PSD Estimation Research Articles

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-Board Random Vibration-Based Robust Detection of Railway Hollow Worn Wheels under Varying Traveling Speeds

The problem of the prompt detection of early-stage hollow worn wheels in railway vehicles via on-board random vibration measurements under normal operation and varying speeds is investigated. This is achieved based on two unsupervised statistical time series (STS) methods which are founded on a multiple-model (MM) framework for the representation of healthy vehicle dynamics. The unsupervised MM power spectral density (U-MM-PSD) method employs Welch-based PSD estimates for wheel wear detection and the unsupervised MM autoregressive (U-MM-AR) method for the parameter vectors of multiple AR models. Both methods are assessed via two case studies using thousands of test cases. The first case study includes Monte Carlo simulations using a SIMPACK-based detailed railway vehicle model, while the second is based on field tests with an Athens Metro train. Wheel wear detection is pursued using lateral or vertical vibration signals from the bogie or the carbody of a trailed vehicle traveling with three different speeds (60, 70, 80 km/h) using wheels under healthy conditions or with early stage hollow wear. Both methods exhibit remarkable performance with the U-MM-AR method to achieve the best overall results, reaching correct detection rates of even 100% with false alarm rates below 5% based on a single accelerometer either on the carbody or bogie.

Quantification of Statistical Error in the Estimate of Strain Power Spectral Density Transmissibility for Operational Strain Modal Analysis

The use of strain modes in structural health monitoring has been constantly increasing because of their superior sensitivity to local structural anomalies. This study aims to investigate the applicability and robustness of power spectral density transmissibility (PSDT) in operational strain modal analysis (OSMA). By noting that OSMA in the frequency domain is vulnerable to the error of spectral estimates, uncertainty quantification stemming from strain spectral estimates and the error propagation analysis in OSMA are conducted from an analytical perspective. The main contributions include the following: (i) the mean and variance of strain PSDT estimates are asymptotically derived based on statistical moment theory and the statistics of PSD estimate error, (ii) the coefficients of variation (c.o.v.) of the strain PSDT estimate and strain spectral estimates are compared with each other through asymptotic analysis to elaborate the robustness of strain PSDT, and (iii) the variability of the strain mode shape is quantified based on the asymptotic formula of strain PSDT estimates tending to local minima of asymptotic zero variance at the resonances. The accuracy and efficiency of the quantification and propagation analysis are validated through numerical and experimental test data accompanied by various parametric studies.

A Constrained Block-Term Tensor Decomposition Framework for Spectrum Cartography

Joint spectrum cartography and disaggregation from sparse spatial observations has been proven to be theoretically feasible based on block-term tensor decomposition (BTD) model. However, the existing BTD framework suffers from inherent drawbacks in terms of numerical stability, complexity and noise robustness. To combat with these drawbacks, we propose a new Constrained-BTD (CBTD) framework in this letter by fully utilizing practical traits of geographical power density spectrum (PSD) and spatial loss field (SLF). The cornerstone of CBTD framework is formulating the joint PSD and SLF estimation as a constrained matrix factorization problem, instead of addressing the factors of BTD. Further, a projection gradient-based (PG) algorithm, which has sublinear convergence, is proposed to handle the restrictions of PSD and SLF by projection on manifolds. Compared with the baseline methods, simulations verify that the proposed approach obtains better performances in terms of stability, complexity and noise robustness.

EEG Based Demarcation of Yogic and Non-Yogic Sleep Patterns Using Power Spectral Analysis

Electroencephalogram (EEG) signals resulting from recordings of polysomnography play a significant role in determining the changes in physiology and behavior during sleep. This study aims at demarcating the sleep patterns of yogic and non-yogic subjects. Frequency domain features based on power spectral density methods were explored in this study. The EEG recordings were segmented into 1s and 0.5s. EEG patterns with four windowing scheme overlaps (0%, 50%, 60% and 75%) to ensure stationarity of the signal in order to investigate the effect of the pre-processing stage. In order to recognize the yoga and non-yoga group through N3 sleep stage, non-linear KNN classifier was introduced and performance was evaluated in terms of sensitivity and specificity. The experimental results show that modified covariance PSD estimate is the best method in classifying the sleep stage N3 of yogic and non-yogic subjects with 95% confidence interval, sensitivity, specificity and accuracy of 97.3%, 98% and 97%, respectively.

