Power Spectral Density Estimation Research Articles

On the Estimation of Power Spectral Density and Lagged Coherence of Time Transformed Nonstationary Seismic Ground Motions and Their Use to Simulate Synthetic Records

ABSTRACT Ground motions could be modelled as amplitude and frequency modulated process. The frequency modulation through a time transformation results in the modelled motions in the new timescale being a stationary process except for the amplitude modulation. The assessment of power spectral density (PSD) and the lagged coherence in the transformed timescale is presented in this study. It is shown theoretically and numerically that the PSD functions obtained through time transformation in the original timescale should not be used as an amplitude modulation function, and that the lagged coherence in the new or auxiliary timescale differs from that in the original timescale.

Optimum step-size control for a variable step-size stereo acoustic echo canceller in the frequency domain

The frequency-domain adaptive filter (FDAF) is a competitive candidate for stereo acoustic echo cancellation (SAEC) because of its good convergence and computational efficiency. However, there is a conflict between the convergence rate and the steady-state misalignment when using a constant step size. In this paper, a variable step-size approach is proposed for the stereo echo canceller in the frequency domain. The proposed method uses a first-order Markov model to describe the time-varying echo paths between the loudspeakers and the microphone. Following a statistical convergence analysis of the two-channel FDAF algorithm, the state recursion of the system distance in each frequency bin is given. The optimal step size is then derived by minimizing the system distance. Several practical problems, including noise power spectral density estimation and echo paths change detection, are discussed in details. Moreover, a close link between the proposed optimum step-size control method and the multichannel state–space frequency-domain adaptive filter is established. We show that the proposed variable step-size approach can also be incorporated into the block extended least-mean-square algorithm to fully exploit their benefits. Finally, computer simulations demonstrate that the proposed algorithm exhibits an excellent convergence performance and is very robust to the double talk.

Horizontal-to-Vertical Spectral Ratio (HVSR) IRIS Station Toolbox

AbstractThe horizontal-to-vertical spectral ratio (HVSR) for seismic ambient noise is a popular method that can be used to estimate the predominant frequency at a given site. In this article, we introduce the Incorporated Research Institutions for Seismology (IRIS) Data Management Center’s (DMC’s) openly available HVSR station toolbox. These tools offer a variety of ways to compute the spectral ratio by providing different averaging routines. The options range from the simple average of spectral ratios to the ratio of spectral averages. Computations take advantage of the available power spectral density estimates of ambient noise for the seismic stations, and they can be used to estimate the predominant frequency of the many three-component seismic stations available from the IRIS DMC. Furthermore, to facilitate the identification of the peaks in HVSR profiles for the assessment of the predominant frequency of station sites, the toolbox can also process the results of HVSR analysis to detect and rank HVSR peaks. To highlight the toolbox capabilities, three different examples of possible use of this toolbox for routine site-effect analysis are discussed: (1) site effects related to thawing in Arctic regions, (2) ground-motion amplification in urban area, and (3) estimation of station VS30.

Hardware-Efficient Bartlett Spectral Density Estimator Based on Optimized R22FFT Processor Using CCSSI Method

This paper offers a novel, low-power, hardware-efficient, yet high-frequency architecture for a power spectral density (PSD) estimator, based on the Bartlett method, for low-power biomedical applications. The Bartlett method is a nonparametric method for PSD estimation. The proposed architecture operates based on a modified multiplierless 64-point optimized radix-22single-path delay feedback (R22SDF) FFT processor. To obtain the final result, it also uses modified safe-scaling in a way that removes the need to use several extra hardware units. It takes advantage of combined coefficient selection and shift-and-add implementation (CCSSI) for computing twiddle factors which is a new algorithm based on digital computer coordinate rotation (CORDIC) for generating trigonometric values. The proposed method has the capability of operating on short word lengths (WLs). Artix-7 is the FPGA used in this research and Verilog is the language used for hardware design. For 8-bit WL and 244-mW power, a frequency of 286 MHz has been achieved. Several vital signals are used for performance comparison of the proposed technique with state-of-the-art designs.

