Spectrum Estimation Research Articles

A Psychoacoustic Quality Criterion for Path-Traced Sound Propagation.

In developing virtual acoustic environments, it is important to understand the relationship between the computation cost and the perceptual significance of the resultant numerical error. In this paper, we propose a quality criterion that evaluates the error significance of path-tracing-based sound propagation simulators. We present an analytical formula that estimates the error signal power spectrum. With this spectrum estimation, we can use a modified Zwicker's loudness model to calculate the relative loudness of the error signal masked by the ideal output. Our experimental results show that the proposed criterion can explain the human perception of simulation error in a variety of cases.

Fast and accurate wideband sparse spatial spectrum estimation in an underwater strong interference environment.

Wideband sparse spatial spectrum estimation is an important direction-of-arrival (DOA) estimation method that can obtain a high resolution with few snapshots and a low signal-to-noise ratio. However, in an underwater strong interference environment, the accuracy of DOA estimation may be seriously affected, and even the weak targets could be completely masked. In this paper, we propose a fast matrix filter design method based on truncated nuclear norm regularization to attenuate strong interferences while passing weak targets. The matrix filter operator and the exact covariance matrix after filtering can be obtained simultaneously by solving a convex optimization problem that contains the output power term and non-Toeplitz error propagation control term. Then the modified sparse spectrum fitting algorithm based on the matrix filter is used to estimate spatial spectrum over closely spaced wideband signals. Compared with existing methods, the proposed method achieves higher DOA estimation accuracy and lower computational time for matrix filter design. Meanwhile, the estimation accuracy of the proposed method is verified with the experimental results.

Enhanced approach to fusing automatic characteristic frequency extraction and adaptive array signals weighting for abnormal machine sound localization

In this paper, an enhanced approach for sound localization is proposed, which fuses automatic extraction of array signal characteristic frequencies and adaptive weighting. The method refines the autoregressive power spectral estimation algorithm and improves density-based spatial clustering of applications with noise algorithm for characteristic frequency extraction. Adaptive weighting technique is introduced to alleviate the problem of frequency mismatch in the localization process. The initial weight of narrowband signals is calculated and normalized using the frequency domain amplitude integration of narrowband signals, followed by adaptive threshold correction to eliminate invalid narrowband signal weights. The adaptive weight vector improves the localization method’s accuracy and interference suppression. The effectiveness and universality of the proposed method are demonstrated with test data from dry transformers and pumps, and its applicability is shown to extend to various spatial spectrum estimation algorithms and deep learning-based sound source localization techniques.

A Separation Method for Electromagnetic Radiation Sources of the Same Frequency

To separate electromagnetic interference sources with an unknown source number, a new separation method is proposed, which includes five key steps: spatial spectrum estimation, source number and direction-of-arrival estimation, mixed matrix estimation, separation matrix estimation, and source signal recovery. A pseudospatial spectrum estimation network based on a convolutional neural network is proposed to estimate the number of electromagnetic radiation sources, their direction of arrival, and the mixing matrix. A new loss function is designed as an optimization criterion for estimating the separation matrix. To ensure generalization, both simulated and measured datasets are used to train the proposed network. Experimental results demonstrate that the proposed separation method outperforms existing source separation techniques in terms of correlation coefficient, root mean square error, and running time. Importantly, it exhibits strong performance in underdetermined cases, as well as in overdetermined or determined cases.

Quantitative interpretations of potential fields: from parametric to geostructural recalculations

The relevance. Need to development of an applied algorithm for combined interpretation of heterogeneous geophysical data based on unified physical analogy, focused on solving the inverse problem of potential theory. The wave approximation of the cross-section of mining massif fits into the paradigm of dissipative structuring of nonequilibrium media acts as a special case of the above analogy. The task of the study is to adapt this algorithm to recalculations of both potential and non-potential geofields. In the list of nonpotential geofields the remote sensing data and digital terrain model are the most interesting as the data with non-regulated access. Practical significance of the research is associated with the approbation of a family of algorithms in production projects of both geological and engineering nature. The aim. To minimize the family of equivalent solutions to the inverse problem by mutual verification of heterogeneous models of the anomaly-forming source. The objects. Development of the geofields combined interpretation algorithm and recalculation of geofields in depth for tracing elements of stratification and geological fractures. The methods. Formed by software and algorithmic development, which is based on deterministic analytical representations: computation of Cauchy integral, iterative application of direct solution, spectrum estimation. The results. Reduced to the set of parametric cross-sections derived with recalculations with minimum a priori geological information with final geological consideration. The combination of visualizations of analytical continuation, singular points and results of automated fitting admits the reconstruction of geostructural model of parametric cross-section with significant reliability. Extension of standard methods of quantitative interpretation by means of wave approximations includes quasi-seismic halftone visualizations verifying the mentioned reconstructions.

