Cross-spectral Measurements Research Articles

Gain and phase calibration of sensor arrays from ambient noise by cross-spectral measurements fitting.

We address the problem of blind gain and phase calibration of a sensor array from ambient noise. The key motivation is to ease the calibration process by avoiding a complex procedure setup. We show that computing the sample covariance matrix in a diffuse field is sufficient to recover the complex gains. To do so, we formulate a non-convex least-square problem based on sample and model covariances. We propose to obtain a solution by low-rank matrix approximation, and two efficient proximal algorithms are derived accordingly. The first algorithm solves the problem modified with a convex relaxation to guarantee that the solution is a global minimizer, and the second algorithm directly solves the initial non-convex problem. We investigate the efficiency of the proposed algorithms by numerical and experimental results according to different sensing configurations. These results show that efficient calibration highly depends on how the measurements are correlated. That is, estimation is achieved more accurately when the field is spatially over-sampled.

Inferring Solar Differential Rotation through Normal-mode Coupling Using Bayesian Statistics

Abstract Normal-mode helioseismic data analysis uses observed solar oscillation spectra to infer perturbations in the solar interior due to global and local-scale flows and structural asphericity. Differential rotation, the dominant global-scale axisymmetric perturbation, has been tightly constrained primarily using measurements of frequency splittings via “a-coefficients.” However, the frequency-splitting formalism invokes the approximation that multiplets are isolated. This assumption is inaccurate for modes at high angular degrees. Analyzing eigenfunction corrections, which respect cross-coupling of modes across multiplets, is a more accurate approach. However, applying standard inversion techniques using these cross-spectral measurements yields a-coefficients with a significantly wider spread than the well-constrained results from frequency splittings. In this study, we apply Bayesian statistics to infer a-coefficients due to differential rotation from cross-spectra for both f-modes and p-modes. We demonstrate that this technique works reasonably well for modes with angular degrees ℓ = 50–291. The inferred a 3-coefficients are found to be within 1 nHz of the frequency-splitting values for ℓ > 200. We also show that the technique fails at ℓ < 50 owing to the insensitivity of the measurement to the perturbation. These results serve to further establish mode-coupling as an important helioseismic technique with which to infer internal structure and dynamics, both axisymmetric (e.g., meridional circulation) and non-axisymmetric perturbations.

Sex Differences in QEEG in Psychopath Offenders.

Introduction. Functional brain differences related to sex in psychopathic behavior represent an important field of neuroscience research; there are few studies on this area, mainly in offender samples. Objective. The aim of this study was to investigate the presence of electrophysiological differences between male and female psychopath offenders; specifically, we wanted to assess whether the results in quantitative EEG, low-resolution electromagnetic tomography (LORETA), and changes in synchronous brain activity could be related to sex influence. Sample and Methods. The study included 31 male and 12 female psychopath offenders, according to the Hare Psychopathy Checklist-Revised criteria from 2 prisons located in Havana City. The EEG visual inspection characteristics and the use of frequency domain quantitative analysis techniques are described. Results. The resting EEG visual analyses revealed a high percentage of EEG abnormalities in both studied groups. Significant statistical differences between the mean parameters of cross spectral measures between psychopathic offender groups were found in the beta band at bilateral frontal derivation and centroparietal areas. LORETA showed differences especially in the paralimbic and parieto-occipital areas Synchronization likelihood revealed a significant group effect in the 26 to 30 Hz band. These results indicate that combining quantitative EEG, LORETA analysis, and synchronization likelihood may improve the neurofunctional differentiation between psychopath offenders of both sexes.

Investigation of Unsteady Pressure Fluctuations in Flow over Backward-Facing Step

Flow over a backward-facing step at , based on the step height, is simulated using the Divergence Free Synthetic Eddy Method of Poletto et al. (“A New Divergence Free Synthetic Eddy Method for the Reproduction of Inlet Flow Conditions for LES,” Flow, Turbulence and Combustion, Vol. 91, No. 3, 2013, pp. 519–539.), implemented in OpenFOAM® 1606, which preserves the instantaneous fluctuating pressure field in the domain, which is normally lost. Examination of the pressure spectra at various positions normal to the wall is well represented by wall-pressure measurements at all but the highest frequencies examined here. Various spectral peaks corresponding to shear-layer movement, discrete vortex shedding from the step, and numerous shear-layer instabilities are investigated using power and cross-spectral measurements of the fluctuating wall pressures. Convective velocities obtained from the cross-spectral phase indicate that the lowest frequencies convect slowly, whereas the higher frequencies near the measured spectral peaks convect at . There is an increase in convective velocity as the measurement locations are moved farther downstream. Additionally, an increase in peak frequency was found in this examination; however, the increase in convective velocity (approximately equal to 33%) and frequency (approximately equal to 7–11%) calculated at different streamwise positions were not found to be directly proportional, indicating that the increase in peak frequency cannot be solely explained by flow acceleration but that the structures are likely undergoing streamwise or spanwise deformation as well.

