Statistical Signal Research Articles

The Farey map exploited in the construction of a Farey mother wavelet

The wavelet analysis of a function passes through its so-called wavelet transform. Such a transform is mathematically defined as a convolution product of the analyzed function with another analyzing function known as the mother wavelet by involving the scale and the translation parameters. This means that the mother wavelet construction is the starting and major point in the wavelet analysis. Besides, the choice of the mother wavelet remains a major problem in wavelet applications such as statistical series, time series, signal, and image processing. This needs more candidates of mother wavelets to be constructed. The main aim of the present paper is to construct a new mother wavelet by exploiting the well-known Farey map. We showed indeed that such a map may be a mother wavelet owing properties such as admissibility, moments, 2-scale relation, and reconstruction rule already necessary in the wavelet analysis of functions. By a suitable choice of translation-dilation parameters on the original Farey map, we succeeded to prove the main properties of a Farey wavelet analysis. The constructed mother looks to be suitable for many complicated applications such as hyperbolic PDEs.

A Novel Data-Driven Fault Detection Method Based on Stable Kernel Representation for Dynamic Systems.

With the steady improvement of advanced manufacturing processes and big data technologies, modern industrial systems have become large-scale. To enhance the sensitivity of fault detection (FD) and overcome the drawbacks of the centralized FD framework in dynamic systems, a new data-driven FD method based on Hellinger distance and subspace techniques is proposed for dynamic systems. Specifically, the proposed approach uses only system input/output data collected via sensor networks, and the distributed residual signals can be generated directly through the stable kernel representation of the process. Based on this, each sensor node can obtain the identical residual signal and test statistic through the average consensus algorithms. In addition, this paper integrates the Hellinger distance into the residual signal analysis for improving the FD performance. Finally, the effectiveness and accuracy of the proposed method have been verified in a real multiphase flow facility.

Data-driven denoising of stationary accelerometer signals

Modern navigation solutions are largely dependent on the performances of the standalone inertial sensors, especially at times when no external sources are available. During these outages, the inertial navigation solution is likely to degrade over time due to instrumental noises sources, particularly when using consumer low-cost inertial sensors. Conventionally, model-based estimation algorithms are employed to reduce noise levels and enhance meaningful information, thus improving the navigation solution directly. However, guaranteeing their optimality often proves to be challenging as sensors performance differ in manufacturing quality, process noise modeling, and calibration precision. In the literature, most inertial denoising models are model-based when recently several data-driven approaches were suggested primarily for gyroscope measurements denoising. Data-driven approaches for accelerometer denoising task are more challenging due to the unknown gravity projection on the accelerometer axes. To fill this gap, we propose several learning-based approaches and compare their performances with prominent denoising algorithms, in terms of pure noise removal, followed by stationary coarse alignment procedure. Based on the benchmarking results, obtained in field experiments, we show that the learning-based models outperform traditional signal processing filtering in terms of pure inertial signal reconstruction. Moreover, they are shown to improve angular errors by one order of magnitude, given a navigation-related task.

Statistical Analysis and EEG Signal Filtering Using Design of Window Function Based on Optimization Methods

The window functions, which are widely used in Finite Impulse Response (FIR) digital filter design with the Fourier Series Methods, aim to eliminate the oscillations adversely affecting the filter performance that occur during the filter design. Window functions, which were developed with different methods in the literature, were designed with three different optimization techniques in this study. By using Particle Swarm Optimization (PSO), Grey Wolf Colony Optimization (GWCO), Cuckoo Search Optimization (CSO) algorithms, which are among current metaheuristic optimization methods, new window functions are designed for FIR digital filter design such that the designed new window functions have different window coefficients and design parameters. The difference of the designed window functions was analyzed with the Friedman and Wilcoxon tests, which are statistical data analysis methods, and the originality of the designed window functions was proven. FIR digital filters that can perform the same operation as the designed window functions have been produced and the results obtained by performing the filtering application of the EEG signal with the produced filters are presented in the study.