Source Spectra of Pg and Lg Waves from North Korean Nuclear Tests Estimated Using a Nonmodel-Based Approach

ABSTRACT In this article, we demonstrate that source spectra for regional seismic waves generated by an underground explosion may be uniquely extracted using a simple linear regression method between the geometrical spreading corrected displacement spectra and epicentral distances as long as the recording stations are well distributed in distances. Using this method, source spectra of Pg and Lg waves from North Korean nuclear tests conducted between 2009 and 2017 are estimated, respectively, and are compared to test the conjecture of Fisk (2006) as well as to determine the relative size between the seismic moment of Lg waves and that of compressional waves. For a specified explosion, the resultant Pg and Lg source spectra approximately have equal low-frequency source level. Based on this result, it is estimated that for the explosions seismic moment of Lg waves would be about 35% of that of compressional waves. In addition, it is shown the Fisk conjecture approximately stands, as for a specified explosion the observed Pg and Lg source spectra share the same manner of high-frequency rolloff as f−2, the source corner frequency of Lg waves is smaller than that of Pg waves by a factor of about 1/3, and the Pg source spectrum exhibits a prominent overshoot, whereas it is not obvious in corresponding Lg source spectrum. The new method for source spectra estimation may have a promising application prospect in monitoring studies. As an example, it is shown that the yield and even buried depths of the North Korean nuclear explosions may be reasonably estimated by fitting the observed Pg source spectra using an MM71- (Mueller and Murphy, 1971) and DJ91 (Denny and Johnson, 1991)-based hybrid source model suggested by Ford and Walter (2013).

Study of the Reasonable Acquisition Frequency Evaluation Method of Midspan Deflection of Medium- and Small-Span Beam Bridges

The objective of this study is to further promote and apply the structural monitoring system to medium and small bridges, given the relative delays in scientific research, technical specifications, and engineering practice for the safety monitoring of small and medium-span girder bridges, as well as the relative simplicity of the structural system of these bridges, their well-defined forces, and the relatively large proportion of live load responses during operation. These concepts are proposed based on the evaluation method of live loading (As therefore, this paper suggests the notion of sensor acquisition frequency and appropriate acquisition frequency based on the live load assessment method and the fundamental reliability theory). Based on the time-history curve depicting the midspan deflection response of the vehicle-bridge coupling system, the frequency domain analysis reveals that the power spectrum at −3 dB corresponds to the response cutoff frequency. Significantly, the cutoff frequency mentioned is double the acquisition frequency considered suitable for the study. Based on the definition of a quasi-static response, it can be deduced that the velocity of a load does not exert any influence on the quasi-static response of a bridge structure. As a result, the derivation of the components related to the midspan deflection of a bridge’s quasi-static response is presented, together with a recommended set of methodological guidelines for the extraction of finite elements. This study introduces a novel approach for determining the cutoff frequency of the structural response by utilizing the characteristics of amplitude spectrum estimation and power spectrum estimation in frequency domain analysis. The cutoff frequency of the signal is determined by analyzing the amplitude-frequency curve of the power spectrum. Subsequently, the probability density function of the original time-history curve data is estimated based on the amplitude spectrum. Finally, reliability analysis is conducted by calculating the ratio of the amplitude spectrum area of the signal obtained through a reasonable acquisition frequency to the area of the amplitude spectrum function of the original signal. This analysis verifies the reliability of the proposed method for determining the midspan deflection acquisition frequency.

