Time-frequency Plane Research Articles

Sinusoidal Fitting Decomposition for Instantaneous Characteristic Representation of Multi-Componential Signal.

The research on how to effectively extract the instantaneous characteristic components of non-stationary signals continues to be both a research hotspot and a very challenging topic. In this paper, a new method of multi-component decomposition is proposed to decompose a signal into finite mono-component signals and extract their Instantaneous Amplitude (IA), Instantaneous Phase (IP), and Instantaneous Frequency (IF), which is called Sinusoidal Fitting Decomposition (SFD). The proposed method can ensure that the IA extracted from the given signal must be positive, the IP is monotonically increasing, and the signal synthesized by both IA and IP must be mono-componential and smooth. It transforms the decomposition process into a synthesis iterative process and does not rely on any dictionary or basis function space or carry out the sifting operation. In addition, the proposed method can describe the instantaneous-frequency-amplitude characteristics of the signal very well on the time-frequency plane. The results of numerical simulation and the qualitative analysis of the amount of calculation show that the proposed method is effective.

Review on application of fractional Fourier transform in LinearFrequencyModulation signal and communication system

Traditional Fourier transform often apply to analyze and process stationary signals, however, it is weak for time-varying non-stationary signals, and fractional Fourier transform (FRFT) can better solve such problems. The FRFT can be comprehended as the expressive methods on the fractional Fourier domain constituted by the spinning coordinate axis of the signal anticlockwise about the origin at arbitrarily Angle in the time-frequency plane. In this paper, the improved fractional Fourier transform is combined with other calculation methods to achieve high precision estimation of chirp signal parameters. And the communication system built on weighted fractional Fourier transform and discrete fractional Fourier transform is studied and simulated respectively, which verifies the feasibility and improves the anti-jamming and anti-interception ability of the communication system.

Gabor Transform Associated with the Dunkl–Bessel Transform and Spectrograms

Time–frequency (or space–phase) analysis plays a key role in signal analysis. In particular, signals that have a very concentrated time–frequency content are of great importance. However, the uncertainty principle sets a limitation to the possible simultaneous concentration of a function and its Dunkl–Bessel transform. For this purpose, we introduce and study a new transformation called Dunkl–Bessel Gabor transform. For this transformation, we define the Toeplitz-type (or time–frequency localization) operators, in order to localize signals on the time–frequency plane. We study these operators; in particular, we give criteria for their boundedness and Schatten class properties. Then, using the special class of concentration operators, which are compact and self-adjoint, we show that their eigenfunctions are maximally time–frequency-concentrated in the region of interest.

Quantitative Assessment of Sand Particulates in Gas-Water Slug Flow Using Deep Learning

Summary The weak collision response excited by micrometer-scale sand particulates is prone to overmixing with strong slug noise, significantly reducing the characterization and monitoring accuracy of sand particulate information in slug flows. Therefore, we developed a quantitative assessment method for sand particulates in slug flow that combines triaxial vibration monitoring and deep learning. First, a migration behavior characterization method of sand particulates is proposed combining nonlinear statistics, multifrequency coherence, and multiscale time frequency. The multifrequency response characteristics corresponding to the multiscale flow behavior of the sand-carrying slug flow were successfully characterized on the 2D time-frequency plane, namely, the mixed sand migration behavior [Intrinsic Mode Function 1 (IMF1)], liquid slug sand carrying (IMF2), forward liquid film and Taylor bubble sand carrying (IMF3), and reflux liquid film sand carrying (IMF4). Furthermore, the influence mechanism of gas superficial velocity (1.5–3.5 m/s), liquid superficial velocity (0.95–2.14 m/s), and sand content (0–20 g) on the triaxial vibration response of slug particulate flow with different migration behaviors is elucidated. Finally, a convolutional neural network (CNN)-gated recurrent unit (GRU)-self-attention mechanism (SATT) model for sand content assessment is developed based on the characterized multiscale migration behavior information and achieves an average recognition accuracy of 95.55% for data sets representing different sand migration behaviors in slug flow. This provides a new method for precisely identifying and monitoring sand production information of multiphase pipe flow.