Genetic diversity and signatures of selection in four indigenous horse breeds of Iran

Indigenous Iranian horse breeds were evolutionarily affected by natural and artificial selection in distinct phylogeographic clades, which shaped their genomes in several unique ways. The aims of this study were to evaluate the genetic diversity and genomewide selection signatures in four indigenous Iranian horse breeds. We evaluated 169 horses from Caspian (n = 21), Turkmen (n = 29), Kurdish (n = 67), and Persian Arabian (n = 52) populations, using genomewide genotyping data. The contemporary effective population sizes were 59, 98, 102, and 113 for Turkmen, Caspian, Persian Arabian, and Kurdish breeds, respectively. By analysis of the population genetic structure, we classified the north breeds (Caspian and Turkmen) and west/southwest breeds (Persian Arabian and Kurdish) into two phylogeographic clades reflecting their geographic origin. Using the de-correlated composite of multiple selection signal statistics based on pairwise comparisons, we detected a different number of significant SNPs under putative selection from 13 to 28 for the six pairwise comparisons (FDR < 0.05). The identified SNPs under putative selection coincided with genes previously associated with known QTLs for morphological, adaptation, and fitness traits. Our results showed HMGA2 and LLPH as strong candidate genes for height variation between Caspian horses with a small size and the other studied breeds with a medium size. Using the results of studies on human height retrieved from the GWAS catalog, we suggested 38 new putative candidate genes under selection. These results provide a genomewide map of selection signatures in the studied breeds, which represent valuable information for formulating genetic conservation and improved breeding strategies for the breeds.

The therapeutic validation of long COVID

The therapeutic validation of long COVID

Advanced mood tracking using waveform statistical signal processing techniques

Tracking one’s mood over time is useful for assessing one’s response to life events and improving self-awareness and emotional regulation. It is also useful for diagnostic purposes for practitioners to determine the emotional stability of their patients using empirical techniques. Most mood trackers however tend to be extremely simplistic and are subject to the subjective analysis of whoever is assessing the results, leading to bias and inaccurate interpretations. Moreover, a manual human analysis is incapable of accurately detecting all patterns and trends in mood given enough data points, which may lead to critical insights being overlooked. Recent advancements in mood tracking mobile apps help alleviate this problem, but they vary widely in their data analysis techniques and tracking scale methodologies. The contents of this paper propose a more sophisticated theoretical framework, which treats mood data points over time as a time series waveform similar to what might be found from a signal in electronic systems. This framework allows standard and robust statistical signal processing techniques to be utilized and can be adapted to any particular numerical mood tracking scale. The calculations of the assessment data provide unbiased empirical analysis metrics which one can simply calculate from the data. When the tracker scale is mapped appropriately, this “mood signal” can also be analyzed in the frequency domain via a Fourier transform, which sheds light onto possible mood periodicities to better determine the source of undesirable behavioral patterns. All of these metrics together allow for a detailed, unbiased, entirely empirical analysis of mood as a function of time.

Advanced Video-Based Processing for Low-Cost Damage Assessment of Buildings under Seismic Loading in Shaking Table Tests.

This paper explores the potential of a low-cost, advanced video-based technique for the assessment of structural damage to buildings caused by seismic loading. A low-cost, high-speed video camera was utilized for the motion magnification processing of footage of a two-story reinforced-concrete frame building subjected to shaking table tests. The damage after seismic loading was estimated by analyzing the dynamic behavior (i.e., modal parameters) and the structural deformations of the building in magnified videos. The results using the motion magnification procedure were compared for validation of the method of the damage assessment obtained through analyses of conventional accelerometric sensors and high-precision optical markers tracked using a passive 3D motion capture system. In addition, 3D laser scanning to obtain an accurate survey of the building geometry before and after the seismic tests was carried out. In particular, accelerometric recordings were also processed and analyzed using several stationary and nonstationary signal processing techniques with the aim of analyzing the linear behavior of the undamaged structure and the nonlinear structural behavior during damaging shaking table tests. The proposed procedure based on the analysis of magnified videos provided an accurate estimate of the main modal frequency and the damage location through the analysis of the modal shapes, which were confirmed using advanced analyses of the accelerometric data. Consequently, the main novelty of the study was the highlighting of a simple procedure with high potential for the extraction and analysis of modal parameters, with a special focus on the analysis of the modal shape's curvature, which provides accurate information on the location of the damage in a structure, while using a noncontact and low-cost method.

