A parametric time frequency-conditional Granger causality method using ultra-regularized orthogonal least squares and multiwavelets for dynamic connectivity analysis in EEGs

Objective: This study proposes a new para-metric TF-CGC (time-frequency conditional Granger causality) method for high-precision connectivity analysis over time and frequency domain in multivariate coupling nonstationary systems, and applies it to source EEG signals to reveal dynamic interaction patterns in oscillatory neo-cortical sensorimotor networks. Methods: The Geweke's spectral measure is combined with the TVARX (time-varying autoregressive with exogenous input) model-ling approach, which uses multiwavelet-based ul-tra-regularized orthogonal least squares (UROLS) algo-rithm aided by APRESS (adjustable prediction error sum of squares), to obtain high-resolution time-varying CGC representations. The UROLS-APRESS algorithm, which adopts both the regularization technique and the ultra-least squares criterion to measure not only the signal themselves but also the weak derivatives of them, is a novel powerful method in constructing time-varying models with good generalization performance, and can accurately track smooth and fast changing causalities. The generalized measurement based on CGC decomposition is able to eliminate indirect influences in multivariate systems. Re-sults: The proposed method is validated on two simulations and then applied to source level motor imagery (MI) EEGs, where the predicted distributions are well recovered with high TF precision, and the detected connectivity patterns of MI-EEGs are physiologically interpretable and yield new insights into the dynamical organization of oscillatory cor-tical networks. Conclusion: Experimental results confirm the effectiveness of the TF-CGC method in tracking rapidly varying causalities of EEG-based oscillatory networks. Significance: The novel TF-CGC method is expected to provide important information of neural mechanisms of perception and cognition

Time–frequency domain local spectral analysis of seismic signals with multiple windows

For a non-stationary seismic signal, time–frequency analysis methods often include a time window function that serves as a weighting function and by which the signal is multiplied to form a segment. The time window function often has the highest weighting coefficient for the central sample of the signal segment. For the rest of the segment, there is no adequate representation in the frequency spectrum. Here I propose to use multiple orthogonal window functions to properly represent the local spectral property in the time–frequency plane and recover the information lost due to time-windowing before applying the Fourier transform. First, I propose to construct multiple window functions directly using a stack of Gaussian functions. The weighted average spectrum of the multiple window functions has a flat passband, which is better than the conventional multiple windows. Taking advantage of the linearity of the Fourier transform, we can apply each window to the analytic signal to generate the instantaneous autocorrelation accordingly and form an averaged instantaneous autocorrelation by a weighted sum before performing the Fourier transform to generate the Wigner–Ville distribution (WVD). This multi-window WVD method successfully represents the local spectrum of the non-stationary seismic signal in the time–frequency plane

Turbulent Velocity Structure in Molecular Clouds

We compare velocity structure in the Polaris Flare molecular cloud at scales ranging from 0.015 pc to 20 pc to simulations of supersonic hydrodynamic and MHD turbulence computed with the ZEUS MHD code. We use several different statistical methods to compare models and observations. The Delta-variance wavelet transform is most sensitive to characteristic scales and scaling laws, but is limited by a lack of intensity weighting. The scanning-beam size-linewidth relation is more robust with respect to noisy data. Obtaining the global velocity scaling behaviour requires that large-scale trends in the maps not be removed but treated as part of the turbulent cascade. We compare the true velocity PDF in our models to velocity centroids and average line profiles in optically thin lines, and find that the line profiles reflect the true PDF better unless the map size is comparable to the total line-of-sight thickness of the cloud. Comparison of line profiles to velocity centroid PDFs can thus be used to measure the line-of-sight depth of a cloud. The observed density and velocity structure is consistent with supersonic turbulence with a driving scale at or above the size of the molecular cloud and dissipative processes below 0.05 pc. Ambipolar diffusion could explain the dissipation. The velocity PDFs exclude small-scale driving such as that from stellar outflows as a dominant process in the observed region. In the models, large-scale driving is the only process that produces deviations from a Gaussian PDF shape consistent with observations. Strong magnetic fields impose a clear anisotropy on the velocity field, reducing the velocity variance in directions perpendicular to the field. (abridged)Comment: 21 pages, 24 figures, accepted by A&A, with some modifications, including change of claimed direct detection of dissipation scale to an upper limi

