Power Spectrum Estimation Method Research Articles

Changes of the Electric and Magnetic Fields on the Ground and in the Ionosphere before and After Several Great Earthquakes

AbstractWe have studied the changes of the geoelectric and geomagnetic fields around the epicentral areas of the Ms8.0 Wenchuan earthquake in Sichuan (2008), the Ms7.3 Yutian quake in Xinjiang (2008) and the Ms7.1 Yushu quake in Qinghai (2010) and their strong aftershocks, and the changes of the ionospheric magnetic field over Wenchuan, Yutian and Yushu. This study is based on processing of the data from the satellite Demeter using the non‐linear power spectrum estimation method (maximum entropy method) and the statistical method of the electric/magnetic field pulse energy. Some significant electromagnetic phenomena are seen, which include the increased power spectrum density and the increased pulse energy of the ELF components of the geoelectric and geomagnetic fields. It is very interesting that such electromagnetic anomalous phenomena appeared on the ground and in the ionosphere in about the same time period. Finally, we have discussed the mechanism of the abnormal electromagnetic phenomena on the ground and in the ionosphere.

Comparative analysis of power spectrum estimation methods

The subject of this paper is the comparative analysis of the eleven most important nonparametric, parametric and subspace power spectrum estimation methods. Theoretically and experimentally we analyse how the frequency resolution of the spectrum estimation methods depends on the signal length, signal-to-noise ratio (SNR) and the order parametric methods.

A New Subband-Weighted MVDR-Based Front-End for Robust Speech Recognition

This paper presents a novel noise-robust feature extraction method for speech recognition. It is based on making the Minimum Variance Distortionless Response (MVDR) power spectrum estimation method robust against noise. This robustness is obtained by modifying the distortionless constraint of the MVDR spectral estimation method via weighting the sub-band power spectrum values based on the sub-band signal to noise ratios. The optimum weighting is obtained by employing the experimental findings of psychoacoustics. According to our experiments, this technique is successful in modifying the power spectrum of speech signals and making it robust against noise. The above method, when evaluated on Aurora 2 task for recognition purposes, outperformed both the MFCC features as the baseline and the MVDR-based features in different noisy conditions.

Comparison of a new frequency domain periodicity detector derived from a temporally stable power spectral representation and zero frequency filtering based periodicity detector.

Recently, an event based periodicity detection method was proposed using zero frequency filtering method [Yegnanarayana et al., ITRW Aalborg 2008]. The authors also introduced a new periodicity detector based on TANDEM‐STRAIGHT [Kawahara et al., ICASSP2008 (2008)], a combination of temporally stable power spectrum estimation method for periodic signals and a spectral envelope recovery method based on consistent sampling [Unser, Proc. IEEE (2000)]. These methods provide a complementary set of information on excitation source signals of speech sounds. MATLAB implementation of these methods was evaluated using publicly available EGG databases and compared with popular existing methods. It was found that the zero frequency filtering based method runs eight times faster than real time even with MATLAB implementation and yielded comparable performance to popular methods. The TANDEM‐STRAIGHT based methods also yielded comparable performance and additional information that is useful to represent diplophonia, for example. Detailed analysis examples and their application for TANDEM‐STRAIGHT will also be discussed.

Wigner-Ville distribution and its application in seismic attenuation estimation

The attenuation of seismic signals is often characterized in the frequency domain using statistical measures of the power spectrum. However, the conventional Fourier transform-based power spectrum estimation methods suffer from time-frequency resolution problems. Wigner-Ville distribution, which is a member of Cohen class time-frequency distributions, possesses many appealing properties, such as time-frequency marginal distribution, time-frequency localization, etc. Therefore, Wigner-Ville distribution offers a new way for estimating the attenuation of seismic signals. This paper initially gives a brief introduction to Wigner-Ville distribution and the smoothed Wigner-Ville distribution that is effective in reducing the cross-term effect, and then presents a method for seismic attenuation estimation based on the instantaneous energy spectrum of the Wigner-Ville distribution. A real data example from central Tarim Basin in western China is presented to illustrate the effectiveness of the proposed method. The results show that the Wigner-Ville distribution-based seismic attenuation estimation method can effectively detect the difference between reef, shoal and lagoon facies by their attenuation properties, indicating that the estimated seismic attenuation can be used for reef and shoal carbonate reservoir characterization.

