Joint Time-frequency Analysis Research Articles

Optical Time-Mapped Spectrograms (II): Fractional Talbot Designs

Real-time implementations of joint time-frequency analysis over instantaneous bandwidths above the GHz range remain challenging. In a companion paper, we have proposed an analog photonic processing scheme that enables computing a short-time Fourier transform (STFT), or spectrogram (SP), of an incoming arbitrary broadband signal, over tens-of-GHz analysis bandwidths, in a continuous, gapless and real-time manner. The proposed method involves a temporal sampling of the signal under test (SUT) with a periodic train of interfering, linearly chirped optical pulses followed by group-velocity dispersion to map the spectra of consecutive and overlapping truncated sections of the SUT along the time domain. This scheme offers a notable design versatility to customize the performance specifications of the computed SP, but it generally involves a sub-optimal non-uniform sampling of the SUT and it requires the use of a bulky and expensive pulsed optical source. In this communication, we show that this previous general scheme can be easily configured to ensure an optimal, uniform sampling of the SUT by simply setting the involved dispersive lines to satisfy a fractional self-imaging condition, while keeping all the advantages (e.g., design versatility) of the original scheme. Moreover, the resulting design is further adapted to entirely avoid the need for a pulsed source, using instead a more efficient and simpler phase-only temporal sampling of the SUT, e.g., implemented through electro-optic phase modulation. We derive the design conditions and performance trade-offs of the proposed time-mapped STFT schemes based on dispersion-induced fractional Talbot self-imaging. Through numerical simulations and experimental demonstration, we confirm the potential of this simple and efficient approach for real-time SP analysis of arbitrary signals over instantaneous bandwidths above a few tens of GHz, with MHz frequency resolutions and ultrahigh processing speeds, approaching billions of FTs per second.

Multi-Featured Sea Ice Classification with SAR Image Based on Convolutional Neural Network

Sea ice is a significant factor in influencing environmental change on Earth. Monitoring sea ice is of major importance, and one of the main objectives of this monitoring is sea ice classification. Currently, synthetic aperture radar (SAR) data are primarily used for sea ice classification, with a single polarization band or simple combinations of polarization bands being common choices. While much of the current research has focused on optimizing network structures to achieve high classification accuracy, which requires substantial training resources, we aim to extract more information from the SAR data for classification. Therefore we propose a multi-featured SAR sea ice classification method that combines polarization features calculated by polarization decomposition and spectrogram features calculated by joint time-frequency analysis (JTFA). We built a convolutional neural network (CNN) structure for learning the multi-features of sea ice, which combines spatial features and physical properties, including polarization and spectrogram features of sea ice. In this paper, we utilized ALOS PALSAR SLC data with HH, HV, VH, and VV, four types of polarization for the multi-featured sea ice classification method. We divided the sea ice into new ice (NI), first-year ice (FI), old ice (OI), deformed ice (DI), and open water (OW). Then, the accuracy calculation by confusion matrix and comparative analysis were carried out. Our experimental results demonstrate that the multi-feature method proposed in this paper can achieve high accuracy with a smaller data volume and computational effort. In the four scenes selected for validation, the overall accuracy could reach 95%, 91%, 96%, and 95%, respectively, which represents a significant improvement compared to the single-feature sea ice classification method.

Multi-Scale Response Analysis and Displacement Prediction of Landslides Using Deep Learning with JTFA: A Case Study in the Three Gorges Reservoir, China

Reservoir water and rainfall, leading to fluctuations groundwater levels, are the main triggering factors that induce landslides in the Three Gorges Reservoir area. This study investigates the response mechanism of landslide deformation under reservoir water and rainfall variations through long-time on-site observations. To address the non-stationary characteristics of the time-series records, joint time-frequency analysis (JTFA) is first introduced into our landslide prediction model. This model employs optimal variational mode decomposition (VMD) to obtain specific signal components with clear physical meaning, such as trend component and periodic components. Then, multi-scale response analysis between the displacement and external factors three wavelet methods was conducted. The analysis results show a 1 year primary cycle of the time series associated with the landslide evolution. The reservoir water level and rainfall show anti-phase fluctuations. The periodic displacement correlates significantly with rainfall, lagging by about two months. The reservoir water is anti-phase with the landslide displacement, preceding it by approximately three months (−51 ± 8° phase difference). For landslide displacement prediction, the gated recurrent units (GRU) neural network model is integrated into the deep learning forecasting architecture. The model takes into account the correlation and hysteresis effect of input variables. Through six experiments, we investigate the effect of data volume on model predictions to determine the optimal model. The results demonstrate that our proposed model ensures high performance in landslide prediction. Moreover, a comparison with six other intelligent algorithms shows the advantages of our model in terms of time-effectiveness and long-sequence forecasting.