Separation of movement direction concepts based on independent component analysis algorithm, linear discriminant analysis, deep belief network, artificial and fuzzy neural networks

Brain signals have various scientific and practical applications, such as Medical Science, Cognitive Science, Neuroscience, and Brain Computer Interfaces. Brain signal analysis is faced with complex challenges including small sample size, high dimensionality and noisy signals. Because of the non-stationarity of brain signals and the impacts of mental states on brain function, brain signals are associated with an inherent uncertainty. In this study, it is tried to present a plausible method for detecting and distinguishing the directions from EEG signals. Recording single-polarized signals was carried out utilizing a 19-channel cap Micromed device with the use of Cz as reference electrode. The statistical population used involved ten 25–35 year old male volunteers. The designed task consisted of 24 slides of up, down, left and right directions. After preprocessing level, ICA algorithm was employed to extract artifacts, to decrease signal dimension and to determine the target signal. In feature extraction section, AR coefficients extracted to feed the ANN, FNN and LDA. Data for Deep Belief Network provided from Autoregressive power spectral density estimate with order of 20 employed on the data set.Classifiers’ results reveal that 2.5 s time window leads to the best separation accuracy.DBN surprisingly leads to the highest level of accuracy in comparison to the other proposed methods.Based on the 10-fold Cross Validation, the performance of the classifiers measured in terms of accuracy, sensitivity and specificity. The obtained average accuracies for LDA, ANN, FNN and DBN respectively are 61.86 ± 1.69 %, 57.18 ± 1.88 %, 66.79 ± 2.14 % and 91.06 ± 0.68.

Automated classification of acoustic startle reflex waveforms in young CBA/CaJ mice using machine learning

BackgroundThe acoustic startle response (ASR) is a simple reflex that results in a whole body motor response after animals hear a brief loud sound and is used as a multisensory tool across many disciplines. Unfortunately, a method of how to record, process, and analyze ASRs has yet to be standardized, leading to high variability in the collection, analysis, and interpretation of ASRs within and between laboratories. New methodASR waveforms collected from young adult CBA/CaJ mice were normalized with features extracted from the waveform, the resulting power spectral density estimates, and the continuous wavelet transforms. The features were then partitioned into training and test/validation sets. Machine learning methods from different families of algorithms were used to combine startle-related features into robust predictive models to predict whether an ASR waveform is a startle or non-startle. ResultsAn ensemble of several machine learning models resulted in an extremely robust model to predict whether an ASR waveform is a startle or non-startle with a mean ROC of 0.9779, training accuracy of 0.9993, and testing accuracy of 0.9301. Comparison with existing methodsASR waveforms analyzed using the threshold and RMS techniques resulted in over 80% of accepted startles actually being non-startles when manually classified versus 2.2% for the machine learning method, resulting in statistically significant differences in ASR metrics (such as startle amplitude and pre-pulse inhibition) between classification methods. ConclusionsThe machine learning approach presented in this paper can be adapted to nearly any ASR paradigm to accurately process, sort, and classify startle responses.

Quantifying the effect of power spectral density uncertainty on gravitational-wave parameter estimation for compact binary sources

In order to perform Bayesian parameter estimation to infer the source properties of gravitational waves from compact binary coalescences (CBCs), the noise characteristics of the detector must be understood. It is typically assumed that the detector noise is stationary and Gaussian, characterized by a power spectral density (PSD) that is measured with infinite precision. We present a new method to incorporate the uncertainty in the power spectral density estimation into the Bayesian inference of the binary source parameters and apply it to the first 11 CBC detections reported by the LIGO- Virgo Collaboration. We find that incorporating the PSD uncertainty only leads to variations in the positions and widths of the binary parameter posteriors on the order of a few percent. Our results are publicly available for download on git [1].