Cosmological constraints from the SDSS luminous red galaxies

We measure the large-scale real-space power spectrum P(k) using luminous red galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS) and use this measurement to sharpen constraints on cosmological parameters from the Wilkinson Microwave Anisotropy Probe (WMAP). We employ a matrix-based power spectrum estimation method using Pseudo-Karhunen-Loeve eigenmodes, producing uncorrelated minimum-variance measurements in 20 k-bands of both the clustering power and its anisotropy due to redshift-space distortions, with narrow and well-behaved window functions in the range 0.01h/Mpc 0.1h/Mpc and associated nonlinear complications, yet agree well with more aggressive published analyses where nonlinear modeling is crucial.

Hybrid estimation of cosmic microwave background polarization power spectra

This paper generalizes the hybrid power spectrum estimation method developed in a previous paper to the estimation of polarization power spectra of the cosmic microwave background radiation. The hybrid power spectrum estimator is unbiased and we show that it is close to optimal at all multipoles, provided the pixel noise satisfies certain constraints. Furthermore, the hybrid estimator is computationally fast and can easily be incorporated in a Monte Carlo chain for Planck-sized data sets, which may be essential to account for realistic noise covariance and systematic errors. Simple formulae are given for the covariance matrices, including uncorrelated inhomogeneous instrumental noise, and these are tested extensively against numerical simulations. We compare the behaviour of simple pseudo-Cℓ (PCL) estimates with maximum-likelihood estimates at low multipoles. For realistic sky cuts, maximum-likelihood estimates reduce very significantly the mixing of E and B modes. To achieve limits on the scalar–tensor ratio of r≪ 0.1 from sky maps with realistic sky cuts, maximum-likelihood methods, or PCL estimators based on unambiguous E and B modes, will be essential.

Methods for Characterizing Flicker and its Applications

Flicker is an important power quality disturbance and has received an increasing concern from power system researchers. Interharmonics are the non-integral frequencies other than harmonic frequencies. Nowadays, research has shown that interharmonics and flicker seem to be closely related. To clarify this relationship, flicker is characterized in the frequency domain. The traditional Fourier-based methods have shown some drawbacks in representing non-stationary, non-periodic power signals and therefore other methods should be investigated for accomplishing this task. This paper introduces the most common signal processing approaches to assess the problem, power spectrum estimation methods and linear transforms. The wavelet transform has shown superior performance comparing to other methods and circumventing the problem time-frequency resolution.

Steady-State VEP-Based Brain-Computer Interface Control in an Immersive 3D Gaming Environment

This paper presents the application of an effective EEG-based brain-computer interface design for binary control in a visually elaborate immersive 3D game. The BCI uses the steady-state visual evoked potential (SSVEP) generated in response to phase-reversing checkerboard patterns. Two power-spectrum estimation methods were employed for feature extraction in a series of offline classification tests. Both methods were also implemented during real-time game play. The performance of the BCI was found to be robust to distracting visual stimulation in the game and relatively consistent across six subjects, with 41 of 48 games successfully completed. For the best performing feature extraction method, the average real-time control accuracy across subjects was 89%. The feasibility of obtaining reliable control in such a visually rich environment using SSVEPs is thus demonstrated and the impact of this result is discussed.

A Digital Power Spectrum Estimation Method for the Adaptation of High-Speed Equalizers

This work presents a method to estimate the power spectrum of digital signals, which is then used to generate an error signal to tune Gbps data rate equalizers for digital communications. The proposed power spectrum estimation method can be realized with standard digital circuits and has been fabricated and tested in 0.35-/spl mu/m CMOS technology for 1-Gbps data rate. Compared with the traditional bandpass filter followed by a rectifier implementation, this method has wider input signal range and is scalable to higher speed technologies beyond the gigahertz range, in addition to largely reduced power dissipation and die area. Also presented are system simulations on the bit-error rate performance and the error space analysis of the proposed method in comparison with the method of using a bandpass filter followed by a rectifier.

Myths and truths concerning estimation of power spectra: the case for a hybrid estimator

It is widely believed that maximum-likelihood estimators must be used to provide optimal estimates of power spectra. Since such estimators require the inversion and multiplication of N d x N d matrices, where N d is the size of the data vector, maximum-likelihood estimators require at least of order N 3 d operations and become computationally prohibitive for N d greater than a few tens of thousands. Because of this, a large and inhomogeneous literature exists on approximate methods of power-spectrum estimation. These range from manifestly suboptimal but computationally fast methods, to near-optimal but computationally expensive methods. Furthermore, much of this literature concentrates on the power-spectrum estimates rather than the equally important problem of deriving an accurate covariance matrix. In this paper, I consider the problem of estimating the power spectrum of cosmic microwave background (CMB) anisotropies from large data sets. Various analytic results on power-spectrum estimators are derived, or collated from the literature, and tested against numerical simulations. An unbiased hybrid estimator is proposed that combines a maximum-likelihood estimator at low multipoles and pseudo-C estimates at high multipoles. The hybrid estimator is computationally fast (i.e. it can be run on a laptop computer for Planck-sized data sets), nearly optimal over the full range of multipoles, and returns an accurate and nearly diagonal covariance matrix for realistic experimental configurations (provided certain conditions on the noise properties of the experiment are satisfied). It is argued that, in practice, computationally expensive methods that approximate the O(N 3 d) maximum-likelihood solution are unlikely to improve on the hybrid estimator, and may actually perform worse. The results presented here can be generalized to CMB polarization and to power-spectrum estimation using other types of data, such as galaxy clustering and weak gravitational lensing.

