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The main difficulty of analyzing the response of nonlinear dynamical systems to fractional Gaussian noise (fGn) is the non-Markov property and non-usefulness of diffusion process theory. Currently, only numerical simulation can be applied to obtain the response of nonlinear systems to fGn. In the present paper, noting the rather flat property of the fGn power spectral density (PSD) in most part of frequency band, the stochastic averaging method for quasi-integrable Hamiltonian systems under wide-band noise excitation is applied to predict the response of quasi-integrable and non-resonant Hamiltonian systems to fGn. By using this method, the averaged Itô stochastic differential equations (SDEs) are established and the probability density function (PDF) of system response can be obtained from solving the corresponding Fokker-Planck-Kolmogorov (FPK) equation. All of the statistics of system response are then obtained from the PDF analytically and verified through the comparison with the simulation results.

This paper presents a signal modeling-based new methodology of automatic seizure detection in EEG signals. The proposed method consists of three stages. First, a multirate filterbank structure is proposed that is constructed using the basis vectors of discrete cosine transform. The proposed filterbank decomposes EEG signals into its respective brain rhythms: delta, theta, alpha, beta, and gamma. Second, these brain rhythms are statistically modeled with the class of self-similar Gaussian random processes, namely, fractional Brownian motion and fractional Gaussian noises. The statistics of these processes are modeled using a single parameter called the Hurst exponent. In the last stage, the value of Hurst exponent and autoregressive moving average parameters are used as features to design a binary support vector machine classifier to classify pre-ictal, inter-ictal (epileptic with seizure free interval), and ictal (seizure) EEG segments. The performance of the classifier is assessed via extensive analysis on two widely used data set and is observed to provide good accuracy on both the data set. Thus, this paper proposes a novel signal model for EEG data that best captures the attributes of these signals and hence, allows to boost the classification accuracy of seizure and seizure-free epochs. [ABSTRACT FROM PUBLISHER]

A method based on the Bivariate Empirical Mode Decomposition (BEMD) is addressed to facilitate radar scene analysis for cognitive radar, building and expanding upon a previous contribution. The method exploits the response of BEMD to the fractional Gaussian character of coherent sea clutter returns. Second-order properties of the intrinsic mode functions are used to form a null hypothesis, which indicates the absence of target(s) if accepted. Extensive experiments on real-world radar data show that the proposed radar scene analysis procedure leads to significantly enhanced statistical separability for target+clutter and clutter-alone data. The results are judged from an information-theoretic perspective using the Kullback-Leibler distance as well as by visual inspection. [ABSTRACT FROM AUTHOR]

Acoustic energy based localization with wireless sensor networks is an interesting solution to locate sources and targets. For simplicity, localization formulation based on the maximum likelihood (ML) approach considers that the source and noise samples are uncorrelated and represented by a Gaussian distribution. However, the acoustic background noise can severely affect the accuracy of the location estimation. This paper proposes an accurate error estimate in which the correlation of the received signals at each wireless sensor is represented by a Hurst exponent and modeled by a fractional Gaussian noise (fGn). The experimental results show that the proposed solution is more appropriate for the source localization estimation under real acoustic noises and even for highly non-stationary sources. [ABSTRACT FROM PUBLISHER]

Fractional Gaussian noise, given as the increment of fractional Brownian motion, is a stationary Gaussian process characterized by the Hurst parameter. In the paper, moments based estimators of the Hurst parameter are presented and analyzed with respect to asymptotic variance. [ABSTRACT FROM PUBLISHER]

In this letter, the linear predictability of discrete-time stationary stochastic processes with 1/\vert f\vert^\alpha-shaped power spectral density (PSD) is considered. In particular, the spectral flatness measure (SFM)—which yields a lower bound for the normalized mean-squared-error (NMSE) of any linear one-step-ahead (OSA) predictor—is obtained analytically as a function of \alpha\in[0,1]. By comparing the SFM bound to the NMSE of the p-tap linear minimum-mean-square error (LMMSE) predictor, it is shown that close to optimal NMSE performance may be achieved for relatively moderate values of p. The performance of the LMMSE predictor for the discrete-time fractional Gaussian noise (DFGN), which may be viewed as the conventional discrete-time counterpart of continuous-time processes with 1/\vert f\vert^\alpha-shaped PSD, shows that the DFGN is more easily predicted than the discrete-time processes considered herein. [ABSTRACT FROM PUBLISHER]

The mutual information between a stochastic signal and this signal plus a fractional Brownian motion (described as an additive fractional Gaussian noise channel) is expressed as the error of an estimation problem that can be naturally associated with this model. If the stochastic signal with the additive fractional Brownian motion occurs multiplied by a scalar parameter, then the rate of change of the mutual information with respect to this parameter is described by the error of another related estimation problem. These results generalize some results for a model where the fractional Brownian motion is a Brownian motion to a model with an arbitrary fractional Brownian motion. [ABSTRACT FROM AUTHOR]

Rhythmic signals from physiological systems usually have memory and long-term correlation. They can be modeled as fractional Brownian motion or fractional Gaussian noise depending on if the signals are derived from cumulative effects of nerves and muscles. That is, they can be treated as signals with fractional dimension, and the value of its fractal dimension can be used to characterize the intensity of physiological signals. In this communication, a novel method of dimension estimation based on the calculation of spectral distribution function of discrete-time fractional Gaussian noise using Legendre polynomials as basis set is proposed. The effectiveness of this proposed method is demonstrated in the dynamic behavior of detrusor of the bladder and external urethral sphincter during micturition. [ABSTRACT FROM AUTHOR]

Empirical mode decomposition (EMD) has recently been pioneered by Huang et al. for adaptively representing nonstationary signals as sums of zero-mean amplitude modulation frequency modulation components. In order to better understand the way EMD behaves in stochastic situations involving broadband noise, we report here on numerical experiments based on fractional Gaussian noise. In such a case, it turns out that EMD acts essentially as a dyadic filter bank resembling those involved in wavelet decompositions. It is also pointed out that the hierarchy of the extracted modes may be similarly exploited for getting access to the Hurst exponent. [ABSTRACT FROM AUTHOR]