Deep convolution neural network for machine health monitoring using spectrograms of vibration signal and its EMD-intrinsic mode functions

A spectrum-image based representation of machine vibration signals with deep convolution neural network is proposed for machine fault classification in which the convolution layer is used for automatic feature extraction as an alternate to the conventional feature-based methods. Two different forms of spectrum representations are proposed, one based on the short time Fourier transform of the original signals and the other based on the short time Fourier transform of the intrinsic mode functions acquired by empirical mode decomposition. Empirical mode decomposition has its own merits in discriminating non stationary signals and the novelty of the work is to use the short time Fourier transform of intrinsic mode functions with deep convolution neural network model. The classification and validation accuracy of the model are investigated with respect to epochs. It is demonstrated that both spectrum-based techniques perform good with 100% model accuracies in a numerical experiment of binary classification on a bearing dataset that comprises of normal and faulty signals. In another experiment using milling data set, short time Fourier transform of intrinsic mode functions representation performs better with 100% training accuracy, F1 score of 0.8933 which is better than that of using short time Fourier transform of raw signals whose training accuracy is 64% and F1 score of 0.7486. The numerical study shows that the empirical mode decomposition based spectrum representation delivers the highest accuracy in the learning model obviating the necessity for independent feature extraction, feature selection, and dimension reduction. The numerical experiment is extended using empirical mode decomposition based spectrums for multiple class classification problems in bearing dataset. The confusion matrix obtained for 10 classes, shows that validation accuracy is 100% for all classes. The performance comparison throws light on the merits of empirical mode decomposition spectrum method over other state of the art methods.

Consensus-Based Time Synchronization Using Bayesian Estimation in Wireless Sensor Networks Under Communication Delays

Time synchronization is crucial for various applications in wireless sensor networks. Consensus-based time synchronization is an essential distributed strategy for its high precision, robustness, and scalability. In practical networks, however, communication delays are not ignorable and make time messages received inaccurate, which is the fundamental limitation for time synchronization. It was pointed out that if a consensus-based time synchronization algorithm does not consider the influence of delays, it may be divergent under the scenario with delays. Making use of the knowledge of statistical signal processing to develop an efficient relative skew estimator is a viable method to restrain communication delays. In this article, we propose a relative skew estimator based on Bayesian estimation theory to counteract the impact of time delays, which improves the estimation accuracy while reducing the memory requirement. By applying the presented estimator to average consensus protocol, precise network-wide synchronization is achieved in the presence of delays. In addition, the proof of convergence of the proposed scheme is given by theoretical analysis. Simulation results demonstrate the effectiveness of the proposed scheme and show that our algorithm outperforms other similar algorithms in terms of synchronization accuracy under random delays.

Blind block timing estimation for Alamouti STBC: An adaptive cyclostationary-based approach

Block timing synchronization, which could be data-aided or non-data-aided, is a critical part of space–time block codes (STBCs) for recovery of transmitted symbols. The data-aided schemes are not suited for some problems like bandwidth efficiency and most of the existing non-data-aided techniques rely on the received signals statistics and channel coefficients estimation increasing their complexity. In this paper, a non-data-aided cyclostationary-based approach is proposed for block timing estimation in Alamouti STBC employing frequency-shifted versions of the received signals. The method is non-statistical with low complexity and requires no knowledge of channel coefficients. Simulation results confirm the effectiveness of the method.

The design and implementation of folded adaptive lattice filter structures in FPGA for ECG signals

An adaptive filter is the utmost essential filter castoff in statistical signal dealing. The fine-tuning of the filter factor in relation to the response signal is the adaptive filter's key feature due to fewer calculations, Least Mean Square (LMS) adaptive filters are widely used to remove noise from Electrocardiograms (ECG). The adaptive filters are realized as signal processing algorithms in Digital Signal Processors (DSPs) or in VLSI Signal Processors (VSPs). The technique provides a way to create a folded adaptive lattice LMS filter, which requires less hardware than an adaptive lattice filter. Folding is an algorithm that uses a time scheduling technique that combines arithmetic operations into one operation which reduces Register and silicon chip areas. The design and implementation of a folded lattice adaptive filter remove Power Line Interference (PLI) noise from ECG signals. The MATLAB Xilinx System Generator tool is used to design the Adaptive Lattice LMS Filter and Folded Adaptive Lattice LMS Filter with Folding Order K = 2 and K = 4 and realized in the Virtex 5 FPGA KIT. The results of the folded architecture show that the area is reduced for K = 2 and K = 4 by 82.60% and 91.05%, respectively compared with a normal adaptive lattice filter.