Power Spectrum Estimation in Strain Border Area using Two Different Fiber Optic Strain Sensor Outputs

It is necessary to estimate the Brillouin scattering power spectrum in a fiber optical strain sensor. This is because optical fiber strain depends on the Brillouin scattering frequency shift. However, this requirement is not met in the strain border area because the Brillouin scattering power spectrum cannot be approximated by one Lorentzian function and therefore the conventional least squares method with linearization cannot be employed. This paper proposes a new power spectrum estimation method that uses two different outputs from a fiber optical strain sensor in the strain border area. The effectiveness of the new method is confirmed by simulation.

First‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: The Angular Power Spectrum

We present the angular power spectrum derived from the first-year Wilkinson Microwave Anisotropy Probe (WMAP) sky maps. We study a variety of power spectrum estimation methods and data combinations and demonstrate that the results are robust. The data are modestly contaminated by diffuse Galactic foreground emission, but we show that a simple Galactic template model is sufficient to remove the signal. Point sources produce a modest contamination in the low frequency data. After masking ~700 known bright sources from the maps, we estimate residual sources contribute ~3500 uK^2 at 41 GHz, and ~130 uK^2 at 94 GHz, to the power spectrum l*(l+1)*C_l/(2*pi) at l=1000. Systematic errors are negligible compared to the (modest) level of foreground emission. Our best estimate of the power spectrum is derived from 28 cross-power spectra of statistically independent channels. The final spectrum is essentially independent of the noise properties of an individual radiometer. The resulting spectrum provides a definitive measurement of the CMB power spectrum, with uncertainties limited by cosmic variance, up to l~350. The spectrum clearly exhibits a first acoustic peak at l=220 and a second acoustic peak at l~540 and it provides strong support for adiabatic initial conditions. Kogut et al. (2003) analyze the C_l^TE power spectrum, and present evidence for a relatively high optical depth, and an early period of cosmic reionization. Among other things, this implies that the temperature power spectrum has been suppressed by \~30% on degree angular scales, due to secondary scattering.

Digital Signal Processing in a Novel Flip Chip Solder Joint Defects Inspection System

Digital signal processing methods in a novel flip chip solder joint quality inspection system are presented. Laser ultrasound and interferometric system is a new approach for solder joint inspection. It has many advantages such as being noncontact, nondestructive, fast, accurate and low cost. Furthermore, it can be used on-line in assembly line or off-line during process development. In this system, signals recorded are ultrasound waveforms. Because noise is present, signal processing methods are developed to increase signal-to-noise ratio, and to extract solder joint quality information from those waveforms. Signals are analyzed both in frequency domain and time domain. In the frequency domain, digital filtering and Bartlett power spectrum estimation method are used, and defects can be detected from the frequency shifting. A series of experimental results are presented, showing that power spectrum estimation can greatly increase the signal-to-noise ratio than when only time domain averaging is used. This speeds up the data acquisition and analysis process. In the time domain, “error ratio” is used to measure the difference between a good chip and a chip with defect. Results indicate that error ratio method not only can detect whether a chip has solder joint defect or not, but can also locate that defect. Overall, signal processing plays a very important role in this flip chip quality inspection system.

Mapping the Cosmic Microwave Background Anisotropy:Combined Analysis of QMAP Flights

We present results from the QMAP balloon experiment, which maps the cosmic microwave background (CMB) and probes its angular power spectrum on degree scales. In two separate flights, data were taken in six channels at two frequency bands between 26 and 46 GHz. We describe our method for mapmaking (removal of 1/f-noise and scan-synchronous offsets) and power spectrum estimation as well as the results of a joint analysis of the data from both flights. This produces a 527 deg2 map of the CMB around the north celestial pole, allowing a wide variety of systematic cross-checks. The frequency dependence of the fluctuations is consistent with CMB and inconsistent with Galactic foreground emission. The anisotropy is measured in three multipole bands from l~40 to l~200, and the angular power spectrum shows a distinct rise that is consistent with the Saskatoon results.

