Cross-spectrum Method Research Articles

Velocity Estimation of Passive Target Based on Sparse Bayesian Learning Cross-Spectrum

To solve the poor performance or even failure of the cross-spectrum (CS) method in hydroacoustic weak-target passive velocimetry, a sparse Bayesian learning cross-spectrum method (SBL-CS), combining phase compensation with sparse Bayesian learning (SBL) is proposed in this paper. Firstly, the cross-correlation sound intensity is taken as the observation quantity and compensates for each frequency point of the cross-spectrum, which enables the alignment of cross-spectrum results at different frequencies. Then, the inter-correlation sound intensity of all frequencies is fused in the iterative estimation of the target velocity, verifying the proposed method’s ability to suppress the background noise when performing multi-frequency processing. The simulation results show that the proposed method is still effective in estimating the target velocity when the CS method fails and that the performance of the proposed method is better than the CS method with a decrease in SNR. As verified using the SWellEx-96 sea trial dataset, the RMSE of the proposed method for surface vessel speed measurement is 0.3545 m/s, which is 46.1% less than the traditional CS method, proving the feasibility and effectiveness of the proposed SBL-CS method for the estimation of the radial speed of a passive target.

Cross-spectrum method for acoustic source identification and visualization of airfoil noise

The identification and visualization of airfoil noise sources are critical for comprehending the interplay between flow and acoustics, and for understanding the generation and propagation of sound. In this paper, we introduce an innovative method, specifically designed to identify and visualize flow-induced noise sources associated with airfoil noise. This approach employs cross power spectral density analysis to distinctly identify flow-induced noise sources. The data for our study comes from large-eddy simulations of a NACA 0012 airfoil, characterized by a Reynolds number of 4×105, a Mach number of 0.058, and an angle of attack of 6.25∘. Different cross-spectrum formulations are examined and evaluated. The analysis includes a comparison of the cross-spectrum method's strengths and limitations relative to established data-driven approaches like dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD). We find that the cross-spectrum method provides both spectral magnitudes and phase topologies, allowing it to effectively compare sound intensities among various sources at specific frequencies, while retaining high-resolution spatiotemporal coherent flow and acoustic dynamics. One of the notable advantages of the cross-spectrum method over DMD or SPOD modes is its lesser reliance on extensive data manipulation in the form of large-size data matrix, making it a more efficient and user-friendly approach for practitioners, particularly when dealing with complex systems or high-dimensional datasets. This characteristic enhances its practicality and accessibility in the field of flow and acoustic visualization. Finally, the newly developed method is applied to three distinct flow transition scenarios to evaluate its proficiency in distinguishing acoustic generation and propagation mechanisms, depending on the specific transition case.

Analysis and application of spatio-temporal correlation characteristics of measured ocean ambient noise

Gain in sonar signal processing is closely linked to the spatio-temporal coherence characteristics of the ocean ambient noise field. The gain relies on the spatio-temporal coherence coefficient of the signal and noise, with the aim of maximizing the former and minimizing the latter. Currently, there has been ample research on the spatial characteristics of the noise field, while studies on the temporal coherence characteristics of single-point noise fields are limited. In this paper, a temporal and spatial coherence model of wind-induced noise is established based on the normal mode theory, and the impact of bandwidth and spectral structure on the time coherence coefficient of wind-induced noise is analyzed.To measure the environmental noise in 103 m of shallow water in the South China Sea, a 64-element vertical array was utilized. The results demonstrate that the measured vertical spatial correlation coefficient aligns closely with the theoretical findings when wind-induced noise is predominant. The measured temporal correlation coefficient of narrowband noise exhibits a cosine function with gradual attenuation of the envelope, and the correlation radius remains independent of frequency. As the bandwidth increases, the measured broadband noise temporal correlation radius gradually decreases. Wind speed has minimal influence on the temporal and spatial correlation coefficients of wind-induced noise. In the presence of interferences such as ships and pulses, the measured temporal and spatial correlation coefficients of wind-induced noise exhibit larger values in certain intervals.Lastly, leveraging the characteristic that the temporal coherence radius of noise is significantly smaller than that of the line spectrum signal, a single-hydrophone cross-spectrum method is proposed to process the line spectrum signal. This approach effectively enhances the signal-to-noise ratio of the line spectrum.