Analytical investigation into error propagation of power spectral density transmissibility (PSDT) based on coherence function

Power spectral density transmissibility (PSDT) has attracted widespread interests because it is insensitive to the nature of excitation and has no demand for measuring the input. The classical spectral estimation procedure is usually subject to measurement and spectral leakage errors, which might cause distortion in the estimation of PSDT. This study investigates how the error of PSD estimation propagates into PSDT estimation based on analytical approximation formulas. Based on perturbation theory in tandem with statistical moments of the ratio of random variables, both first- and second-order asymptotic expressions of the mean and variance of PSDT estimation are derived in terms of coherence functions, PSDT measurements, and the number of averages. Given these theoretical findings, it is further revealed that the variance of PSDT estimation around the system poles approaches zero, and the variances of the magnitude and phase of the mode shape decrease to local minima. The performance of the analytical error propagation formulas is validated through numerical and field test data. Parametric studies into the effects of recording durations, window types, and reference outputs on the statistics of PSDT estimation and mode shape estimation are also conducted.

A noise PSD estimation algorithm using derivative-based high-pass filter in non-stationary noise conditions

The minimum mean-square error (MMSE)-based noise PSD estimators have been used widely for speech enhancement. However, the MMSE noise PSD estimators assume that the noise signal changes at a slower rate than the speech signal— which lacks the ability to track the highly non-stationary noise sources. Moreover, the performance of the MMSE-based noise PSD estimator largely depends upon the accuracy of the a priori SNR estimation in practice. In this paper, we introduce a noise PSD estimation algorithm using a derivative-based high-pass filter in non-stationary noise conditions. The proposed method processes the silent and speech frames of the noisy speech differently to estimate the noise PSD. It is due to the non-stationary noise that can be mixed with silent and speech-dominated frames non-uniformly. We first introduce a spectral-flatness-based adaptive thresholding technique to detect the speech activity of the noisy speech frames. Since the silent frame of the noisy speech is completely filled with noise, the noise periodogram is directly computed from it without applying any filtering. Conversely, a 4th order derivative-based high-pass filter is applied during speech activity of the noisy speech frame to filter out the clean speech components while leaving behind mostly the noise. The noise periodogram is computed from the filtered signal—which counteracts the leaking of clean speech power. The noise PSD estimate is obtained by recursively averaging the previously estimated noise PSD and the current estimate of the noise periodogram. The proposed method is found to be effective in tracking the rapidly changing as well as the slowly varying noise PSD than the competing methods in non-stationary noise conditions for a wide range of signal-to-noise ratio (SNR) levels. Extensive objective and subjective scores on the NOIZEUS corpus demonstrate that the application of the proposed noise PSD with MMSE-based speech enhancement methods produce higher quality and intelligible enhanced speech than the competing methods.

Image Process of Rock Size Distribution Using DexiNed-Based Neural Network

In an aggregate crushing plant, the crusher performances will be affected by the variation from the incoming feed size distribution. Collecting accurate measurements of the size distribution on the conveyors can help both operators and control systems to make the right decisions in order to reduce overall power consumption and avoid undesirable operating conditions. In this work, a particle size distribution estimation method based on a DexiNed edge detection network, followed by the application of contour optimization, is proposed. The proposed framework was carried out in the four main steps. The first step, after image preprocessing, was to utilize a modified DexiNed convolutional neural network to predict the edge map of the rock image. Next, morphological transformation and watershed transformation from the OpenCV library were applied. Then, in the last step, the mass distribution was estimated from the pixel contour area. The accuracy and efficiency of the DexiNed method were demonstrated by comparing it with the ground-truth segmentation. The PSD estimation was validated with the laboratory screened rock samples.