Model reduction of fractional impedance spectra for time–frequency analysis of batteries, fuel cells, and supercapacitors

AbstractJoint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells, batteries, and supercapacitors. To increase the reliability of time–frequency analysis, a theoretical correlation between frequency‐domain stationary analysis and time‐domain transient analysis is urgently required. The present work formularizes a thorough model reduction of fractional impedance spectra for electrochemical energy devices involving not only the model reduction from fractional‐order models to integer‐order models and from high‐ to low‐order RC circuits but also insight into the evolution of the characteristic time constants during the whole reduction process. The following work has been carried out: (i) the model‐reduction theory is addressed for typical Warburg elements and RC circuits based on the continued fraction expansion theory and the response error minimization technique, respectively; (ii) the order effect on the model reduction of typical Warburg elements is quantitatively evaluated by time–frequency analysis; (iii) the results of time–frequency analysis are confirmed to be useful to determine the reduction order in terms of the kinetic information needed to be captured; and (iv) the results of time–frequency analysis are validated for the model reduction of fractional impedance spectra for lithium‐ion batteries, supercapacitors, and solid oxide fuel cells. In turn, the numerical validation has demonstrated the powerful function of the joint time–frequency analysis. The thorough model reduction of fractional impedance spectra addressed in the present work not only clarifies the relationship between time‐domain transient analysis and frequency‐domain stationary analysis but also enhances the reliability of the joint time–frequency analysis for electrochemical energy devices.

A New Signal Processing Method Based on Notch Filtering and Wavelet Denoising in Wire Rope Inspection

Wire rope is a necessary tool in practical applications especially in crane, elevator and bridge construction, which plays an important role in the national economy and daily life, and safety inspection for wire rope is the key to ensure people’s life and property. However, detection signals are usually complicated due to the twining structures, which make the wire rope defect signal and strand signal mix together. What’s more, no reports and studies have appeared to solve this problem. In view of the situation and challenges above, this paper proposes a combined signal processing method based on notch filtering and wavelet denoising to process detected wire rope signals. Basic time domain, frequency domain and joint time–frequency analysis are first conducted, thereafter, conventional signal processing methods such as low-pass filtering and adaptive analysis are presented according to the signal characterizations. These comparisons and results demonstrate that a conventional single method is incapable of wire-rope-detection signal identification and differentiation. Nonetheless, after the notch filter design and calculation, the processing results for the typical wire rope inspection signals in the experiments indicate that the combined methods can not only distinguish steel wire rope defect signal and strand signal effectively but also with high detection accuracy, even for the inner defect. Finally, the feasibility and reliability are verified by a series of signal processing results and comparisons, which demonstrate that this new method has great application potential and is of vital significance to the development of wire rope safety inspection.

A Review on the Applications of Time-Frequency Methods in ECG Analysis

The joint time-frequency analysis method represents a signal in both time and frequency. Thus, it provides more information compared to other one-dimensional methods. Several researchers recently used time-frequency methods such as the wavelet transform, short-time Fourier transform, empirical mode decomposition and reported impressive results in various electrophysiological studies. The current review provides comprehensive knowledge about different time-frequency methods and their applications in various ECG-based analyses. Typical applications include ECG signal denoising, arrhythmia detection, sleep apnea detection, biometric identification, emotion detection, and driver drowsiness detection. The paper also discusses the limitations of these methods. The review will form a reference for future researchers willing to conduct research in the same field.