Properties of the Octonion Linear Canonical Transform

Abstract The linear canonical transform is a widely utilized integral transform in the field of signal analysis, characterized by three independent parameters. It not only facilitates rotation of the time-frequency plane but also enables expansion and contraction of the frequency domain, thereby playing a crucial role in handling non-stationary signals. In recent years, the linear canonical transform has been extended to octonion domains, which possess a more generalized form and offer greater research potential. This extension effectively harnesses the processing capabilities of the linear canonical transform for non-stationary signals in high-dimensional spaces. In this paper, we explore the definition and the conjugacy of the left side octonion linear canonical transform. Moreover, we thoroughly examine the differential properties of octonion linear canonical transform. The study of these properties is helpful for understanding the characteristics and applications of geometric transformations as well as expanding the scope of mathematical theory and practical applications.

Iterative local maximum synchrosqueezing-extracting transform

Recently, there has been significant interest in time-varying signal analysis. Multisynchrosqueezing transform (MSST) and improved multisynchrosqueezing transform (IMSST) have shown promise in overcoming the limitations of conventional methods. Although progress has been made, challenges still exist, such as the presence of non-reassigned time–frequency (TF) points and the presence of noise in the TF plane when processing noisy time-varying signals. In this paper, we introduce an innovative TF analysis method known as the iterative local maximum synchrosqueezing-extracting transform (ILMSSTSEO). First, the proposed method extracts the local maximum value of the instantaneous frequency (IF) during each iteration to eliminate non-reassigned TF points. Additionally, a synchroextracting operator is introduced unconventionally to enhance the concentration of TF energy and reduce noise in the TF representation. By doing so, the method effectively solves many challenges faced by existing methods and provides a new extraction framework for synchrosqueezing transform-based TF analysis methods.

Study on the detection of power line operation anomalies in the Hexi Corridor based on multi-scale filtering of BeiDou satellite signals

In the artificial intelligence detection of power line anomalies, the identification effect is determined by the positioning process of two-dimensional map, which is also a difficult point in this field Therefore, this paper proposes a method to detect the abnormal operation of power lines in Hexi Corridor based on multi-scale filtering of Beidou satellite signals. Multi-scale processing is carried out by wavelet transform to obtain multiple wavelet basis functions of different scales. On this basis, a two-dimensional time–frequency diagram is drawn according to the results of continuous wavelet transform. The adaptive multi-time frequency entropy method is selected to divide the two-dimensional time–frequency map into multiple layers and scales, and the adaptive multi-scale time–frequency entropy of the time–frequency plane is calculated. After smoothing the obtained power line position signal by S-G filtering method, the power line position signal of Hexi Corridor is obtained by GPS/ Beidou dual-mode satellite positioning system, and the positioning signal is optimized by using the positioning mechanism of multiple receiving stations. Realize the abnormal operation detection of power lines in Hexi Corridor. The experimental results show that this method can obtain more accurate positioning signals, and the geometric accuracy factor GDOP fluctuates in the range of 0 ∼ 2. The unsmooth signal can be effectively removed; The maximum error result of abnormal position detection is 1.22kn；; At the same time, the abnormal displacement section of the line can be determined.

The linear canonical W-transform

The time-frequency spectrum of seismic data is commonly used as an attribute in the analysis and interpretation of nonstationary seismic signals. To improve the capability of the W-transform to analyze nonstationary data, we introduce the linear canonical W-transform (LCWT) by implementing an affine matrix along with scaling parameters to generate high resolution and energy-concentrated time-frequency spectra. More features of nonstationary signals can be explored in the time-linear canonical frequency domain by transforming the time-frequency plane, which makes the algorithm more applicable to seismic signals. For the completeness of the LCWT, we also develop the inverse LCWT to extend its applications. Examples of synthetic and field seismic data show that a highly resolved and energy-concentrated time-frequency spectrum can be estimated with the LCWT with negligible additional computational burden. In addition, our algorithm is promising for several seismic data processing and interpretation techniques, such as reservoir characterization and thin layer identification.