Generation of strongly non-Gaussian stochastic processes by iterative scheme upgrading phase and amplitude contents

Random excitations, such as wind velocity, always exhibit non-Gaussian features. Sample realisations of stochastic processes satisfying given features should be generated, in order to perform the dynamical analysis of structures under stochastic loads based on the Monte Carlo simulation. In this paper, an efficient method is proposed to generate stationary non-Gaussian stochastic processes. It involves an iterative scheme that produces a class of sample processes satisfying the following conditions. (1) The marginal cumulative distribution function of each sample process is perfectly identical to the prescribed one. (2) The ensemble-averaged power spectral density function of these non-Gaussian sample processes is as close to the prescribed target as possible. In this iterative scheme, the underlying processes are generated by means of the spectral representation method that recombines the upgraded power spectral density function with the phase contents of the new non-Gaussian processes in the latest iteration. Numerical examples are provided to demonstrate the capabilities of the proposed approach for four typical non-Gaussian distributions, some of which deviate significantly from the Gaussian distribution. It is found that the estimated power spectral density functions of non-Gaussian processes are close to the target ones, even for the extremely non-Gaussian case. Furthermore, the capability of the proposed method is compared to two other methods. The results show that the proposed method performs well with convergence speed, accuracy, and random errors of power spectral density functions.

A signal decomposition method based on repeated extraction of maximum energy component for offshore structures

Contrary to most signal decomposition methods that usually decompose an original signal into a series of components simultaneously, a novel approach based on repeated extraction of Maximum Energy Component (MEC) is proposed. The approach starts from determination of the MEC referring to the estimated Power Spectral Density (PSD) function, and then represents the MEC by employing an exponential function to fit the original signal. By defining a stopping criterion based on two adjacent estimated PSDs, each MEC can be accurately extracted with an improved performance throughout the entire signal decomposition. To verify the proposed method, a single degree-of-freedom system subject to harmonic loads has been examined. Numerical results show that the analytical response can not only be decomposed into four MECs corresponding to the excitation and the system, respectively, but also provide an accurate estimation of natural frequency and damping ratio of the system. Meanwhile, by observing results from the Ensemble Empirical Mode Decomposition (EEMD), Variational Mode Decomposition (VMD) and Prony based on state-space model (Prony-SS), an improved decomposition accuracy has been achieved from the proposed approach. Furthermore, experimental data from the Norwegian Deepwater Programme and two sets of field-test data from one fixed offshore platform and an offshore wind turbine have been used to demonstrate the correctness of the developed signal decomposition method. It is noted that divergence in results by Prony-SS can be observed when a very large model order is used, while the proposed method provides the better decomposition and reconstruction of signals.

Subspace-Based Blood Power Spectral Capon Combined with Wiener Postfilter to Provide a High-Quality Velocity Waveform with Low Mathematical Complexity

In Doppler analysis, the power spectral density (PSD), which accounts for the axial velocity distribution of the blood scatterers, is estimated. The conventional spectral estimator is Welch's method, which suffers from frequency leakage at small observation window length. The performance of adaptive techniques such as blood power Capon (BPC) has been promising at the cost of higher computation complexity. Reducing the computational complexity while retaining the benefits of BPC would be necessary for real-time implementation. The purpose of the work described here was to investigate whether it is possible to decrease the computation load in BPC and still obtain acceptable results. The computation complexity in BPC is owing primarily to the matrix inversion required for computing the PSD estimate. We here propose the subspace blood power Capon technique, which employs a data covariance matrix with reduced number of rows in estimation of the weight vector. In maximum velocity estimation in the spectra, the signal noise slope intersection envelop estimator that makes use of the integrated power spectrum is employed. The evaluations are made based on both simulated and in vivo data. The results indicate that it is possible to reduce the order of complexity to almost 12.25% at the cost of 2.31% and 2.24% increases in the relative standard deviation and relative bias of the estimates. Moreover, the Wiener post-filter as a post-weighting factor, which will be multiplied by the final weight vector of the spectral estimator, estimates the power of the desired signal and the power of the interference plus noise to improve the contrast. The proposed estimator has exhibited a promising performance at beam-to-flow angles of 45°, 60° and 75°. Furthermore, the robust performance of the proposed estimator against variation in the flow rate is also documented.

