Power Spectral Density Estimation Research Articles

Modeling and Estimation of Adaptive Optics-Corrected long-exposure Point Spread Function Using Gaussian Sum Approximation

Abstract Adaptive optics (AO) enhances astronomical images by correcting perturbations in the optical system, resulting in complex point spread function (PSF) shapes, which provide critical information for optical design, calibration, and diagnostics. This paper presents a parametric model for an AO-corrected long-exposure PSF that adapts to complex shapes and various seeing conditions. A complementary estimation method is also introduced, addressing the inverse problem of estimating the atmospheric PSF or power spectral density (PSD) from observed PSF data. The model, based on Gaussian sum approximation (GSA), was tested using simulated PSF data from the OOMAO toolbox for Fried parameter (r0) values ranging from 0.10 to 0.20 m and on-sky data from the Very Large Telescope’s MUSE instrument. Two approaches were analyzed: (i) direct PSF estimation using GSA, and (ii) PSF estimation derived from atmospheric PSD estimation. Both methods were evaluated using root mean square error (RMSE). While approach (i) provided the best performance, approach (ii) produced more accurate atmospheric PSF estimates compared to the Moffat approximation and the Fetick method. Additionally, approach (ii) enabled the estimation of key physical parameters, such as the Fried parameter (r0) and residual AO variance ($\sigma _{AO}^2$). The proposed methods effectively estimate atmospheric PSF and PSD, even for complex PSF shapes influenced by spiders, central obstructions, or static aberrations.

A straightforward method for estimating evolutionary power spectral density of non-stationary typhoon wind speed

PurposeA precise estimation of the evolutionary power spectral density (EPSD) of typhoon wind speed is a difficult and significant undertaking in the analysis of turbulence effects on large-expansive structures. A majority of the prevailing EPSD estimation techniques rely on complex signal processing methodologies, such as wavelet decomposition, Hilbert–Huang transformation and time-varying autoregressive moving average (ARMA) model. However, these approaches often pose challenges in terms of comprehensibility and practical implementation for engineers. In light of this issue, the present study introduces a straightforward and effective EPSD estimation method tailored specifically for typhoon wind speed, aiming to facilitate its understanding and application in engineering contexts.Design/methodology/approachFirstly, the mathematical model of a uniformly modulated non-stationary process is employed to represent the typhoon wind speed. Secondly, the reverse arrangement test serves as an auxiliary tool in conjunction with wavelet transform or empirical mode decomposition, aiding in the determination of the optimal slowly varying mean wind speed. Thirdly, Kernel regression technique is utilized to discern the time-dependent standard deviation of wind speed fluctuations. Finally, the power spectral density (PSD) of wind speed residuals is computed to facilitate the estimation of the EPSD.FindingsFirstly, the reverse arrangement test-assisted approach enables the determination of an optimal time-dependent mean from the candidate results obtained through discrete wavelet transform (DWT) and empirical mode decomposition (EMD). Secondly, the application of the Kernel regression technique facilitates accurate identification of the time-dependent variance from the fluctuating wind speed data. Thirdly, due to the influence of the extreme weather, the Gaussianity of the reduced turbulent fluctuations in typhoon wind is easily disturbed, resulting in the obvious non-Gaussian features.Originality/valueThis paper employs the mathematical model of uniformly modulated non-stationary process to characterize typhoon wind speeds and then proposes a straightforward and efficient method for estimating the EPSD of typhoon wind. The accuracy and efficacy of the presented estimation method are verified using the field-measured wind speed data from Typhoon Rammasun. The proposed EPSD estimation method for typhoon wind exhibits suitability for engineering applications owing to its simplicity and computational efficiency.

High-pass Filter Periodogram: An Improved Power Spectral Density Estimator for Unevenly Sampled Data

Accurate time series analysis is essential for studying variable astronomical sources, where detecting periodicities and characterizing power spectral density (PSD) are crucial. The Lomb–Scargle periodogram, commonly used in astronomy for analyzing unevenly sampled time series data, often suffers from noise introduced by irregular sampling. This paper presents a new high-pass filter (HPF) periodogram, a novel implementation designed to mitigate this sampling-induced noise. By applying a frequency-dependent HPF before computing the periodogram, the HPF method enhances the precision of PSD estimates and periodicity detection across a wide range of signal characteristics. Simulations and comparisons with the Lomb–Scargle periodogram demonstrate that the HPF periodogram improves accuracy and reliability under challenging sampling conditions, making it a valuable complementary tool for more robust time series analysis in astronomy and other fields dealing with unevenly sampled data.