Quantile Cross-Spectral Measures of Dependence between Economic Variables

In this paper we introduce quantile cross-spectral analysis of multiple time series which is designed to detect general dependence structures emerging in quantiles of the joint distribution in the frequency domain. We argue that this type of dependence is natural for economic time series but remains invisible when the traditional analysis is employed. To illustrate how such dependence structures can arise between variables in different parts of the joint distribution and across frequencies, we consider quantile vector autoregression processes. We define new estimators which capture the general dependence structure, provide a detailed analysis of their asymptotic properties and discuss how to conduct inference for a general class of possibly nonlinear processes. In an empirical illustration we examine one of the most prominent time series in economics and shed new light on the dependence of bivariate stock market returns.

Flow dynamics in the wakes of low-aspect-ratio wall-mounted obstacles

The influence of shape and relative submergence (the ratio of flow depth to obstacle height, d/H) on the wake dynamics around low-aspect-ratio wall-mounted obstacles is documented for flows at Re H = 17,800 in a thin boundary layer. The obstacles investigated consisted of semi-ellipsoids with the major axes of the base ellipses aligned in the streamwise and transverse directions, and two cylinders with aspect ratios matching the ellipsoids (H/D = 0.89 and 0.67, where D is the maximum transverse dimension). Thermal anemometry was employed to provide insight into the wake dynamics, and thus, augment knowledge of the mean structure of these wakes presented by Hajimirzaie et al. (Exp Fluids 53:1943–1962, 2012). Weak symmetric shedding was observed at St = 0.183 and 0.188 in the wakes of streamwise and transverse ellipsoids at d/H = 3.9, while cross-spectral measurements confirmed downstream and upstream tilting of arch structures shed by the transverse and streamwise ellipsoids, respectively. Much weaker peaks in the power spectrum were observed for the low- and high-aspect-ratio cylinders at St = 0.084 and 0.065, respectively. While the dominant Strouhal number remained constant as the relative submergence was reduced to d/H = 2.5 for the ellipsoids, it increased significantly at d/H = 1 to St = 0.357 and 0.345 for the streamwise and transverse ellipsoids, respectively, and transitioned to an antisymmetric mode. The shedding behavior was similarly antisymmetric for both cylinders at d/H = 1, with dominant Strouhal numbers of 0.248 and 0.243 for the cylinders of H/D = 0.67 and 0.89, respectively. When calculating Strouhal number using wake width as the length scale, the values for d/H = 1 were found to fall more in line with those typical of two-dimensional bluff bodies.

Alterations in brain connectivity underlying beta oscillations in Parkinsonism.

Cortico-basal ganglia-thalamocortical circuits are severely disrupted by the dopamine depletion of Parkinson's disease (PD), leading to pathologically exaggerated beta oscillations. Abnormal rhythms, found in several circuit nodes are correlated with movement impairments but their neural basis remains unclear. Here, we used dynamic causal modelling (DCM) and the 6-hydroxydopamine-lesioned rat model of PD to examine the effective connectivity underlying these spectral abnormalities. We acquired auto-spectral and cross-spectral measures of beta oscillations (10–35 Hz) from local field potential recordings made simultaneously in the frontal cortex, striatum, external globus pallidus (GPe) and subthalamic nucleus (STN), and used these data to optimise neurobiologically plausible models. Chronic dopamine depletion reorganised the cortico-basal ganglia-thalamocortical circuit, with increased effective connectivity in the pathway from cortex to STN and decreased connectivity from STN to GPe. Moreover, a contribution analysis of the Parkinsonian circuit distinguished between pathogenic and compensatory processes and revealed how effective connectivity along the indirect pathway acquired a strategic importance that underpins beta oscillations. In modelling excessive beta synchrony in PD, these findings provide a novel perspective on how altered connectivity in basal ganglia-thalamocortical circuits reflects a balance between pathogenesis and compensation, and predicts potential new therapeutic targets to overcome dysfunctional oscillations.

