Time-varying Signals Research Articles

Synchrosqueezing-Based Short-Time Fractional Fourier Transform

A novel synchrosqueezing transform to the time-frequency representation based on short-time fractional Fourier transform for strong time-varying signals is proposed in this paper. To finely describe the local characteristics of nonstationary signal in the short-time fractional Fourier transform domain, a new instantaneous frequency estimator, a new instantaneous fractional frequency estimator and the corresponding energy reassignment operators are given by time-fractional frequency basis. The discrete implementation and signal reconstruction of the proposed method are investigated. Furthermore, the calculation of the optimal fractional order, computational complexity and limitation of the proposed method are discussed. Various strong time-varying signal experiments and time-frequency spectrum energy attenuation gradient extraction experiments of real synthetic aperture radar (SAR) images are conducted to verify the effectiveness and superiority of the proposed method over some advanced time-frequency analysis methods in energy concentration, time-frequency localization, signal reconstruction and clutter suppression.

Online Edge Flow Imputation on Networks

An online algorithm for missing data imputation for networks with signals defined on the edges is presented. Leveraging the prior knowledge intrinsic to real-world networks, we propose a bi-level optimization scheme that exploits the causal dependencies and the flow conservation, respectively via <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(i)</i> a sparse line graph identification strategy based on a group-Lasso and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(ii)</i> a Kalman filtering-based signal reconstruction strategy developed using simplicial complex (SC) formulation. The advantages of this first SC-based attempt for time-varying signal imputation have been demonstrated through numerical experiments using EPANET models of both synthetic and real water distribution networks.

NEAR–OPTIMUM DETECTION OF SIGNALS IN UNDERWATER ACOUSTIC NOISE USING LOCALLY OPTIMAL DETECTOR IN TIGERS RIVER

Signal detection has been considered important in under-water signal processing and digital communications, and depending upon noise statistics’ knowledge, near-optimum signal detections in the under-water acoustic noises (UWANs) may be realized in a more effective manner. The theory of the normal (i.e. Gaussian) noise permits using matched filter (MF) detectors; for that reason, a locally optimal (LO) detector has been designed in the present work for improving the probability of the detection ( based on knowing the probability density function (PDF) of noise. Under-water noise that has been utilized for the validation represents the real data that had been gathered from the sea with the use of the broad-band hydrophones at Abo Dali district -Kazem Al Ali Village-Tigris Beaches-Baghdad-Iraq. The LO detector performance is compared after that to the conventional matched filter detector and those have been assessed based on their values. For time-varying signals, the probability of false alarms has been identified as 0.010, and of 90%, energy-to-noise ratios (ENRs) of LO are more efficient compared to the ones of Matched Filter by 4.1dB and for the signals with a fixed frequency, LO is more efficient compared to matched filter by 4.7dB.

Spike encoding techniques for IoT time-varying signals benchmarked on a neuromorphic classification task.

Spiking Neural Networks (SNNs), known for their potential to enable low energy consumption and computational cost, can bring significant advantages to the realm of embedded machine learning for edge applications. However, input coming from standard digital sensors must be encoded into spike trains before it can be elaborated with neuromorphic computing technologies. We present here a detailed comparison of available spike encoding techniques for the translation of time-varying signals into the event-based signal domain, tested on two different datasets both acquired through commercially available digital devices: the Free Spoken Digit dataset (FSD), consisting of 8-kHz audio files, and the WISDM dataset, composed of 20-Hz recordings of human activity through mobile and wearable inertial sensors. We propose a complete pipeline to benchmark these encoding techniques by performing time-dependent signal classification through a Spiking Convolutional Neural Network (sCNN), including a signal preprocessing step consisting of a bank of filters inspired by the human cochlea, feature extraction by production of a sonogram, transfer learning via an equivalent ANN, and model compression schemes aimed at resource optimization. The resulting performance comparison and analysis provides a powerful practical tool, empowering developers to select the most suitable coding method based on the type of data and the desired processing algorithms, and further expands the applicability of neuromorphic computational paradigms to embedded sensor systems widely employed in the IoT and industrial domains.