Maximum entropy spectral analysis: an application to gravitational waves data analysis

The maximum entropy spectral analysis (MESA) method, developed by Burg, offers a powerful tool for spectral estimation of a time-series. It relies on Jaynes’ maximum entropy principle, allowing the spectrum of a stochastic process to be inferred using the coefficients of an autoregressive process AR(p) of order p. A closed-form recursive solution provides estimates for both the autoregressive coefficients and the order p of the process. We provide a ready-to-use implementation of this algorithm in a Python package called memspectrum, characterized through power spectral density (PSD) analysis on synthetic data with known PSD and comparisons of different criteria for stopping the recursion. Additionally, we compare the performance of our implementation with the ubiquitous Welch algorithm, using synthetic data generated from the GW150914 strain spectrum released by the LIGO-Virgo-Kagra collaboration. Our findings indicate that Burg’s method provides PSD estimates with systematically lower variance and bias. This is particularly manifest in the case of a small (O(5000)) number of data points, making Burg’s method most suitable to work in this regime. Since this is close to the typical length of analysed gravitational waves data, improving the estimate of the PSD in this regime leads to more reliable posterior profiles for the system under study. We conclude our investigation by utilising MESA, and its particularly easy parametrisation where the only free parameter is the order p of the AR process, to marginalise over the interferometers noise PSD in conjunction with inferring the parameters of GW150914

Non-Intrusive System for Honeybee Recognition Based on Audio Signals and Maximum Likelihood Classification by Autoencoder.

Artificial intelligence and Internet of Things are playing an increasingly important role in monitoring beehives. In this paper, we propose a method for automatic recognition of honeybee type by analyzing the sound generated by worker bees and drone bees during their flight close to an entrance to a beehive. We conducted a wide comparative study to determine the most effective preprocessing of audio signals for the detection problem. We compared the results for several different methods for signal representation in the frequency domain, including mel-frequency cepstral coefficients (MFCCs), gammatone cepstral coefficients (GTCCs), the multiple signal classification method (MUSIC) and parametric estimation of power spectral density (PSD) by the Burg algorithm. The coefficients serve as inputs for an autoencoder neural network to discriminate drone bees from worker bees. The classification is based on the reconstruction error of the signal representations produced by the autoencoder. We propose a novel approach to class separation by the autoencoder neural network with various thresholds between decision areas, including the maximum likelihood threshold for the reconstruction error. By classifying real-life signals, we demonstrated that it is possible to differentiate drone bees and worker bees based solely on audio signals. The attained level of detection accuracy enables the creation of an efficient automatic system for beekeepers.

High-performance power spectral/bispectral estimator for biomedical signal processing applications using novel memory-based FFT processor

This research paper proposes a novel robust high-performance power spectrum estimator, and bispactral power density analyzer that has outstanding capabilities in estimating noisy biomedical signal's power spectrum, and bispectrum. Biomedical signals usually are exposed to several sources of noises such as electrical noise from environmental noise from external sources, electrical equipment, and biological noise from the body. Therefore, accuracy and reliability are the most important feature of these systems in processing non-stationary biomedical signals. The proposed computationally-efficient architecture is based on a radix-8 memory-based 1024-point Blackman-Tuckey method power spectral density (PSD) estimator. The proposed nonparametric estimator uses a novel shared-resource CORDIC-Ⅱ unit to avoid multiplications in FFT computation, as well as filtering operations implemented in folded architectures. In order to merge two FFTs, the module uses bidirectional fractional delay filters to estimate half delay samples. By using modified safe-scaling, valid final output would be achieved, without any averaging operation. The proposed and competing designs are implemented on Artix-7 FPGA which is an ideal option for DSP applications. As final results demonstrate, the hardware has a remarkable capability in operating in short word-lengths which allows high-performance in low-power applications to compute the power spectrum and bicoherence of a vital signal.