Fault signature extraction of rolling bearings under variable speed via time–frequency overlap group sparse representation

The high-fidelity extraction of the nonperiodic fault transients of rolling bearings under variable speed is of significant importance, while still a challenge for early-stage fault diagnosis of major equipment such as aero engines and wind turbines. A method termed continuous symmetric Laplace wavelet transform (CSLWT) enhanced time–frequency overlap group sparse (OGS) representation is proposed in this paper. A symmetric Laplace mother wavelet function is proposed which could satisfy the admissibility condition of wavelet decomposition and reconstruction, upon which the CSLWT is fabricated and adopted as the sparse representation dictionary to match the nonperiodic fault transients. Since the decomposition coefficients of nonperiodic fault impulses via the CSLWT exhibit group sparsity on the time–frequency plane with unknown intervals, the time–frequency OGS model is adopted and then solved for extraction of the nonperiodic fault transients. Moreover, a data driven, multi-objective optimization strategy is presented for determining the hyper-parameters of the sparse model. The correlated kurtosis of angular envelope signal (CK-AE) and harmonic-to-noise energy ratio of the order spectrum (HNR-OS) are introduced as the optimization objectives, and the Pareto front is solved based on the NSGA-II algorithm, upon which the acceptable solutions set is chosen from the Pareto front, and the proper hyper-parameters are further determined via proposed normalized solutions distance density sorting of the acceptable solutions set. The performance of the proposed method is validated via processing both simulated and experimental vibration signals, as well as compared with some tradition fault diagnosis methods.

Refined linear chirplet transform for time–frequency analysis of non-stationary signals

Time-Frequency Analysis (TFA) stands as a pivotal technique for unraveling the inherent properties of signals, which are omnipresent across natural phenomena. Current methodologies encounter significant challenges in the analysis of non-stationary signals, especially those characterized by closely-spaced or intersecting instantaneous frequencies. In this study, we present the refined linear chirplet transform (RLCT), inspired by the concept of the generalized linear chirplet transform (GLCT), to derive the time–frequency representation of non-stationary signals. By increasing the number of chirp rate searches in GLCT, one can derive higher time–frequency concentration, however, this costs much higher computational resources. In the proposed RLCT, the capacity in searching the optimal chirp rates, or equivalently the rotation angles on the time–frequency plane, is dramatically improved by adopting a local search strategy for mono-component signals. As a sequence, the resolution for the multi-component signals, even with overlapping instantaneous frequency, is greatly enhanced by adopting the idea of the adaptive linear chirplet transform (ALCT), where the components with high energy concentration are consecutively detected and subtracted from consideration. Two critical metrics are employed to assess the performance (accuracy and resolution) of the TFA methods: total energy and energy ratio. The latter is defined as the proportion of energy within a narrowly defined frequency band centered around the actual instantaneous frequency, relative to the total energy. The validation examples demonstrate that the LCT-based methods dramatically enhance the accuracy compared to short-time Fourier transform, in terms of total energy. Furthermore, among the LCT family investigated, the proposed method offers marked improvements in resolution, in terms of energy ratio, while maintaining algorithmic simplicity. The seismic responses of a lighthouse during a severe earthquake are investigated by the RLCT to reveal its frequency drop and recovery due to the opening and closing of the existing cracks.

A Multidimensional Health Indicator Based on Autoregressive Power Spectral Density for Machine Condition Monitoring.

Condition monitoring (CM) is the basis of prognostics and health management (PHM), which is gaining more and more importance in the industrial world. CM, which refers to the tracking of industrial equipment's state of health during operations, plays, in fact, a significant role in the reliability, safety, and efficiency of industrial operations. This paper proposes a data-driven CM approach based on the autoregressive (AR) modeling of the acquired sensor data and their analysis within frequency subbands. The number and size of the bands are determined with negligible human intervention, analyzing only the time-frequency representation of the signal of interest under normal system operating conditions. In particular, the approach exploits the synchrosqueezing transform to improve the signal energy distribution in the time-frequency plane, defining a multidimensional health indicator built on the basis of the AR power spectral density and the symmetric Itakura-Saito spectral distance. The described health indicator proved capable of detecting changes in the signal spectrum due to the occurrence of faults. After the initial definition of the bands and the calculation of the characteristics of the nominal AR spectrum, the procedure requires no further intervention and can be used for online condition monitoring and fault diagnosis. Since it is based on the comparison of spectra under different operating conditions, its applicability depends neither on the nature of the acquired signal nor on a specific system to be monitored. As an example, the effectiveness of the proposed method was favorably tested using real data available in the Case Western Reserve University (CWRU) Bearing Data Center, a widely known and used benchmark.