Mixed Reality Visualization System for the 3D sound intensity using PAGE method and spatial interpolation

In the our previous study, we proposed the visualization system of three-dimensional sound intensity measured by handy 4-ch microphones using Mixed Reality. In the previous system, since the sound intensity was estimated by the cross-spectrum method. the error at the higher frequency than the spatial Nyquist frequency becomes larger due to the microphone intervals. In addition, visibility of sound intensity map was degraded because the microphone array was moved by hands and the intervals of measurement points for sound intensity map are irregular. In this study, we improve the previous mixed reality system for sound intensity by applying the PAGE method (Phase and Amplitude Gradient Estimation), which can accurately estimate the sound intensity up to higher frequencies. Furthermore, by using spatial interpolation of an irregularly-sampled intensity map, we improve visibility of sound intensity map with mixed reality. The proposed system interpolates sound intensities at equal intervals from the sound intensities measured at irregular intervals. For evaluation, we conducted visualization experiments of sound intensities surrounding single loudspeaker.

Ultra-high-resolution time-frequency analysis of EEG to characterise brain functional connectivity with the application in Alzheimer’s disease

Objective. This study aims to explore the potential of high-resolution brain functional connectivity based on electroencephalogram, a non-invasive low-cost technique, to be translated into a long-overdue biomarker and a diagnostic method for Alzheimer’s disease (AD). Approach. The paper proposes a novel ultra-high-resolution time-frequency nonlinear cross-spectrum method to construct a promising biomarker of AD pathophysiology. Specifically, using the peak frequency estimated from a revised Hilbert–Huang transformation (RHHT) cross-spectrum as a biomarker, the support vector machine classifier is used to distinguish AD from healthy controls (HCs). Main results. With the combinations of the proposed biomarker and machine learning, we achieved a promising accuracy of 89%. The proposed method performs better than the wavelet cross-spectrum and other functional connectivity measures in the temporal or frequency domain, particularly in the Full, Delta and Alpha bands. Besides, a novel visualisation approach developed from topography is introduced to represent the brain functional connectivity, with which the difference between AD and HCs can be clearly displayed. The interconnections between posterior and other brain regions are obviously affected in AD. Significance. Those findings imply that the proposed RHHT approach could better track dynamic and nonlinear functional connectivity information, paving the way for the development of a novel diagnostic approach.

Passive estimation of target velocity based on cross-spectrum histogram.

In underwater acoustic target parameter estimation, the cross-spectrum method estimates the velocity of the target by the interference structure of the cross-correlated fields in two ranges. However, with the increase in interference in the marine environment, the performance of conventional cross-spectrum target velocity estimation methods gradually declines or even fails. To solve this problem, a cross-spectrum histogram method that combines the multi-line spectrum characteristics of the target is proposed in this paper. First, each frequency point of all line spectra is compensated by the cross-spectrum compensation method. Then the target velocity estimation value is obtained by performing probability distribution statistics on the velocity estimation results for all frequency points. Under different signal-to-noise ratios, simulations and experiments are carried out to verify the effectiveness of the proposed method. The results show that the proposed method is still effective in estimating the target velocity when the conventional method fails.

Research on sound power measurement of multi-element ultrasonic focusing transducer based on cross-spectrum method.

In this paper, aiming at the problem that a multi-array focused ultrasonic transducer working in a high power range has a nonlinear influence on the measurement accuracy, a study of acoustic power measurement based on the near field cross-spectrum method was carried out. The focused acoustic field of a multi-array transducer was derived theoretically by combining the cross-spectrum method and the Westervelt nonlinear acoustic propagation equation. Finite element simulation was used to establish the model of the focused sound field of the multi-array transducer under different excitation conditions, and the influence law of each harmonic on the total sound power under specific excitation conditions was obtained. A cross-spectrum measurement system was built to scan the two near focusing planes under different excitation conditions. The total energy, each harmonic energy, and their proportion in the focusing region under the corresponding excitation were obtained through calculation and processing. The theoretical and simulation results were verified, and the harmonic energies were compensated in the calculation of the total ultrasonic power. The measurement results were compared with those obtained by radiation force balances. It was found that the maximum measurement deviation of compensated ultrasonic power was 7.89%, which met the requirements of acoustic measurement. The accuracy of the method and conclusion was verified under the power range of 10-60W.