Improved method for drone sound event detection system aiming at the impact of background noise and angle deviation

Drones pose a hidden threat to public safety, and effective and accurate detection technology for the drone that exist in the environment is imminent, in which how to weaken the influence of target sound source localization deviation and strong background interference noise on the detection task is the key to improve the accuracy of drone sound event detection. In this paper, a method has been proposed to improve the accuracy of drone acoustic event detection, named as the linear shrinkage-subspace projection-power spectral density filter method (LSP). This method mainly including covariance matrix reconstruction, steering vector recalibration, and filter coefficient redesign method. Firstly, based on Minimum Variance Distortionless Response, the linear shrinkage method is used to suppress the interference and noise components in the signal plus interference covariance matrix, and the sample covariance matrix is reconstructed to eliminate background interference noise. Then, the correlation between the steering vector and the eigenvector is used to eliminate the angle correlation term, and the subspace projection method is combined to recalibrate the steering vector, so as to improve the ability of the beamforming method to resist the angle deviation and realize the correction of the target source positioning deviation. Next, a redesign method for wiener filter coefficients based on the estimated power spectral density is used to further weaken background interference noise. In order to verify the accuracy of the proposed method, a complete drone sound event detection system is constructed by combining the deep learning drone sound event detection classifier, and the evaluation is carried out according to different angular deviations and interference sound distances. In addition, a new evaluation criterion is proposed, named as the Machine-Human Extreme Hearing Distance Rate (MHDR), which analogizes the system's detection ability with the ear's auditory detection ability. The research results of this article indicate that the detection accuracy of the detection system shows satisfactory accuracy when the proposed method is applied to circular microphone array, that improved by 15.12 % compared to existing methods. The proposed method improves the detection accuracy of the drone acoustic event detection task under the influence of sound source position deviation and strong background speech interference, and provides a reference for the development of anti-drone technology.

Postfilter for Dual Channel Speech Enhancement Using Coherence and Statistical Model-Based Noise Estimation.

A multichannel speech enhancement system usually consists of spatial filters such as adaptive beamformers followed by postfilters, which suppress remaining noise. Accurate estimation of the power spectral density (PSD) of the residual noise is crucial for successful noise reduction in the postfilters. In this paper, we propose a postfilter utilizing proposed a posteriori speech presence probability (SPP) and noise PSD estimators, which are based on both the coherence and the statistical models. We model the coherence-based a posteriori SPP as a simple function of the magnitude of coherence between two microphone signals and combine it with a single-channel SPP based on statistical models. The coherence-based estimator for the PSD of the noise remaining in the beamformer output in the presence of speech is derived using the pseudo-coherence considering the effect of the beamformers, which is used to construct the coherence-based noise PSD estimator. Then, the final noise PSD estimator is obtained by combining the coherence-based and statistical model-based noise PSD estimators with the proposed SPP. The spectral gain function is also modified, incorporating the proposed SPP. Experimental results demonstrate that the proposed method led to more accurate noise PSD estimation and perceptual evaluation of speech quality scores in various diffuse noise environments, and did not degrade the speech quality under the presence of directional interference, although the proposed method utilizes the coherence information.

Ambient Seismic Noise Tomography Within the Floridan Aquifer System, Santa Fe River‐Sink Rise, Florida, US

AbstractThis study utilized ambient seismic noise tomography to investigate correlations of hydrogeological systems with heterogeneous porosity with the internal velocity structure of karst aquifers using the Floridan Aquifer System (FAS) as an example. We conducted a seismic signal analysis with 30 days of vertical component seismic data acquired within the Santa Fe River Sink‐Rise system (Sink‐Rise System), using power spectral density estimates and frequency‐wavenumber analysis to identify any noise source biases. Empirical Green's functions were derived through phase cross‐correlations and phase‐weighted stacking. The functions allowed extraction of group velocity dispersion measurements, which were inverted to generate 2D tomographic images at various periods. Tomographic images show multiple layers with varying group velocities that aligned with known hydrogeological features of the FAS, including its base, low‐porosity and low‐permeability dolostone semiconfining units characterized by elevated velocities, and zones of elevated porosity from karstification with reduced seismic velocities. Our results show how ambient seismic noise can be used to evaluate aquifer physical properties, identify unknown features, and identify the location and continuity of aquifer units.

