Power Spectrum Estimation Research Articles

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.

Efficient processing of water wave records via compressive sensing and joint time-frequency analysis via harmonic wavelets

A methodology is proposed for efficient processing of sea wave field data via compressive sensing (CS), and joint time-frequency analysis via harmonic wavelets (HWs) based evolutionary power spectrum (EPS) estimation. In this regard, it is possible to record and store relatively long wave data sequences, whereas the commonly adopted in-practice assumption of stationary data is abandoned. Currently, most wave records are measured by buoys, which acquire data for a time interval representative of stationary time series. Next, following a Fourier transform processing, only few spectral parameters are stored. Thus, detailed information about localized-in-time phenomena are completely lost. Herein, it is shown that CS can be adopted for efficiently compressing and reconstructing wave data, while retaining localized information. For this purpose, CS is used in conjunction with a HW basis for processing long time series. In particular, storage capacity demands are drastically decreased as only the HW coefficients need to be saved. These are determined from a randomly-sampled record by invoking a L1/2 norm minimization procedure. The resulting reconstructed record, being longer than conventional wave time series, can no longer be regarded as stationary; thus, a HW based EPS estimate is employed for describing the joint time-frequency features of the record. Finally, the reliability of the methodology is assessed by analyzing wave field data measured at the Natural Ocean Engineering Laboratory (NOEL) of Reggio Calabria. Specifically, comparisons between original and reconstructed records demonstrate a satisfactory agreement regarding the time-histories, and the estimated EPS and relevant statistical quantities, even for up to 60% missing/removed data.

Lp-norm minimization for stochastic process power spectrum estimation subject to incomplete data

Abstract A general L p norm ( 0 p ≤ 1 ) minimization approach is proposed for estimating stochastic process power spectra subject to realizations with incomplete/missing data. Specifically, relying on the assumption that the recorded incomplete data exhibit a significant degree of sparsity in a given domain, employing appropriate Fourier and wavelet bases, and focusing on the L 1 and L 1 / 2 norms, it is shown that the approach can satisfactorily estimate the spectral content of the underlying process. Further, the accuracy of the approach is significantly enhanced by utilizing an adaptive basis re-weighting scheme. Finally, the effect of the chosen norm on the power spectrum estimation error is investigated, and it is shown that the L 1 / 2 norm provides almost always a sparser solution than the L 1 norm. Numerical examples consider several stationary, non-stationary, and multi-dimensional processes for demonstrating the accuracy and robustness of the approach, even in cases of up to 80% missing data.

An analytical method to simulate the H i 21-cm visibility signal for intensity mapping experiments

Simulations play a vital role in testing and validating H i 21-cm power spectrum estimation techniques. Conventional methods use techniques like N-body simulations to simulate the sky signal which is then passed through a model of the instrument. This makes it necessary to simulate the H i distribution in a large cosmological volume, and incorporate both the light-cone effect and the telescope's chromatic response. The computational requirements may be particularly large if one wishes to simulate many realizations of the signal. In this paper, we present an analytical method to simulate the H i visibility signal. This is particularly efficient if one wishes to simulate a large number of realizations of the signal. Our method is based on theoretical predictions of the visibility correlation which incorporate both the light-cone effect and the telescope's chromatic response. We have demonstrated this method by applying it to simulate the H i visibility signal for the upcoming Ooty Wide Field Array Phase I.

Multitaper and multisegment spectral estimation of line-edge roughness

Line-edge roughness (LER) has important impacts on the quality of semiconductor device performance, and power spectrum estimates are useful tools in characterizing it. These estimates are often obtained by taking measurements of many lines and averaging a classical power spectrum estimate from each one. While this approach reduces the uncertainty of the estimates, there are disadvantages to the collection of many measurements. We propose techniques with widespread application in other fields that simultaneously reduce data requirements and the uncertainty of LER power spectrum estimates over current approaches at the price of computational complexity. Multitaper spectral analysis uses an orthogonal collection of data windowing functions or tapers to obtain a set of approximately statistically independent spectrum estimates. The Welch overlapped segment averaging is an earlier approach to reduce the uncertainty of power spectrum estimates. There are known techniques to evaluate the uncertainty of power spectrum estimates. We simulate random rough lines using the Thorsos method.

