Power Spectrum Estimation Research Articles

Self-similarity and multifractality in human brain activity: A wavelet-based analysis of scale-free brain dynamics

BackgroundThe temporal structure of macroscopic brain activity displays both oscillatory and scale-free dynamics. While the functional relevance of neural oscillations has been largely investigated, both the nature and the role of scale-free dynamics in brain processing have been disputed. New methodHere, we offer a novel method to rigorously enrich the characterization of scale-free brain activity using a robust wavelet-based assessment of self-similarity and multifractality. For this, we analyzed human brain activity recorded with magnetoencephalography (MEG) while participants were at rest or performing a visual motion discrimination task. ResultsFirst, we report consistent infraslow (from 0.1 to 1.5 Hz) scale-free dynamics (i.e., self-similarity and multifractality) in resting-state and task data. Second, we observed a fronto-occipital gradient of self-similarity reminiscent of the known hierarchy of temporal scales from sensory to higher-order cortices; the anatomical gradient was more pronounced in task than in rest. Third, we observed a significant increase of multifractality during task as compared to rest. Additionally, the decrease in self-similarity and the increase in multifractality from rest to task were negatively correlated in regions involved in the task, suggesting a shift from structured global temporal dynamics in resting-state to locally bursty and non Gaussian scale-free structures during task. Comparison with existing method(s)We showed that the wavelet leader based multifractal approach extends power spectrum estimation methods in the way of characterizing finely scale-free brain dynamics. ConclusionsAltogether, our approach provides novel fine-grained characterizations of scale-free dynamics in human brain activity.

Calibrating magnification bias for the EG statistic to test general relativity

We assess the effect of magnification bias on the $E_G$ statistic for probing gravity. $E_G$, a statistic constructed from power spectrum estimates of both weak lensing and redshift space distortions (RSD), directly tests general relativity (GR) while in principle being independent of clustering bias. This property has motivated its recent use in multiple tests of GR. Recent work has suggested that the magnification bias of galaxies due to foreground matter perturbations breaks the bias-independence of the $E_G$ statistic. The magnitude of this effect is very sensitive to the clustering and magnification biases of the galaxy sample. We show that for realistic values of the clustering and magnification biases, the effect for magnification bias is small relative to statistical errors for most spectroscopic galaxy surveys but large for photometric galaxy surveys. For the cases with significant magnification bias, we propose a method to calibrate magnification bias using measurements of the lensing auto-power spectrum. We test this calibration method using simulations, finding that our calibration method can calibrate $E_G$ from 2-4 times the simulation error to well within the errors, although its accuracy is sensitive to the precision of the measured redshift distribution and magnification bias, but not the clustering bias. This work gives strong evidence that this method will work increasingly well in future CMB lensing surveys.

Erratum: “PAPER-64 Constraints on Reionization: The 21 cm Power Spectrum at z = 8.4” (2015, ApJ, 809, 61)

Erratum: “PAPER-64 Constraints on Reionization: The 21 cm Power Spectrum at <i>z</i> = 8.4” (2015, ApJ, 809, 61)

Power Spectrum Consistency among Systems and Transducers

Use of the reference phantom method for computing acoustic attenuation and backscatter is widespread. However, clinical application of these methods has been limited by the need to acquire reference phantom data. We determined that the data acquired from 11 transducers of the same model and five clinical ultrasound systems of the same model produce equivalent estimates of reference phantom power spectra. We describe that the contribution to power spectral density variance among systems and transducers equals that from speckle variance with 59 uncorrelated echo signals. Thus, when the number of uncorrelated lines of data is small, speckle variance will dominate the power spectral density estimate variance introduced by different systems and transducers. These results suggest that, at least for this particular transducer and imaging system combination, one set of reference phantom calibration data is highly representative of the average among equivalent transducers and systems that are in good working order.