Performance comparison and stability analysis of ACM and ENLC controlled SEPIC PFC converter

In this study, a detailed comparison between two power factor correction (PFC) controls, viz., average current mode (ACM) control and enhanced non-linear carrier (ENLC) control for single-ended primary inductance converter (SEPIC) are made. In ACM control, a linear current reference, generated using the conventional method is compared with the inductor current. In ENLC control, a non-linear carrier current reference, generated using passive components is compared with switch current. The proposed ENLC control uses reduced components and sensors compared to ACM and conventional non-linear carrier control methods. The evolving of nonlinear phenomena during load variation is investigated along with the electromagnetic interference (EMI) study with power spectral density estimation. For stability enhancement and EMI mitigation, a detailed simulation study is performed using MATLAB/Simulink platform. Mathematical bifurcation analysis, by deriving critical phase angle is carried out to obtain a better insight of stability boundaries in order to access the system behaviour. Owing to the advantages of ENLC, an experimental setup of ENLC controlled SEPIC PFC converter was built to support the results.

Experimental investigations on power spectral density estimation in heterogeneous dispersion unmanaged transmissions

In this paper, we present and verify by experiments a semi-analytical model to estimate the power spectral density of the noise-to-signal ratio in dispersion unmanaged transmissions over heterogeneous fiber types. The model combines an experimental calibration and an analytical formula. After a one-span profiling calibration, the overall system performance is assessed by joining the calibration results with a cumulative summing formula, targeting as a performance estimate the spectral density of the noise-to-signal ratio. After recalling the fundamental theoretical developments, we report experimental validations for four-span long dispersion unmanaged heterogeneous testbeds. According to the experimental results, the estimation error on the signal-to-noise ratio is always below 0.3 dB. Moreover, thanks to spectral knowledge, we show that we can account for some digital signal processing performed at the transceiver, which impacts system performance, such as the carrier-phase estimation. We demonstrate that without altering the experimental calibration, we can predict the performance adaptively to the carrier-phase estimation implemented at the receiver, capping the estimation error to < 0.5 dB.

Parametric Power Spectral Density Estimation-Based Breakthrough Detection for Orthopedic Bone Drilling with Acoustic Emission Signal Analysis

Manual bone drilling in orthopedic surgical operations may cause injury to patient tissues if the drill bit continues to progress after exiting the bone. In this study, a new bone breakthrough detection algorithm based on acoustic emission (AE) signal analysis has been developed to minimize temporary and permanent injuries that can be caused by surgeon-controlled surgical drills. Three parametric estimation methods, Burg, Yule–Walker and Modified Covariance were used to estimate Power Spectral Density (PSD) of the AE signal during the drilling operation. Four frequency features, Mean Frequency, Median Frequency, Mean–Median and Power Bandwidth were calculated for each PSD estimate. An artificial neural network-based breakthrough detection classification was constructed from the extracted features. The highest breakthrough detection performance was obtained with the features extracted by the Burg method with an accuracy rate of 90.95 ± 0.97% in the training phase and 92.37 ± 1.09% in the test phase. In the detection of Not-Breakthrough situations, the highest accuracy was obtained with features extracted with the Covariance method as 99.04 ± 0.03% in the training phase and 99.05 ± 0.08% in the testing phase. This new approach which could be integrated into conventional drills with minimum configuration changes and without any major cost has the potential to increase the performance and safety of bone drilling procedures.