Automatic Detection of Subglacial Water Bodies in the AGAP Region, East Antarctica, Based on Short-Time Fourier Transform

Subglacial water bodies are critical components in analyzing the instability of the Antarctic ice sheet. Their detection and identification normally rely on geophysical and remote sensing methods such as airborne radar echo sounding (RES), ground seismic, and satellite/airborne altimetry and gravity surveys. In particular, RES surveys are able to detect basal terrain with a relatively high accuracy that can assist with the mapping of subglacial hydrology systems. Traditional RES processing methods for the identification of subglacial water bodies mostly rely on their brightness in radargrams and hydraulic flatness. In this study, we propose an automatic method with the main objective to differentiate the basal materials by quantitatively evaluating the shape of the A-scope waveform near the basal interface in RES radargrams, which has been seldom investigated. We develop an automatic algorithm mainly based on the traditional short-time Fourier transform (STFT) to quantify the shape of the A-scope waveform in radargrams. Specifically, with an appropriate window width applied on the main peak of each A-scope waveform in the RES radargram, STFT shows distinct and contrasting frequency responses at the ice-water interface and ice-rock interface, which is largely dependent upon their different reflection characteristics at the basal interface. We apply this method on 882 RES radargrams collected in the Antarctic’s Gamburtsev Province (AGAP) in East Antarctica. There are 8822 identified A-scopes with the calculated detection value larger than the set threshold, out of the overall 1,515,065 valid A-scopes in these 882 RES radargrams. Although these identified A-scopes only takes 0.58% of the overall A-scope population, they show exceptionally continuous distribution to represent the subglacial water bodies. Through a comprehensive comparison with existing inventories of subglacial lakes, we successfully verify the validity and advantages of our method in identifying subglacial water bodies using the detection probability for other basal materials of theoretically the highest along-track resolution. The frequency signature obtained by the proposed joint time–frequency analysis provides a new corridor of investigation that can be further expanded to multivariable deep learning approaches for subglacial and englacial material characterization, as well as subglacial hydrology mapping.

Joint time-frequency analysis on space-time-coding digital metasurfaces

Space-time and time-varying metastructures have attracted a lot of research interest in recent years. On the other hand, digital programmable metasurfaces have also gained great attention owing to their powerful capabilities in controlling electromagnetic (EM) fields and waves in real time, which is very suitable for implementing spatiotemporal modulations in a digital manner. Accordingly, space-time-coding (STC) digital metasurfaces have recently been proposed to realize advanced manipulations of EM wavefronts and digital information, allowing simultaneous control of propagation directions in the space domain and harmonic distributions in the frequency domain. However, their instantaneous responses and the connection between the time- and frequency-domain characteristics have not yet been fully revealed. Here, we present a joint time-frequency analysis method to revisit STC digital metasurfaces, in which the time-domain instantaneous scattering patterns and frequency-domain equivalent excitations are investigated to analyze the spatial-spectral distributions of the modulated waves. This joint time-frequency analysis method helps to better explain the basic working principle of STC digital metasurfaces and is expected to facilitate more applications in wireless communications, radar, imaging, and beamforming.

Underwater variable frequency vibrating dipole detection of artificial lateral line based on the joint time-frequency analysis

Inspired by the lateral line system (LLS) of fish, an underwater pressure sensor array, aka, artificial lateral line system (ALLS) was proposed for underwater perception. The Fourier transform (FT) was the most widely used method to extract features from the ALLS signals. However, the FT lost efficacy when the vibrating condition of the dipole such as frequency varied over time. To overcome this problem, four joint time-frequency analysis (JTFA) methods were employed to transform the original pressure signal into the frequency domain and time domain. The short-time Fourier transform (STFT) and wavelet transform (WT) showed better performance in the dipole vibrating frequency evaluation. Later, the results of JTFA were input into a convolutional neural network (CNN) model to identify the motion pattern and position of the dipole. In this paper, different frequency rise/drop duration represented different motion patterns of variable frequency dipole. The position of the dipole indicated the coordinate of the dipole relative to the ALLS. The experiment result showed that the identification result of dipole motion pattern and position could reach 99.93 % and 2.134 mm respectively. Lastly, the ALLS pressure signals were discussed under the external flow and multiple dipole targets based on the tank experiment and computational fluid dynamics (CFD) simulation. The pressure drifting generated by the external flow was affected by both the flow velocity and the water depth variation. The distinction between JTFA results of different ALLS sensors exhibited correspondence with the state of multiple dipoles. The underwater feature extraction method of ALLS signal based on the JTFA proposed in this paper showed a promising way in the perception of the target in more challenging motion states.