Event Extraction with Spectrum Estimation Using Neural Networks Linear Methods

The timely extraction of event information from enormous amounts of textual data is a critical research problem. Event extraction using deep learning technology has gained academic attention as a result of the fast growth of deep learning. Event extraction requires costly, expert-level, high-quality human annotations. As a result, developing a data-efficient event extraction model that can be trained using only a few labelled samples has emerged as a key difficulty. Existing research work focuses mainly on the structured data with supervised models. The proposed work focuses on Movie Scene Event Extraction, a practical media analysis problem that seeks to extract structured events from unstructured movie screenplays. We suggest using the correlation between various argument roles in situations where different argument roles in a movie scene share similar qualities. This can be beneficial to the Movie Scene Argument Extraction (argument classification and identification) and film scene trigger extraction (Trigger recognition and classifying). In order to represent the relation between different roles in argument and their respective roles, we propose a Superior Concept of Role (SRC) as a top-level idea of a role that is based on the classic argument role, as well as an SRC-based Graph Attention System (GAT). To assess the efficacy of the model we designed, we constructed the dataset MovieSceneEvent to extract movies’ scene-related events. Additionally, we conducted tests on an existing dataset in order to compare results with different models. Results from the experiments like extraction of words, aspect keywords from the documents indicate that our model does better than other models. Furthermore, the information on the relationship between the argument roles helps improve the effectiveness of film scene extraction of events.

Non-stationary astrophysical stochastic gravitational-wave background: a new probe to the high-redshift population of binary black holes

ABSTRACTThe astrophysical stochastic gravitational-wave background (SGWB) originates from the mergers of compact binary objects that are otherwise undetected as individual events, along with other sources such as supernovae, magnetars, etc. The individual gravitational-wave (GW) signal is time-varying over a time-scale that depends on the chirp mass of the coalescing binaries. Another time-scale that plays a role is the time-scale at which the sources repeat, which depends on the merger rate. The combined effect of these two leads to a breakdown of the time translation symmetry of the observed SGWB and a correlation between different frequency modes in the signal covariance matrix of the SGWB. Using an ensemble of SGWB due to binary black hole coalescence, calculated using simulations of different black hole mass distributions and merger rates, we show how the structure of the signal covariance matrix varies. This structure in the signal covariance matrix brings additional information about the sources on top of the power spectrum. We show that there is a significant improvement in the figure of merit by using this additional information in comparison to only power spectrum estimation for the LIGO–Virgo–KAGRA (LVK) network of detectors with the design sensitivity noise with 2 yr of observation. The inclusion of the off-diagonal correlation in the covariance of the SGWB in the data analysis pipelines will be beneficial in the quest for the SGWB signal in LVK frequency bands as well as in lower frequencies and in getting an insight into its origin.

Multi-taper S-transform method for estimating Wigner-Ville and Loève spectra of quasi-stationary harmonizable processes

Current non-stationary load models based on the evolutionary power spectral density (EPSD) may lead to overestimation and ambiguity of structural responses. The quasi-stationary harmonizable process with its Wigner-Ville spectrum (WVS) and Loève spectrum, which do not suffer from the deficiencies of EPSD, is suitable for modeling non-stationary loads and analyzing their induced structural responses. In this study, the multi-taper S-transform (MTST) method for estimating WVS and Loève spectrum of multi-variate quasi-stationary harmonizable processes is presented. The analytical biases and variances of the WVS, Loève spectrum, and time-invariant and time-varying coherence estimators from the MTST method are provided under the assumption that the target multi-variate harmonizable process is Gaussian. Using a numerical case of a bivariate harmonizable wind speed process, the superiority and reliability of the MTST method are demonstrated through comparisons with several existing methods for the WVS and Loève spectrum estimations. Finally, the MTST method is applied to two pieces of ground motion acceleration records measured during the Turkey earthquake in 2023.

Inductive Matrix Completion and Root-MUSIC-Based Channel Estimation for Intelligent Reflecting Surface (IRS)-Aided Hybrid MIMO Systems

This paper studies the estimation of cascaded channels in passive intelligent reflective surface (IRS)-aided multiple-input multiple-output (MIMO) systems employing hybrid precoders and combiners. We propose a low-complexity solution that estimates the channel parameters progressively. The angles of departure (AoDs) and angles of arrival (AoAs) at the transmitter and receiver, respectively, are first estimated using inductive matrix completion (IMC) followed by root-MUSIC-based super-resolution spectrum estimation. Forward-backward spatial smoothing (FBSS) is applied to address the coherence issue. Using the estimated AoAs and AoDs, the training precoders and combiners are then optimized and the angle differences between the AoAs and AoDs at the IRS are estimated using the least squares (LS) method followed by FBSS and the root-MUSIC algorithm. Finally, the composite path gains of the cascaded channel are estimated using on-grid sparse recovery with a small-size dictionary. The simulation results suggest that the proposed estimator can achieve improved channel parameter estimation performance with lower complexity as compared to several recently reported alternatives, thanks to the exploitation of the knowledge of the array responses and low-rankness of the channel using low-complexity algorithms at all the stages.