Rethinking CMB foregrounds: systematic extension of foreground parametrizations

Future high-sensitivity measurements of the cosmic microwave background (CMB) anisotropies and energy spectrum will be limited by our understanding and modeling of foregrounds. Not only does more information need to be gathered and combined, but also novel approaches for the modeling of foregrounds, commensurate with the vast improvements in sensitivity, have to be explored. Here, we study the inevitable effects of spatial averaging on the spectral shapes of typical foreground components, introducing a moment approach, which naturally extends the list of foreground parameters that have to be determined through measurements or constrained by theoretical models. Foregrounds are thought of as a superposition of individual emitting volume elements along the line of sight and across the sky, which then are observed through an instrumental beam. The beam and line of sight averages are inevitable. Instead of assuming a specific model for the distributions of physical parameters, our method identifies natural new spectral shapes for each foreground component that can be used to extract parameter moments (e.g., mean, dispersion, cross-terms, etc.). The method is illustrated for the superposition of power-laws, free-free spectra, gray-body and modified blackbody spectra, but can be applied to more complicated fundamental spectral energy distributions. Here, we focus on intensity signals but the method can be extended to the case of polarized emission. The averaging process automatically produces scale-dependent spectral shapes and the moment method can be used to propagate the required information across scales in power spectrum estimates. The approach is not limited to applications to CMB foregrounds but could also be useful for the modeling of X-ray emission in clusters of galaxies.

Combined analysis of galaxy cluster number count, thermal Sunyaev-Zel’dovich power spectrum, and bispectrum

The thermal Sunyaev-Zel’dovich (tSZ) effect is a powerful probe of the evolution of structures in the universe, and is thus highly sensitive to cosmological parameters σ8 and Ωm, though its power is hampered by the current uncertainties on the cluster mass calibration. In this analysis we revisit constraints on these cosmological parameters as well as the hydrostatic mass bias, by performing (i) a robust estimation of the tSZ power-spectrum, (ii) a complete modeling and analysis of the tSZ bispectrum, and (iii) a combined analysis of galaxy clusters number count, tSZ power spectrum, and tSZ bispectrum. From this analysis, we derive as final constraints σ8 = 0.79 ± 0.02, Ωm = 0.29 ± 0.02, and (1−b) = 0.71 ± 0.07. These results favor a high value for the hydrostatic mass bias compared to numerical simulations and weak-lensing based estimations. They are furthermore consistent with both previous tSZ analyses, CMB derived cosmological parameters, and ancillary estimations of the hydrostatic mass bias.

Time-frequency Research of Pulse Rate Variability Based on the EEMD

In this paper, based on the feature of ensemble empirical mode decomposition(EEMD) which is very suitable for analyzing non-stationary and nonlinear signals, the pulse rate variability (PRV) signal is decomposed into multiple intrinsic mode function (IMF) components by EEMD, to calculate the energy of each IMF component respectively, and high-frequency energy(EHF), low-frequency energy(ELF) and very low-frequency energy(EVLF) of PRV were reconstructed from the energy of the IMF components according to the characteristics of each IMF component spectrum. This method is compared with the traditional AR power spectrum estimation method through the experiment. The results show that the correlation coefficient of each frequency domain parameter corresponding to PRV obtained by the two methods is higher than 0.96, which indicates that the method can truly reflect the sympathetic nerve and vagus nerve activity.

Simulated predictions for H i at z = 3.35 with the Ooty Wide Field Array – I. Instrument and the foregrounds

Foreground removal is the most important step in detecting the large-scale redshifted HI 21-cm signal. Modelling foreground spectra is challenging and is further complicated by the chromatic response of the telescope. We present a multi-frequency angular power spectrum (MAPS) estimator for use in a survey for redshifted HI 21-cm emission from z~3.35, and demonstrate its ability to accurately characterize the foregrounds. This survey will be carried out with the two wide-field interferometer modes of the upgraded Ooty Radio Telescope, called the Ooty Wide Field Array (OWFA), at 326.5 MHz. We have tailored the two-visibility correlation for OWFA to estimate the MAPS and test it with simulated foregrounds. In the process, we describe a software model that encodes the geometry and the details of the telescope, and simulates a realistic model for the bright radio sky. This article presents simulations which include the full chromatic response of the telescope, in addition to the frequency dependence intrinsic to the foregrounds. We find that the visibility correlation MAPS estimator recovers the input angular power spectrum accurately, and that the instrument response to the foregrounds dominates the systematic errors in the recovered foreground power spectra.

