Power Spectrum Estimation Research Articles

Analysis and Estimation of Power Spectrum by EEG During the Kraepelin Test with or Without Rhythm

In this paper, by measuring EEG during the Kraepelin test, it was clarified that the optimal rhythm which maximized the number of answers was found to be 1.2-times, when the rhythm answering without rhythm was set at 1.0-times. It was clarified that when the optimum rhythm was listened to, the ratio of power spectrum for relaxation/concentration was higher, the standard deviation of that ratio was smaller, and the activation of the left and right brains was not unbalanced. The power spectrum of the EEG while listening to the rhythm and answering the Kraepelin test was estimated from the EEG when answering without rhythm, and the error was less than 10%.

Recent Advances in Attenuation Estimation.

This chapter reviews some of the recent advances in the estimation of the local and the total attenuation, with an emphasis on reducing the bias and variance of the estimates. A special focus is put on describing the effect of power spectrum estimation on bias and variance, the introduction of regularization strategies, as well as on eliminating the need to use reference phantoms for compensating for system dependent effects.

The tracking tapered gridded estimator for the power spectrum from drift scan observations

ABSTRACT Intensity mapping with the redshifted 21-cm line is an emerging tool in cosmology. Drift scan observations, where the antennas are fixed to the ground and the telescope’s pointing centre (PC) changes continuously on the sky due to earth’s rotation, provide broad sky coverage and sustained instrumental stability needed for 21-cm intensity mapping. Here, we present the Tracking Tapered Grided Estimator (TTGE) to quantify the power spectrum of the sky signal estimated directly from the visibilities measured in drift scan radio interferometric observations. The TTGE uses the data from the different PC to estimate the power spectrum of the signal from a small angular region located around a fixed tracking centre (TC). The size of this angular region is decided by a suitably chosen tapering window function that serves to reduce the foreground contamination from bright sources located at large angles from the TC. It is possible to cover the angular footprint of the drift scan observations using multiple TC, and combine the estimated power spectra to increase the signal-to-noise ratio. Here, we have validated the TTGE using simulations of $154 \, {\rm MHz}$ Murchison Wide-field Array drift scan observations. We show that the TTGE can recover the input model angular power spectrum Cℓ within $20 {{\ \rm per\ cent}}$ accuracy over the ℓ range 40 < ℓ < 700.

The control of astronomical cycles on lacustrine fine-grained event Sedimentation—A case study of the Chunshang sub-member of the upper Es4 in the Dongying Sag

Fine-grained lacustrine sedimentation controlled by astronomical cycles remains a research weakness in sedimentology studies, as most studies have concentrated on how astronomical cycles affect the normal lacustrine fine-grained sedimentation, but how they affect the lacustrine fine-grained event sedimentation has been rarely studied. Therefore, this work researched the characteristics of event sedimentation by systematically observing the cores from 30 cored wells in the Shahejie Formation of the Dongying Sag at a depth of over 1800 m, with more than 4000 thin sections being authenticated and over 1000 whole rocks being analyzed by X-ray diffraction (XRD). The research object was the Chunshang Sub-member of Upper Es4 in the Fanye 1 well, as it had the most comprehensive analysis data and underwent the most continuous coring. We divided astronomical cycles into different orders and made corresponding curves using the gamma-ray (GR) curve, spectral analysis, power spectrum estimation, and module extreme values, there were 6 long eccentricity periods, 22 short eccentricity periods, 65.5 obliquity cycles, and 110.5 precession cycles in this sub-member. On this basis, this study analyzed the control of astronomical cycles on the lacustrine fine-grained event sedimentation, and the research shows deposits were developed by slide-slump, turbidities, hyperpycnites, and tempestites in the Chunshang Sub-member of the Upper Es4, with higher long eccentricity, the monsoon climate contributes to the formation of storm currents, while with lower long eccentricity, the surface deposits are severely eroded by rivers and rainfalls, thus developing the slide-slump, turbidities, and hyperpycnites. The relationship between the lacustrine fine-grained event sedimentation and astronomical cycles was studied in this case study, which can promote research on fine-grained sedimentary rocks in genetic dynamics and boost the theoretical and disciplinary development in fine-grained sedimentology.