Adjustable proportional-integral multivariable observer-based FDI attack dynamic reconstitution and secure control for cyber-physical systems

This paper investigates the false data injection (FDI) attack dynamic reconstitution and secure control problems for cyber-physical systems (CPSs) with disturbances. The FDI attacks on the actuator channel and sensor channel are considered simultaneously, and the attack signals acting on the system side are regarded as time-varying signals. Firstly, a novel adjustable proportional-integral multivariable observer (APIMO) scheme is designed to synchronously reconstitute the system states, actuator FDI attacks, and sensor FDI attacks. In particular, the impacts of instantaneous increment of attack signals are attenuated, which enables the proposed APIMO scheme more advantageous in reconstituting time-varying attack signals. Secondly, incorporating a robust attenuation technique, an APIMO-based security controller with corrective capability is designed, such that the discrete-time CPSs achieve asymptotic stability with H∞ performance index. Finally, the simulation example and experiment compared with existing results are realized to examine the feasibility and advantages of the developed strategy.

Multiple squeezing based on velocity synchronous chirplet transform with application for bearing fault diagnosis

Traditional constant basis time–frequency analysis (TFA) methods are limited by the frequency smearing effect when dealing with time-varying synchronous multi-component signals, which makes it difficult to obtain a clear time–frequency representation (TFR) for signals with closely-spaced frequencies. Therefore, it is still a challenge to segregate the synchronous components and to concentrate the energy of frequency components in the TFR. As such, a new nonlinear basis TFA method is proposed in this paper, named multiple squeezing based on velocity synchronous chirplet transform (MSVSCT). In the MSVSCT, the second-order velocity-synchronous chirplet transform is used to generate a nonlinear basis that has a consistent trend complying the instantaneous frequency (IF) variations, so that synchronous components can be separated even in a closely spaced situation. The multi-squeezing technique is adopted to further improve the energy concentration and the accuracy of the TFR. Simulated and experimental signals are employed for validations. The analysis results confirm that MSVSCT has higher accuracy, more robustness to noise, better observability, and higher fidelity of signal reconstruction over other popular TFA methods when processing synchronous multi-component signals.

Adaptive Detector for FDA-Based Ambient Backscatter Communications

Ambient backscatter communication (AmBC), whose passive tags transmit information to readers through radio frequency (RF) signals in the air, has attracted much attention due to its promising prospects in green internet of things (IoTs). However, AmBC detection has faced a new challenge at the reader because the received signal is mainly a hybrid signal from direct link and backscatter link, which makes it difficult to detect symbols of the backscatter tag. To address this problem, in this paper, frequency diverse array (FDA) is utilized to transmit time-variant ambient signal, which can separate the two link signals received by the reader. We propose an adaptive dual-threshold detector by employing the time-variant characteristic of FDA RF signal, which is based on the position of the boundary backscatter tag defined. Specifically, the closed form expressions for maximum likelihood (ML) threshold and adaptive thresholds are derived, respectively. Furthermore, the computational complexities are analyzed. Finally, numerical results are presented to show that the proposed adaptive dual-threshold detector achieves better bit error rate (BER) performance than the conventional ML detector.

Time-varying signal recovery based on low rank and graph-time smoothness

Time-varying data recovery problem exists extensively in computer vision, image processing, environment monitoring, etc. In recent years, the emerging field of graph signal processing provides a new way to solve this problem, deriving the graph signal matrix completion (GSMC) which incorporates the correlation among data entries. The model-based methods of GSMC are more interpretable, but their reconstruction quality is still not satisfactory, especially when observations are sparse. In this paper, we propose a new matrix completion method to solve the time-varying data recovery problem. By adopting the time series analysis method to capture the evolution of data in the time dimension, we obtain a method based on Low Rank and Graph-Time Smoothness (LRGTS). The proposed method has high recovery accuracy by using the second-order information associated with the problem. Numerical results on three real-world datasets demonstrate that our scheme has better reconstruction performance when known entries are sparse, compared with existing matrix completion approaches.

