Frequency Domain Connectivity Identification: An Application of Partial Directed Coherence in fMRI

Functional magnetic resonance imaging (fMRI) has become an important tool in Neuroscience due to its noninvasive and high spatial resolution properties compared to other methods like PET or EEG. Characterization of the neural connectivity has been the aim of several cognitive researches, as the interactions among cortical areas lie at the heart of many brain dysfunctions and mental disorders. Several methods like correlation analysis, structural equation modeling, and dynamic causal models have been proposed to quantify connectivity strength. An important concept related to connectivity modeling is Granger causality, which is one of the most popular definitions for the measure of directional dependence between time series. In this article, we propose the application of the partial directed coherence (PDC) for the connectivity analysis of multisubject fMRI data using multivariate bootstrap. PDC is a frequency domain counterpart of Granger causality and has become a very prominent tool in EEG studies. The achieved frequency decomposition of connectivity is useful in separating interactions from neural modules from those originating in scanner noise, breath, and heart beating. Real fMRI dataset of six subjects executing a language processing protocol was used for the analysis of connectivity. Hum Brain Mapp 30:452-461, 2009. (C) 2007 Wiley-Liss, Inc.

Frequency-domain receiver design for doubly-selective channels

This work is devoted to the broadband wireless transmission techniques, which are serious candidates to be implemented in future broadband wireless and cellular systems, aiming at providing high and reliable data transmission and concomitantly high mobility. In order to cope with doubly-selective channels, receiver structures based on OFDM and SC-FDE block transmission techniques, are proposed, which allow cost-effective implementations, using FFT-based signal processing. The first subject to be addressed is the impact of the number of multipath components, and the diversity order, on the asymptotic performance of OFDM and SC-FDE, in uncoded and for different channel coding schemes. The obtained results show that the number of relevant separable multipath components is a key element that influences the performance of OFDM and SC-FDE schemes. Then, the improved estimation and detection performance of OFDM-based broadcasting systems, is introduced employing SFN (Single Frequency Network) operation. An initial coarse channel is obtained with resort to low-power training sequences estimation, and an iterative receiver with joint detection and channel estimation is presented. The achieved results have shown very good performance, close to that with perfect channel estimation. The next topic is related to SFN systems, devoting special attention to time-distortion effects inherent to these networks. Typically, the SFN broadcast wireless systems employ OFDM schemes to cope with severely time-dispersive channels. However, frequency errors, due to CFO, compromises the orthogonality between subcarriers. As an alternative approach, the possibility of using SC-FDE schemes (characterized by reduced envelope fluctuations and higher robustness to carrier frequency errors) is evaluated, and a technique, employing joint CFO estimation and compensation over the severe time-distortion effects, is proposed. Finally, broadband mobile wireless systems, in which the relative motion between the transmitter and receiver induces Doppler shift which is different or each propagation path, is considered, depending on the angle of incidence of that path in relation to the direction of travel. This represents a severe impairment in wireless digital communications systems, since that multipath propagation combined with the Doppler effects, lead to drastic and unpredictable fluctuations of the envelope of the received signal, severely affecting the detection performance. The channel variations due this effect are very difficult to estimate and compensate. In this work we propose a set of SC-FDE iterative receivers implementing efficient estimation and tracking techniques. The performance results show that the proposed receivers have very good performance, even in the presence of significant Doppler spread between the different groups of multipath components.

Single-carrier frequency domain equalisation for hammerstein communication systems using complex-valued neural networks

Single-carrier (SC) block transmission with frequency-domain equalisation (FDE) offers a viable transmission technology for combating the adverse effects of long dispersive channels encountered in high-rate broadband wireless communication systems. However, for high bandwidthefficiency and high power-efficiency systems, the channel can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such nonlinear Hammerstein channels, the standard SC-FDE scheme no longer works. This paper advocates a complex-valued (CV) B-spline neural network based nonlinear SC-FDE scheme for Hammerstein channels. Specifically, We model the nonlinear HPA, which represents the CV static nonlinearity of the Hammerstein channel, by a CV B-spline neural network, and we develop two efficient alternating least squares schemes for estimating the parameters of the Hammerstein channel, including both the channel impulse response coefficients and the parameters of the CV B-spline model. We also use another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse B-spline neural network model obtained in time domain. Extensive simulation results are included to demonstrate the effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels.