A Revised Hilbert-Huang Transformation to Track Non-Stationary Association of Electroencephalography Signals.

The time-varying cross-spectrum method has been used to effectively study transient and dynamic brain functional connectivity between non-stationary electroencephalography (EEG) signals. Wavelet-based cross-spectrum is one of the most widely implemented methods, but it is limited by the spectral leakage caused by the finite length of the basic function that impacts the time and frequency resolutions. This paper proposes a new time-frequency brain functional connectivity analysis framework to track the non-stationary association of two EEG signals based on a Revised Hilbert-Huang Transform (RHHT). The framework can estimate the cross-spectrum of decomposed components of EEG, followed by a surrogate significance test. The results of two simulation examples demonstrate that, within a certain statistical confidence level, the proposed framework outperforms the wavelet-based method in terms of accuracy and time-frequency resolution. A case study on classifying epileptic patients and healthy controls using interictal seizure-free EEG data is also presented. The result suggests that the proposed method has the potential to better differentiate these two groups benefiting from the enhanced measure of dynamic time-frequency association.

Multimodal Two-Phase Flow Measurement Using Dual Plane ECT and GRT

This work assesses the accuracy of two-phase flow measurement, based on cross correlation (XC) and cross-spectrum (CS) velocity computation, using dual plane nonintrusive electrical capacitance tomography (ECT), over a broad spectrum of horizontal flow configurations, combined with fraction distribution measurements from gamma-ray tomography (GRT). The measurement of two-phase flow encompasses the measurement of both the velocity and the phase concentration of the flow components. The accuracy of the flow velocity is still an open discussion and remains a key challenge in the field of multiphase flow measurement. The velocities of the two-phase components vary, both in between them and across the pipe cross section. This study assesses the use of XC techniques as methods for calculating the cross-sectional velocity distribution by deriving the transit time of the fluid flowing through two parallel ECT sensor arrays mounted on the perimeter of a pipe. The spectral distribution of the velocities is assessed for improved accuracy of individual component velocities. A dual-plane ECT is adopted for the velocity measurements and is combined with state-of-the-art density-based cross-sectional phase fraction distribution from a GRT system to measure the volumetric flow rates of the two phases. The results show that the CS method provides enhanced velocity estimation for both flow phases over the conventional XC technique. Further improvement was reported using a simple predictive correction model resulting in flowrate estimation accuracy of ±10%. The method for two-phase flow measurement suggested in this work leverages the accuracy of the tomography systems on accurate fraction measurement and fast data acquisition to lead to potential enhancement in process control by enabling a more accurate prediction of components velocities.

Cross-Spectrum Measurement Statistics: Uncertainties and Detection Limit

The cross-spectrum method consists in measuring a signal c(t) simultaneously with two independent instruments. Each of these instruments contributes to the global noise by its intrinsic (white) noise, whereas the signal c(t) that we want to characterize could be a (red) noise. We first define the real part of the cross spectrum as a relevant estimator. Then, we characterize the probability density function (pdf) of this estimator knowing the noise level (direct problem) as a Variance-gamma (VG) distribution. Next, we solve the "inverse problem" due to Bayes' theorem to obtain an upper limit of the noise level knowing the estimate. Checked by massive Monte Carlo simulations, VG proves to be perfectly reliable for any number of degrees of freedom (DOFs). Finally, we compare this method with another method using the Karhunen-Loève transform (KLT). We find an upper limit of the signal level slightly different as the one of VG since KLT better considers the available information.

The Study of Ocean Wave and Wave Power Observations by Synthetic Aperture Radar in Nearshore Waters