Control a Robot via VEP Using Emotiv EPOC

Antud töö kirjeldab visuaalse stiimuliga esilekutsutud potentsiaalidel põhinevat aju ning arvuti vahelist liidest (AAL), mis loodi antud töö praktilise osana. AALi saab kasutada aju ja seadme vahelise otsese suhtluskanali loomiseks, mis tähendab, et seadmega suhtlemiseks pole vaja nuppe vajutada, piisab vaid visuaalsete stiimulite vaatamisest. Efektiivne AAL võimaldaks raske puudega isikutel näiteks elektroonilist ratastooli juhtida. Antud töö osana loodud AAL kasutab tuntud kanoonilise korrelatsiooni- ja võimsusspektri analüüsi meetodeid ning uuendusena kombineerib need kaks meetodit üheks teineteist täiendavaks meetodiks. Kahe meetodi kombinatsioon muudab AALi täpsemaks. AALi testiti antud töös vaid pealiskaudselt ning tulemused on järgnevad: ühe käsu edastamise aeg 2,61 s, täpsus 85,81% ning informatsiooni edastamise kiirus 27,73 bitt/min. Antud AAL on avatud lähtekoodiga, kirjutatud Python 2.7 programmeerimiskeeles, sisaldab graafilist kasutajaliidest ning kasutab aju tegevuse mõõtmiseks elektroensefalograafia (EEG) seadet Emotiv EPOC. AALi kasutamiseks on vaja ainult arvutit ja Emotiv EPOC seadet. Koodi muutes on võimalik kasutada ka teisi EEG seadmeid.This thesis describes an SSVEP-based BCI implemented as a practical part of this work. One possible usage of a BCI that efficiently implements a communication channel between the brain and an external device would be to help severely disabled people to control devices that currently require pushing buttons, for example an electric wheelchair. The BCI implemented as a part of this thesis uses widely known PSDA and CCA feature extraction methods and introduces a new way to combine these methods. Combining different methods improves the performance of a BCI. The application was tested only superficially and the following results were obtained: 2.61 s target detection time, 85.81% accuracy and 27.73 bits/min ITR. The implemented BCI is open-source, written in Python 2.7, has graphical user interface and uses inexpensive EEG device called Emotiv EPOC. The BCI requires only a computer and Emotiv EPOC, no additional hardware is needed. Different EEG devices could be used after modifying the code

The estimation of geoacoustic properties from broadband acoustic data, focusing on instantaneous frequency techniques

The compressional wave velocity and attenuation of marine sediments are fundamental to marine science. In order to obtain reliable estimates of these parameters it is necessary to examine in situ acoustic data, which is generally broadband. A variety of techniques for estimating the compressional wave velocity and attenuation from broadband acoustic data are reviewed. The application of Instantaneous Frequency (IF) techniques to data collected from a normal-incidence chirp profiler is examined. For the datasets examined the best estimates of IF are obtained by dividing the chirp profile into a series of sections, estimating the IF of each trace in the section using the first moments of the Wigner Ville distribution, and stacking the resulting IF to obtain a composite IF for the section. As the datasets examined cover both gassy and saturated sediments, this is likely to be the optimum technique for chirp datasets collected from all sediment environments