Dynamic identification of structures: experimental assessment of modal parameteres through methods in frequency domain, in time-frequency domain and model updating

Among the experimental methods commonly used to define the behaviour of a full scale system, dynamic tests are the most complete and efficient procedures. A dynamic test is an experimental process, which would define a set of characteristic parameters of the dynamic behaviour of the system, such as natural frequencies of the structure, mode shapes and the corresponding modal damping values associated. An assessment of these modal characteristics can be used both to verify the theoretical assumptions of the project, to monitor the performance of the structural system during its operational use. The thesis is structured in the following chapters: The first introductive chapter recalls some basic notions of dynamics of structure, focusing the discussion on the problem of systems with multiply degrees of freedom (MDOF), which can represent a generic real system under study, when it is excited with harmonic force or in free vibration. The second chapter is entirely centred on to the problem of dynamic identification process of a structure, if it is subjected to an experimental test in forced vibrations. It first describes the construction of FRF through classical FFT of the recorded signal. A different method, also in the frequency domain, is subsequently introduced; it allows accurately to compute the FRF using the geometric characteristics of the ellipse that represents the direct input-output comparison. The two methods are compared and then the attention is focused on some advantages of the proposed methodology. The third chapter focuses on the study of real structures when they are subjected to experimental test, where the force is not known, like in an ambient or impact test. In this analysis we decided to use the CWT, which allows a simultaneous investigation in the time and frequency domain of a generic signal x(t). The CWT is first introduced to process free oscillations, with excellent results both in terms of frequencies, dampings and vibration modes. The application in the case of ambient vibrations defines accurate modal parameters of the system, although on the damping some important observations should be made. The fourth chapter is still on the problem of post processing data acquired after a vibration test, but this time through the application of discrete wavelet transform (DWT). In the first part the results obtained by the DWT are compared with those obtained by the application of CWT. Particular attention is given to the use of DWT as a tool for filtering the recorded signal, in fact in case of ambient vibrations the signals are often affected by the presence of a significant level of noise. The fifth chapter focuses on another important aspect of the identification process: the model updating. In this chapter, starting from the modal parameters obtained from some environmental vibration tests, performed by the University of Porto in 2008 and the University of Sheffild on the Humber Bridge in England, a FE model of the bridge is defined, in order to define what type of model is able to capture more accurately the real dynamic behaviour of the bridge. The sixth chapter outlines the necessary conclusions of the presented research. They concern the application of a method in the frequency domain in order to evaluate the modal parameters of a structure and its advantages, the advantages in applying a procedure based on the use of wavelet transforms in the process of identification in tests with unknown input and finally the problem of 3D modeling of systems with many degrees of freedom and with different types of uncertainty.

Mean sea surface modelling from multi-satellite altimetry utilising frequency domain techniques

A technique is presented for the development of a high precision and resolution Mean Sea Surface (MSS) model. The model utilises Radar altimetric sea surface heights extracted from the geodetic phase of the ESA ERS-1 mission. The methodology uses a modified Le Traon et al. (1995) cubic-spline fit of dual ERS-1 and TOPEX/Poseidon crossovers for the minimisation of radial orbit error. The procedure then uses Fourier domain processing techniques for spectral optimal interpolation of the mean sea surface in order to reduce residual errors within the model. Additionally, a multi-satellite mean sea surface integration technique is investigated to supplement the first model with additional enhanced data from the GEOSAT geodetic mission.The methodology employs a novel technique that combines the Stokes' and Vening-Meinsz' transformations, again in the spectral domain. This allows the presentation of a new enhanced GEOSAT gravity anomaly field.