Measurement and Visualization System of Eigenmode Shapes Considering Orthogonal Modes on Circular Membrane

This work proposes a visualization system of eigenmode shapes of a tapped circular membrane of membranophones. Under tapped membrane vibration, it is not enough to divide modes in frequency domain, because of the existence of eignmodes whose frequencies are close to each other including orthogonal modes. Therefore, we structured this visualization system of eigenmode shapes, which could divide the orthogonal modes appearing at slightly different frequencies. This system firstly measures the sound pressures emitted from the vibration on tapped circular membrane of membranophone with a circular microphone array placed in proximity to the membrane. Secondly, it extracts the circumferential shape of each eigenfrequency. In this system, dominant frequencies of estimated power spectrum density obtained by Yule-Walker method are considered as approximate eigenfrequences of this vibration. Multiple eigenmodes whose azimuthal mode order is different, are divided by Fourier series expansion of the circumferential shapes of each eigenfrequency. In addition, orthogonal modes, which have the same mode order and slightly different frequencies are divided by considering the orthogonality of mode shapes, sine and cosine functions. Lastly, the system estimates the eigenmode shape of the whole membrane using the Bessel function of the first kind correspond to each mode order as radial shape, and shows them to users. It is expected that user could recognize the unbalance of tension distribution intuitively using this system. It is also expected the system to be applied to the tuning assistive system of the tuning of circular membranophone.

Wideband Spectrum Sensing Based on Single-Channel Sub-Nyquist Sampling for Cognitive Radio.

Spectrum sensing is an important task in cognitive radio. However, currently available Analog-to-Digital Converters (ADC) can hardly satisfy the sampling rate requirement for wideband signals. Even with such an ADC, the cost is extremely high in terms of price and power consumption. In this paper, we propose a spectrum-sensing method based on single-channel sub-Nyquist sampling. Firstly, a serial Multi-Coset Sampling (MCS) structure is designed to avoid mismatches among sub-ADCs in the traditional parallel MCS. Clocks of the sample/hold and ADC are provided by two non-uniform sampling clocks. The cooperation between these two non-uniform sampling clocks shifts the high sampling rate burden from the ADC to the sample/hold. Secondly, a power spectrum estimation method using sub-Nyquist samples is introduced, and an efficient spectrum-sensing algorithm is proposed. By exploiting the frequency-smoothing property, the proposed efficient spectrum-sensing algorithm only needs to estimate power spectrum at partial frequency bins to conduct spectrum sensing, which will save a large amount of computational cost. Finally, the sampling pattern design of the proposed serial MCS is given, and it is proved to be a minimal circular sparse ruler with an additional constraint. Simulations show that mismatches in traditional parallel MCS have a serious impact on spectrum-sensing performance, while the proposed serial MCS combined with the efficient spectrum-sensing algorithm exhibits outstanding spectrum-sensing performance at much lower computational cost.

Evidence for solar influence in a Holocene speleothem record (Père Noël cave, SE Belgium)

We present a decadal-centennial scale Holocene climate record based on trace elements contents from a 65 cm stalagmite from Belgian Père Noël cave. “Père Noël” (PN) stalagmite covers the last 12.7 ka according to U/Th dating. High spatial resolution measurements of trace elements (Sr, Ba and Mg) were done by Laser-Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS). Trace elements profiles were interpreted as environmental and climate changes in the Han-sur-Lesse region. Power spectrum estimators and continuous wavelet transform were applied on trace elements time series to detect any statistically significant periodicities in the PN stalagmite. Spectral analyses reveal decadal to millennial periodicities (i.e., 68–75, 133–136, 198–209, 291–358, 404–602, 912–1029 and 2365–2670 yr) in the speleothem record. Results were compared to reconstructed sunspot number data to determine whether solar signal is presents in PN speleothem. The occurrence of significant solar periodicities (i.e., cycles of Gleissberg, de Vries, unnamed 500 years, Eddy and Hallstatt) supports for an impact of solar forcing on PN speleothem trace element contents. Moreover, several intervals of significant rapid winter change were detected during the Holocene at 10.3, 9.3–9.5, around 8.2, 6.4–6.2, 4.7–4.5, and around 2.7 ka BP. Those intervals are similar to the cold winter events evidenced in different natural paleoclimate archives, suggesting common climate forcing mechanisms related to changes in solar irradiance.

Wideband compressive beamforming tomography for drive-by large-scale acoustic source mapping.

Noise-mapping is an effective sound visualization tool for the identification of urban noise hotspots, which is crucial to taking targeted measures to tackle environmental noise pollution. This paper develops a high-resolution wideband acoustic source mapping methodology using a portable microphone array, where the joint localization and power spectrum estimation of individual sources sparsely distributed over a large region are achieved by tomographic imaging with the multi-frequency delay-and-sum beamforming power outputs from multiple array positions. Exploiting the fact that a wideband source has a common spatial signal-support across the frequency spectrum, two-dimensional tomographic maps are produced by applying compressive sensing techniques including group least absolute shrinkage selection operator formulation and sparse Bayesian learning to promote group sparsity over multiple frequency bands. The high-resolution mapping is demonstrated with experimental data recorded with a microphone array mounted atop an electric vehicle driven along a road while playing audio clips from a loudspeaker positioned within the adjacent open field.

