Related papers: The Bispectrum and Its Relationship to Phase-Ampli…
Phase-amplitude coupling (PAC), a form of cross-frequency interaction, has been implicated in various cognitive functions and, by extension, in neural communication and information integration. Accurately detecting and characterising PAC is…
Phase-amplitude coupling (PAC) describes the phenomenon where the power of a high-frequency oscillation evolves with the phase of a low-frequency one. We propose a model that explains the emergence of PAC in two commonly-accepted…
Recent evidence has revealed cross-frequency coupling and, particularly, phase-amplitude coupling (PAC) as an important strategy for the brain to accomplish a variety of high-level cognitive and sensory functions. However, decoding PAC is…
Background: In electrical brain signals such as Local Field Potential (LFP) and Electroencephalogram (EEG), oscillations emerge as a result of neural network activity. The oscillations extend over several frequency bands. Between their…
Neural control of grasping arises from nonlinear interactions across multiple brain rhythms, yet EEG-based motor decoding has largely relied on linear, second-order spectral features. Here, we examine whether higher-order cross-frequency…
Several methods have been developed to extract information from electroencephalograms (EEG). One of them is Phase-Amplitude Coupling (PAC) which is a type of Cross-Frequency Coupling (CFC) method, consisting in measure the synchronization…
The bispectrum stands out as a revolutionary tool in frequency domain analysis, leaping the usual power spectrum by capturing crucial phase information between frequency components. In our innovative study, we have utilized the bispectrum…
Brain cognitive functions arise through the coordinated activity of several brain regions, which actually form complex dynamical systems operating at multiple frequencies. These systems often consist of interacting subsystems, whose…
Higher-order spectra (or polyspectra), defined as the Fourier Transform of a stationary process' autocumulants, are useful in the analysis of nonlinear and non Gaussian processes. Polyspectral means are weighted averages over Fourier…
Higher Order Spectral (HOS) analysis is often applied effectively to analyze many bio-medical signals to detect nonlinear and non-Gaussian processes. One of the most basic HOS methods is the bispectral estimation, which extracts the degree…
In the standard picture of structure formation, initially random-phase fluctuations are amplified by non-linear gravitational instability to produce a final distribution of mass which is highly non-Gaussian and has highly coupled Fourier…
This paper presents a general framework for modeling dependence in multivariate time series. Its fundamental approach relies on decomposing each signal in a system into various frequency components and then studying the dependence…
The direction and magnitude of energy transfer between turbulence scale brought about by external forcing on a turbulent boundary layer are uncovered through the bispectrum, bicoherence, and biphase. The bispectrum is a third-order,…
In recent years, the cross spectrum has received considerable attention as a means of characterising the variability of astronomical sources as a function of wavelength. While much has been written about the statistics of time and phase…
This paper introduces the novel class of modulated cyclostationary processes, a class of non-stationary processes exhibiting frequency coupling, and proposes a method of their estimation from repeated trials. Cyclostationary processes also…
The analysis of gravitational wave interferometer data requires estimates for the noise covariance matrix. For stationary noise, this amounts to estimating the power spectrum. Classical methods such as Welch averaging are used in many…
Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely…
Bicoherence analysis is a well established method for identifying the quadratic nonlinearity of stationary processes. However, it is often applied without checking the basic assumptions of stationarity and convergence. The classic…
To investigate and specify the statistical properties of cosmological fields with particular attention to possible non-Gaussian features, accurate formulae for the bispectrum and the bispectrum covariance are required. The bispectrum is the…
We focus on an alignment-free method to estimate the underlying signal from a large number of noisy randomly shifted observations. Specifically, we estimate the mean, power spectrum, and bispectrum of the signal from the observations. Since…