Estimation of the combustion-related noise transfer matrix of a multi-cylinder diesel engine

In the present paper, a procedure for estimating an engine-platform-dependent transfer matrix that relates in-cylinder pressures to radiated noise resulting from processes associated with the combustion process is described. A knowledge of that transfer matrix allows the combustion-related component of the noise radiated by a diesel engine to be estimated from a knowledge of cylinder pressure signals. The procedure makes use of multi-input/multi-output (MIMO) system modeling concepts in conjunction with cross-spectral measurements. To date, the empirical prediction of diesel engine combustion noise has usually been achieved by combining a cylinder pressure with a single, smooth structural attenuation function (e.g., the Lucas combustion noise meter) regardless of the specifications of the engine. In comparison, the procedure described in the present work provides the structural attenuation characteristics of a particular engine in the form of a transfer matrix, thus allowing accurate prediction by accounting fully for inter-cylinder correlation, cylinder-to-cylinder variation and the detailed characteristics of an engine structure. The procedure was applied to a six-cylinder diesel engine, and the various aspects of the new procedure are described.

Cross spectral measurement of head related speech transfer functions using speaker’s own voice

A cross spectrum method is applied to measure sound pressure variations around the head using the speaker’s own speech sounds. The variations are represented as transfer functions from the mouth reference point to a set of measuring points. Preliminary tests indicated that there are systematic frequency response variations depending on vowel colors. This vowel color dependency was not replicated in the classical measurement of speech radiation characteristics by J. L. Flanagan. However, taking into account the large (sometimes exceeding 20 dB) amount of variations, it is not likely to be negligible. A set of calibration and normalization procedures were introduced to reduce artifacts due to background noise, room acoustics, zeros in the speech spectra. A series of M-sequence based transfer function measurements were also conducted using a head and torso simulator to evaluate intrinsic errors in the cross spectral measurements. It was found that the standard errors in the cross spectral measurements using recorded speech sounds are around 1 dB. Based on these reference data and confidence interval calculations based on coherence, it is safe to conclude that the vowel color dependency is significantly modifying the transfer functions. [Work supported by JSPS.]

Coherent structure in the turbulent planar jet. Part 1. Extraction of proper orthogonal decomposition eigenmodes and their self-similarity

In this paper the coherent structure in the similarity region of the turbulent planar jet is examined experimentally by application of the proper orthogonal decomposition (POD). In particular, twin cross-stream rakes of X-wire probes are used to take cross-spectral measurements with different spanwise separations between the rakes and at several locations throughout the similarity region. The resulting POD spatial eigenfunctions for each of the three velocity components depend on cross-stream spatial coordinate, Strouhal number, and spanwise wavenumber. Corresponding eigenvalue distributions are obtained in Strouhal number–spanwise wavenumber space. Eigenvalue convergence is demonstrated to be rapid. When properly scaled the eigenfunctions and eigenvalues are shown to exhibit self-similarity though the streamwise location at which this commences depends on the particular velocity component. The results suggest that the flow supports a planar structure aligned in the spanwise direction as well as an essentially three-dimensional structure with asymmetrical shape in the cross-stream direction and pseudo-periodically distributed in the spanwise direction. Comparison of the single- and dual-rake implementations of the POD presented in this paper demonstrate that measurements confined to a single plane are incapable of properly extracting the planar modes. Rather, the single-rake implementation results in modes that appear to be a weighted sum of modes corresponding to different spanwise wavenumbers.

On the Mach- and Reynolds-Number Dependence of the Flat-Plate Turbulent Boundary Layer Wall-Pressure Spectrum