Studying large-scale structure probes of modified gravity with COLA

We study the effect of two Modified Gravity (MG) theories, f(R) and nDGP, on three probes of large-scale structure, the real space power spectrum estimator Q 0, bispectrum and voids, and validate fast approximate COLA simulations against full N-body simulations for the prediction of these probes.We find that using the first three even multipoles of the redshift space power spectrum to estimate Q 0 is enough to reproduce the MG boost factors of the real space power spectrum for both halo and galaxy catalogues. By analysing the bispectrum and reduced bispectrum of Dark Matter (DM), we show that the strong MG signal present in the DM bispectrum is mainly due to the enhanced power spectrum. We warn about adopting screening approximations in simulations as this neglects non-linear contributions that can source a significant component of the MG bispectrum signal at the DM level, but we argue that this is not a problem for the bispectrum of galaxies in redshift space where the signal is dominated by the non-linear galaxy bias. Finally, we search for voids in our mock galaxy catalogues using the ZOBOV watershed algorithm.To apply a linear model for Redshift-Space Distortion (RSD) in the void-galaxy cross-correlation function, we first examine the effects of MG on the void profiles entering into the RSD model. We find relevant MG signals in the integrated-density, velocity dispersion and radial velocity profiles in the nDGP theory. Fitting the RSD model for the linear growth rate, we recover the linear theory prediction in an nDGP model, which is larger than the ΛCDM predictionat the 3σ level. In f(R) theory we cannot naively compare the results of the fit with the linear theory prediction as this is scale-dependent, but we obtain results that are consistent with the ΛCDM prediction.

Application of Bispectrum Dimensionality Reduction Method in Ultrasonic Echo Signal Processing

Processing ultrasonic echo signals to obtain high-precision residual thickness information of the pipeline wall is the key to nondestructive testing of corrosion of a long-distance pipeline. The traditional power spectrum estimation method assumes that an analyzed echo signal is Gaussian, and the useful information is insufficiently extracted, which leads to errors in the processing results. In this paper, to solve this problem, the bispectrum, which requires the least amount of computation in higher-order spectral estimation, is proposed to process an echo signal with a non-minimum phase and non-Gaussian characteristics. The bispectrum is projected onto a one-dimensional frequency space using the dimensionality reduction method, and one-dimensional diagonal slices of the bispectrum are extracted to analyze the characteristics of the echo signal, which significantly improves the intuitiveness of data processing. The experimental results show that the bispectrum dimensionality reduction method has high accuracy in processing ultrasonic echo signals, and the relative error of the residua wall thickness is below 2%. A C-scan image displaying the shape, size, depth, and other characteristics of pipeline corrosion obtained by the proposed method is much better than that using the traditional power spectrum estimation method. Therefore, the proposed method is suitable for nondestructive testing of corrosion of long-distance pipelines.

Towards optimal foreground mitigation strategies for interferometric H i intensity mapping in the low-redshift Universe

Abstract We conduct the first case study towards developing optimal foreground mitigation strategies for neutral hydrogen (H i) intensity mapping using radio interferometers at low redshifts. A pipeline for simulation, foreground mitigation, and power spectrum estimation is built, which can be used for ongoing and future surveys using MeerKAT and Square Kilometre Array Observatory. It simulates realistic sky signals to generate visibility data-given instrument and observation specifications, which is subsequently used to perform foreground mitigation and power spectrum estimation. A quadratic estimator formalism is developed to estimate the temperature power spectrum in visibility space. Using MeerKAT telescope specifications for observations in the redshift range, $z$ ∼ 0.25–0.30, corresponding to the MeerKAT International GHz Tiered Extragalactic Exploration (MIGHTEE) survey, we present a case study, where we compare different approaches of foreground mitigation. We find that component separation in visibility space provides a more accurate estimation of H i clustering when compared with foreground avoidance, with the uncertainties being 30 per cent smaller. Power spectrum estimation from image is found to be less robust with larger bias and more information loss when compared with estimation in visibility. We conclude that for the considered sub-band of $z$ ∼ 0.25–0.30, the MIGHTEE survey will be capable of measuring the H i power spectrum from $k\sim 0.5$ to $k\sim 10\, {\rm Mpc^{-1}}$ with signal-to-noise ratio being ∼3. We are the first to show that, at low redshift, component separation in visibility space suppresses foreground contamination at large line-of-sight scales, allowing measurement of H i power spectrum closer to the foreground wedge, crucial for data analysis towards future detections.