Wan, Y.; Zheng, C.W.; Zhang, J.; Dai, Y.; Li, L.; Qu, X., and Zhang, X., 2020. The Study of Ocean Wave and Wave Power Observations by Synthetic Aperture Radar in Nearshore Waters. In: Zheng, C.W.; Wang, Q.; Zhan, C., and Yang, S.B. (eds.),Air-Sea Interaction and Coastal Environments of the Maritime Polar Silk Roads.Journal of Coastal Research, Special Issue No. 99, pp. 9-15. Coconut Creek (Florida), ISSN 0749-0208.Based on 2 RADARSAT-2 SAR (Synthetic Aperture Radar) SLC (Single Look Complex) data and the cross-spectrum method, the distributions of significant wave heights and mean wave periods of ocean wave were inverted, and the distributions of the wave power density, which can represent the wave power, were calculated. Some comparisons between the results of the SAR and those of the ECMWF (European Center for Medium-Range Weather Forecasts) dataset were carried out, and the observation ability for the distribution characteristics of wave and wave power by the SAR was studied in detail. The results show that compared with buoys, which are single-point observations, and wave models, which are simulated observations, the SAR is an ideal tool for extensive wave observations in nearshore waters. The advantage of SAR observations is that some fine structure and microcosmic changes in wave and wave power can be found, which helps us understand the internal structure and transformation patterns of wave better. Therefore, the SAR showed extremely extensive application prospects in the field of wave observations. The contributions in this paper will provide some references for researchers aiming for ocean wave detection by remote sensing and promote the application level of SAR in the detection of wave and wave power.

1/f spectrum estimation based on α-stable distribution in colored Gaussian noise environments

The main goal of this paper is to suppress the effect of unavoidable colored Gaussian noise on declining accuracy of transistor 1/f spectrum estimation. Transistor noises are measured by a nondestructive cross-spectrum measurement method, which is first to amplify the voltage signals through ultra-low noise amplifiers, then input the weak signals into data acquisition card. The data acquisition card collects the voltage signals and outputs the amplified noise for further analysis. According to our studies, the output 1/f noise can be characterized more accurately as non-Gaussian α-stable distribution rather than Gaussian distribution. Therefore, by utilizing the properties of α-stable distribution, we propose a cross-spectrum method effective in noisy environments based on samples normalized cross-correlation function. Simulation results and diodes output noise spectrum estimation results confirm the effectiveness of our method.

Fast radio burst search: cross spectrum vs. auto spectrum method

The search for fast radio bursts (FRBs) is a hot topic in current radio astronomy studies. In this work, we carry out a single pulse search with a very long baseline interferometry (VLBI) pulsar observation data set using both auto spectrum and cross spectrum search methods. The cross spectrum method, first proposed in Liu et al., maximizes the signal power by fully utilizing the fringe phase information of the baseline cross spectrum. The auto spectrum search method is based on the popular pulsar software package PRESTO, which extracts single pulses from the auto spectrum of each station. According to our comparison, the cross spectrum method is able to enhance the signal power and therefore extract single pulses from data contaminated by high levels of radio frequency interference (RFI), which makes it possible to carry out a search for FRBs in regular VLBI observations when RFI is present.

Correction: to “Measurement of the Spectrum of Phase Noise of Harmonic Ultrahigh-Frequency Signals by the Cross-Spectrum Method,”

The acknowledgement on page 944 should read This work was supported by the Ministry of Education and Science of the Russian Federation under the agreement of 14.577.21.0279 of 26.09.2017, identifi er RFMEFI57717X0279.

Measurement of the Spectrum of Phase Noise of Harmonic Ultrahigh-Frequency Signals by the Cross-Spectrum Method

We consider various methods of measurements of the spectra of amplitude and phase noises of harmonic microwave signals and choose the most sensitive method of synchronous demodulation with two independent channels and the determination of the cross-spectrum. The results of measurements of the spectra performed by using a model of two-channel low-frequency analyzer, as well as the results of measurements of the spectra of phase noises of ultrahigh-frequency sources of various intensities, are presented and compared with the data of reference measurements.

Identification of aerodynamic admittance functions of a flat closed-box deck in different grid-generated turbulent wind fields

Wind tunnel tests of synchronous measurements of the buffeting lifts and moments on six separated strips of a motionless 1:45 scale sectional model of a flat closed-box bridge deck were carried out in three turbulent flow conditions. The longitudinal and vertical components of turbulent wind speed were also measured synchronously with the buffeting forces at the positions just over the windward edges of the six strips. Three typical methods, including the auto-spectral method based on the measured auto-spectrum of buffeting force (auto-spectrum method), the cross-spectral method based on the measured cross-spectra between buffeting force and fluctuating turbulence components (cross-spectrum method), and the colligated least square method based on a colligated residue of the above-mentioned auto- and cross-spectra (colligated least square method), were then used, respectively, to identify the aerodynamic admittance functions of the flat closed-box deck. The aerodynamic admittance function components of a buffeting force with respect to the longitudinal and vertical components of fluctuating wind speed were effectively separated using the colligated least square method while only a weighted average value, often called the equivalent aerodynamic admittance function, was obtained using the auto-spectrum method. Meanwhile, the reproduced auto-spectra of the buffeting forces had very high accuracies when the aerodynamic admittance functions identified with the colligated least square method were employed, but deviated significantly from the measured ones when the aerodynamic admittance functions identified with the cross-spectrum method were used. Furthermore, the influence of the span-wise position of the wind probe on the values of aerodynamic admittance function module was confirmed to be very small. Finally, the aerodynamic admittance function components with respect to the longitudinal and vertical fluctuating wind speeds were found to be significantly affected by both the intensities and integral scales of the oncoming turbulence wind.