FREQUENCY DOMAIN CHARACTERIZATION OF OPTIC FLOW AND VISION-BASED OCELLAR SENSING FOR ROTATIONAL MOTION

The structure of an animal’s eye is determined by the tasks it must perform. While vertebrates rely on their two eyes for all visual functions, insects have evolved a wide range of specialized visual organs to support behaviors such as prey capture, predator evasion, mate pursuit, flight stabilization, and navigation. Compound eyes and ocelli constitute the vision forming and sensing mechanisms of some flying insects. They provide signals useful for flight stabilization and navigation. In contrast to the well-studied compound eye, the ocelli, seen as the second visual system, sense fast luminance changes and allows for fast visual processing. Using a luminance-based sensor that mimics the insect ocelli and a camera-based motion detection system, a frequency-domain characterization of an ocellar sensor and optic flow (due to rotational motion) are analyzed. Inspired by the insect neurons that make use of signals from both vision sensing mechanisms, advantages, disadvantages and complementary properties of ocellar and optic flow estimates are discussed.

Information theoretic interpretation of frequency domain connectivity measures

In order to provide adequate multivariate measures of information flow between neural structures, modified expressions of partial directed coherence (PDC) and directed transfer function (DTF), two popular multivariate connectivity measures employed in neuroscience, are introduced and their formal relationship to mutual information rates are proved.

Atrial activation during sinus rhythm in patients with rheumatic and non-rheumatic paroxysmal atrial fibrillation. Frequency-domain analysis using signal-averaged electrocardiography

OBJECTIVE: Using P-wave signal-averaged electrocardiography, we assessed the patterns of atrial electrical activation in patients with idiopathic atrial fibrillation as compared with patterns in patients with atrial fibrillation associated with structural heart disease. METHODS: Eighty patients with recurrent paroxysmal atrial fibrillation were divided into 3 groups as follows: group I - 40 patients with atrial fibrillation associated with non-rheumatic heart disease; group II - 25 patients with rheumatic atrial fibrillation; and group III - 15 patients with idiopathic atrial fibrillation. All patients underwent P-wave signal-averaged electrocardiography for frequency-domain analysis using spectrotemporal mapping and statistical techniques for detecting and quantifying intraatrial conduction disturbances. RESULTS: We observed an important fragmentation in atrial electrical conduction in 27% of the patients in group I, 64% of the patients in group II, and 67% of the patients in group III (p=0.003). CONCLUSION: Idiopathic atrial fibrillation has important intraatrial conduction disturbances. These alterations are similar to those observed in individuals with rheumatic atrial fibrillation, suggesting the existence of some degree of structural involvement of the atrial myocardium that cannot be detected with conventional electrocardiography and echocardiography.

Time- and frequency-domain modeling of passive interconncection structured in field and circuit analysis

PEEC, computational electromagnetics

Frequency-Domain and Wide-Pulse Time-Domain Measurements of Lanthanide Luminescence and Lanthanide-Based Resonance Energy Transfer

Resonance energy transfer (RET) is a non-radiative transfer of the excitation energy from the initially excited luminescent donor to an acceptor. The requirements for the resonance energy transfer are: i) the spectral overlap between the donor emission spectrum and the acceptor absorption spectrum, ii) the close proximity of the donor and the acceptor, and iii) the suitable relative orientations of the donor emission and the acceptor absorption transition dipoles. As a result of the RET process the donor luminescence intensity and the donor lifetime are decreased. If the acceptor is luminescent, a sensitized acceptor emission appears. The rate of RET depends strongly on the donor–acceptor distance (r) and is inversely proportional to r6. The distance dependence of RET is utilized in binding assays. The proximity requirement and the selective detection of the RET-modified emission signal allow homogeneous separation free assays. The term lanthanide-based RET is used when luminescent lanthanide compounds are used as donors. The long luminescence lifetimes, the large Stokes’ shifts and the intense, sharply-spiked emission spectra of the lanthanide donors offer advantages over the conventional organic donor molecules. Both the organic lanthanide chelates and the inorganic up-converting phosphor (UCP) particles have been used as donor labels in the RET based binding assays. In the present work lanthanide luminescence and lanthanide-based resonance energy transfer phenomena were studied. Luminescence lifetime measurements had an essential role in the research. Modular frequency-domain and time-domain luminometers were assembled and used successfully in the lifetime measurements. The frequency-domain luminometer operated in the low frequency domain ( 100 kHz) and utilized a novel dual-phase lock-in detection of the luminescence. One of the studied phenomena was the recently discovered non-overlapping fluorescence resonance energy transfer (nFRET). The studied properties were the distance and temperature dependences of nFRET. The distance dependence was found to deviate from the Förster theory and a clear temperature dependence was observed whereas conventional RET was completely independent of the temperature. Based on the experimental results two thermally activated mechanisms were proposed for the nFRET process. The work with the UCP particles involved the measurement of the luminescence properties of the UCP particles synthesized in our laboratory. The goal of the UCP particle research is to develop UCP donor labels for binding assays. In the present work the effect of the dopant concentrations and the core–shell structure on the total up-conversion luminescence intensity, the red–green emission ratio, and the luminescence lifetime was studied. Also the non-radiative nature of the energy transfer from the UCP particle donors to organic acceptors was demonstrated for the first time in aqueous environment and with a controlled donor–acceptor distance.

