Power Spectrum Values Research Articles

A comparison of various linear and non-linear signal processing techniques to separate uterine EMG records of term and pre-term delivery groups

Various linear and non-linear signal-processing techniques were applied to three-channel uterine EMG records to separate term and pre-term deliveries. The linear techniques were root mean square value, peak and median frequency of the signal power spectrum and autocorrelation zero crossing; while the selected non-linear techniques were estimation of the maximal Lyapunov exponent, correlation dimension and calculating sample entropy. In total, 300 records were grouped into four groups according to the time of recording (before or after the 26th week of gestation) and according to the total length of gestation (term delivery records--pregnancy duration >or=37 weeks and pre-term delivery records--pregnancy duration <37 weeks). The following preprocessing band-pass Butterworth filters were tested: 0.08-4, 0.3-4, and 0.3-3 Hz. With the 0.3-3 Hz filter, the median frequency indicated a statistical difference between those term and pre-term delivery records recorded before the 26th week (p = 0.03), and between all term and all pre-term delivery records (p = 0.012). With the same filter, the sample entropy indicated statistical differences between those term and pre-term delivery records recorded before the 26th week (p = 0.035), and between all term and all pre-term delivery records (p = 0.011). Both techniques also showed noticeable differences between term delivery records recorded before and after the 26th week (p <or= 0.001).

Minimum-Variance Multitaper Spectral Estimation on the Sphere

We develop a method to estimate the power spectrum of a stochastic process on the sphere from data of limited geographical coverage. Our approach can be interpreted either as estimating the global power spectrum of a stationary process when only a portion of the data are available for analysis, or estimating the power spectrum from local data under the assumption that the data are locally stationary in a specified region. Restricting a global function to a spatial subdomain -- whether by necessity or by design -- is a windowing operation, and an equation like a convolution in the spectral domain relates the expected value of the windowed power spectrum to the underlying global power spectrum and the known power spectrum of the localization window. The best windows for the purpose of localized spectral analysis have their energy concentrated in the region of interest while possessing the smallest effective bandwidth as possible. Solving an optimization problem in the sense of Slepian (1960) yields a family of orthogonal windows of diminishing spatiospectral localization, the best concentrated of which we propose to use to form a weighted multitaper spectrum estimate in the sense of Thomson (1982). Such an estimate is both more representative of the target region and reduces the estimation variance when compared to estimates formed by any single bandlimited window. We describe how the weights applied to the individual spectral estimates in forming the multitaper estimate can be chosen such that the variance of the estimate is minimized.

Objective quantification of acetylcholine receptor aggregation using fast Fourier transforms

A new approach for objectively analyzing the aggregation of acetylcholine receptors (AChRs) through power spectrum analysis derived from fast Fourier transform (FFT) of images has been developed. Presently, detection of AChR aggregates at neuromuscular junctions is not easily accomplished. Though the formation of AChR clusters results in periodic gray-level variations that differ with time, no study reporting their correlation with frequency information in the Fourier domain for aggregates’ detection purposes exists. To this end, we processed time-lapse images of AChR aggregates’ formation on murine myotubes to extract peak values of power spectra. To validate interpretation of the Fourier spectra analysis, a computer routine was developed to semi-automatically count AChR aggregates. We found: (1) logarithmic maxima of Fourier spectra correlated significantly with experimentation time; (2) cluster count correlated significantly with time only after clusters were discernable from images, signifying that this method heavily depended on definitive growth data and thresholding values; (3) exponents of Fourier maxima versus time and cluster count versus time profiles during this phase compared favorably, indicating that both methods were analyzing identical cluster growth rates. Our observations suggest that analysis via FFT power spectrum is sensitive and robust enough to automatically quantify AChR aggregates.

Statistical characteristics of surrogate data based on geophysical measurements

Abstract. In this study, the statistical properties of a range of measurements are compared with those of their surrogate time series. Seven different records are studied, amongst others, historical time series of mean daily temperature, daily rain sums and runoff from two rivers, and cloud measurements. Seven different algorithms are used to generate the surrogate time series. The best-known method is the iterative amplitude adjusted Fourier transform (IAAFT) algorithm, which is able to reproduce the measured distribution as well as the power spectrum. Using this setup, the measurements and their surrogates are compared with respect to their power spectrum, increment distribution, structure functions, annual percentiles and return values. It is found that the surrogates that reproduce the power spectrum and the distribution of the measurements are able to closely match the increment distributions and the structure functions of the measurements, but this often does not hold for surrogates that only mimic the power spectrum of the measurement. However, even the best performing surrogates do not have asymmetric increment distributions, i.e., they cannot reproduce nonlinear dynamical processes that are asymmetric in time. Furthermore, we have found deviations of the structure functions on small scales.