Revising the application of cross-spectrum processing in motion parameter estimation for harmonic sources

Single-receiver motion parameter estimation is an effective and economical technology for passive source localization and train-bearing fault diagnosis, in which time-consuming time-frequency analysis (TFA) methods are widely used to suppress noise when extracting the continuous Doppler shift of the overhead pass. Cross-spectrum processing is a potential way to improve the computational efficiency of TFA methods, but its application is overshadowed by the phenomena of unknown Doppler shift offset and power spectrum estimation error. In this paper, conventional cross-spectrum processing is proven to be an approximation trick for power spectrum estimation in a small frequency interval, and the two phenomena are fully explained by the frequency aliasing of bandpass sampling and the approximation error. On this basis, an revised framework for applying the cross-spectrum processing is provided. Processing results of the SWellEx-96 experiment data demonstrate that the computational efficiencies of spectrogram and a parameterized TFA method could be improved up to 85% and 88.2%, respectively, without a noticeable impact on the accuracy of parameter estimates.

BCI Wheelchair Control Using Expert System Classifying EEG Signals Based on Power Spectrum Estimation and Nervous Tics Detection

The constantly developing biomedical engineering field and newer and more advanced BCI (brain–computer interface) systems require their designers to constantly develop and search for various innovative methods used in their creation. In response to practical requirements and the possibility of using the system in real conditions, the authors propose an advanced solution using EEG (electroencephalography) signal analysis. A BCI system design approach using artificial intelligence for the advanced analysis of signals containing facial expressions as control commands was used. The signals were burdened with numerous artifacts caused by simulated nervous tics. The proposed expert system consisted of two neural networks. The first one allowed for the analysis of one-second samples of EEG signals from selected electrodes on the basis of power spectrum estimation waveforms. Thus, it was possible to generate an appropriate control signal as a result of appropriate facial expression commands. The second of the neural networks detected the appearance and type of nervous tics in the signal. Additionally, the participants were affected by interference such as street and TV or radio sound, Wi-Fi and radio waves. The system designed in such a way is adapted to the requirements of the everyday life of people with disabilities, in particular those in wheelchairs, whose control is based on BCI technology.

Accurate predictions from small boxes: variance suppression via the Zel'dovich approximation

Simulations have become an indispensable tool for accurate modelling of observables measured in galaxy surveys, but can be expensive if very large dynamic range in scale is required. We describe how to combine Lagrangian perturbation theory models with N-body simulations to reduce the effects of finite computational volume in the prediction of ensemble average properties in the simulations within the context of control variates. In particular we use the fact that Zel'dovich displacements, computed during initial condition generation for any simulation, correlate strongly with the final density field. Since all the correlators of biased tracers can be computed with arbitrary precision for these displacements, pairing the Zel'dovich `simulation' with the N-body realization allows hundredfold reductions in sample variance for power spectrum or correlation function estimation. Zel'dovich control variates can accurately extend matter or tracer field emulators to larger scales than previously possible, as well as improving measurements of statistics in simulations which are inherently limited to small volumes, such as hydrodynamical simulations of galaxy formation and reionization.

KiDS and Euclid: Cosmological implications of a pseudo angular power spectrum analysis of KiDS-1000 cosmic shear tomography