A note on spike localization for line spectrum estimation

A note on spike localization for line spectrum estimation

A guide to Whittle maximum likelihood estimator in MATLAB.

The assessment of physiological complexity via the estimation of monofractal exponents or multifractal spectra of biological signals is a recent field of research that allows detection of relevant and original information for health, learning, or autonomy preservation. This tutorial aims at introducing Whittle's maximum likelihood estimator (MLE) that estimates the monofractal exponent of time series. After introducing Whittle's maximum likelihood estimator and presenting each of the steps leading to the construction of the algorithm, this tutorial discusses the performance of this estimator by comparing it to the widely used detrended fluctuation analysis (DFA). The objective of this tutorial is to propose to the reader an alternative monofractal estimation method, which has the advantage of being simple to implement, and whose high accuracy allows the analysis of shorter time series than those classically used with other monofractal analysis methods.

Lifting Wavelets with OGS for Doppler Profile Estimation

This article discusses the second-generation wavelet transform concept and technique and its application to the noise removal problem of MST radar data. Located near Gadanki in Andhra Pradesh, India, the MST radar is collecting data on climate change. To obtain weather data, the signal collected by the radar needs to be analyzed, which usually requires power spectrum estimation. Most parametric and non-parametric methods cannot predict Doppler at an altitude above 14 KM, which makes to search for introduction of new denoising methods. More research is predominantly done on many denoising algorithms and tested with the simulated signal with various thresholds. It is observed that Lifting wavelets (LWT) with OGS is more effective in denoising the signals. Split, predict, and update are the three phases of lifting transform which on application of these steps reduces noise effectively. The LWT with OGS is applied to MST radar data and the research results shows that the noise level is reduced at higher altitudes and the signal-to-noise ratio is improved.

Fetal heart rate spectral analysis in raw signals and PRSA-derived curve: normal and pathological fetuses discrimination.

Cardiotocography (CTG) is the most common technique for electronic fetal monitoring and consists of the simultaneous recording of fetal heart rate (FHR) and uterine contractions. In analogy with the adult case, spectral analysis of the FHR signal can be used to assess the functionality of the autonomic nervous system. To do so, several methods can be employed, each of which has its strengths and limitations. This paper aims at performing a methodological investigation on FHR spectral analysis adopting 4 different spectrum estimators and a novel PRSA-based spectral method. The performances have been evaluated in terms of the ability of the various methods to detect changes in the FHR in two common pregnancy complications: intrauterine growth restriction (IUGR) and gestational diabetes. A balanced dataset containing 2178 recordings distributed between the 32nd and 38th week of gestation was used. The results show that the spectral method derived from the PRSA better differentiates high-risk pregnancies vs. controls compared to the others. Specifically, it more robustly detects an increase in power percentage within the movement frequency band and a decrease in high frequency between pregnancies at high risk in comparison to those at low risk.

Adaptive Beamforming with Small Samples and Low Complexity for Large-Scale Arrays

In this paper, we propose a novel adaptive beamforming method based on interference plus noise covariance matrix (INCM) reconstruction with few samples and low complexity. Unlike existing techniques, we make use of the fact that large-scale antenna arrays can significantly increase the spectral analysis’s resolution by estimating the steering vector (SV) and power of the interfering signal using the discrete Fourier transform (DFT). In addition, a simple spatial rotation operation is employed to resolve the power “leakage” problem of the DFT spectrum and increase estimation precision. The proposed method achieves a high output SINR by reconstructing an accurate INCM with the advantage of simple implementation and low computation complexity. Finally, we verify the effectiveness of the proposed method by numerical simulation and result analysis.

Robust power spectral density estimation via a performance-weighted blend of order statistics

Loud transients introduce bias to background spectrum estimates based on the sample mean, like the Welch Overlapped Segment Averaging (WOSA) [1967]. The Schwock and Abadi [2021] Welch Percentile (SAWP) estimator avoids the loud transient bias by replacing the averaging of the WOSA with a scaled order statistic (OS) of the sample power spectrum. While the scaling ensures the SAWP is unbiased regardless of which OS is chosen, the 80th percentile minimizes the variance of the SAWP estimator in a scenario without loud transients. However, the 80th percentile SAWP is still vulnerable to bias and increased variance from more frequent loud transients. Also, the rate of occurrence of loud transients may change with time, requiring the SAWP to adapt which percentile is used. To approach this challenge, this talk proposes a Universal SAWP estimator which is a weighted sum across different fixed percentile SAWP estimators. At each iteration, the Universal SAWP updates the blend weights to promote the percentile with the lowest sample variance over recent observations. In computer simulations, the Universal SAWP quickly assigns higher weights to the lowest variance estimators as the occurrence of loud transients increases. Overall, the Universal SAWP achieves equal or lower variance as the best fixed percentile SAWP estimator. [Work supported by ONR Code 321US.]