Numerical investigations on the beating behavior of self-excited combustion instability in a hydrogen-fueled Rijke type combustor

Beating, a specific oscillation mode of combustion instability, occurred in a premixed hydrogen fueled Rijke tube was investigated. A two-dimensional transient numerical model for the self-excited combustion instability was developed and well validated. In a beating cycle, the amplitude of pressure oscillations increased to 1400 Pa and then decreased to 70 Pa, exhibiting an obvious feature of low frequency modulation. The joint time-frequency analysis showed that the dominant frequency shifted from 230 Hz to 330 Hz over time at each cycle. To shed lights on the inherent mechanisms of beating instability, the coupling processes between the combustion and flow dynamics were investigated. At each beating cycle, the shapes of flame were relatively stable in growing stage, while strongly fluctuated in transition stage and recovered to stable state in decaying stage. Notably, due to the large amplitude of pressure oscillations, an obvious recirculation zone was formed around the flame and sucked the high temperature exhausted gas to the flame root during the transition stage. Accordingly, the high temperature area was formed around the flame and affected the oscillation mode. By employing the proper orthogonal decomposition analysis, the apparent oscillations at 1 Hz were observed in the modes of heat release rate, velocity vectors and temperature. Later, it was found that with the increase of the amplitude of pressure oscillations, the mass flow rate of air supply at tube inlet dramatically decreased, which reduced the oxygen around the flame and changed the fluctuation mode of heat release rate. The coupling process was also identified by the phase difference and Rayleigh index.

Research and Implementation of Emotional Classification of Traditional Folk Songs Based on Joint Time-Frequency Analysis

Traditional folk music is built on traditional folk songs. The five types of emotions of patriotism, homesickness, affection, friendship, and love are all depicted in modern Chinese folk songs, which show the rich and colorful emotions of people of all ethnic groups in China. Modern Chinese folk songs that express these emotions have a variety of artistic features in terms of melody, rhythm, mode, and mood and provide the audience with unique aesthetic experiences. This paper focuses on JTFA- (Joint Time-Frequency Analysis-) based emotional classification of traditional folk songs, as well as PCA (principal component analysis) and KPCA (Kernel-Based Principle Component Analysis) methods for nonstationary signal feature dimension reduction. The simulation results show that the number of features in KPCA is less than in PCA for the same accuracy. When the number of features is equal to the number of principal components, the accuracy is higher than PCA, indicating that KPCA has a better effect in dimension reduction and feature extraction. Furthermore, in all categories, the double-layer classification model maintains a relatively high recall rate and accuracy rate, demonstrating the effectiveness of the double-layer multimusic emotion classification model.

Lifetime assessment of porous journal bearings using joint time-frequency analysis of real-time sensor data

In this work, we employed a custom-built tribometer that allows simultaneous testing of five porous journal bearing systems to perform lifetime tests on combinations of bearing materials and lubricants at various temperatures. Test parameters and contact conditions were tailored to promote mixed/boundary lubrication and accelerated wear tests. Failure and wear data were evaluated ex-post, leading to survival probability curves based on Weibull fitting that allow quantitative ranking of bearing life as well as qualitative assessment of the failure behavior. Friction torque and accelerometer data were recorded either continuously or at regular time intervals, with the potential for on-the-fly evaluation. Using joint time-frequency analysis, we produced spectograms of the accelerometer data, which can characterize the state of operation and allow a clear disambiguation of the running-in phase, steady-state behavior, and critical operation before failure.