Fully automated operational modal identification based on scale-space peak picking algorithm and power spectral density estimation

Modal analysis is a fundamental and essential research direction in the field of structural engineering. The ultimate goal is to determine the modal parameters of the structures. However, the existing modal analysis algorithms often require a large number of parameter adjustments and manual intervention during operation, which cannot be fully automated. In order to realize the automatic identification of modal parameters, the automatic operational modal identification method (AOMI) is proposed based on the interpolated power spectral density estimation (IPSE). To achieve more precise spectrum analysis in the low-frequency band, IPSE is employed to perform Fourier transform on the original frequency domain segment with optimized frequency resolution. This enhances the sharpness of the obtained spectrum in the low-frequency range, making peak frequencies more discernible. Subsequently, the scale-space peak picking algorithm is used to automatically obtain the peak of the power spectral density (PSD), thus enabling the automatic identification of the natural frequency. Finally, the frequency domain decomposition method (FDD) is used to identify modal parameters based on the natural frequencies. The effectiveness of AOMI is verified through the modal identification of the old steel truss bridge and the three layer framework. Under the environmental excitation, the frequencies identified by the IPSE method is close to that of FDD, Bayesian fast fourier transform (FFT) and covariance driven stochastic subspace identification (SSI-COV). Furthermore, the PSD obtained through IPSE has sharper peak than that of FDD and the Welch’s method. The damping ratio identification accuracy and modal assurance criterion (MAC) are satisfactory in AOMI, which can improve the automatic performance.

Large-Area Thickness Measurement of Transparent Films Based on a Multichannel Spectral Interference Sensor

Thickness measurement of thin films is essential for quality control in the manufacturing process of the semiconductor and display industries. Real-time monitoring of film thickness during production is an urgent technical problem to be solved. In this study, a method for large-area thickness measurement of transparent films based on a multichannel spectral interference sensor is proposed. The sensor simultaneously acquires multichannel spectral interference signals through a combination of fan-out fiber optic bundles, detection probes, and an imaging spectrometer. The spectral data are calibrated and transformed into the wavenumber dimension, and then the power spectral density estimation method is used to demodulate the data frequency to swiftly derive the film thickness. The thickness measurement capacity of the proposed system is successfully validated on two standard film samples with a relative deviation of less than 0.38% and a relative standard deviation of less than 0.044%. The total spectral acquisition and calculation time for a single multichannel measurement was approximately 7.5 ms. The experimental results on polyimide films show that the measurement efficiency of the system is at least 4 times higher than that of the traditional system, indicating the potential of the multichannel spectral interference sensor for online monitoring in film production.

Structural EEG signal analysis for sleep apnea classification.

Diagnosing the sleep apnea can be critical in preventing the person having sleep disorder from unhealthy results. The aim of this study is to obtain a sleep apnea scoring approach by comparing parametric and non-parametric power spectral density (PSD) estimation methods from EEGsignals recorded from different brain regions (C4-M1 and O2-M1) for transient signal analysis of sleep apnea patients. Power Spectral Density (PSD) methods (Burg, Yule-Walker, periodogram, Welch and multi-taper) are examined for the detection of apnea transition states including pre-apnea, intra-apnea and post-apnea together with statistical methods. In the experimental studies, EEG recordings available in the database were analyzed with PSD methods. Results showed that there are statistically significant differences between parametric and non-parametric methods applied for PSD analysis of apnea transition states in delta, theta, alpha and beta bands. Moreover, it was also revealed that PSD of EEG signals obtained from C4-M1 and O2-M1 channels were also found statistically different as proved by classification using the K-nearest neighbour (KNN) method. It was concluded that not only applying different PSD methods, but also EEG signals from different brain regions provided different statistical results in terms of apnea transition states as obtained from KNN classification.

Background Seismic Noise Levels among the Caribbean Network and the Role of Station Proximity to Coastline