Modeling and Unsupervised Unmixing Based on Spectral Variability for Hyperspectral Oceanic Remote Sensing Data with Adjacency Effects

In a previous paper, we introduced (i) a specific hyperspectral mixing model for the sea bottom, based on a detailed physical analysis that includes the adjacency effect, and (ii) an associated unmixing method that is supervised (i.e., not blind) in the sense that it requires a prior estimation of various parameters of the mixing model, which is constraining. We here proceed much further, by first analytically showing that the above model can be seen as a specific member of the general class of mixing models involving spectral variability. Therefore, we then process such data with the IP-NMF unsupervised (i.e., blind) unmixing method that we proposed in previous works to handle spectral variability. Such variability especially occurs when the sea depth significantly varies over the considered scene. We show that IP-NMF then yields significantly better pure spectra estimates than a classical method from the literature that was not designed to handle such variability. We present test results obtained with realistic synthetic data. These tests address several reference water depths, up to 7.5 m, and clear or standard water. For instance, they show that when the reference depth is set to 7.5 m and the water is clear, the proposed approach is able to distinguish various classes of pure materials when the water depth varies up to ±0.2 m around this reference depth, over all pixels of the analyzed scene or over a “subscene”: the overall scene may first be segmented, to obtain smaller depths variations over each subscene. The proposed approach is therefore effective and can be used as a building block in performing the subpixel classification of the sea bottom for shallow water.

Sub-Nyquist sampling-based wideband spectrum sensing: a compressed power spectrum estimation approach

Sub-Nyquist sampling-based wideband spectrum sensing: a compressed power spectrum estimation approach

A novel approach to investigate the stability analysis and the dynamics of reaction–diffusion SVIR epidemic model

Understanding the behaviour of nonlinear dynamical systems is crucial in epidemiological modelling. Stability analysis is one of the important concepts in assessing the qualitative behaviour of such systems. This technique has been widely implemented on deterministic models involving ordinary differential equations (ODEs). Nevertheless, the application of stability analysis to distinct complex systems involving partial differential equations (PDEs) has been infrequent. In this paper, an in-depth investigation is conducted on the stability analysis and the dynamics of a reaction–diffusion SVIR model with partial immunity. Firstly, numerical simulation is performed for the proposed PDE model under several realistic scenarios to demonstrate the crucial factors that may affect the qualitative dynamics of the epidemiological model. Our numerical simulation findings highlight the occurrence of disease-free equilibrium when the transmission rates are sufficiently low, preventing the spread of the disease. However, an endemic situation is observed when the transmission rates are moderate (or high) enough to sustain ongoing transmission, leading to a stable endemic steady state. Other epidemiological factors such as vaccination and treatment (or recovery) strategies also play important roles in controlling disease outbreaks. The transition between disease-free equilibrium (DFE) and endemic equilibrium (EE), resulting from switching stability between equilibria, is of particular interest in epidemiology, due to its implications for public health interventions and strategies. This insight helps to inform decision-making processes regarding the control and prevention of diseases. To examine the stability of steady states in this PDE model, we employ a novel technique called numerical range approaches, which relies on the application of operator theory. Typically, discretising differential operators in the PDE model leads to spectral complexity and a wide range of eigenvalues. Our analysis has demonstrated that employing the numerical range (NR) and the cubic numerical range (CNR) techniques make it feasible to estimate each individual eigenvalue in the spectral range. For the DFE (respectively, EE) scenario, the spectrum of eigenvalues for the PDE system agrees with CNR estimates in which the eigenvalues are real-valued and bounded above by zero (respectively, complex conjugates pairs with negative real parts); these numerical estimations have also been verified analytically. Despite the challenges posed, the use of numerical range techniques provides a good estimation of the eigenvalues spectrum, thereby overcoming the difficulties associated with discretisation, and providing a more comprehensive understanding of the dynamics of the epidemiological system.