EEG-Based Demarcation of Yogic and Non-Yogic Sleep Patterns Using Power Spectral Analysis

Electroencephalogram (EEG) signals resulting from recordings of polysomnography play a significant role in determining the changes in physiology and behavior during sleep. This study aims at demarcating the sleep patterns of yogic and non-yogic subjects. Frequency domain features based on power spectral density methods were explored in this study. The EEG recordings were segmented into 1s and 0.5s. EEG patterns with four windowing scheme overlaps (0%, 50%, 60% and 75%) to ensure stationarity of the signal in order to investigate the effect of the pre-processing stage. In order to recognize the yoga and non-yoga group through N3 sleep stage, non-linear KNN classifier was introduced and performance was evaluated in terms of sensitivity and specificity. The experimental results show that modified covariance PSD estimate is the best method in classifying the sleep stage N3 of yogic and non-yogic subjects with 95% confidence interval, sensitivity, specificity and accuracy of 97.3%, 98% and 97%, respectively.

How Processing Methodologies Can Distort and Bias Power Spectral Density Estimates of Seismic Background Noise

AbstractPower spectral density (PSD) estimates are widely used in seismological studies to characterize background noise conditions, assess instrument performance, and study quasi-stationary signals that are difficult to observe in the time domain. However, these studies often utilize different processing techniques, each of which can inherently bias the resulting PSD estimates. The level of smoothing, the size of the data window, and the method used for actually estimating the spectral content can all have strong influences on PSD estimates and background noise statistics. We show that although smoothing reduces the variance of the PSD estimate, the corresponding decrease in frequency resolution can eliminate or distort features of interest. For instance, popular software packages such as Incorporated Research Institutions for Seismology Modular Utility for STAatistical kNowledge Gathering (MUSTANG) and earlier versions of Portable Array Seismic Studies of the Continental Lithosphere Quick Look eXtended (PQLX), which were designed for data quality control and are effective in that regard, are less suitable for scientific studies that require accurate resolution of spectral peaks, even for peaks as broad as the primary (∼14 s period) and secondary (∼7 s period) microseisms. We also demonstrate how the 1 and 3 hr data windows used in MUSTANG and PQLX can be strongly influenced by energy generated from moderate-size (M>∼4.8) teleseismic earthquakes. The ubiquity of these events is likely skewing median ambient-noise estimates by as much as 5 dB upward, for periods of 10–50 s at high-quality broadband stations. Finally, we illustrate that many of the discrepancies between global low-noise models are attributable to processing methodologies rather than fundamental differences in the underlying seismic data.

Effects of high stimulus presentation rate on EEG template characteristics and performance of c-VEP based BCIs

Objective: This study aims at investigating the effects of high stimulus presentation rates on the characteristics of c-VEP responses along with the change in performance depending on the stimulus presentation rate by utilizing a c-VEP based speller BCI. Approach: Twenty subjects participated in three different experiments with refresh rates of 60 Hz (E1), 120 Hz (E2) and 240 Hz (E3), where a 127-bit m-sequence is used. To observe the change in frequency content of c-VEP responses, PSD estimates of c-VEP responses were evaluated. Principal component analysis (PCA) was applied to observe how many distinguishable responses could be evoked with a 127-bit length m-sequence for three different refresh rates. Main Results: Average ITR and accuracy values are 85.87 bits min−1 and 92% for E1, 94.21 bits min−1 and 97% for E2, and 78.65 bits min−1 and 87% for E3 respectively. The c-VEP responses are band-limited although the bandwidth of the input signal significantly increases as the refresh rate increases. The spectral densities of c-VEP templates are concentrated on several frequency intervals, especially for E3, which eventually results in a target misclassification. PCA shows that the number of well distinguishable responses decreases with the increasing refresh rate. Considering all results and observations, we suggest that 120 Hz refresh rate is best to use in BCIs with high number of targets whereas 240 Hz refresh rate may be prefered for low number of targets. Significance: This study mainly investigates the alterations in the characteristics of c-VEP responses according to the stimulus presentation rate which have never been investigated thoroughly before. Our results show that increasing refresh rate does not necessarily increase the overall performance of the system due to the changes in characteristics of c-VEP responses. Further applications and designs of a c-VEP based BCIs will benefit from the observations and results of this study.