Wall-pressure measurements are performed using an array of pinhole microphones mounted into the test wall of a low noise, low turbulence flow facility. The frequency–wave-number spectra for both streamwise and spanwise directions are obtained through the spatial Fourier transformation of cross-spectral measurements in the said directions. The results of the wind-tunnel measurements reveal an interesting behavior of the low wave-number portion of the wall-pressure spectrum. Namely, this portion of the spectrum does not exhibit any Mach-number dependence for nearly incompressible flows. A low Mach-number analysis accounting for finite Reynolds-number effects is performed. This analysis shows the wall-pressure spectrum to have a leading term independent of the Mach number. The frequency dependence of the theoretical spectrum agrees well with that of the experimental spectrum. The physical mechanism for the Mach-number independence of the spectrum is attributed to a hydrodynamic dipole contribution to the wall pressure resulting from the Stokes layer induced by the turbulent eddies. The higher differential order of the viscous equations of motion allows for the existence of such Stokes layers. They have no counterpart in invisicd theories wherein no such Mach-number independence of the spectrum has been observed. A simple model problem is devised which isolates the viscous mechanism responsible for the modification of the wall pressure and the corresponding sound field. It is argued that the physical process involved is akin (albeit inversely) to that operative in the boundary-layer receptivity problem for nearly incompressible flows.

The effects of stochastic galvanic vestibular stimulation on human postural sway.

Galvanic vestibular stimulation serves to modulate the continuous firing level of the peripheral vestibular afferents. It has been shown that the application of sinusoidally varying, bipolar galvanic currents to the vestibular system can lead to sinusoidally varying postural sway. Our objective was to test the hypothesis that stochastic galvanic vestibular stimulation can lead to coherent stochastic postural sway. Bipolar binaural stochastic galvanic vestibular stimulation was applied to nine healthy young subjects. Three different stochastic vestibular stimulation signals, each with a different frequency content (0-1 Hz, 1-2 Hz, and 0-2 Hz), were used. The stimulation level (range 0.4-1.5 mA, peak to peak) was determined on an individual basis. Twenty 60-s trials were conducted on each subject - 15 stimulation trials (5 trials with each stimulation signal) and 5 control (no stimulation) trials. During the trials, subjects stood in a relaxed, upright position with their head facing forward. Postural sway was evaluated by using a force platform to measure the displacements of the center of pressure (COP) under each subject's feet. Cross-spectral measures were used to quantify the relationship between the applied stimulus and the resulting COP time series. We found significant coherency between the stochastic vestibular stimulation signal and the resulting mediolateral COP time series in the majority of trials in 8 of the 9 subjects tested. The coherency results for each stimulation signal were reproducible from trial to trial, and the highest degree of coherency was found for the 1- to 2-Hz stochastic vestibular stimulation signal. In general, for the nine subjects tested, we did not find consistent significant coherency between the stochastic vestibular stimulation signals and the anteroposterior COP time series. This work demonstrates that, in subjects who are facing forward, bipolar binaural stochastic galvanic stimulation of the vestibular system leads to coherent stochastic mediolateral postural sway, but it does not lead to coherent stochastic anteroposterior postural sway. Our finding that the coherency was highest for the 1- to 2-Hz stochastic vestibular stimulation signal may be due to the intrinsic dynamics of the quasi-static postural control system. In particular, it may result from the effects of the vestibular stimulus simply being superimposed upon the quiet-standing COP displacements. By utilizing stochastic stimulation signals, we ensured that the subjects could not predict a change in the vestibular stimulus. Thus, our findings indicate that subjects can act as "responders" to galvanic vestibular stimulation.

Propagation characteristics and relation between electrostatic and magnetic fluctuations in DIT

An account is given of experiments on the DITE tokamak, using a fast reciprocating set of combined Langmuir and magnetic probes in the same discharge to compare the propagation characteristics of the turbulent electrostatic and magnetic perturbations with those expected from the measured local electric field and pressure gradient, and to investigate the effect of shear on cross-field transport. In addition, the relation between the electrostatic and magnetic aspects of the turbulence is investigated using direct cross-spectral measurements. The results are consistent with a picture in which magnetic fluctuations in the edge are due to the currents driven by the basically electrostatic turbulence, whose own propagation behaviour is dominated by the effects of the sheared E*B/B2 velocity

Spectral measurements of temperature and longitudinal velocity fluctuations in fully developed pipe flow

It is known that for fully developed flows the similarity between heat and momentum transfer can be studied in terms of the temperature and longitudinal velocity fluctuations at a point. Results of spectral and cross-spectral measurements are presented which show that a strong relationship exists between the velocity and temperature field at low wavenumbers but not at high wavenumbers. Considerable flow energy was found associated with wavelengths much larger than the tube diameter and new information about spectral shapes is revealed. From Taylor's hypothesis and time delayed cross-correlations, the streamwise extent of the correlation between the two fields is described.