Validating a novel angular power spectrum estimator using simulated low frequency radio-interferometric data

The “Tapered Gridded Estimator” (TGE) is a novel way to directly estimate the angular power spectrum from radio-interferometric visibility data that reduces the computation by efficiently gridding the data, consistently removes the noise bias, and suppresses the foreground contamination to a large extent by tapering the primary beam response through an appropriate convolution in the visibility domain. Here we demonstrate the effectiveness of TGE in recovering the diffuse emission power spectrum through numerical simulations. We present details of the simulation used to generate low frequency visibility data for sky model with extragalactic compact radio sources and diffuse Galactic synchrotron emission. We then use different imaging strategies to identify the most effective option of point source subtraction and to study the underlying diffuse emission. Finally, we apply TGE to the residual data to measure the angular power spectrum, and assess the impact of incomplete point source subtraction in recovering the input power spectrum Cℓ of the synchrotron emission. This estimator is found to successfully recovers the Cℓ of input model from the residual visibility data. These results are relevant for measuring the diffuse emission like the Galactic synchrotron emission. It is also an important step towards characterizing and removing both diffuse and compact foreground emission in order to detect the redshifted 21 cm signal from the Epoch of Reionization.

Factor Analysis for Spectral Estimation.

Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model where a signal is given by a random linear combination of fixed, yet unknown, stochastic sources. Given multiple such signals, we estimate the subspace spanned by the power spectra of these fixed sources. Projecting individual power spectrum estimates onto this subspace increases estimation accuracy. We provide accuracy guarantees for this method and demonstrate it on simulated and experimental data from cryo-electron microscopy.

Efficient simulations of large-scale structure in modified gravity cosmologies with comoving Lagrangian acceleration

We implement an adaptation of the COLA approach, a hybrid scheme that combines Lagrangian perturbation theory with an N-body approach, to model non-linear collapse in chameleon and symmetron modified gravity models. Gravitational screening is modeled effectively through the attachment of a suppression factor to the linearized Klein-Gordon equations. The adapted COLA approach is benchmarked, with respect to an N-body code both for the $\Lambda$CDM scenario and for the modified gravity theories. It is found to perform well in the estimation of the dark matter power spectra, with consistency of 1 % to $k\sim2.5$ h/Mpc. Redshift space distortions are shown to be effectively modeled through a Lorentzian parameterization with a velocity dispersion fit to the data. We find that COLA performs less well in predicting the halo mass functions, but has consistency, within $1\sigma$ uncertainties of our simulations, in the relative changes to the mass function induced by the modified gravity models relative to $\Lambda$CDM. The results demonstrate that COLA, proposed to enable accurate and efficient, non-linear predictions for $\Lambda$CDM, can be effectively applied to a wider set of cosmological scenarios, with intriguing properties, for which clustering behavior needs to be understood for upcoming surveys such as LSST, DESI, Euclid and WFIRST.

Measurement of acoustic velocity components in a turbulent flow using LDV and high-repetition rate PIV

The present study provides theoretical details and experimental validation results to the approach proposed by Minotti et al. (Aerosp Sci Technol 12(5):398–407, 2008) for measuring amplitudes and phases of acoustic velocity components (AVC) that are waveform parameters of each component of velocity induced by an acoustic wave, in fully turbulent duct flows carrying multi-tone acoustic waves. Theoretical results support that the turbulence rejection method proposed, based on the estimation of cross power spectra between velocity measurements and a reference signal such as a wall pressure measurement, provides asymptotically efficient estimators with respect to the number of samples. Furthermore, it is shown that the estimator uncertainties can be simply estimated, accounting for the characteristics of the measured flow turbulence spectra. Two laser-based measurement campaigns were conducted in order to validate the acoustic velocity estimation approach and the uncertainty estimates derived. While in previous studies estimates were obtained using laser Doppler velocimetry (LDV), it is demonstrated that high-repetition rate particle image velocimetry (PIV) can also be successfully employed. The two measurement techniques provide very similar acoustic velocity amplitude and phase estimates for the cases investigated, that are of practical interest for acoustic liner studies. In a broader sense, this approach may be beneficial for non-intrusive sound emission studies in wind tunnel testings.

Design of a CMOS multi‐rate adaptive continuous‐time equalizer based on power spectrum estimation

SummaryAn adaptive continuous‐time equalizer for reliable short‐haul high‐speed serial communications is described in this paper. The adaptive equalizer uses the spectrum‐balancing technique to adapt its response to changes in the bandwidth, amplitude, and bit rate of the input signal. In this way, it is able to compensate the frequency response of a 1‐mm diameter step‐index plastic optical fiber, for lengths up to 50 m, and bit rates ranging from 400 Mb/s to 2.5 Gb/s. Experimental results are shown to demonstrate its feasibility. Copyright © 2017 John Wiley & Sons, Ltd.