Temporal novelty detection and multiple timescale integration drive Drosophila orientation dynamics in temporally diverse olfactory environments.

To survive, insects must effectively navigate odor plumes to their source. In natural plumes, turbulent winds break up smooth odor regions into disconnected patches, so navigators encounter brief bursts of odor interrupted by bouts of clean air. The timing of these encounters plays a critical role in navigation, determining the direction, rate, and magnitude of insects' orientation and speed dynamics. Disambiguating the specific role of odor timing from other cues, such as spatial structure, is challenging due to natural correlations between plumes' temporal and spatial features. Here, we use optogenetics to isolate temporal features of odor signals, examining how the frequency and duration of odor encounters shape the navigational decisions of freely-walking Drosophila. We find that fly angular velocity depends on signal frequency and intermittency-the fraction of time signal can be detected-but not directly on durations. Rather than switching strategies when signal statistics change, flies smoothly transition between signal regimes, by combining an odor offset response with a frequency-dependent novelty-like response. In the latter, flies are more likely to turn in response to each odor hit only when the hits are sparse. Finally, the upwind bias of individual turns relies on a filtering scheme with two distinct timescales, allowing rapid and sustained responses in a variety of signal statistics. A quantitative model incorporating these ingredients recapitulates fly orientation dynamics across a wide range of environments and shows that temporal novelty detection, when combined with odor motion detection, enhances odor plume navigation.

CAR-T Cells and the Kidney: Insights from the WHO Safety Database.

Chimeric antigen receptor T (CAR-T) cells have proven to be a game changer for treating several hematologic malignancies. Randomized controlled trials have highlighted potential life-threatening adverse drug reactions (ADRs), including cytokine release syndrome (CRS). Acute renal failure (ARF) has also been reported in 20% of the patients treated. However, an analysis of renal safety supported by large-scale real-life data seems warranted. We queried VigiBase® for all reports of the Standardised MedDRA Query "acute renal failure" (ARF) involving a CAR-T cell, registered until 24 July 2022. Disproportionality for this ADR was analyzed through calculation of the Information Component [IC (95% confidence interval)]. A positive lower end of the 95% confidence interval of the IC is the threshold used in statistical signal detection in VigiBase®. The same analysis was carried out for various hydroelectrolytic disorders. We gathered 224 reports of ARF, and 125 reports of hydroelectrolytic disorders involving CAR-T cells. CAR-T cells were disproportionately reported with ARF [IC 1.5 (1.3-1.7)], even after excluding reports mentioning CRS. A significant disproportionate reporting was also found for hypernatremia [IC 3.1 (2.2-3.8)], hyperphosphatemia [IC 3.1 (1.8-3.9)], hypophosphatemia [IC 2.0 (0.6-2.9)], metabolic acidosis [IC 1.8 (1.2-2.2)], hyponatremia [IC 1.6 (1.1-2.0)], and hypercalcemia [IC 1.4 (0.5-2.1)]. There was no disproportionate reporting of dyskalemia. This study is limited by the inherent flaws of pharmacovigilance approaches. Nonetheless, our findings suggest that ARF and an array of hydroelectrolytic disorders are potential ADRs of CAR-T cell therapy, in real-life settings and in a nonselected population.

Impact of policy uncertainty on gold price in India: evidence from multi commodity exchange (MCX) India and World Gold Council prices

ABSTRACT India is one of the largest consumers of gold but remains largely unexplored and requires proper attention from investors, regulators and policymakers. Our study aims to uncover the relationship between policy uncertainty and gold prices in India, considering a timeline from 2004 to 2023. Using India EPU and geopolitical uncertainty-related index, the empirical estimation was performed in a time series framework using standard OLS and augmented regression using data from MCX-India and WGC prices. Our statistical investigation signals that policy uncertainty and gold prices in India are positively associated. This implies a higher degree of policy uncertainty and a higher gold price. Monetary policy uncertainty and interest rate changes shows an asymmetric impact on the gold price in India; the effects were more pronounced after 2015. Furthermore, policy uncertainty contains information explaining gold futures prices and has a two-month lag impact. Thus, gold trading in India is sensitive to the economic outlook of the economy and policy uncertainty. Gold imports in India have an adverse effect on gold prices. It is also reported that the INR/USD exchange rate plays a vital role in gold price setting. Hence, the study suggest that India’s government should develop a healthy gold ecosystem and gold-policy.