Abstract The amplitude and frequency content of background seismic noise is highly variable with geographic location. Understanding the characteristics and behavior of background seismic noise as a function of location can inform approaches to improve network performance and in turn increase earthquake detection capabilities. Here, we calculate power spectral density estimates in one-hour windows for over 15 yr of vertical-component data from the nine-station Caribbean network (CU) and look at background noise within the 0.05–300 s period range. We describe the most visually apparent features observed at the CU stations. One of the most prominent features occurs in the 0.75–3 s band for which power levels are systematically elevated and decay as a function of proximity to the coastline. Further examination of this band on 1679 contiguous USArray Transportable Array stations reveals the same relationship. Such a relationship with coastal distance is not observed in the 4–8 s range more typical of globally observed secondary microseisms. A simple surface-wave amplitude decay model fits the observed decay well with geometric spreading as the most important factor for stations near the coast (<∼50 km). The model indicates that power levels are strongly influenced by proximity to coastline at 0.75–3 s. This may be because power from nearshore wave action at 0.75–3 s overwhelms more distant and spatially distributed secondary microseism generation. Application of this basic model indicates that a power reduction of ∼25 dB can be achieved by simply installing the seismometer 25 km away from the coastline. This finding may help to inform future site locations and array design thereby improving network performance and data quality, and subsequently earthquake detection capabilities.

Random vibration-based progressive fatigue damage monitoring in thermoplastic coupons: a preliminary investigation

In recent years there has been an increasing trend towards the utilization of composites, particularly thermoplastics, in various components of aerostructures. The prelusion of such materials has underscored the significance of investigating their fatigue behavior and developing reliable methods for detecting fatigue damage. In this context, vibration-based techniques hold significant potential as they leverage the inherent excitation provided by in-flight noise and turbulence. This study aims at assessing the progressively accumulated fatigue damage in thermoplastic coupons via random vibration signals while accounting for operational and inter-structural uncertainties. The experimental process consists of preliminary tension and fatigue tests, interrupted fatigue tests, C-Scan inspection tests, and non-contact random vibration tests. Consecutive fatigue states are obtained by performing fatigue tests at intervals of 10 000 cycles for a population of 7 coupons. At each interruption, ultrasonic C-Scan and vibration inspection tests are performed, allowing for the visualization of fatigue damage and random vibration signal analysis. Welch Power Spectral Density estimates are employed and are shown to have good potential for distinguishing among different fatigue states despite the inevitable population and experimental uncertainty. Furthermore, fatigue damage is found to progress symmetrically and laterally along the free edges of the test coupons, which is explained by the free edge effect.

Development of software for information-measuring Systems for frequency analysis of binary-quantized Signals

The article discusses the methodology and design template for a complex of structurally, functionally, informationally and metrologically compatible software modules that implement algorithms for calculating estimates of the PSD power spectral density based on binary-signed analog-stochastic quantization with reduced multiplicative complexity. Algorithmic support makes it possible to calculate PSD estimates by the method of averaged modified periodograms and by the correlogram method using time correlation windows based on a discrete-event representation of the results of binary-sign analog-stochastic quantization. This approach made it possible to perform integration operations analytically, which eliminates the methodological error caused by performing these operations in digital form. In addition, the multiplication operations degenerate into procedures that basically require the execution of logical operations and simple arithmetic operations of summing and subtracting the values of the correlation windows, which significantly reduces the complexity of estimating the PSD.

On Digital Signal Processing of Time Series for Spectrum Estimation.

We present a study of power spectral density (PSD) estimation from data sampled in the time domain. This work was motivated by our recent development of digital radiometry, where radiation spectra were obtained by processing the digitally sampled signal. The PSD estimation can be generalized by a quadratic estimator and minimization of mean squared error of the estimator leads to the optimal window choice. The bounds of the variance and the bias are formulated in order to quantify the uncertainty associated with non-ideal PSD estimation in digital signal processing. Windowed estimates of spectrum measurements are presented for comparison in terms of computational efficiency and amplitude measurement precision. A few examples on real and simulated data are shown for comparison.

Uncovering acoustic signatures of pore formation in laser powder bed fusion

We present a machine learning workflow to discover signatures in acoustic measurements that can be utilized to create a low-dimensional model to accurately predict the location of keyhole pores formed during additive manufacturing processes. Acoustic measurements were sampled at 100 kHz during single-layer laser powder bed fusion (LPBF) experiments, and spatio-temporal registration of pore locations was obtained from post-build radiography. Power spectral density (PSD) estimates of the acoustic data were then decomposed using non-negative matrix factorization with custom varvec{k}-means clustering (NMFvarvec{k}) to learn the underlying spectral patterns associated with pore formation. NMFvarvec{k} returned a library of basis signals and matching coefficients to blindly construct a feature space based on the PSD estimates in an optimized fashion. Moreover, the NMFvarvec{k} decomposition led to the development of computationally inexpensive machine learning models which are capable of quickly and accurately identifying pore formation with classification accuracy of supervised and unsupervised label learning greater than 95% and 90%, respectively. The intrinsic data compression of NMFk, the relatively light computational cost of the machine learning workflow, and the high classification accuracy makes the proposed workflow an attractive candidate for edge computing toward in-situ keyhole pore prediction in LPBF.