Time-frequency analysis of QRS applied to wavelet transform in patient with myocardial infarction; A way of signal averaged method for using integral values of power spectrum.

Time-frequency analysis of QRS applied to wavelet transform in patient with myocardial infarction; A way of signal averaged method for using integral values of power spectrum.

Multifractal modelling and spectrum analysis: Methods and applications to gamma ray spectrometer data from southwestern Nova Scotia, Canada

Multifractal spectrum, autocorrelation/semivariogram and power spectrum are three different functions characterizing a field or measure from different aspects. These functions are interre- lated in such that the autocorrelation/semivariogram and power spectrum are related to the low order statistical moments (0 to 2 nd) which may determine the local multifractality ( τ ²(1)) of a multifractal measure. A better understanding of the interrelationships among these three functions is important because, on one hand, the multifractal modelling characterizes a multifractal measure in a more de- tailed manner since it involves moments of all orders. On the other hand, the commonly used semivariogram and power spectrum functions can be used as alternatives to study the dominant multifractal properties around the mean measure. Moreover, semivariogram and power-spectrum functions provide spatial and spectral information, which is highly valued in geological applications. A new fractal relation found between area and power-spectrum will be useful for investigation of new meth- ods of spatial-spectral analysis for pattern recognition, anomaly separation, classification, etc. These results have been demonstrated with the case study of modelling gamma ray spectrometer data from the mineral district, southwestern Nova Scotia, Canada. The results have shown that the values of uranium (U), thorium (Th) and potassium (K) may possess monofractal properties whereas the ratios of these values show high multifractality. The values of the ratios U/K and U/Th show relatively large variances and may provide more information for distinguishing the distinct phases of the granites, country rocks as well as possible gold mineralization-associated regional hydrothermal alteration zones. In addition, the power spectra for U, Th, K, U/Th and U/K consistently show two distinct power-law relationships for two ranges of wave number 12≤ ω ≤160 km and 0≤ ω ≤12 km. These properties might provide useful thresholds for separating the power-spectrum values into two types of patterns to reflect different influences of possible geological processes such as hydrothermal alteration in the study area.

A noise-estimation algorithm for highly non-stationary environments

A noise-estimation algorithm is proposed for highly non-stationary noise environments. The noise estimate is updated by averaging the noisy speech power spectrum using time and frequency dependent smoothing factors, which are adjusted based on signal-presence probability in individual frequency bins. Signal presence is determined by computing the ratio of the noisy speech power spectrum to its local minimum, which is updated continuously by averaging past values of the noisy speech power spectra with a look-ahead factor. The local minimum estimation algorithm adapts very quickly to highly non-stationary noise environments. This was confirmed with formal listening tests which indicated that the proposed noise-estimation algorithm when integrated in speech enhancement was preferred over other noise-estimation algorithms.

Short distance and initial state effects in inflation: Stress tensor and decoherence

We present a consistent low energy effective field theory framework for parameterizing the effects of novel short distance physics in inflation, and their possible observational signatures in the Cosmic Microwave Background. We consider the class of general homogeneous, isotropic initial states for quantum scalar fields in Robertson-Walker (RW) spacetimes, subject to the requirement that their ultraviolet behavior be consistent with renormalizability of the covariantly conserved stress tensor which couples to gravity. In the functional Schr\"odinger picture such states are coherent, squeezed, mixed states characterized by a Gaussian density matrix. This Gaussian has parameters which approach those of the adiabatic vacuum at large wave number, and evolve in time according to an effective classical Hamiltonian. The one complex parameter family of $\alpha$ squeezed states in de Sitter spacetime does not fall into this UV allowed class, except for the special value of the parameter corresponding to the Bunch-Davies state. We determine the finite contributions to the inflationary power spectrum and stress tensor expectation value of general UV allowed adiabatic states, and obtain quantitative limits on the observability and backreaction effects of some recently proposed models of short distance modifications of the initial state of inflation. For all UV allowed states, the second order adiabatic basis provides a good description of particles created in the expanding RW universe. Due to the absence of particle creation for the massless, minimally coupled scalar field in de Sitter space, there is no phase decoherence in the simplest free field inflationary models. We apply adiabatic regularization to the renormalization of the decoherence functional in cosmology to corroborate this result.