Influence of beat phenomenon on direction of arrival estimation based on a single vector hydrophone

The vector hydrophone can measure sound pressure and orthogonal components of particle velocity co-locately in space and simultaneously in time. DOA (direction of arrival) estimation based on a single vector hydrophone has attracted extensive attention. Beat phenomenon can cause confusion in the DOA estimation results. In this paper, the impact mechanism of beat phenomenon to DOA estimation by cross spectrum method and average acoustic intensity method is explored through theoretical study and simulation. The result shows that beat phenomenon causes the change of sound pressure and vibration velocity amplitude with time and leads to DOA estimation results of these two methods are instability eventually. First, DOA is estimated by the average sound intensity method, if the temporal resolution is smaller than the minimum envelope period, the DOA estimation will change over time; Second, DOA is estimated by the cross spectral method, if the FFT frequency resolution is greater than frequency difference, it is unable to distinguish the frequency of these two signals. Subsequent operations will also be confused by two signal energy, causing error estimates. In the end, the solutions and application examples are proposed. The conclusion could be applied to improve the DOA estimation performance of a single vector hydrophone.

Cross-Spectrum PM Noise Measurement, Thermal Energy, and Metamaterial Filters.

Virtually all commercial instruments for the measurement of the oscillator PM noise make use of the cross-spectrum method (arXiv:1004.5539 [physics.ins-det], 2010). High sensitivity is achieved by correlation and averaging on two equal channels, which measure the same input, and reject the background of the instrument. We show that a systematic error is always present if the thermal energy of the input power splitter is not accounted for. Such error can result in noise underestimation up to a few decibels in the lowest-noise quartz oscillators, and in an invalid measurement in the case of cryogenic oscillators. As another alarming fact, the presence of metamaterial components in the oscillator results in unpredictable behavior and large errors, even in well controlled experimental conditions. We observed a spread of 40 dB in the phase noise spectra of an oscillator, just replacing the output filter.

Investigating Long-run Relationship between Money, Income and Price for Bangladesh: Application of Econometrics and Cross Spectra Methods

This study examines the long-run causation between the three major macroeconomic variables namely real GDP, money supply and price level in the Bangladesh context. The results obtained by applying time series econometric techniques reveal that unidirectional causation exists between real GDP and prices. The study also suggests that causation runs from money supply to prices but price level does not causes money supply. However, co-integration analysis ascertains long run relationship between these three variables. Moreover, in order to decompose Granger causality between real GDP, money supply and prices in the frequency-domain, Lemmens et al. (2008) method of cross spectra analysis has been used which imply that money supply granger causes real GDP over the short-run, but in the long run, money supply Granger causes prices, not real GDP.Journal of Science Foundation, January 2016;14(1):17-25

Numerical study of hydrodynamic process in Chaohu Lake

In this paper, the hydrodynamic characteristics of water flow in Chaohu Lake are studied by using the finite volume coastal ocean model (FVCOM), which is verified by the observed data. The typical flow field and the 3-D flow structure are obtained for the lake. The flow fields under extreme conditions are analyzed to provide a prospective knowledge of the water exchange and the transport process. The influence of the wind on the flow is determined by the cross spectrum method. The results show that the wind-driven flow dominates most area of the lake. Under prevailing winds in summer and winter, the water flows towards the downwind side at the upper layer while towards the upwind side at the lower layer in most area except that around the Chaohu Sluice. The extreme wind speed is not favorable for the water exchange while the sluice's releasing water accelerates the process. The water velocity in the lake is closely related with the wind speed.