Adaptive multivariate chirp mode decomposition

Multivariate signal processing methods are becoming more prevalent as sensors and modern science and technology improve. However, most existing multivariate signal decomposition methods suffer from the following challenges: (i) requiring prior knowledge of multivariate signal modes; (ii) limiting to narrowband signal analysis; (iii) presenting mode mixing. To overcome the challenges mentioned above, this study proposes a novel method, named adaptive multivariate chirp mode decomposition (AMCMD). The method captures time-varying joint modes one-by-one in a recursive framework without knowing the precise number of modes. Specifically, a multivariate chirp mode (MCM) is modeled first based on AM–FM signals, with the constraint that there is a joint frequency component between all signal channels. Furthermore, demodulation techniques are used to entail the wideband multivariate signal mode exhibit narrowband characteristics. Finally, the objective function is established and the modes of each channel signal are estimated one by one. The efficacy and superiority of the method are verified by a series of numerical examples. In addition, the analysis of real-world time-varying vibration signals also confirms the practicality of the method. The findings demonstrate that the proposed method can converge faster to the same satisfactory results as existing state-of-the-art methods at a faster rate, even without knowing the precise number of modes.

Online Distributed ADMM Algorithm With RLS-Based Multitask Graph Filter Models

This article establishes a multitask graph filter model based on the recursive least square (RLS) method and proposes an online distributed alternating direction method of multipliers (ODADMM) algorithm. We are interested in the time-varying graph signal, i.e., the graph filter is estimated from streaming data. Considering that current popular graph shift operators' energy can not be preserved, which will lead to slow estimation speed, so the RLS method is adopted in graph filters (GFs) to improve the convergence rate. Besides, a multitask GFs model is proposed for node-variant GFs, where each vertex cooperates with neighbours to improve the estimation performance by utilizing the correlation of tasks. Then, according to our model, a distributed alternating direction method of multipliers (DADMM) algorithm is designed, while it has enormous computational complexity. To address this drawback, an ODADMM algorithm is further developed, and the algorithm can converge to an optimal point that is validated. Numerical results verify that the proposed algorithm is more competitive in convergence speed and performance than other related algorithms, and two real scenes are tested to verify the effectiveness of the algorithm.

Distributed Dynamic Weighted Average Consensus for Disturbed Multiagent Systems in Fixed Time

This article addresses the dynamic weighted average consensus (DWAC) problem of disturbed first-order multiagent systems, where a group of agents work cooperatively to track the weighted average of multiple time-varying signals. A class of distributed continuous-time algorithms are proposed to achieve DWAC within a fixed settling time, regardless of the initial conditions of the agents' states. Our first algorithm achieves accurate tracking of the desired trajectory by taking advantage of the variable structure property of sign functions. The second algorithm achieves uniformly bounded tracking with adjustable tracking error bounds by applying the continuous control law. Lyapunov method based stability analysis shows that both the algorithms achieve the fixed-time tracking control even when the single-integrator agent dynamics are affected by bounded disturbances. Moreover, the relationships between controller parameters and tracking performance are derived and the upper bounds of settling time are estimated. Finally, the proposed algorithms are applied to solve the distributed time-varying quadratic optimization problem, and the simulation results confirm the effectiveness of the proposed distributed fixed-time DWAC algorithms.

Speech Signal Analysis With a Refined Iterative Adaptive Method

A new speech signal analysis method referred to as a refined iterative adaptive method (RIAM) is introduced in this paper. Based on time-varying adaptive sinusoidal modeling, the RIAM method tries to determine in an iterative adaptive manner the instantaneous components of time-varying quasi-periodic multi-component signals such as voiced speech. The proposed method can adjust the current analysis parameters to the time-varying characteristics of the speech signal. This is done using a refined iterative sinusoidal parameter estimation algorithm based on a frequency correction mechanism combined with an adaptive scheme. The experiments on voiced speech demonstrate that the proposed RIAM algorithm outperforms some well-known state-of-the-art approaches. The RIAM algorithm provides a higher signal to reconstruction error ratio (SRER) of 42.267 dB with an improvement of 19.752 dB, 5.054 dB, and 2.552 dB compared to the conventional sinusoidal model (SM), adaptive harmonic model (aHM), and extended adaptive quasi harmonic model (eaQHM), respectively.