Adhesive debonding inspection with a small EMAT in resonant mode

In this paper, a noncontact ultrasonic testing method with using a small electromagnetic acoustic transducer (EMAT) in resonant mode is proposed for metal-based adhesive debonding inspection. The small EMAT with a new magnet configuration and a small coil is developed firstly to improve the spatial resolution and detecting ability for minute defects. Different from conventional pulse echo method using short pulse excitation for debonding inspection, a new method based on power spectrum estimation of the resonant ultrasonic signal with long burst excitation is applied to increase the signal-to-noise ratio (SNR) and detecting ability of the small EMAT. Finally, ultrasonic C-scan images of specimens with various adhesive bonding are obtained to demonstrate the capability of this technique.

Fast algorithm for the computation of the CMB polarization TE power spectrum using non-circular beam

A precise measurement of the Cosmic Microwave Background (CMB) anisotropy has been one of the foremost concerns in modern cosmology as it provides a valuable information on the cosmology of the Universe. The estimation of the CMB power spectrum is complicated by different systematics. For the polarization experiments, the signals are rather fainter in comparison with the CMB total intensity, which might lead to an important bias in the estimation of the angular power spectrum. One of the most important source of bias in CMB polarization experiment is the beam asymmetry. In this paper, we present a semi-analytical framework using the pseudo-Cl estimator to compute the power spectrum TE of the temperature anisotropy and the E-component of the polarization radiation field using non-circular beams. We assume that the beam is non-rotating. We adopt a model of beams obtained from a perturbative expansion of the beam around a circular (axisymmetric) beam in harmonic space. We compute the resulting bias matrix which relates the true power spectrum with the observed one by using an efficient algorithm for rapid computation. We show that for a multipole up to lmax=500, the bias matrix can be computed in less than one second with a single CPU processor at 2.53 GHz. We find that the systematic effect induced by the beam asymmetry in the temperature and polarization power spectrum at the peak of the bias matrix for WMAP and Planck experiments can be as large as a few 10 to 20% (upper limit for Planck LFI 30 GHz).

KiDS+GAMA: cosmology constraints from a joint analysis of cosmic shear, galaxy–galaxy lensing, and angular clustering

We present cosmological parameter constraints from a joint analysis of three cosmological probes: the tomographic cosmic shear signal in $\sim$450 deg$^2$ of data from the Kilo Degree Survey (KiDS), the galaxy-matter cross-correlation signal of galaxies from the Galaxies And Mass Assembly (GAMA) survey determined with KiDS weak lensing, and the angular correlation function of the same GAMA galaxies. We use fast power spectrum estimators that are based on simple integrals over the real-space correlation functions, and show that they are practically unbiased over relevant angular frequency ranges. We test our full pipeline on numerical simulations that are tailored to KiDS and retrieve the input cosmology. By fitting different combinations of power spectra, we demonstrate that the three probes are internally consistent. For all probes combined, we obtain $S_8\equiv \sigma_8 \sqrt{\Omega_{\rm m}/0.3}=0.800_{-0.027}^{+0.029}$, consistent with Planck and the fiducial KiDS-450 cosmic shear correlation function results. Marginalising over wide priors on the mean of the tomographic redshift distributions yields consistent results for $S_8$ with an increase of $28\%$ in the error. The combination of probes results in a $26\%$ reduction in uncertainties of $S_8$ over using the cosmic shear power spectra alone. The main gain from these additional probes comes through their constraining power on nuisance parameters, such as the galaxy intrinsic alignment amplitude or potential shifts in the redshift distributions, which are up to a factor of two better constrained compared to using cosmic shear alone, demonstrating the value of large-scale structure probe combination.