Joint time-frequency analysis and non-linear estimation for fetal ECG extraction

This paper proposes a novel algorithm based on joint time–frequency analysis for extracting the fetal ECG using single-channel abdominal ECG. Stockwell transform is the time–frequency tool used in combination with Shannon Energy Entropy for identifying the maternal peaks. The single maternal beat is constructed as a Maximum likelihood estimator. The abdominal ECG free from the maternal component is again processed using S-transform to identify the fetal peaks. Masking and thresholding is done in the time–frequency domain to eliminate the high frequency and background noises. Inverse Stockwell transform combined with proposed region selective amplitude scaling (RSAS) is performed to denoise the FECG. Identifying maternal and fetal peaks in the time–frequency domain enables higher performance even in overlapping beats and further avoids the need for an explicit pre-processing approach. The proposed algorithm's performance is validated using Daisy database, Physionet Challenge 2013 Set-a dataset (PCDB), and Abdominal direct fetal ECG database (ABDFECGDB). Further to validate the consistency of proposed algorithm’s performance, results obtained using real-time recordings acquired using Powerlab data acquisition hardware and data from Non-Invasive Fetal ECG Arrhythmia Database are included. The obtained results show the proposed algorithm's superiority with97.37% of accuracy, 98.61% of sensitivity,98.72% of positive predictive value, and98.67% of F1 measure using PCDB database and 98.55% of accuracy, 99.16% of sensitivity,99.38% of positive predictive value, and99.27% of F1 measure using ABDFECGDB.Further, the algorithm shows consistent results using real-time data and arrhythmia dataset.

SISO Radar-Based Human Movement Direction Determination Using Micro-Doppler Signatures

Human movement direction determination (HMDD) is a significant task in human detection and recognition applications, but it remains a challenge when utilizing single-input and single-output (SISO) radar because angle information cannot be accessed without multiple receiving antennas. Moreover, adopting multiple-output radar systems for this task would limit their applicability in a broader range of scenarios, as these systems require a larger placement area and a more extensive calibration procedure than SISO radar. Tackling this problem, this paper presents an effective method for the SISO-radar-based human movement direction determination task. Our method combines the joint time-frequency analysis (JTFA) technique with a proposed bio-inspired feature extraction process, thereby producing an accurate perception of moving direction based on the analysis of micro-Doppler signatures. The radar simulation and measurements are separately conducted and used to establish the corresponding dataset, so the superior performance of our method could be verified on the HMDD task. Furthermore, this article delves into why existing criteria for evaluating an HMDD model’s performance are insufficient in multi-direction situations, followed by an introduction of “small error concentration" and “omnidirectional error uniformity", as well as their evaluation protocols, to describe and measure the bias of an HMDD model’s results on multi-direction determination problems. By comparing with existing both traditional and deep-learning methods, we confirm our method’s superior in the HMDD task, and we believe that our research will aid in the advancement of human detection and recognition applications using SISO radar.

Vibration-based terrain classification recognition using a six-axis accelerometer

Aging is a key problem in our daily life which demands more technology such as the terrain classification recognition for the detailed path planning. In this article, a six-axis accelerometer was placed on the base of a walking stick to capture walking gait vibration information. The signal features in the collected information were used to reflect the terrain. We used a matching tracking method to decompose the signal data into linear combinations of Gabor atoms and a joint time-frequency analysis method to perform analysis on the topographic features in a three-dimensional space. Three types of terrains were classified from space-time data. Results show that the proposed algorithm could achieve an average accuracy rate of 88.6%, which is 4% higher than conventional methods.

Nonlinear dynamics of a self-mixing thin-slice solid-state laser subjected to Doppler-shifted optical feedback.

Chaotic oscillations of a linearly polarized single longitudinal-mode thin-slice Nd:GdVO_{4} laser placed in a self-mixing laser Doppler velocity scheme were dynamically characterized in terms of the intensity probability distribution, joint time-frequency analysis, and short-term Fourier transformation of temporal evolutions, and the degree of disorder in the amplitude and phase of the long-term temporal evolutions. The transition from chaotic relaxation oscillations (ROs) to chaotic spiking oscillations (SOs) was explored via the chaotic itinerancy (CI) regime by increasing the feedback ratio toward the laser from a rotating scattering object. The intensity probability distribution was found to change from an exponential decay in the RO regime to an inverse power law in the SO regime, which manifests itself in self-organized critical behavior, while stochastic subharmonic frequency locking among the two periodicities of RO and SO takes place in the CI regime featuring quantum-noise (spontaneous-emission)-induced order in the amplitude and phase of the spiking oscillations. All of the experimental results were reproduced by numerical simulations of a model equation of a single-mode self-mixing solid-state laser subjected to Doppler-shifted optical feedback from a rotating scattering object.