A non-linear time–frequency tool for machinery fault diagnosis under varying speed condition

Vibration signals acquired from rotating machines operating under varying speed condition often exhibit strong frequency modulation. Conventional time–frequency analysis techniques cannot accurately capture the rapid changing dynamic of such signals where the time–frequency representation often suffers from the diffused energy problem. A new technique binding the demodulation technique and synchroextracting transform (SET) is thus proposed in this paper to overcome this problem. A theoretical analysis is also presented in the study to show the underlying mechanism that the SET technique has certain limitations in dealing with strong time-varying signals, whereas the proposed technique can effectively overcome such limitations. Several numerical examples and two sets of bearing experimental data are used to verify the effectiveness of the proposed technique in the analysis of time-varying signals and for bearing fault diagnosis.

Development of an Early Fire Detection Technique Using a Passive Infrared Sensor and Deep Neural Networks

Early detection of fire is key to mitigate fire related damages. This paper presents a differential pyro-electric infrared (PIR) sensor and deep neural networks (DNNs) based method to detect fire in real-time. Since the PIR sensor is sensitive to sudden body motions and emits a continuous time-varying signal, experiments are carried out to collect human and fire motions using a PIR sensor. These signals are processed using one-dimensional continuous wavelet transform to perform feature extraction. The corresponding wavelet coefficients are converted into RGB spectrum images that are then used as inputs for a deep convolutional neural network. Various pre-trained DNN architectures are adopted to train and identify the collected data for background (no motion), human motion, and fire categories: small quasi-static and spreading fires. Experimental results show that the ShuffleNet architecture yields the highest prediction accuracy of 87.8%. Experimental results for the real-time strategy which works at a speed of 12 frames-per-second show 95.34% and 92.39% fire and human motion detection accuracy levels respectively.

Exploring the benefits of spatial and temporal block-wise filtering architectures

Spatial block-wise filtering architectures improve noise stationarity locally, making SVD-based filtering more robust (Song et al., 2017). Temporal block-wise filtering has been proposed to augment spatial block-wise methods for 3D Doppler data acquired via mechanical translation (Chen et al., 2021) and compensate for bulk motion in cardiac power Doppler imaging (Zhang et al., 2021). We combine spatial and temporal block-wise architectures to suppress noise through depth and better capture time-varying signals with power Doppler. We show that a combination of spatial and temporal block-wise methods provides improved CNR (3.9 dB gain), SNR (0.9 dB gain), and CR (11.7 dB gain) over spatial block-wise alone and propose two methods for selecting temporal block sizes. First, we select temporal ensembles from systole, early-, and late-diastole from matched ECG data. Second, we derive a temporal SVD cutoff between the blood and noise subspaces for the entire ensemble. We use that cutoff as a proxy for correlation length and select ensembles accordingly. We collected 2 s of liver data from a healthy volunteer (nine angled plane waves at 600 Hz PRF and 4.1667 MHz center frequency) and applied spatial and temporal block-wise SVD filtering with 100-sample ensembles and 50-sample temporal block sizes overlapped at 20%.

Parametermeasurement of aircraft-radiated noise from a single acoustic sensor node in three-dimensional space

A line spectrum presents the form of a narrow-band time-varying signal due to Doppler effect when the single hydrophone node observes flight-radiated noise. The modulation law of the time-varying signal contains a large number of feature information of moving targets, which can be used for detection and classification. This paper studies the possibility of using instantaneous frequency measurements from the hydrophone node to improve the precision of the flight parameter estimates when the source spectrum contains a harmonic line of constant frequency. First of all, we build up and analyze the underwater sound field excited by the aircraft using the ray theory model; then the Doppler shift in the two isospeed media, which is caused by the aircraft, is established; finally, a robust time–frequency transform describes the time–frequency distribution of the received signal, and a geometric approach solves the flying parameters.

Multivariate time-varying complex signal processing framework and its application in rotating machinery rotor-bearing system