The hydrogen epoch of reionization array dish III: measuring chromaticity of prototype element with reflectometry

The experimental efforts to detect the redshifted 21 cm signal from the Epoch of Reionization (EoR) are limited predominantly by the chromatic instrumental systematic effect. The delay spectrum methodology for 21 cm power spectrum measurements brought new attention to the critical impact of an antenna's chromaticity on the viability of making this measurement. This methodology established a straightforward relationship between time-domain response of an instrument and the power spectrum modes accessible to a 21 cm EoR experiment. We examine the performance of a prototype of the Hydrogen Epoch of Reionization Array (HERA) array element that is currently observing in Karoo desert, South Africa. We present a mathematical framework to derive the beam integrated frequency response of a HERA prototype element in reception from the return loss measurements between 100-200 MHz and determined the extent of additional foreground contamination in the delay space. The measurement reveals excess spectral structures in comparison to the simulation studies of the HERA element. Combined with the HERA data analysis pipeline that incorporates inverse covariance weighting in optimal quadratic estimation of power spectrum, we find that in spite of its departure from the simulated response, HERA prototype element satisfies the necessary criteria posed by the foreground attenuation limits and potentially can measure the power spectrum at spatial modes as low as $k_{\parallel} > 0.1h$~Mpc$^{-1}$. The work highlights a straightforward method for directly measuring an instrument response and assessing its impact on 21 cm EoR power spectrum measurements for future experiments that will use reflector-type antenna.

Beyond the plane-parallel approximation for redshift surveys

Redshift space distortions privilege the location of the observer in cosmological redshift surveys, breaking the translational symmetry of the underlying theory. This violation of statistical homogeneity has consequences for the modeling of clustering observables, leading to what are frequently called `wide angle effects'. We study these effects analytically, computing their signature in the clustering of the multipoles in configuration and Fourier space. We take into account both physical wide angle contributions as well as the terms generated by the galaxy selection function. Similar considerations also affect the way power spectrum estimators are constructed. We quantify, in an analytical way the biases which enter and clarify the relation between what we measure and the underlying theoretical modeling. The presence of an angular window function is also discussed. Motivated by this analysis we present new estimators for the three dimensional Cartesian power spectrum and bispectrum multipoles written in terms of spherical Fourier-Bessel coefficients. We show how the latter have several interesting properties, allowing in particular a clear separation between angular and radial modes.

Mobile e-Commerce Recommendation System Based on Multi-Source Information Fusion for Sustainable e-Business

A lack of in-depth excavation of user and resources information has become the main bottleneck restricting the predictive analytics of recommendation systems in mobile commerce. This article provides a method which makes use of multi-source information to analyze consumers’ requirements for e-commerce recommendation systems. Combined with the characteristics of mobile e-commerce, this method employs an improved radial basis function (RBF) network in order to determine the weights of recommendations, and an improved Dempster–Shafer theory to fuse the multi-source information. Power-spectrum estimation is then used to handle the fusion results and allow decision-making. The experimental results illustrate that the traditional method is inferior to the proposed approach in terms of recommendation accuracy, simplicity, coverage rate and recall rate. These achievements can further improve recommendation systems, and promote the sustainable development of e-business.

EEG power spectrum as a biomarker of autism: a pilot study

The aim of this study was to assess whether power spectrum estimates of electroencephalogram (EEG) can be used as a biomarker for autism spectrum disorder (ASD). EEG collected from ASD and control participants performing a short-memory task was preprocessed to remove noise and artefacts, power spectral density (PSD) estimates were obtained by the modified covariance method and used as the study features that were subjected next to the Kruskal-Wallis analysis of differences. After verifying that the features (PSD estimates) were statistically different between the autistic and control subjects, these PSD estimates were classified using the 'k nearest neighbour' (KNN) classification algorithm with the average accuracy of 89.29%. This result indicates that EEG of autistic and control individuals may contain statistically different features; therefore, EEG power spectrum may be used as a biomarker for autism.

EEG power spectrum as a biomarker of autism: a pilot study

The aim of this study was to assess whether power spectrum estimates of electroencephalogram (EEG) can be used as a biomarker for autism spectrum disorder (ASD). EEG collected from ASD and control participants performing a short-memory task was preprocessed to remove noise and artefacts, power spectral density (PSD) estimates were obtained by the modified covariance method and used as the study features that were subjected next to the Kruskal-Wallis analysis of differences. After verifying that the features (PSD estimates) were statistically different between the autistic and control subjects, these PSD estimates were classified using the 'k nearest neighbour' (KNN) classification algorithm with the average accuracy of 89.29%. This result indicates that EEG of autistic and control individuals may contain statistically different features; therefore, EEG power spectrum may be used as a biomarker for autism.