Task-driven optimization of CT tube current modulation and regularization in model-based iterative reconstruction

Tube current modulation (TCM) is routinely adopted on diagnostic CT scanners for dose reduction. Conventional TCM strategies are generally designed for filtered-backprojection (FBP) reconstruction to satisfy simple image quality requirements based on noise. This work investigates TCM designs for model-based iterative reconstruction (MBIR) to achieve optimal imaging performance as determined by a task-based image quality metric. Additionally, regularization is an important aspect of MBIR that is jointly optimized with TCM, and includes both the regularization strength that controls overall smoothness as well as directional weights that permits control of the isotropy/anisotropy of the local noise and resolution properties. Initial investigations focus on a known imaging task at a single location in the image volume. The framework adopts Fourier and analytical approximations for fast estimation of the local noise power spectrum (NPS) and modulation transfer function (MTF)—each carrying dependencies on TCM and regularization. For the single location optimization, the local detectability index (d′) of the specific task was directly adopted as the objective function. A covariance matrix adaptation evolution strategy (CMA-ES) algorithm was employed to identify the optimal combination of imaging parameters. Evaluations of both conventional and task-driven approaches were performed in an abdomen phantom for a mid-frequency discrimination task in the kidney. Among the conventional strategies, the TCM pattern optimal for FBP using a minimum variance criterion yielded a worse task-based performance compared to an unmodulated strategy when applied to MBIR. Moreover, task-driven TCM designs for MBIR were found to have the opposite behavior from conventional designs for FBP, with greater fluence assigned to the less attenuating views of the abdomen and less fluence to the more attenuating lateral views. Such TCM patterns exaggerate the intrinsic anisotropy of the MTF and NPS as a result of the data weighting in MBIR. Directional penalty design was found to reinforce the same trend. The task-driven approaches outperform conventional approaches, with the maximum improvement in d′ of 13% given by the joint optimization of TCM and regularization. This work demonstrates that the TCM optimal for MBIR is distinct from conventional strategies proposed for FBP reconstruction and strategies optimal for FBP are suboptimal and may even reduce performance when applied to MBIR. The task-driven imaging framework offers a promising approach for optimizing acquisition and reconstruction for MBIR that can improve imaging performance and/or dose utilization beyond conventional imaging strategies.

Fatigue Induced Changes of the EMG Profile of Select Lower Extremity Muscles in Competitive Cyclists

PURPOSE: To determine the effect of fatigue on the median frequency (MF) and amplitude (AMP) of select lower extremity muscles in competitive cyclists. METHODS: Five category 4 or above cyclists (29.6 yrs ± 16.0) were recruited for this pilot study. Data collection consisted of 2 sessions. At session one, the subject’s maximum work load (MWL) was determined during an incremental cycling test. At session two, EMG activity of the rectus femoris (RF), vastus medialis (VM) and lateralis (VL), semitendinosus (ST), biceps femoris (BF), gastrocnemius (GS), tibialis anterior (TA) and gluteus maximus (GM) were recorded bilaterally at 2400 Hz using surface electrodes during a fatigue protocol. The fatigue protocol consisted of a 4-minute warm-up at 55% of their MWL followed by 5, alternating efforts at 90% and 55% of their MWL for 1 and 2-minutes respectively. This was followed by a continuous cycling effort at 90% of their MWL until fatigue (pedaling rate < 80 RPM). For each muscle, the EMG data were band pass filtered and the MF was determined using a time-frequency analysis based on power spectra estimation (short-time Fourier transform). The average MF and average peak AMP was calculated for each trial. The average change in MF and average peak AMP from the 1st trial to the fatigue trial for each muscle were calculated. RESULTS: The average MF for the RF, VM, VL, ST, BF, and TA increased by 3.0, 3.4, 5.8, 4.2, 1.2, and 0.6 %, respectively from trial 1 to the fatigue trial while the MF for the GM and GS decreased by 7.3 and 5.8%, respectively. The average peak AMP for the RF, VM, VL, ST, BF, and GM increased by 44.9, 27.5, 23.4, 18.6, 38.3, and 51.6%, respectively while the average peak AMP for the TA and GS decreased by 2.0 and 6.3%, respectively. CONCLUSION: According to Luttmann et al’s (1996) joint analysis of EMG spectrum and amplitude theory, the quadriceps (RF, VM, VL) and hamstring (BF, ST) muscles demonstrated an increase in force production, while the GS and TA exhibited a decrease force production during fatigue. Only the GM exhibited a classical fatigue pattern of activity (decrease MF, increase AMP). These results suggest that in the current testing paradigm both central and peripheral fatigue may be contributing to the inability to maintain pedaling rate. Funding was provided in part by the 2016 NEACSM Undergraduate Research Experience Grant.