Multiplicity of coprime pairs for extension of coprime sensor arrays

This research finds the optimum period of a basic coprime sensor array (CSA) needed to reduce the PSL height to -13 dB for both minimum and product processing methods. Our design does not have the constraint that the subarray lengths be one integer apart unlike in [Adhikari et al., 2014]. We apply MUSIC algorithm to the optimized CSA and compare the PSD estimate obtained by Vaidyanathan and Pal’s covariance matrix estimation using a single sensor pair versus our covariance matrix estimated using all available sensor pairs. We show that minimum processing requires fewer periods than product processing to reach the PSL height of -13 dB. Larger coprime pairs require fewer periods and cause an increase in variance and a decrease in the number of lags available between the two subarrays. This decrease lowers the accuracy of the covariance matrix estimation. However, using all available sensor pairs to generate the covariance matrix greatly increases the accuracy compared to using a single sensor pair. When only one signal is present, both covariance estimates produce a similar, accurate DOA, but as the number of signals increases, our covariance estimate performs better. [Work supported by Louisiana Tech University.]

Automatic Noise PSD Estimation for Restoration of Archived Audio

Automatic Noise PSD Estimation for Restoration of Archived Audio

A Novel Posture for Better Differentiation Between Parkinson's Tremor and Essential Tremor.

Due to a lack of reliable non-invasive bio-markers, misdiagnosis between Parkinson's disease and essential tremor is common. Although some assistive engineering approaches have been proposed, little acceptance has been obtained for these methods lack well-studied mechanisms and involve operator-dependent procedures. Aiming at a better differentiation between the two tremor causes, we present a novel posture, termed arm-rested posture, to ameliorate the quality of recorded tremor sequences. To investigate its efficacy, the posture was compared with another common posture, called arm-stretching posture, in fundamental aspects of tremor intensity and dominant frequency. A tremor-affected cohort comprising 50 subjects (PD = 26, ET = 24) with inhomogeneous tremor manifestation were recruited. From each subject, acceleration data of 5 min in terms of each posture were recorded. In the overall process, no operator-dependent procedures, such as data screening, was employed. The differentiation performance of the two postures were assessed by the index of discrimination coefficient and a receiver operating characteristic analysis based on binary logistic regression. The results of the differentiation assessment consistently demonstrate a better performance with the arm-rested posture than with the arm-stretching posture. As a by-product, factors of disease stage (incipient, progressed stage), spectrum estimate (PSD, bispectrum) and recording length (5–300s) were investigated. The significant effect of disease stage was only found in PD in terms of tremor intensity [F(1, 516) = 7.781, P < 0.05]. The bispectrum estimate was found to have better performance than the PSD estimate in extracting dominant frequency in terms of the discrimination coefficient. By extending the recording length, we noticed an increase in the performance of dominant frequency. The best result of the arm-rested posture was obtained with the maximum recording length of 300 s (area under the curve: 0.944, sensitivity: 92%, 1-specificity: 0%, accuracy: 96%), which is better than that of the arm-stretching posture in the same condition (area under the curve: 0.734, sensitivity: 54%, 1-specificity: 12%, accuracy: 72%). Thus, we conclude that the arm-rested posture can assist in improving tremor differentiation between Parkinson's disease and essential tremor and may act as a universal tool to analyze tremor for both clinical and research purpose.

Binaural noise reduction via cue-preserving MMSE filter and adaptive-blocking-based noise PSD estimation

Binaural noise reduction, with applications for instance in hearing aids, has been a very significant challenge. This task relates to the optimal utilization of the available microphone signals for the estimation of the ambient noise characteristics and for the optimal filtering algorithm to separate the desired speech from the noise. The additional requirements of low computational complexity and low latency further complicate the design. A particular challenge results from the desired reconstruction of binaural speech input with spatial cue preservation. The latter essentially diminishes the utility of multiple-input/single-output filter-and-sum techniques such as beamforming. In this paper, we propose a comprehensive and effective signal processing configuration with which most of the aforementioned criteria can be met suitably. This relates especially to the requirement of efficient online adaptive processing for noise estimation and optimal filtering while preserving the binaural cues. Regarding noise estimation, we consider three different architectures: interaural (ITF), cross-relation (CR), and principal-component (PCA) target blocking. An objective comparison with two other noise PSD estimation algorithms demonstrates the superiority of the blocking-based noise estimators, especially the CR-based and ITF-based blocking architectures. Moreover, we present a new noise reduction filter based on minimum mean-square error (MMSE), which belongs to the class of common gain filters, hence being rigorous in terms of spatial cue preservation but also efficient and competitive for the acoustic noise reduction task. A formal real-time subjective listening test procedure is also developed in this paper. The proposed listening test enables a real-time assessment of the proposed computationally efficient noise reduction algorithms in a realistic acoustic environment, e.g., considering time-varying room impulse responses and the Lombard effect. The listening test outcome reveals that the signals processed by the blocking-based algorithms are significantly preferred over the noisy signal in terms of instantaneous noise attenuation. Furthermore, the listening test data analysis confirms the conclusions drawn based on the objective evaluation.