A Diagnostic Strategy via Multiresolution Synchrosqueezing Transform on Obsessive Compulsive Disorder.

This research presents a new method for detecting obsessive-compulsive disorder (OCD) based on time-frequency analysis of multi-channel electroencephalogram (EEG) signals using the multi-variate synchrosqueezing transform (MSST). With the evolution of multi-channel sensor implementations, the employment of multi-channel techniques for the extraction of features arising from multi-channel dependency and mono-channel characteristics has become common. MSST has recently been proposed as a method for modeling the combined oscillatory mechanisms of multi-channel signals. It makes use of the concepts of instantaneous frequency (IF) and bandwidth. Electrophysiological data, like other nonstationary signals, necessitates both joint time-frequency analysis and independent time and frequency domain studies. The usefulness and effectiveness of a multi-variate, wavelet-based synchrosqueezing algorithm paired with a band extraction method are tested using electroencephalography data obtained from OCD patients and control groups in this research. The proposed methodology yields substantial results when analyzing differences between patient and control groups.

Analysis and Research on Radar Gesture Micro-motion Feature Extraction Method

Radar gesture recognition technology is widely used in daily life, and the micro motion feature is the key information to distinguish the feature quantity of different gestures. The extraction of micro motion feature is the key step of radar gesture recognition. Joint time-frequency analysis is a common method for radar signal micro motion feature extraction. Firstly, this paper makes a theoretical analysis of the common joint time-frequency analysis methods; Then radar gesture model is completed, and the performance of different JTFA is compared by extracting the time-frequency features of the motion gesture echo; Finally, the measured data are collected under the condition of microwave anechoic chamber. After analysis, the theoretical simulation results are consistent with the measured data, which verifies the reliability of the simulation.

Parametric Decomposition of Pulsed Lidar Signals with Noise Corruption Using FRFT Spectrum Analysis

The parametric decomposition of full-waveform Lidar data is challenging when faced with heavy noise scenarios. In this paper, we report a fractional Fourier transform (FRFT)-based approach for accurate parametric decomposition of pulsed Lidar signals with noise corruption. In comparison with other joint time-frequency analysis (JTFA) techniques, FRFT is found to present a one-dimensional Lidar signal by a particular two-dimensional spectrum, which can exhibit the mathematical distribution of the multiple components in Lidar signals even with a heavy noise interference. A FRFT spectrum-processing solution with histogram clustering and moving LSM fitting is designed to extract the amplitude, time offset, and pulse width contained in the mathematical distribution. Extensive experimental results demonstrate that the proposed FRFT spectrum analysis method can remarkably outperform the conventional Levenberg–Marquardt-based method. In particular, it can accurately decompose the amplitudes, time offsets, and pulse widths of the pulsed Lidar signal with a −10-dB signal-to-noise-ratio by mean deviation ratios of 4.885%, 0.531%, and 7.802%, respectively.

Joint time‐frequency analysis of visible laser reflections in a sheep heart

Limited methods exist to confirm the position of cardiovascular devices in the superior vena cava or right atrium of the heart. The aim of this study was to design, test and validate the feasibility of whether an optical fiber-based instrument could accurately distinguish when a cardiovascular catheter was located in the superior vena cava vs in the right atrium. An optical fiber was placed in a cardiovascular catheter which was inserted into a living sheep and guided to the vicinity of the heart where diode laser-based reflection intensity data were simultaneously gathered from two visible wavelengths of light reflected from the venous and atrial tissue surfaces near the cavoatrial junction. The time series data were postoperatively analyzed using methods of joint time-frequency analysis and validated against catheter positions determined with fluoroscopy and ECG. The system was successful in distinguishing the location of the superior vena cava from the right atrium.