STRUCTURE IN THE 3D GALAXY DISTRIBUTION: III. FOURIER TRANSFORMING THE UNIVERSE: PHASE AND POWER SPECTRA.

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Impact of modelling foreground uncertainties on future CMB polarization satellite experiments

We present an analysis of errors on the tensor-to-scalar ratio due to residual diffuse foregrounds. We use simulated observations of a CMB polarization satellite, the Cosmic Origins Explorer, using the specifications of the version proposed to ESA in 2010 (COrE). We construct a full pipeline from microwave sky maps to $r$ likelihood, using two models of diffuse Galactic foregrounds with different complexity, and assuming component separation with varying degrees of accuracy. Our pipeline uses a linear mixture (Generalized Least Squares) solution for component separation, and a hybrid approach for power spectrum estimation, with a Quadratic Maximum Likelihood estimator at low $\ell$s and a pseudo-$C_{\ell}$ deconvolution at high $\ell$s. In the likelihood for $r$, we explore modelling foreground residuals as nuisance parameters. Our analysis aims at measuring the bias introduced in $r$ by mismodelling the foregrounds, and to determine what error is tolerable while still successfully detecting $r$. We find that $r=0.01$ can be measured successfully even for a complex sky model and in the presence of foreground parameters error. However, the detection of $r=0.001$ is a lot more challenging, as inaccurate modelling of the foreground spectral properties may result in a biased measurement of $r$. Once biases are eliminated, the total error on $r$ allows setting an upper limit rather than a detection, unless the uncertainties on the foreground spectral indices are very small, i.e. equal or better than 0.5\% error for both dust and synchrotron. This emphasizes the need for pursuing research on component separation and foreground characterization in view of next-generation CMB polarization experiments.

Making maps of cosmic microwave background polarization for B-mode studies: the POLARBEAR example

Analysis of cosmic microwave background (CMB) datasets typically requires some filtering of the raw time-ordered data. For instance, in the context of ground-based observations, filtering is frequently used to minimize the impact of low frequency noise, atmospheric contributions and/or scan synchronous signals on the resulting maps. In this work we have explicitly constructed a general filtering operator, which can unambiguously remove any set of unwanted modes in the data, and then amend the map-making procedure in order to incorporate and correct for it. We show that such an approach is mathematically equivalent to the solution of a problem in which the sky signal and unwanted modes are estimated simultaneously and the latter are marginalized over. We investigated the conditions under which this amended map-making procedure can render an unbiased estimate of the sky signal in realistic circumstances. We then discuss the potential implications of these observations on the choice of map-making and power spectrum estimation approaches in the context of B-mode polarization studies. Specifically, we have studied the effects of time-domain filtering on the noise correlation structure in the map domain, as well as impact it may haveon the performance of the popular pseudo-spectrum estimators. We conclude that although maps produced by the proposed estimators arguably provide the most faithful representation of the sky possible given the data, they may not straightforwardly lead to the best constraints on the power spectra of the underlying sky signal and special care may need to be taken to ensure this is the case. By contrast, simplified map-makers which do not explicitly correct for time-domain filtering, but leave it to subsequent steps in the data analysis, may perform equally well and be easier and faster to implement. We focused on polarization-sensitive measurements targeting the B-mode component of the CMB signal and apply the proposed methods to realistic simulations based on characteristics of an actual CMB polarization experiment, POLARBEAR. Our analysis and conclusions are however more generally applicable.

Modal analysis of annual runoff volume and sediment load in the Yangtze river-lake system for the period 1956-2013.

This study focuses on detecting trends in annual runoff volume and sediment load in the Yangtze river-lake system. Times series of annual runoff volume and sediment load at 19 hydrological gauging stations for the period 1956-2013 were collected. Based on the Mann-Kendall test at the 1% significance level, annual sediment loads in the Yangtze River, the Dongting Lake and the Poyang Lake were detected with significantly descending trends. The power spectrum estimation indicated predominant oscillations with periods of 8 and 20 years are embedded in the runoff volume series, probably related to the El Niño Southern Oscillation (2-7 years) and Pacific Decadal Oscillation (20-30 years). Based on dominant components (capturing more than roughly 90% total energy) extracted by the proper orthogonal decomposition method, total change ratios of runoff volume and sediment load during the last 58 years were evaluated. For sediment load, the mean CRT value in the Yangtze River is about -65%, and those in the Dongting Lake and the Poyang Lake are -92.2% and -87.9% respectively. Particularly, the CRT value of the sediment load in the channel inflow of the Dongting Lake is even -99.7%. The Three Gorges Dam has intercepted a large amount of sediment load and decreased the sediment load downstream.