Hilbert-Huang Transform and Welch's Method for Motor imagery based Brain Computer Interface

The features extraction is the main step in a Brain-Computer Interface (BCI) design. Its goal is to create features easy to be interpreted in order to produce the most accurate control commands. For this end, these features must include all the original signal characteristics. The generated brain's signals' non-stationary and nonlinearity constitute a limitation to the improvement of the performances of systems based on traditional signal processing such as Fourier Transform. This work deals with the comparison of features extraction between Hilbert-Huang Transform (HHT) and Welch's method for Power Spectral Density estimation (PSD) then on the creation of an adaptive method combining the two. The parameters optimization of each method is firstly performed to reach the best classification accuracy rate. The study shows that the PSD estimation is sensitive to the parametric variation whereas the HHT method is mainly robust. The classification results show that an adaptive joint method can reach 90% of accuracy rate for a mental activity period of 1s.

Correction to "Maximum Likelihood PSD Estimation for Speech Enhancement in Reverberation and Noise" [Sep 16 1599-1612

Presents corrections to the paper, A Novel Approach Based on Marine Radar Data Analysis for High-Resolution Bathymetry Map Generation.

An Analysis of Adaptive Recursive Smoothing with Applications to Noise PSD Estimation

First-order recursive smoothing filters using a fixed smoothing constant are in general unbiased estimators of the mean of a random process. Due to their efficiency in terms of memory consumption and computational complexity, they are of high practical relevance and are also often used to track the first-order moment of nonstationary random processes. However, in single-channel speech-enhancement applications, e.g., for the estimation of the noise power spectral density, an adaptively changing smoothing factor is often employed. Here, the adaptivity is used to avoid speech leakage by raising the smoothing factor when speech is likely to be present. In this paper, we investigate the properties of adaptive first-order recursive smoothing factors applied to noise power spectral density estimators. We show that in contrast to a smoothing with fixed smoothing factors, adaptive smoothing is in general biased. We propose different methods to quantify and to compensate for the bias. We demonstrate that the proposed correction methods reduce the estimation error and increases the perceptual evaluation of speech quality scores in a speech enhancement framework.

Optimization of the Removal Function of Dual-Rotation Magnetorheological Finishing

Magnetorheological finishing (MRF) is an advanced polishing technique capable of rapidly converging to the required surface figure. In this article, dual-rotation MRF tool is used to generate centrosymmetric removal function that can be W-shaped or Gaussian-shaped. Using W-shaped removal function and Gaussian-shaped removal function respectively, this article compares the convergence of surface error by simulating the finishing process through iterative calculations. Furthermore, it compares mid-spatial-frequency surface error caused by the two removal functions, through 2D FFT and PSD estimation in the frequency domain. From simulation, this article proves that Gaussian-shaped removal function is more advantageous than W-shaped removal function. To solve the problem that the removal function obtained in dual-rotation MRF is W-shaped, this paper presents the method of adjusting the distance between the axes of self-rotation and co-rotation to secure Gaussian-shaped removal function. Finally, experiments have been conducted to demonstrate validity of the method.

Lomb algorithm versus fast Fourier transform in heart rate variability analyses of pain in premature infants.

Heart rate variability analysis is a promising method for measuring pain in premature infants. The Lomb algorithm was adapted and compared with fast Fourier transform (FFT) for the purposes of PSD estimation. Both FFT and the Lomb algorithm had similar low frequency (LF) estimation error rates. However, the Lomb algorithm had a significant smaller error rate than FFT when estimating high frequency (HF). In addition, the ECG signals of two premature infants in the newborn intensive care unit were analyzed while undergoing a routine heel stick, a common painful procedure. The Lomb algorithm performed as expected marking a decrease in both LF and HF power in the presence of pain.