Window Functions and Their Applications in Signal Processing

Window functions—otherwise known as weighting functions, tapering functions, or apodization functions—are mathematical functions that are zero-valued outside the chosen interval. They are well established as a vital part of digital signal processing. Window Functions and their Applications in Signal Processing presents an exhaustive and detailed account of window functions and their applications in signal processing, focusing on the areas of digital spectral analysis, design of FIR filters, pulse compression radar, and speech signal processing. Comprehensively reviewing previous research and recent developments, this book: Provides suggestions on how to choose a window function for particular applications Discusses Fourier analysis techniques and pitfalls in the computation of the DFT Introduces window functions in the continuous-time and discrete-time domains Considers two implementation strategies of window functions in the time- and frequency domain Explores well-known applications of window functions in the fields of radar, sonar, biomedical signal analysis, audio processing, and synthetic aperture rada

Window Functions and Their Applications in Signal Processing

Window functions—otherwise known as weighting functions, tapering functions, or apodization functions—are mathematical functions that are zero-valued outside the chosen interval. They are well established as a vital part of digital signal processing. Window Functions and their Applications in Signal Processing presents an exhaustive and detailed account of window functions and their applications in signal processing, focusing on the areas of digital spectral analysis, design of FIR filters, pulse compression radar, and speech signal processing. Comprehensively reviewing previous research and recent developments, this book: Provides suggestions on how to choose a window function for particular applications Discusses Fourier analysis techniques and pitfalls in the computation of the DFT Introduces window functions in the continuous-time and discrete-time domains Considers two implementation strategies of window functions in the time- and frequency domain Explores well-known applications of window functions in the fields of radar, sonar, biomedical signal analysis, audio processing, and synthetic aperture rada

The framework for satellite gravity data assimilation into land surface models

The Gravity Recovery and Climate Experiment (GRACE) mission has provided an unprecedented global, homogeneous observational dataset of the time variation in terrestrial water storage (TWS) since 2002. This product has seen widespread use in the study of processes in hydrology, oceanography, the cryosphere, and is particularly critical to inform, improve, and validate computational models of the Earth system. Assimilation of the GRACE TWS fields into current land surface models can correct model deficiencies due to errors in the model structure, atmospheric forcing datasets, parameters, etc. However, the assimilation process is complicated by spatial and temporal resolution discrepancies between the model and observational datasets, characterization of the error in each, and requires tuning to the unique characteristics of satellite gravity data. This study establishes a framework for hydrological data assimilation of terrestrial water storage data from GRACE, closes the loop between GRACE product development and its scientific use, and analyzes the assimilated results for use with current GRACE products and future satellite gravity missions. The framework fuses the strengths of the observational and land surface model datasets into an assimilated product representative of the signal strength and large scale structures of the GRACE dataset effectively downscaled to the high resolution land surface dynamics. The data assimilation framework was developed through a comprehensive analysis of the deficiencies and potential improvements of the satellite data products, the assimilation procedures and error characterization, and the assimilation effectiveness over time. This analysis motivated the development of a higher frequency GRACE dataset more representative of the hydrometeorological signal content with reduced temporal aliasing of the TWS signal. Three innovations were implemented in the product development: regularization, sliding windows, and mascon basis functions, to develop a high-fidelity daily gravity field product (RSWM). The signal and error profile of the RSWM product was comprehensively analyzed via an end-to-end simulation analysis of the GRACE mission. The simulation analysis developed an error covariance representative of the magnitude, correlation, and spatial pattern of error in the RSWM dataset available for use in the data assimilation system. The assimilation algorithms and tools were advanced to optimally incorporate the GRACE TWS data and error covariance information. Daily assimilation was performed globally at the one degree gridcell level, significantly reducing spatial and temporal smoothing of the assimilation update from previous basin-scale assimilation of the monthly mean GRACE datasets. Framework elements additionally defined the mechanisms of the assimilation process: (i) the Gaspari-Cohn localization radius to spatially smooth the coarser resolution GRACE data, (ii) the necessary assimilation update rate to balance assimilation performance and computational efficiency, and (iii) open-loop error growth after assimilation has conditioned the system to advise data latency requirements. The GRACE data assimilation framework is versatile and adaptable to other land surface models, different formulations of data from the current GRACE mission, and future satellite gravity datasets.Aerospace Engineerin