Measuring the Galaxy Power Spectrum with Future Redshift Surveys

Precision measurements of the galaxy power spectrum P(k) require a data analysis pipeline that is both fast enough to be computationally feasible and accurate enough to take full advantage of high-quality data. We present a rigorous discussion of different methods of power spectrum estimation, with emphasis on the traditional Fourier method and linear (Karhunen-Loeve; KL) and quadratic data compression schemes, showing in what approximations they give the same result. To improve speed, we show how many of the advantages of KL data compression and power spectrum estimation may be achieved with a computationally faster quadratic method. To improve accuracy, we derive analytic expressions for handling the integral constraint, since it is crucial that finite volume effects are accurately corrected for on scales comparable to the depth of the survey. We also show that for the KL and quadratic techniques, multiple constraints can be included via simple matrix operations, thereby rendering the results less sensitive to Galactic extinction and misestimates of the radial selection function. We present a data analysis pipeline that we argue does justice to the increases in both quality and quantity of data that upcoming redshift surveys will provide. It uses three analysis techniques in conjunction: a traditional Fourier approach on small scales, a pixelized quadratic matrix method on large scales, and a pixelized KL eigenmode analysis to probe anisotropic effects such as redshift-space distortions.

SAR imaging via modern 2-D spectral estimation methods

This paper discusses the use of modern 2D spectral estimation algorithms for synthetic aperture radar (SAR) imaging. The motivation for applying power spectrum estimation methods to SAR imaging is to improve resolution, remove sidelobe artifacts, and reduce speckle compared to what is possible with conventional Fourier transform SAR imaging techniques. This paper makes two principal contributions to the field of adaptive SAR imaging. First, it is a comprehensive comparison of 2D spectral estimation methods for SAR imaging. It provides a synopsis of the algorithms available, discusses their relative merits for SAR imaging, and illustrates their performance on simulated and collected SAR imagery. Some of the algorithms presented or their derivations are new, as are some of the insights into or analyses of the algorithms. Second, this work develops multichannel variants of four related algorithms, minimum variance method (MVM), reduced-rank MVM (RRMVM), adaptive sidelobe reduction (ASR) and space variant apodization (SVA) to estimate both reflectivity intensity and interferometric height from polarimetric displaced-aperture interferometric data. All of these interferometric variants are new. In the interferometric contest, adaptive spectral estimation can improve the height estimates through a combination of adaptive nulling and averaging. Examples illustrate that MVM, ASR, and SVA offer significant advantages over Fourier methods for estimating both scattering intensity and interferometric height, and allow empirical comparison of the accuracies of Fourier, MVM, ASR, and SVA interferometric height estimates.

Non-Gaussian sampling effects on the estimation of the cosmic microwave background power spectrum

We introduce a non-Gaussian model of structure formation, and show how it produces surprising sampling effects on the estimation of the CMB power spectrum. Estimates of the average power spectrum based on small sky patches produce qualitatively different results from patch to patch, and vary also with the patch size. For instance a system of secondary Doppler peaks is observed in small enough patches, but at different positions in different patches. However, no secondary Doppler peaks are observed in large sky patches. These effects question usual methods of power spectrum estimation, and techniques like bootstrapping. The non-Gaussianity of this model fails to be detected by standard tests.

Analysis of Optical Disk Readout Signal Deterioration Caused by Dust on the Substrate

A noise power spectrum estimation method is presented for optical disk readout signal influenced by dust on the substrate. The noise due to dust has been modeled using geometrical optics and assuming the Poisson distribution for the dust particles. The noise power spectrum consists of two components: one comes from the effect of individual dust particles passing across the light beam, and the other comes from the effect of overlapping area of a particle and the inverted image of another particle. The feasibility of a thin-substrate optical disk was studied using this model. Dust will not have a serious effect on the readout signal when a 0.6 mm-thick substrate is used in place of the conventional 1.2 mm-thick substrate.

Diffraction analysis of optical-disk readout signal deterioration caused by mark-profile fluctuation

A noise power-spectrum estimation method for mark-profile fluctuation is presented for optical-disk readout signals. The diffraction by marks is modeled by use of the Fraunhofer diffraction theory, and mark-profile fluctuations are taken into account through statistical averaging. The change in the readout signal is assumed to be linear to the change in the mark profile. The calculated results for a high-definition video disk agree well with the experimental results. Fluctuations in the mark-edge position is the major source of noise in the present high-definition video-disk system.