Separation characteristics between time domain and frequency domain of wireless power communication signal in wind farm

Understanding the intrinsic characteristics of wind power is important for the safe and efficient parallel function of wind turbines in large-scale wind farms. Current research on the spectrum characteristics of wind power focuses on estimation of power spectral density, particularly the structural characteristics of Kolmogorov’s scaling law. In this study, the wavelet Mallat algorithm, which is different from the conventional Fourier transform, with compactly supported characteristics is used to extract the envelope of the signal and analyze the instantaneous spectral characteristics of wind power signals. Then, the theory for the change in the center frequency of the wind power is obtained. The results showed that within a certain range, the center frequency decreases as the wind power increases by using enough wind farm data. In addition, the center frequency remains unchanged when the wind power is sufficiently large. Together with the time domain characteristics of wind power fluctuation, we put forward the time-frequency separation characteristics of wind power and the corresponding physical parameter expressions, which corresponds to wind speed’s amplitude and frequency modulation characteristics. Lastly, the physical connotation of the time-frequency separation characteristics of wind power from the perspective of atmospheric turbulent energy transport mechanism and wind turbine energy transfer mechanism is established.

Recognizing human actions with multiple Fourier transforms

Abstract In this paper we present an approach for action recognition that uses various applications of Fourier transform. The main idea is to classify video sequences based on action representations obtained using shape descriptors. For shape representation we use the Two-Dimensional Fourier Descriptor, Generic Fourier Descriptor and UNL-Fourier Descriptor. For each sequence of binary silhouettes we derive a set of shape descriptors and match the descriptor of the first frame with the rest of descriptors to obtain a vector of similarities (correlation coefficients or C1 correlations) or dissimilarities (Euclidean distances). Then normalized vectors are transformed into action representations using discrete Fourier transform, power spectral density estimate or a combination of both. Classification is performed using leave-one-out cross-validation and various matching measures. Additionally, we incorporate a coarse classification step that distinguish between actions performed in place and actions with changing location of a silhouette. Extensive experiments are carried out to investigate all possible combinations of selected processing steps, and experimental results are promising.

Microphone Array Wiener Post Filtering Using Monotone Operator Splitting

For array-based acoustic source enhancement, variants of multi-channel Wiener filters are commonly used. The approach includes a Wiener post-filter that requires the simultaneous estimation of the power spectral density (PSD) of the target source and of noise sources for each time-frame. Conventional methods generally do not exploit prior knowledge , such as sparsity of the source, in solving this simultaneous estimation problem. We show that, for common scenarios, the simultaneous PSD estimation with consideration of prior knowledge can be formulated as a convex optimization problem with linear constraints. We use monotone operator splitting (MOS) to solve the constrained optimization problem. Our experiments confirm that the proposed method improves the accuracy of the noise PSD estimation, and that the resulting enhanced target signal is of higher quality.

Task Sensitivity in Continuous Electroencephalogram Person Authentication

This research investigates on the task sensitivity in multimodal stimulation task for continuous person authentication using the electroencephalogram (EEG) signals. Pattern analysis aims to train from historical examples for prediction on the unseen data. However, data trials in EEG stimulation consists of inseparable cognitive information that is difficult to ensure that the testing trials contain the cognitive information matching to the training data. Since the EEG signals are unique across individuals, we assume that multimodal stimulation task in EEG analysis is not sensitive in train-test data trials control. Data trial inconsistency during training and testing can still be used as biometrics to authenticate a person. The EEG signals were collected using the 10-20 systems from 20 healthy subjects. During data acquisition, subjects were asked to operate a computer and perform various computer-related tasks (e.g.: mouse click, mouse scrolling, keyboard typing, browsing, reading, video watching, music listening, playing computer games, and etc.) as their preferences, without interruption. Features extracted from Welch’s estimated Power Spectral Density in different frequency bands were tested. The designed authentication approach computed intra- and inter-personal variability using Mahalanobis distance to authenticate subject. The proposed EEG continuous authentication approach has succeeded. Data collected from multimodal stimulus disregard of task sensitivity able to authenticate subject, where the highest verification performance shown in the low-Beta frequency band. Evidence found that effective frequency region on the middle band was anticipated due to the data collected was based on subject voluntary actions. Future research will focus on the effect of subject voluntary and involuntary actions on the effective frequency region.