A metaplectic perspective of uncertainty principles in the linear canonical transform domain

We derive Heisenberg uncertainty principles for pairs of Linear Canonical Transforms of a given function, by resorting to the fact that these transforms are just metaplectic operators associated with free symplectic matrices. The results obtained synthesize and generalize previous results found in the literature, because they apply to all signals, in arbitrary dimension and any metaplectic operator (which includes Linear Canonical Transforms as particular cases). Moreover, we also obtain a generalization of the Robertson-Schrödinger uncertainty principle for Linear Canonical Transforms. We also propose a new quadratic phase-space distribution, which represents a signal along two intermediate directions in the time-frequency plane. The marginal distributions are always non-negative and permit a simple interpretation in terms of the Radon transform. We also give a geometric interpretation of this quadratic phase-space representation as a Wigner distribution obtained upon Weyl quantization on a non-standard symplectic vector space. Finally, we derive the multidimensional version of the Hardy uncertainty principle for metaplectic operators and the Paley-Wiener theorem for Linear Canonical Transforms.

Deep learning based event reconstruction for cyclotron radiation emission spectroscopy

The objective of the cyclotron radiation emission spectroscopy (CRES) technology is to build precise particle energy spectra. This is achieved by identifying the start frequencies of charged particle trajectories which, when exposed to an external magnetic field, leave semi-linear profiles (called tracks) in the time–frequency plane. Due to the need for excellent instrumental energy resolution in application, highly efficient and accurate track reconstruction methods are desired. Deep learning convolutional neural networks (CNNs) - particularly suited to deal with information-sparse data and which offer precise foreground localization—may be utilized to extract track properties from measured CRES signals (called events) with relative computational ease. In this work, we develop a novel machine learning based model which operates a CNN and a support vector machine in tandem to perform this reconstruction. A primary application of our method is shown on simulated CRES signals which mimic those of the Project 8 experiment—a novel effort to extract the unknown absolute neutrino mass value from a precise measurement of tritium β −-decay energy spectrum. When compared to a point-clustering based technique used as a baseline, we show a relative gain of 24.1% in event reconstruction efficiency and comparable performance in accuracy of track parameter reconstruction.

Investigating Fire–Atmosphere Interaction in a Forest Canopy Using Wavelets

Wildland fire–atmosphere interaction generates complex turbulence patterns, organized across multiple scales, which inform fire-spread behaviour, firebrand transport, and smoke dispersion. Here, we utilize wavelet-based techniques to explore the characteristic temporal scales associated with coherent patterns in the measured temperature and the turbulent fluxes during a prescribed wind-driven (heading) surface fire beneath a forest canopy. We use temperature and velocity measurements from tower-mounted sonic anemometers at multiple heights. Patterns in the wavelet-based energy density of the measured temperature plotted on a time–frequency plane indicate the presence of fire-modulated ramp–cliff structures in the low-to-mid-frequency band (0.01–0.33 Hz), with mean ramp durations approximately 20% shorter and ramp slopes that are an order of magnitude higher compared to no-fire conditions. We then investigate heat- and momentum-flux events near the canopy top through a cross-wavelet coherence analysis. Briefly before the fire-front arrives at the tower base, momentum-flux events are relatively suppressed and turbulent fluxes are chiefly thermally-driven near the canopy top, owing to the tilting of the flame in the direction of the wind. Fire-induced heat-flux events comprising warm updrafts and cool downdrafts are coherent down to periods of a second, whereas ambient heat-flux events operate mainly at higher periods (above 17 s). Later, when the strongest temperature fluctuations are recorded near the surface, fire-induced heat-flux events occur intermittently at shorter scales and cool sweeps start being seen for periods ranging from 8 to 35 s near the canopy top, suggesting a diminishing influence of the flame and increasing background atmospheric variability thereat. The improved understanding of the characteristic time scales associated with fire-induced turbulence features, as the fire-front evolves, will help develop more reliable fire behaviour and scalar transport models.