Markov chain reconstruction of the 2dF Galaxy Redshift Survey real-space power spectrum

The real-space power spectrum of L* galaxies measured from the 2dF Galaxy Redshift Survey (2dFGRS) is presented. Markov-Chain Monte-Carlo (MCMC) sampling was used to fit radial and angular modes resulting from a Spherical Harmonics decomposition of the 2dFGRS overdensity field (described in Percival et al. 2004) with 16 real-space power spectrum values and linear redshift-space distortion parameter \beta(L*,0). The recovered marginalised band-powers are compared to previous estimates of galaxy power spectra. Additionally, we provide a simple model for the 17 dimensional likelihood hyper-surface in order to allow the likelihood to be quickly estimated given a set of model band-powers and \beta(L*,0). The likelihood surface is not well approximated by a multi-variate Gaussian distribution with model-independent covariances. Instead, a model is presented in which the distribution of each band-power has a Gaussian distribution in a combination of the band-power and its logarithm. The relative contribution of each component was determined by fitting the MCMC output. Using these distributions, we demonstrate how the likelihood of a given cosmological model can be quickly and accurately estimated, and use a simple set of models to compare estimated likelihoods with likelihoods calculated using the full Spherical Harmonics procedure. All of the data are made publically available (from this http URL, enabling the Spherical Harmonics decomposition of the 2dFGRS of Percival et al. (2004) to be easily used as a cosmological constraint.

Hybrid nonlinear joint transform correlator that operates at a high frame rate.

A joint transform correlator has been constructed by a spatial light modulator that uses the electroabsorption effect of GaAs crystal and operates at a high frame rate a TV camera with logarithmic response and a personal computer. In the system, logarithmic values of joint power spectra generated in an optical system were electrically digitized and inverse-Fourier transformed. The system has accomplished the operation of correlation with a throughput time smaller than 10 ms per an input image.

Noise optimized IIR digital filter design—tutorial and some new aspects

IIR digital filters can be implemented in a large number of different structures. In addition, there are various possibilities for the individual realization of these structures, depending on coefficient format, state variable format, quantization points and used overflow characteristics. An overview is given about the whole filter design procedure for cascades with second order sections (SOS) in the direct forms and in the state space form, including scaling and calculation of the noise figure for the selected structures and hardware realizations. For SOS in the state space form a noise optimized transformation is evaluated as a closed solution. The best pairing and ordering of poles and zeros within the cascade is calculated by “Dynamic Programming”, an efficient optimization method for the allocation problem. Optimization is possible by the mean noise power as well as by the peak value of the noise power spectrum. Based on the exact solutions, rules of thumb are examined and further improved. The methods for optimized filter implementations are tested by an ensemble of filters with varying zero and pole positions. The results illustrate that, according to the transfer function, an appropriate choice of the SOS forms together with an optimization of pairing and ordering is useful for different hardware realizations.

EROICA: Exploring regions of interest with cluster analysis in large functional magnetic resonance imaging data sets

AbstractWe describe a divide and conquer strategy for an exploratory data analysis (EDA) of large functional magnetic resonance imaging (fMRI) data sets. The need for an EDA to precede and complement a confirmatory model‐based analysis is now well established. For complex fMRI experiments, where a prior model of the expected response cannot be posited, the sole option is to conduct an initial EDA. An EDA often discovers unanticipated behavior, allowing the experimenter to augment or even change the original hypothesis. In addition, the gross artifact behavior that EDA makes evident may aid the experimenter in deciding whether the data set is even usable, some additional preprocessing step is required, or the one used has introduced spurious effects. The proposed strategy, named EROICA for exploring regions of interest with cluster analysis, evolved from an empirical observation that a typical cluster of activation or artifact time series can be partitioned into three subsets: time series corrupted by significant trends and time series above and below some noise level. Moreover, the sought‐after common temporal behavior among the cluster time series can be extracted in an uncorrupted form from the above noise level time series alone. Thus, the key feature of EROICA is the initial partition of the data set into trendy and below the noise level time series, followed by the fuzzy cluster analysis (FCA) of the above the noise level time series to extract common cluster behavior patterns (centroids). The initial partition is based on a test statistic in the power spectrum domain. This step has significant ramifications: it greatly speeds up the FCA because of the much smaller number of time series to cluster; it makes the clustering results more robust because they are no longer affected by the trendy and noisy time series; the above the noise level time series can be further grouped according to the location of the spectral peak on the frequency axis, and these groups can be used to create a subset of initial centroids that greatly improves the convergence rate of the FCA; and the group of below the noise level time series (referred to as the noise pool) can be used as a data‐driven representation of the underlying noise source. In the final step, each time series is modeled as a linear combination of the closest centroid plus noise. The noise pool is very convenient for obtaining thresholds when testing the significance of the model parameter without having to model or assume the distributional properties of the underlying noise source. To limit the number of false positives in the activation maps, the significance test also tests the time series power spectrum values at the frequency locations determined by the cluster centroid. EROICA is one of the analysis options offered by the general image‐processing package EvIdent®. © 2003 Wiley Periodicals, Inc. Concepts Magn Reson 16A: 50–62, 2003