Affected by multi-field coupling factors, the vibration response of rotating machinery similar to the hydro-generator unit often exhibits strong time-varying frequency components, which makes rotor fault detection more challenging. The fusion analysis of the vibration signals of multiple bearing sections of the rotor has been proved to be a very effective method for rotor vibration fault diagnosis. However, how to more accurately and synchronously extract the instantaneous features of rotor non-stationary vibration signals associated with multiple sections has been unresolved. To this end, a framework for multivariate time-varying complex signal decomposition of the rotor-bearing system (RBS) is proposed, namely multivariate complex nonlinear chirp mode decomposition. First, the decomposition of multivariate time-varying complex signals is realized by two-stage processing. Second, instantaneous orbit features (IOFs) are obtained through the proposed framework. Finally, a three-dimensional instantaneous orbit map reflecting the time-varying process is constructed through the IOFs. The framework not only realizes the decomposition of the multi-channel time-varying complex signals of the rotor but also simultaneously extracts the instantaneous features of the multi-channel signals. In addition, it also realizes the description of the instantaneous vibration state of the RBS in the non-stationary process (such as startup and shutdown). Simulation experiments show that the framework is superior to other multi-channel signal processing methods in processing time-varying complex signals. The results based on field-measured signals show that the framework can guide the real-time analysis of the signals generated by rotating machinery, which improves the intuition of condition monitoring.

An algorithm for identifying reference signals under the environment of complex fuzzy sets

In this paper, we have discussed some new operations and results of set theory for complex fuzzy sets (CFSs). Moreover, we developed the basic results of CFSs under the basic operations such as complex fuzzy simple difference, bounded sum, bounded difference, dot product, bounded product, union, intersection, and Cartesian product. We explored the CFSs and discussed the related properties with examples such as complex fuzzy bounded sum over the intersection, complex fuzzy dot product over the union, etc. Identifying the reference signals under the environment of CFSs have always been a challenging. Many algorithms based on set theoretic operations and distance measures have been proposed for identifying a reference signal using any common system. But linear time invariant (LTI) system is considered easy to analyze the linear and time-varying signals. We used CFSs in signals and systems. We developed an algorithm based on convolution product and LTI system under the complex fuzzy environment. We identified a high degree of resemblance (reference signal) of the received signals to the reference signal in a linear time-invariant (LTI) system that receives an input signal and produces an output signal.

Earth orientation parameters prediction based on the hybrid SSA + LS + SVM model

The high-precision prediction of Earth orientation parameters (EOPs) is essential for astro-geodynamics, high-precision space navigation and positioning, on-board autonomous orbits determination and deep space exploration. However, the prediction accuracy of existing models is much lower than the estimation accuracy of geodetic technical solutions, which affects certain high-precision real-time users. To improve the prediction accuracy of EOP in short- and long-term period, we propose a hybrid model by combining the singular spectrum analysis (SSA), least squares (LSs) and support vector machine (SVM) in the study. Through SSA algorithm, the deterministic time-varying signal of EOP time series can be more precisely and reasonably detected and modeled. Based on the optimization theory, we reconstruct the EOP sequences using SSA and establish the LS extrapolation model based on the reconstructed series. Then, the residuals from SSA reconstruction and those from the LS model, are used for SVM training and prediction. The results of two-year prediction experiments based on the EOP 14 C04 series show that the proposed hybrid model has significant improvements in polar motion (PM) and length of day (LOD) for different prediction intervals (1–360 d) compared with the LS + autoregression (AR) model. The prediction error for x-component of polar motion (PMX) is reduced by 40.2%, 31.0% and 51.4% while that for y-component of polar motion (PMY) is 22.1%, 23.3% and 55.6% for prediction period of 30, 90 and 180 d respectively. For LOD, the maximum prediction improvement can reach to 53.8% during the predicted 360 d. In addition, the proposed method has better accuracy in mid- and long-term PM(x, y) predictions compared to the Bulletin A, with a 360 d prediction error of 27.273 and 21.741 mas.

Distributed reconstruction of time-varying graph signals via a modified Newton’s method

This paper develops a distributed reconstruction algorithm, that can be implemented efficiently, for time-varying graph signals. The reconstruction problem is formulated as an unconstrained optimization problem that minimizes the weighted sum of the data fidelity term and the regularization term. The regularizer used is the nonsmoothness measure of the temporal difference signal. The classical Newton’s method can be used to solve the optimization problem. However, computation of the Hessian matrix inverse is required, and this does not scale well with the graph size. Furthermore, a distributed implementation is not possible. An approximation to the inverse Hessian, that exploits the graph topology, is developed here. The resulting iterative algorithm can be implemented in a distributed manner, and scales well with the graph size. Convergence analysis of the algorithm is presented, which shows convergence to the global optimum. Numerical results, using both synthetic and real world datasets, will demonstrate the superiority of the proposed reconstruction algorithm over existing methods.