Robust speed estimation for a moving harmonic acoustic source with a single stationary sensor.

A noise-insensitive cost function was developed for estimating the speed of harmonic acoustic sources in uniform linear motion. This function weighs and integrates the energy distribution of received tones in the time-frequency plane to enhance the robustness of parameter estimation under low signal-to-noise ratio conditions, where weight values are intentionally combined with the law of observed instantaneous frequency. As the cost function is differentiable, the procedure of parameter estimations also has high computing efficiency. Processing data of SWellEx-96 experiments with real ocean noise confirmed the anti-noise capabilities of this cost function to conventional processing methods.

Fast adaptive time-varying window length STFT for compound track short-wave defects identification

Track short-wave defect, as a common defect of railway tracks, can cause dynamic response on both vehicle and its components and thus severely affect the stability and safety of running vehicle. The vibration signal, collected by an accelerator mounted on the axle box of vehicle, is a kind of vehicle dynamic response signal. It consists of complex periodic and impact signal components, which poses challenges for track short-wave defects identification. In this paper, the forms and features of vibration signal of vehicle dynamic response are analyzed at first. Then, based on short-time Fourier transform (STFT), a fast adaptive time-varying window length STFT (FATW-STFT) is developed for compound track short-wave defect analysis. Specifically, by quickly calculating a series of time-frequency planes with various window length, modified kurtosis, boundary function, and Rényi entropy are introduced to sift the time-frequency planes and optimize the window lengths at each time point. Unlike other STFT-based methods, FATW-STFT uses fully adaptive window length optimization to distinguish both periodic and impactive signal components, which helps to detect multiform track short-wave defects such as corrugation and impact of welded joint. Both the simulated and measured results indicate that the proposed approach can rapidly and effectively identify the compound track short-wave defects and possesses potential prospect of practical applications.

ADAMS Simulation and HHT Feature Extraction Method for Bearing Faults of Coal Shearer

Aiming at the problem of difficult fault diagnosis work caused by the difficulty of data acquisition of the bearing in the traction part of a coal mining machine, a method of ADAMS simulation and HHT feature extraction of the bearing fault of a coal mining machine is proposed. First of all, take the traction section bearing as the research object, use the virtual prototype in the establishment of the healthy state of coal mining machine traction section model based on the establishment of the bearing inner ring fault, rolling body fault, outer ring fault of the coal mining machine traction section dynamics model, and then after the EMD decomposition, each IMF component of the Hilbert transform, to obtain the signal in the time-frequency plane of the time-frequency joint characteristics, to get the HHT marginal spectra and to different Under different working conditions, the bearing vibration signal features are mined by quantitative feature extraction. Finally, a variety of mainstream machine learning algorithms are introduced to classify the features, and the results show that the feature extraction method in this paper is universal and provides valuable theoretical support and technical guidance for the field application of coal mining machine-bearing fault diagnosis.

УСУНЕННЯ ЗАВАД У ДИНАМІЧНИХ СПЕКТРАХ ЗА НАЯВНОСТІ ПОТУЖНОГО СИГНАЛУ ЧАСТИНА 1. ПОТУЖНІ ШИРОКОСМУГОВІ ІМПУЛЬСИ ТА ЛІНІЙНО ЧАСТОТНО-МОДУЛЬОВАНІ ЗАВАДИ