We present a tomographic weak lensing analysis of the Kilo Degree Survey Data Release 4 (KiDS-1000), using a new pseudo angular power spectrum estimator (pseudo-Cℓ) under development for the ESA Euclid mission. Over 21 million galaxies with shape information are divided into five tomographic redshift bins, ranging from 0.1 to 1.2 in photometric redshift. We measured pseudo-Cℓ using eight bands in the multipole range 76 < ℓ < 1500 for auto- and cross-power spectra between the tomographic bins. A series of tests were carried out to check for systematic contamination from a variety of observational sources including stellar number density, variations in survey depth, and point spread function properties. While some marginal correlations with these systematic tracers were observed, there is no evidence of bias in the cosmological inference. B-mode power spectra are consistent with zero signal, with no significant residual contamination from E/B-mode leakage. We performed a Bayesian analysis of the pseudo-Cℓ estimates by forward modelling the effects of the mask. Assuming a spatially flat ΛCDM cosmology, we constrained the structure growth parameter S8 = σ8(Ωm/0.3)1/2 = 0.754−0.029+0.027. When combining cosmic shear from KiDS-1000 with baryon acoustic oscillation and redshift space distortion data from recent Sloan Digital Sky Survey (SDSS) measurements of luminous red galaxies, as well as the Lyman-α forest and its cross-correlation with quasars, we tightened these constraints to S8 = 0.771−0.032+0.006. These results are in very good agreement with previous KiDS-1000 and SDSS analyses and confirm a ∼3σ tension with early-Universe constraints from cosmic microwave background experiments.

Constraints on τ NL from Planck temperature and polarization

We update constraints on the amplitude of the primordial trispectrum, using the final Planck mission temperature and polarization data. In the squeezed limit, a cosmological local trispectrum would be observed as a spatial modulation of small-scale power on the CMB sky. We reconstruct this signal as a source of statistical anisotropy via quadratic estimator techniques. We systematically demonstrate how the estimated power spectrum of a reconstructed modulation field can be translated into a constraint on τ NL via likelihood methods, demonstrating the procedures effectiveness by inferring known τ NL signal(s) from simulations. Our baseline results constrain τ NL < 1700 at the 95% confidence level, providing the most stringent constraints to date.

COMAP Early Science. III. CO Data Processing

We describe the first-season CO Mapping Array Project (COMAP) analysis pipeline that converts raw detector readouts to calibrated sky maps. This pipeline implements four main steps: gain calibration, filtering, data selection, and mapmaking. Absolute gain calibration relies on a combination of instrumental and astrophysical sources, while relative gain calibration exploits real-time total-power variations. High-efficiency filtering is achieved through spectroscopic common-mode rejection within and across receivers, resulting in nearly uncorrelated white noise within single-frequency channels. Consequently, near-optimal but biased maps are produced by binning the filtered time stream into pixelized maps; the corresponding signal bias transfer function is estimated through simulations. Data selection is performed automatically through a series of goodness-of-fit statistics, including χ 2 and multiscale correlation tests. Applying this pipeline to the first-season COMAP data, we produce a data set with very low levels of correlated noise. We find that one of our two scanning strategies (the Lissajous type) is sensitive to residual instrumental systematics. As a result, we no longer use this type of scan and exclude data taken this way from our Season 1 power spectrum estimates. We perform a careful analysis of our data processing and observing efficiencies and take account of planned improvements to estimate our future performance. Power spectrum results derived from the first-season COMAP maps are presented and discussed in companion papers.

Low-Cost Millimeter Wave Frequency Scanning Based Synthesis Aperture Imaging System for Concealed Weapon Detection

In this article, a novel low-cost frequency scanning-based synthetic aperture radar (F-SAR) system is proposed for high-resolution imaging. F-SAR scheme is demonstrated for personal screening for the first time. A hybrid scanning model is presented to illuminate the human body, namely, frequency control beam steering in cross-track and mechanical scanning in along-track. A frequency scanning-based tomographic SAR focusing algorithm is proposed. Accordingly, a power spectrum estimation algorithm in cross-track and synthetical aperture processing in along-track are compounded in the signal processing framework. Unlike a variety of multiple input multiple output (MIMO) array imaging which illuminates the object by switching different channels sequentially over separate time intervals, the F-SAR concept sweeps across all swaths over each chirp by employing a frequency scanned beam. Herein imaging time and hardware cost can be significantly cut down by dimensionality reduction from the MIMO system to a single input single output (SISO) system. Furthermore, to fulfill the particular scheme of the F-SAR system, a novel combo antenna module, leaky-wave slotted waveguide combined with a cylindrical lens, is proposed and achieved at 78–92-GHz band, by which a steering fan-beam focused at the object under test (OUT) plane is radiated. The radiation beam is focalized by the cylindrical lens accompanied by frequency sweeping, while is diffused in along-track. The frequency-controlled beam-steering concept and the fan-beam focusing mechanism are verified by the chamber measurements. The measured scanning range is 23°. Beamwidth of 11–16 mm is obtained at the focal plane. Beam steering in cross-track together with mechanical scanning in along-track can attain a field of view (FoV) of 0.54 2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}^{2}$ </tex-math></inline-formula> . Through-clothes imaging of person-borne concealed objects and the real-time capability are demonstrated by experiments. Resolutions in both along-track and cross-track can reach 5 mm.