Linear perturbations in spherically symmetric dust cosmologies including a cosmological constant

We study the dynamical behaviour of gauge-invariant linear perturbations in spherically symmetric dust cosmologies including a cosmological constant. In contrast to spatially homogeneous FLRW models, the reduced degree of spatial symmetry causes a non-trivial dynamical coupling of gauge-invariant quantities already at first order perturbation theory and the strength and influence of this coupling on the spacetime evolution is investigated here. We present results on the underlying dynamical equations augmented by a cosmological constant and integrate them numerically. We also present a method to derive cosmologically relevant initial variables for this setup. Estimates of angular power spectra for each metric variable are computed and evaluated on the central observer's past null cone. By comparing the full evolution to the freely evolved initial profiles, the coupling strength will be determined for a best fit radially inhomogeneous patch obtained in previous works (see [1]). We find that coupling effects are not noticeable within the cosmic variance limit and can therefore safely be neglected for a relevant cosmological scenario. On the contrary, we find very strong coupling effects in a best fit spherical void model matching the distance redshift relation of SNe which is in accordance with previous findings using parametric void models.

Towards optimal extraction of cosmological information from nonlinear data

One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics of clusters, density peaks or voids etc.), along with the corresponding covariance matrices. However, this approach is computationally prohibitive and has not been shown to be exhaustive in terms of information content. Here we instead develop a hierarchical Bayesian approach, expanding the likelihood around the maximum posterior of linear modes, which we solve for using optimization methods. By integrating out the modes using perturbative expansion of the likelihood we construct an initial power spectrum estimator, which for a fixed forward model contains all the cosmological information if the initial modes are gaussian distributed. We develop a method to construct the window and covariance matrix such that the estimator is explicitly unbiased and nearly optimal. We then generalize the method to include the forward model parameters, including cosmological and nuisance parameters, and primordial non-gaussianity. We apply the method in the simplified context of nonlinear structure formation, using either simplified 2-LPT dynamics or N-body simulations as the nonlinear mapping between linear and nonlinear density, and 2-LPT dynamics in the optimization steps used to reconstruct the initial density modes. We demonstrate that the method gives an unbiased estimator of the initial power spectrum, providing among other a near optimal reconstruction of linear baryonic acoustic oscillations.

Deconvolving the wedge: maximum-likelihood power spectra via spherical-wave visibility modelling

Direct detection of the Epoch of Reionization (EoR) via the red-shifted 21-cm line will have unprecedented implications on the study of structure formation in the infant Universe. To fulfill this promise, current and future 21-cm experiments need to detect this weak EoR signal in the presence of foregrounds that are several orders of magnitude larger. This requires extreme noise control and improved wide-field high dynamic-range imaging techniques. We propose a new imaging method based on a maximum likelihood framework which solves for the interferometric equation directly on the sphere, or equivalently in the $uvw$-domain. The method uses the one-to-one relation between spherical waves and spherical harmonics (SpH). It consistently handles signals from the entire sky, and does not require a $w$-term correction. The spherical-harmonics coefficients represent the sky-brightness distribution and the visibilities in the $uvw$-domain, and provide a direct estimate of the spatial power spectrum. Using these spectrally-smooth SpH coefficients, bright foregrounds can be removed from the signal, including their side-lobe noise, which is one of the limiting factors in high dynamics range wide-field imaging. Chromatic effects causing the so-called "wedge" are effectively eliminated (i.e. deconvolved) in the cylindrical ($k_{\perp}, k_{\parallel}$) power spectrum, compared to a power spectrum computed directly from the images of the foreground visibilities where the wedge is clearly present. We illustrate our method using simulated LOFAR observations, finding an excellent reconstruction of the input EoR signal with minimal bias.

Pengaruh Latar Belakang Warna pada Objek Gambar terhadap Hasil Ekstraksi Sinyal EEG

In this study, observation on the differences in features quality of EEG records as a result of training on subjects has been made. The features of EEG records were extracted using two different methods, the root mean square which is acquired from the range between 0.5 and 5 seconds and the average of power spectrum estimation from the frequency range between 20 and 40Hz. All of the data consists of a 4-channel recording and produce good quality classification on artificial neural network, with each of which generates training data accuracy over 90%. However, different results are occured when the trained system is tested on other test data. The test results show that the two systems which are trained using training data with object with color background produce higher accuracy than the other two systems which are trained using training data with object without background color, 63.98% and 60.22% compared to 59.68% and 56.45% accuracy respectively. From the use of the features on the artificial neural network classification system, it can be concluded that the training system using EEG data records derived from the visualization of object with color background produces better features than the visualization of object without color background.