicability of the proposed method is tested by means of numerical simulations on low-dimensional time series.

Time series analysis of chaotic signals

The Box-Jenkins time series analysis is applied to obtain the amount of chaos for one-dimensional mappings and to characterize the non-chaotic part.