DeepMMSE: A Deep Learning Approach to MMSE-Based Noise Power Spectral Density Estimation

An accurate noise power spectral density (PSD) tracker is an indispensable component of a single-channel speech enhancement system. Bayesian-motivated minimum mean-square error (MMSE)-based noise PSD estimators have been the most prominent in recent time. However, they lack the ability to track highly non-stationary noise sources due to current methods of a priori signal-to-noise (SNR) estimation. This is caused by the underlying assumption that the noise signal changes at a slower rate than the speech signal. As a result, MMSE-based noise PSD trackers exhibit a large tracking delay and produce noise PSD estimates that require bias compensation. Motivated by this, we propose an MMSE-based noise PSD tracker that employs a temporal convolutional network (TCN) a priori SNR estimator. The proposed noise PSD tracker, called DeepMMSE makes no assumptions about the characteristics of the noise or the speech, exhibits no tracking delay, and produces an accurate estimate that requires no bias correction. Our extensive experimental investigation shows that the proposed DeepMMSE method outperforms state-of-the-art noise PSD trackers and demonstrates the ability to track abrupt changes in the noise level. Furthermore, when employed in a speech enhancement framework, the proposed DeepMMSE method is able to outperform state-of-the-art noise PSD trackers, as well as multiple deep learning approaches to speech enhancement. Availability: DeepMMSE is available at: https://github.com/anicolson/DeepXi .

Spatial Coherence-Aware Multi-Channel Wind Noise Reduction

Outdoor recording is particularly challenging in the presence of wind, which induces highly non-stationary noise in the microphone signals. To enhance a desired signal, e.g., speech, a dedicated noise reduction processing is required. The reduction is usually performed by estimating an unknown set of parameters, e.g., the noise and the speech power spectral densities (PSDs). In contrast to the commonly used assumption of uncorrelated wind noise in multi-channel recordings, we assume the spatial correlation of wind noise contributions to be non-zero at low frequencies when closely-spaced microphones are employed. In our earlier work, we assumed that the spatial coherence was known, i.e., given by a model which depends on the free-field speed and direction of the air stream. As these quantities are unknown in practice, we propose in this work a method to recursively estimate the spatial coherence matrix based on the microphone observations. In addition, we prove the equivalence of two recently developed noise PSD estimation methods when uncorrelated wind noise is assumed, and we propose an approximation of both estimators which is independent of the propagation vector of the speech source at sufficiently low frequency and for a small inter-microphone distance. An evaluation in terms of improvements in speech quality, signal-to-noise ratio and intelligibility is carried out using both simulated and measured wind noise samples.

Roughness-induced vehicle energy dissipation from crowdsourced smartphone measurements through random vibration theory

Abstract We propose, calibrate, and validate a crowdsourced approach for estimating power spectral density (PSD) of road roughness based on an inverse analysis of vertical acceleration measured by a smartphone mounted in an unknown position in a vehicle. Built upon random vibration analysis of a half-car mechanistic model of roughness-induced pavement–vehicle interaction, the inverse analysis employs an L2 norm regularization to estimate ride quality metrics, such as the widely used International Roughness Index, from the acceleration PSD. Evoking the fluctuation–dissipation theorem of statistical physics, the inverse framework estimates the half-car dynamic vehicle properties and related excess fuel consumption. The method is validated against (a) laser-measured road roughness data for both inner city and highway road conditions and (b) road roughness data for the state of California. We also show that the phone position in the vehicle only marginally affects road roughness predictions, an important condition for crowdsourced capabilities of the proposed approach.