Effects in the Solarp‐Mode Power Spectrum from Scattering on a Turbulent Background Flow with Stochastic Wave Sources

This work demonstrates how the scattered wave field, in combination with stochastic wave sources, influences the p-mode power spectrum. I adopt a zone with random fluctuations in sound speed and velocity (characterized by the respective correlation functions). I present a general formalism (for plane-parallel conditions) to calculate the expectation value of the p-mode power spectrum. The power due to the direct field from the sources dominates, and depends only on the source correlation function. Smaller, but significant, are due to scattered wave field components. These corrections depend in general on the correlation functions of the fluctuations in the medium. I adopt a simple waveguide for the purpose of clear demonstration, and show that the corrections generate three important effects: (1) the line profiles are shifted along the wavenumber (frequency) axis, with varying effects depending on which turbulent physical quantity we consider; (2) the shapes and widths of the line profiles are altered; and (3) the troughs between the line profiles are to some extent filled in, contributing to the solar background power. It is demonstrated that boundary zones can generate important contributions to the power spectrum.

A new surface characterization technique: RIMAPS (Rotated Image with Maximum Average Power Spectrum).

This work introduces a new imaging technique, Rotated Image with Maximum Average Power Spectrum (RIMAPS), for use in determining orientation and characteristics of surface topography. It consists of computing the maximum value of the averaged power spectrum, given by one step of the two-dimensional Fourier transform, for each angle of rotation of a digitized image. The basic measurement science of this technique is described and different cases are studied. The characterization of simple geometrical figures explains the meaning of peaks and their angular positions given by RIMAPS analysis. A known surface pattern made on a sample of pure copper, mechanically ground, is used to study reproducibility, dependence on image quality and topography scale relative to pixel size and magnification. Samples of pure zinc, mechanically ground and chemically etched, were used to show the main features of RIMAPS analysis when characterizing a more complicated pattern on a real surface. All the studies performed under different conditions for observation and acquisition of images give strong evidence of the stability and robustness of RIMAPS as a technique for the characterization of topography.

A novel approach for the forecasting of mean hourly wind speed time series

This paper presents a novel method for the forecasting of mean hourly wind speed data using time series analysis. The initial point for this approach is mainly the fact that none of the forecasting approaches for hourly data, that can be found in the literature, based on time series analysis or meteorological models, gives significantly lower prediction error than the elementary persistent approach. This was combined with the characteristics of the wind speed data, which are determined by the power spectrum values, distinguished by the spectral gap in intervals between 20 minutes and 2 hours. The finally proposed methodology is based on the multi-step forecasting of 10 minutes averaged data and the subsequent averaging to generate mean hourly predictions. When applied to two independent data sets, this approach outperformed by a factor of four, the conventional one which utilizes past mean hourly wind speed values as inputs to the forecasting models.

Diurnal changes in the power spectral characteristics of eye movements and heart rate variability in the human fetus at term.

It is well known that 1/f characteristics in power spectral patterns exist in various biological factors including heart rate variability. In the present study, we tried to elucidate the diurnal variation in spectral properties of eye movement and heart rate variability in the human fetus at term, via continuous 24-h observation of both these parameters. Studied were five uncomplicated fetuses at term. We observed eye movement and fetal heart rate (FHR) with real-time ultrasound and Doppler cardiotocograph, respectively, and analyzed the diurnal change in spectral properties, using the maximum entropy method. In four of five cases, the slope values of power spectra for both eye movement frequency and FHR, ranging approximately between 0.5 and 1.8, indicated diurnal variation, where the slopes tended to have high values during the day and low values at night. These findings suggest that, in the human fetus at term, eye movement and FHR are under the control of a common central mechanism, and this center changes its complexity as seen through diurnal rhythm.