Detecting slow narrowband modulation in EEG signals

BackgroundWe observed an unusual modulatory phenomenon in the electroencephalogram (EEG) of pediatric patients with acquired brain injury. The modulation is orders of magnitude slower than the fast EEG background activity, necessitating new analysis procedures to systematically detect and quantify the phenomenon. New methodWe propose a method for analyzing spatial and temporal relationships associated with slow, narrowband modulation of EEG. We extract envelope signals from physiological frequency bands of EEG. Then, we construct a sparse representation of the spectral content of the envelope signal across sliding windows. For the latter, we use an augmented LASSO regression to incorporate spatial and temporal filtering into the solution. The method can be applied to windows of variable length, depending on the desired frequency resolution. ResultsThe sparse estimates of the envelope power spectra enable the detection of narrowband modulation in the millihertz frequency range. Subsequently, we are able to assess non-stationarity in the frequency and spatial relationships across channels. The method can be paired with unsupervised anomaly detection to identify windows with significant modulation. We validated such findings by applying our method to a control set of EEGs. Comparison with existing methodsTo our knowledge, no methods have been previously proposed to quantify second order modulation at such disparate time-scales. ConclusionsWe provide a general EEG analysis framework capable of detecting signal content below 0.1 Hz, which is especially germane to clinical recordings that may contain multiple hours worth of continuous data.

Transcranial Direct Current Stimulation Over the Left Dorsolateral Prefrontal Cortex Reduced Attention Bias Toward Negative Facial Expression: A Pilot Study in Healthy Subjects.

Research in the cognitive neuroscience field has shown that individuals with a stronger attention bias for negative information had higher depression risk, which may be the underlying pathogenesis of depression. This dysfunction of affect-biased attention also represents a decline in emotion regulation ability. Clinical studies have suggested that transcranial direct current stimulation (tDCS) treatment can improve the symptoms of depression, yet the neural mechanism behind this improvement is still veiled. This study aims to investigate the effects of tDCS on affect-biased attention. A sample of healthy participants received 20 min active (n = 22) or sham tDCS (n = 19) over the left dorsolateral prefrontal cortex (DLPFC) for 7 consecutive days. Electroencephalographic (EEG) signals were recorded while performing the rest task and emotional oddball task. The oddball task required response to pictures of the target (positive or negative) emotional facial stimuli and neglecting distracter (negative or positive) or standard (neutral) stimuli. Welch power spectrum estimation algorithm was applied to calculate frontal alpha asymmetry (FAA) in the rest task, and the overlapping averaging method was used to extract event-related potentials (ERP) components in the oddball task. Compared to sham tDCS, active tDCS caused an obvious increment in FAA in connection with emotion regulation (p < 0.05). Also, participants in the active tDCS group show greater P3 amplitudes following positive targets (p < 0.05) and greater N2 amplitudes following negative distracters (p < 0.05), reflecting emotion-related attention biases. These results offer valuable insights into the relationship between affect-biased attention and the effects of tDCS, which may be of assistance in exploring the neuropathological mechanism of depression and anxiety and new treatment strategies for tDCS.

Improved Gibbs samplers for cosmic microwave background power spectrum estimation

We study different variants of the Gibbs sampler algorithm from the perspective of their applicability to the estimation of power spectra of the cosmic microwave background (CMB) anisotropies. These include approaches studied earlier in the CMB literature as well as new ones which are proposed in this work. We demonstrate all these variants on full- and cut-sky simulations and compare their performance, assessing both their computational and statistical efficiency. For this we employ a consistent comparison metric, an effective sample size per second, commonly used in this context in the statistical literature. We show that one of the proposed approaches, referred to as Centered overrelax, which capitalizes on additional, auxiliary variables to minimize the computational time needed per sample, uses overrelaxation to decorrelate subsequent samples, and performs better than the standard Gibbs sampler by a factor between one and two orders of magnitude in the nearly full-sky, satellitelike cases. It therefore potentially provides an interesting alternative to the currently favored approaches.