A frequency-domain pseudo-force method for dynamic structural analysis nonlinear systems and nonproportional damping

A frequency-domain method for nonlinear analysis of structural systems with viscous, hysteretic, nonproportional and frequency-dependent damping is presented. The nonlinear effects and nonproportional damping are considered through pseudo-force terms. The modal coordinates uncoupled equations are iteratively solved. The treatment of initial conditions in the frequency domain which is necessary for the treatment of the uncoupled equations is initially adressed.

Non-negative matrix decomposition approaches to frequency domain analysis of music audio signals

On étudie l’application des algorithmes de décomposition matricielles tel que la Factorisation Matricielle Non-négative (FMN), aux représentations fréquentielles de signaux audio musicaux. Ces algorithmes, dirigés par une fonction d’erreur de reconstruction, apprennent un ensemble de fonctions de base et un ensemble de coef- ficients correspondants qui approximent le signal d’entrée. On compare l’utilisation de trois fonctions d’erreur de reconstruction quand la FMN est appliquée à des gammes monophoniques et harmonisées: moindre carré, divergence Kullback-Leibler, et une mesure de divergence dépendente de la phase, introduite récemment. Des nouvelles méthodes pour interpréter les décompositions résultantes sont présentées et sont comparées aux méthodes utilisées précédemment qui nécessitent des connaissances du domaine acoustique. Finalement, on analyse la capacité de généralisation des fonctions de bases apprises par rapport à trois paramètres musicaux: l’amplitude, la durée et le type d’instrument. Pour ce faire, on introduit deux algorithmes d’étiquetage des fonctions de bases qui performent mieux que l’approche précédente dans la majorité de nos tests, la tâche d’instrument avec audio monophonique étant la seule exception importante.

A MATLAB GUI for learning controller design in the frequency domain

A MATLAB GUI is presented which is used to help students learn to design controllers in the frequency domain. It complements the author’s two previous GUIs for plotting and identification of systems in the frequency domain. It also incorporates the concept used in the “electronic calculator that makes students think” to assist learning. Positive student feedback affirms that the GUI has helped their understanding.

B-spline neural network based single-carrier frequency domain equalisation for Hammerstein channels

A practical single-carrier (SC) block transmission with frequency domain equalisation (FDE) system can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such Hammerstein channels, the standard SC-FDE scheme no longer works. We propose a novel Bspline neural network based nonlinear SC-FDE scheme for Hammerstein channels. In particular, we model the nonlinear HPA, which represents the complex-valued static nonlinearity of the Hammerstein channel, by two real-valued B-spline neural networks, one for modelling the nonlinear amplitude response of the HPA and the other for the nonlinear phase response of the HPA. We then develop an efficient alternating least squares algorithm for estimating the parameters of the Hammerstein channel, including the channel impulse response coefficients and the parameters of the two B-spline models. Moreover, we also use another real-valued B-spline neural network to model the inversion of the HPA’s nonlinear amplitude response, and the parameters of this inverting B-spline model can be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse Bspline neural network model obtained in time domain. The effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels is demonstrated in a simulation study.