Ambulatory ECG and analysis of heart rate variability in Parkinson's disease

OBJECTIVESCardiovascular reflex tests have shown both sympathetic and parasympathetic failure in Parkinson's disease. These tests, however, describe the autonomic responses during a restricted time period and have great individual variability,...

Large-scale power spectrum and structures from the ENEAR galaxy peculiar velocity catalogue

We estimate the mass density fluctuations power spectrum (PS) on large scales by applying a maximum likelihood technique to the peculiar velocity data of the recently completed redshift—distance survey of early-type galaxies (hereafter ENEAR). Parametric cold dark matter (CDM)-like models for the PS are assumed, and the best-fitting parameters are determined by maximizing the probability of the model given the measured peculiar velocities of the galaxies, their distances and estimated errors. The method has been applied to CDM models with and without COBE normalization. The general results are in agreement with the high-amplitude power spectra found from similar analyses of other independent all-sky catalogue of peculiar velocity data such as MARK III and SFI, in spite of the differences in the way these samples were selected, the fact that they probe different regions of space and galaxy distances are computed using different distance relations. For example, at k = 0.1 h Mpc−1 the power spectrum value is P(k)Ω1.2 = (6.5 ± 3) × 103(h−1 Mpc)3 and η8 ≡ σ8Ω0.6 = 1.1−0.35+0.2; the quoted uncertainties refer to 3σ error level. We also find that, for ΛCDM and OCDM COBE-normalized models, the best-fitting parameters are confined by a contour approximately defined by Ω h1.3 = 0.377 ± 0.08 and Ω h0.88 = 0.517±0.083 respectively. Γ-shape models, free of COBE normalization, result in the weak constraint of Γ≥0.17 and in the rather stringent constraint of η8 = 1.0 ± 0.25. All quoted uncertainties refer to 3σ confidence level (c.l.). The calculated PS has been used as a prior for Wiener reconstruction of the density field at different resolutions and the three-dimensional velocity field within a volume of radius ≈80 h−1 Mpc. All major structures in the nearby Universe are recovered and are well matched to those predicted from all-sky redshift surveys. The robustness of these features has been tested with constrained realizations (CR). Analysis of the reconstructed three-dimensional velocity field yields a small bulk-flow amplitude (∼160±60 km s−1 at 60 h−1 Mpc) and a very small rms value of the tidal field (∼60 km s−1). The results give further support to the picture that most of the motion of the Local Group arises from mass fluctuations within the volume considered.

A Bayesian Estimate of the Skewness of the Cosmic Microwave Background

We propose a formalism for estimating the skewness and angular power spectrum of a general Cosmic Microwave Background data set. We use the Edgeworth Expansion to define a non-Gaussian likelihood function that takes into account the anisotropic nature of the noise and the incompleteness of the sky coverage. The formalism is then applied to estimate the skewness of the publicly available 4 year Cosmic Background Explorer (COBE) Differential Microwave Radiometer data. We find that the data is consistent with a Gaussian skewness, and with isotropy. Inclusion of non Gaussian degrees of freedom has essentially no effect on estimates of the power spectrum, if each $C_\ell$ is regarded as a separate parameter or if the angular power spectrum is parametrized in terms of an amplitude (Q) and spectral index (n). Fixing the value of the angular power spectrum at its maxiumum likelihood estimate, the best fit skewness is $S=6.5\pm6.0\times10^4(\muK)^3$; marginalizing over Q the estimate of the skewness is $S=6.5\pm8.4\times10^4(\muK)^3$ and marginalizing over n one has $S=6.5\pm8.5\times10^4(\muK)^3$.

Effect of Noise on Analog Circuit Testing

The effect of test environment noise (tester noise) on test waveforms is considered. We show that tests generated ignoring the tester noise characteristics are prone to failure when actually applied to the circuit-under-test (CUT). The failure may result in the good circuit being declared faulty or the faulty circuit being declared good. This failure is independent of the fault model and nature of the test, i.e., AC or DC, time domain or frequency domain. We characterize the total noise at the primary outputs (PO‘s) of the circuit using second order statistics. We use the noise power spectrum and root mean square (RMS) values to make decisions about the test waveforms and recommend more noise-robust tests. For non-linear circuits we use the Central Limit Theorem of statistics to approximate narrow band noise at a primary input (PI) by a sum of sinusoidal distributions, and we use Monte-Carlo simulations to determine the noise at the PO‘s in the time domain. Results of experiments on an instrumentation amplifier, a biquadratic filter, and a Gilbert multiplier are presented, which prove that valid tests in a noise-free environment are invalid when tester noise is considered.