A multiscale feature fusion network based on attention mechanism for motor imagery EEG decoding

The decoding of motor imagery (MI) electroencephalogram (EEG) is an essential component of the brain–computer interface (BCI), which can help patients with motor impairment communicate directly with the outside world through assistive devices. The key to motor imagery electroencephalogram (MI-EEG) classification is to extract multiple temporal, spatial, and spectral features, to obtain more comprehensive and representative information. However, current deep learning methods must fully consider the depth of temporal features and multi-spectral knowledge in EEG and often ignore the temporal or spectrum dependence in MI-EEG. In addition, the lack of effective feature fusion methods can lead to information redundancy, which affects decoding performance. To solve the above problems, this paper proposes a novel MI-EEG decoding method, named multi-scale feature fusion network based on attention mechanism (MSFF-SENet). Firstly, the multi-scale spatio-temporal module (MS-STM) and the multi-scale temporal module (MSTM) extract spatial and high-dimensional temporal features from the original signal. Then, the power spectral density estimation (PSD) convolution module (PSD-Conv module) acquires the multi-spectral features of the MI-EEG signal. Secondly, the feature fusion module fuses spatio-temporal and multi-spectral features to generate integrated feature mappings and establish the dependencies between different features. Finally, we conducted a visual analysis of the results, explaining the neural activity patterns of various motor imagery tasks in different frequency ranges and revealing the potential relationship between body movement and changes related to brain activity. The experimental results show that the classification accuracy of this model in BCI Competition IV 2a (BCI IV 2a) and High Gamma (HGD) datasets is 85.37% and 96.60%, respectively, which is superior to the most advanced methods.

The Thermal Structure of Central Te Riu a Māui/Zealandia Continent as Determined From the Depth to Base of Magnetic Sources

AbstractTo investigate the thermal structure of central Te Riu a Māui/Zealandia continent we estimate the depth to base of magnetic sources (DBMS), using an updated compilation of magnetic data. We calculate thousands of power spectral density estimates and solve an analytic solution for the fractal distribution of magnetization using a Bayesian method constrained by a sediment thickness model. Our DBMS results are broadly similar to a global model yet show complex relationships with independent models of crust and elastic thicknesses, and depth to base of seismicity (D90). Across central Zealandia, DBMS occurs above, coincident with, and below the Moho reflecting that factors additional to temperature influence DBMS. Away from subduction zones crustal thickness likely modulates DBMS while plate margins show varying influence dependent on margin characteristics. In the Taupō Volcanic Zone we interpret DBMS to reflect Curie point temperature at an average depth of 9–11 km. Error analysis shows that the choice of prior influences the posterior standard deviation and can result in counter intuitive error versus DBMS relationships. We use the DBMS as a basal temperature isotherm in heat flow models to compare with heat flow derived from borehole temperature measurements. Using the standard Curie point temperature of 580°C we find that DBMS derived heat flow models over estimate heat flow in areas underlain by plutonic rocks. We propose this reflects a higher titanomagnetite content in these rocks, although detailed studies of the magnetic mineralogy of Zealandia's plutonic rocks are required.

Performance evaluation of sound source localisation and tracking methods using multiple drones

This study evaluates methods to improve sound source localisation and tracking performance using microphone arrays from multiple drones. Previous studies have demonstrated the feasibility of multi-drone sound source tracking by triangulating their respective direction estimations using the MUltiple SIgnal Classification (MUSIC) algorithm. In addition, we evaluate techniques to reduce the influence of rotor noise. Namely, this includes a Wiener filter that utilises rotor noises' power spectral density (PSD) estimations and a noise correlation matrix (NCM) estimation scheme exploiting the geometries of the drone and the microphone array. This is to reduce the rotor noise's influence on the microphone array input correlation matrix prior to localising with MUSIC. Results show that applying the rotor noise reduction method improves localisation and tracking accuracy under a wider range of signal-to-noise ratios, regardless of the sound source tracking method.