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Independent component analysis, a new concept?

Statistical Analysis with Missing Data

Fundamentals Of Statistical Signal Processing

Heart rate variability (HRV) is a reliable reflection of the many physiological factors modulating the normal rhythm of the heart. In fact, they provide a powerful means of observing the interplay between the sympathetic and parasympathetic nervous systems. It shows that the structure generating the signal is not only simply linear, but also involves nonlinear contributions. Heart rate (HR) is a nonstationary signal; its variation may contain indicators of current disease, or warnings about impending cardiac diseases. The indicators may be present at all times or may occur at random-during certain intervals of the day. It is strenuous and time consuming to study and pinpoint abnormalities in voluminous data collected over several hours. Hence, HR variation analysis (instantaneous HR against time axis) has become a popular noninvasive tool for assessing the activities of the autonomic nervous system. Computer based analytical tools for in-depth study of data over daylong intervals can be very useful in diagnostics. Therefore, the HRV signal parameters, extracted and analyzed using computers, are highly useful in diagnostics. In this paper, we have discussed the various applications of HRV and different linear, frequency domain, wavelet domain, nonlinear techniques used for the analysis of the HRV.

Heart rate variability: a review

A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher-order statistics to practical problems is demonstrated. Most of the results are given for one-dimensional processes, but some extensions to vector processes and multichannel systems are discussed. The topics covered include cumulant-polyspectra formulas; impulse response formulas; autoregressive (AR) coefficients; relationships between second-order and higher-order statistics for linear systems; double C(q,k) formulas for extracting autoregressive moving average (ARMA) coefficients; bicepstral formulas; multichannel formulas; harmonic processes; estimates of cumulants; and applications to identification of various systems, including the identification of systems from just output measurements, identification of AR systems, identification of moving-average systems, and identification of ARMA systems. >

Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications

It is the purpose of this tutorial paper to place bispectrum estimation in a digital signal processing framework in order to aid engineers in grasping the utility of the available bispectrum estimation techniques, to discuss application problems that can directly benefit from the use of the bispectrum, and to motivate research in this area Three general reasons are behind the use of bispectrum in signal processing and are addressed in the paper: to extract information due to deviations from normality, to estimate the phase of parametric signals, and to detect and characterize the properties of nonlinear mechanisms that generate time series

Bispectrum estimation: A digital signal processing framework

Higher order spectra contain information about random processes that is not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality. Estimation of the bispectrum, which is a third-order spectrum, has been applied in various fields to obtain information regarding quadratic phase coupling among harmonic components and non-Gaussianness of processes. Existing methods of bispectrum estimation are patterned after the conventional methods of power spectrum estimation which are known to possess certain limitations. The paper proposes a parametric approach to bispectrum estimation based on a non-Gaussian white noise driven autoregressive (AR) model. The AR parameter estimates are obtained by solving the third-order recursion equations which may be Toeplitz in form but not symmetric. It is shown that the method provides bispectral estimates that are far superior to the conventional estimates in terms of bispectral fidelity and that in the case of detecting phase coupling among sinusoids, the method provides significantly better resolution.

Bispectrum estimation: A parametric approach

Bispectrum estimation via AR modeling

Higher order spectra provide information about processes not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality. The bispectrum which is a third order spectrum provides information about quadratic phase coupling among harmonic components. Bispectrum estimation has been applied in diverse fields principally to obtain such information. Existing methods for bispectrum estimation are patterned after the conventional methods for power spectrum estimation which are known to possess certain limitations. The paper proposes a parametric approach to bispectrum estimation based on AR modeling of time series. The definition and properties of a parametric bispectrum estimator in the general ARMA case are stated. The third moment recursion equations that follow from the model assumptions for the proposed AR bispectrum estimator are presented. The estimates are derived using biased estimates of the third moments in these equations. Results from preliminary experiments suggest that the resulting method does possess certain attractive features when compared with existing methods.

M.R. Raghuveer

Papers

Bispectrum estimation: A digital signal processing framework

Bispectrum estimation: A parametric approach

Bispectrum estimation via AR modeling

A parametric approach to bispectrum estimation