An empirical nonlinear power spectrum overdensity response

Context.The overdensity inside a cosmological sub-volume and the tidal fields from its surroundings affect the matter distribution of the region. The resulting difference between the local and global power spectra is characterized by the response function.Aims.Our aim is to provide a new, simple, and accurate formula for the power spectrum overdensity response at highly nonlinear scales based on the results of cosmological simulations and paying special attention to the lognormal nature of the density field.Methods.We measured the dark matter power spectrum amplitude as a function of the overdensity (δW) inN-body simulation subsamples. We show that the response follows a power-law form in terms of (1 + δW), and we provide a new fit in terms of the variance,σ(L), of a sub-volume of sizeL.Results.Our fit has a similar accuracy and a comparable complexity to second-order standard perturbation theory on large scales, but it is also valid for nonlinear (smaller) scales, where perturbation theory needs higher-order terms for a comparable precision. Furthermore, we show that the lognormal nature of the overdensity distribution causes a previously unidentified bias: the power spectrum amplitude for a subsample with an average density is typically underestimated by about −2σ2. Although this bias falls to the sub-percent level above characteristic scales of 200 Mpc h−1, taking it into account improves the accuracy of estimating power spectra from zoom-in simulations and smaller high-resolution surveys embedded in larger low-resolution volumes.

A DC Series Arc Fault Detection Method Based on a Lightweight Convolutional Neural Network Used in Photovoltaic System

Although photovoltaic (PV) systems play an essential role in distributed generation systems, they also suffer from serious safety concerns due to DC series arc faults. This paper proposes a lightweight convolutional neural network-based method for detecting DC series arc fault in PV systems to solve this issue. An experimental platform according to UL1699B is built, and current data ranging from 3 A to 25 A is collected. Moreover, test conditions, including PV inverter startup and irradiance mutation, are also considered to evaluate the robustness of the proposed method. Before fault detection, the current data is preprocessed with power spectrum estimation. The lightweight convolutional neural network has a lower computational burden for its fewer parameters, which can be ready for embedded microprocessor-based edge applications. Compared to similar lightweight convolutional network models such as Efficientnet-B0, B2, and B3, the Efficientnet-B1 model shows the highest accuracy of 96.16% for arc fault detection. Furthermore, an attention mechanism is combined with the Efficientnet-B1 to make the algorithm more focused on arc features, which can help the algorithm reduce unnecessary computation. The test results show that the detection accuracy of the proposed method can be up to 98.81% under all test conditions, which is higher than that of general networks.

Euclid: Covariance of weak lensing pseudo-Cℓ estimates

An accurate covariance matrix is essential for obtaining reliable cosmological results when using a Gaussian likelihood. In this paper we study the covariance of pseudo-Cℓ estimates of tomographic cosmic shear power spectra. Using two existing publicly available codes in combination, we calculate the full covariance matrix, including mode-coupling contributions arising from both partial sky coverage and non-linear structure growth. For three different sky masks, we compare the theoretical covariance matrix to that estimated from publicly available N-body weak lensing simulations, finding good agreement. We find that as a more extreme sky cut is applied, a corresponding increase in both Gaussian off-diagonal covariance and non-Gaussian super-sample covariance is observed in both theory and simulations, in accordance with expectations. Studying the different contributions to the covariance in detail, we find that the Gaussian covariance dominates along the main diagonal and the closest off-diagonals, but farther away from the main diagonal the super-sample covariance is dominant. Forming mock constraints in parameters that describe matter clustering and dark energy, we find that neglecting non-Gaussian contributions to the covariance can lead to underestimating the true size of confidence regions by up to 70 per cent. The dominant non-Gaussian covariance component is the super-sample covariance, but neglecting the smaller connected non-Gaussian covariance can still lead to the underestimation of uncertainties by 10–20 per cent. A real cosmological analysis will require marginalisation over many nuisance parameters, which will decrease the relative importance of all cosmological contributions to the covariance, so these values should be taken as upper limits on the importance of each component.