Subject and Purpose. The writers aim at developing and testing a new method of interference mitigation, proceeding from the example of radio emissions from Jupiter. Its effectiveness is compared with the results of other workers, equally relating to the case of a significant overlapping, within the time-frequency window under analysis, of the areas occupied by the useful signal and the interference. Methods and Methodology. The analysis has revealed several fundamental limitations associated with the use of standard statis- tical methods for identifying sources of interference. A new approach is proposed that allows separating useful signals from inter- ference in the time-frequency plane. It is based on the idea of transferring the statistical analysis from the space of signal amplitudes to such of linear patterns which are formed by maximal readings while the spectrograms are being scanned in time, frequency or otherwise. Results. Methods of statistical data processing have been suggested which allow analysis of signals of a variety of power lev- els against the background of interference of comparable intensity. This enables a detailed analysis of the time-frequency patterns demonstrated by signals with a broad range of parameter variations. The algorithms developed demonstrate stability against changes in the interference background conditions that may be caused either by human activity or by natural factors, such as, e.g. ionospheric perturbations, changes in the frontend frequency response of a receiver resulting from a changed antenna beam orientation, or else from Faraday’s polarization plane rotation in the radio emission being received. Conclusions. The necessity of creating new interference mitigation techniques is stipulated both by worsening of the general level of interference at radio frequencies, and by the growth of complexity in the sporadically emerging time-frequency patterns that result from the improved time and frequency resolutions in the course of signal reception. A significant progress has been achieved, owing exclusively to the fundamental modifications of the signal processing algorithms that are based on varying the direction of analysis in the time-frequency plane.

Generalized adaptive singular spectrum decomposition and its application in fault diagnosis of rotating machinery under varying speed

Rotating machinery fault signals often consist of multiple components with time varying frequencies under variable speed conditions. Spectral overlap exists among these components, making it difficult to independently separate the features of the components. Singular spectrum decomposition (SSD), a singular spectrum analysis-based signal decomposition method, has shown its great potential in suppressing background noise and extracting fault-related components in complex background noise environments. However, SSD is a frequency domain decomposition method with equivalent filtering characteristics, and it is susceptible to the mode mixing when processing signals with spectral overlap. Moreover, the choice of a key parameter in the iteration decomposition process of SSD, the embedding dimension, is determined using an empirical formula, which might cause suboptimal decomposition outcomes. To address these issues, this paper proposes a generalized adaptive singular spectrum decomposition (GASSD) method, which combines generalized demodulation with improved embedding dimension selection for SSD. GASSD incorporates SSD into the framework of adaptive generalized demodulation to separate specific frequency domain features. Firstly, for an effective generalized demodulation analysis, a region block synchronous ridge extraction method is proposed to accurately estimate the instantaneous frequency ridges from the time-frequency plane, which helps construct proper demodulation phase functions. Secondly, to achieve optimal analysis of SSD, a Gini moderation decomposition index is designed to improve the construction of the trajectory matrix by determining an appropriate embedding dimension. Finally, the reliability of the proposed method is demonstrated by analyzing wind turbine generator bearing fault signals and rotor rubbing fault signals.

Sharp detection of oscillation packets in rich time-frequency representations of neural signals.

Brain oscillations most often occur in bursts, called oscillation packets, which span a finite extent in time and frequency. Recent studies have shown that these packets portray a much more dynamic picture of synchronization and transient communication between sites than previously thought. To understand their nature and statistical properties, techniques are needed to objectively detect oscillation packets and to quantify their temporal and frequency extent, as well as their magnitude. There are various methods to detect bursts of oscillations. The simplest ones divide the signal into band limited sub-components, quantifying the strength of the resulting components. These methods cannot by themselves cope with broadband transients that look like genuine oscillations when restricted to a narrow band. The most successful detection methods rely on time-frequency representations, which can readily show broadband transients and harmonics. However, the performance of such methods is conditioned by the ability of the representation to localize packets simultaneously in time and frequency, and by the capabilities of packet detection techniques, whose current state of the art is limited to extraction of bounding boxes. Here, we focus on the second problem, introducing two detection methods that use concepts derived from clustering and topographic prominence. These methods are able to delineate the packets' precise contour in the time-frequency plane. We validate the new approaches using both synthetic and real data recorded in humans and animals and rely on a super-resolution time-frequency representation, namely the superlets, as input to the detection algorithms. In addition, we define robust tests for benchmarking and compare the new methods to previous techniques. Results indicate that the two methods we introduce shine in low signal-to-noise ratio conditions, where they only miss a fraction of packets undetected by previous methods. Finally, algorithms that delineate precisely the border of spectral features and their subcomponents offer far more valuable information than simple rectangular bounding boxes (time and frequency span) and can provide a solid foundation to investigate neural oscillations' dynamics.