Retinal motion statistics during natural locomotion.

Walking through an environment generates retinal motion, which humans rely on to perform a variety of visual tasks. Retinal motion patterns are determined by an interconnected set of factors, including gaze location, gaze stabilization, the structure of the environment, and the walker's goals. The characteristics of these motion signals have important consequences for neural organization and behavior. However, to date, there are no empirical in situ measurements of how combined eye and body movements interact with real 3D environments to shape the statistics of retinal motion signals. Here, we collect measurements of the eyes, the body, and the 3D environment during locomotion. We describe properties of the resulting retinal motion patterns. We explain how these patterns are shaped by gaze location in the world, as well as by behavior, and how they may provide a template for the way motion sensitivity and receptive field properties vary across the visual field.

Noisy Fading Channel Distributions Parameter Estimation and Reconstruction based on Truncation

In this paper, Rayleigh and Nakagami-m fading channels are considered that are positively correlated. The received signal statistics specifically mean and variance of sum of fading and noise variables in cases where fading distributions are considered ranging from zero to infinity compared to cases where the fading and noise distributions are truncated due to applying the energy criterion to each distribution are considered. Average number of required bits are derived by calculating Shannon entropy for each case investigated. The number of measurements required for distribution reconstruction based on CS reduced complexity method for each case are also computed. Furthermore, the Bit-Error-Rate (BER) curves for all respective cases are derived and directly compared. The results impose the effect of truncation on the quantification of variances as well as average number of bits as measures of uncertainty and number of measurements for reconstruction. The BER curves produced account for the Gaussian statistical assumption adopted. Applications to 5G communications are provided and future directions are highlighted.

Frequency Estimation with Co-prime DFT Filter Bank and Half Nyquist Frequency Shift

When processing wide sense stationary (WSS) signals, the sampled data rate of conventional MN bands DFT filter bank is at least MN, while the co-prime DFT filter bank (co-prime DFTFB) only needs M+N, that sharply lowers the sampling rate. Here, M and N are co-prime pair of integers. However, practical FIR filter imperfections and correlation detection mode arouse spurious peaks in signal power spectrogram, that greatly limits the application of co-prime DFTFB. In this paper, we propose a modified co-prime DFTFB by adding a real valued multiplier to the original one, where M and N are both odd numbers. Together with original co-prime DFTFB, we get a 2MN bands filter bank. In the simulation section, two BPSK signals with random carrier frequencies are employed. The results of detection probability versus SNR curves through 500 Monte Carlo experiments verify the effectiveness of our method.

Correlation-Based Maximal Invariant Statistic for Spectrum Sensing

In this letter, spectrum sensing for wide-sense stationary signals with temporal correlation is studied. In order to perform uniformly most powerful invariant test (UMPIT) or locally most powerful invariant test (LMPIT), the ratio of the distributions of the maximum invariant statistics is derived in closed-form using Wijsman’s theorem. This ratio shows that UMPIT can be obtained when the signal-to-noise ratio (SNR) and the normalized auto-correlation matrix of the primary user signal are both known. In addition, the LMPIT with nominal SNR (LMPIT-NSNR) and the LMPIT with improved sample auto-correlation matrix (LMPIT-ISAC) are proposed based on this ratio. LMPIT-NSNR and LMPIT-ISAC are suitable for the case where the normalized auto-correlation matrix is known and the SNR is unknown, and for the case where both the normalized auto-correlation matrix and the SNR are unknown, respectively. Simulation results show that the performance of LMPIT-NSNR is robust to the fixed nominal SNR value and can approach the performance of UMPIT, and the LMPIT-ISAC performs better than the traditional covariance-based test.

Approximately low-rank recovery from noisy and local measurements by convex program

Abstract Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with the $\ell _1$ norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensor-norm-constrained estimator for the recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regularizer is designed to adapt to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching by applying Maurey’s empirical method to tensor products of Banach spaces. The estimator provides a near-optimal error bound in a minimax sense and admits a polynomial-time algorithm for these applications.