Adaptive Time Frequency Distribution Based on Linear Chirp Modulated Gaussian Functions

We propose a method that uses linear chirp modulated Gaussian functions as the elementary functions, by adaptively adjusting variances, time frequency centers and sweep rates, to decompose signals. By taking WVD, an improved adaptive time frequency distribution is developed, which is non negative, free of cross term interference, and of better time frequency resolution. The paper presents an effective numerical algorithm to estimate the optimal parameters of the basis. Simulations indicate that the proposed approach is effective in analyzing signal's time frequency behavior.

The time and frequency system of the Tianma 65 m radio telescope

A time and frequency system is a critical component of Very Long Baseline Interferometry(VLBI)stations,providing stable and reliable standards that directly impact data processing quality.At the Tianma 65 m radio telescope(TMRT),this system has been meticulously designed to ensure long-term reliability and high performance.It incorporates high-performance hydrogen atomic clocks,high-precision time standards,automatic signal switching,and robust system software.This comprehensive approach has enabled the system to achieve long-term reliable operation,successfully supporting both major national engineering tasks and daily scientific observations.The effectiveness of the system is evidenced by its consistent delivery of the precision and stability required for radio astronomy.This article provides an in-depth exploration of the design and operation of the time and frequency system at the Tianma 65 m telescope,examining various aspects of its architecture,implementation,and performance.By sharing these insights,we aim to contribute knowledge that could benefit similar systems at other VLBI stations,greatly advancing radio astronomy infrastructure.

Few-shot working condition recognition of a sucker-rod pumping system based on a 4-dimensional time-frequency signature and meta-learning convolutional shrinkage neural network

The accurate and intelligent identification of the working conditions of a sucker-rod pumping system is necessary. As onshore oil extraction gradually enters its mid-to late-stage, the cost required to train a deep learning working condition recognition model for pumping wells by obtaining enough new working condition samples is expensive. For the few-shot problem and large calculation issues of new working conditions of oil wells, a working condition recognition method for pumping unit wells based on a 4-dimensional time-frequency signature (4D-TFS) and meta-learning convolutional shrinkage neural network (ML-CSNN) is proposed. First, the measured pumping unit well workup data are converted into 4D-TFS data, and the initial feature extraction task is performed while compressing the data. Subsequently, a convolutional shrinkage neural network (CSNN) with a specific structure that can ablate low-frequency features is designed to extract working conditions features. Finally, a meta-learning fine-tuning framework for learning the network parameters that are susceptible to task changes is merged into the CSNN to solve the few-shot issue. The results of the experiments demonstrate that the trained ML-CSNN has good recognition accuracy and generalization ability for few-shot working condition recognition. More specifically, in the case of lower computational complexity, only few-shot samples are needed to fine-tune the network parameters, and the model can be quickly adapted to new classes of well conditions.

High-Precision Doppler Frequency Estimation Based Positioning Using OTFS Modulations by Red and Blue Frequency Shift Discriminator

Orthogonal Time Frequency and Space(OTFS) modulation is expected to provide high-speed and ultra-reliable communications for emerging mobile applications, including low-orbit satellite communications. Using the Doppler frequency for positioning is a promising research direction on communication and navigation integration. To tackle the high Doppler frequency and low signal-to-noise ratio(SNR) in satellite communication, this paper proposes a Red and Blue Frequency Shift Discriminator(RBFSD) based on the pseudo-noise(PN) sequence.The paper derives that the cross-correlation function on the Doppler domain exhibits the characteristic of a Sinc function. Therefore, it applies modulation onto the Delay-Doppler domain using PN sequence and adjusts Doppler frequency estimation by red-shifting or blue-shifting. Simulation results show that the performance of Doppler frequency estimation is close to the Cramér-Rao Lower Bound when the SNR is greater than -15dB. The proposed algorithm is about 1/D times less complex than the existing PN pilot sequence algorithm, where D is the resolution of the fractional Doppler.

Performance Analysis for Orthogonal Time Frequency Space Modulation Systems with Generalized Waveform

Orthogonal time-frequency space(OTFS),which exhibits beneficial advantages in high-mobility scenarios,has been considered as a promising technology in future wireless communication systems.In this paper,a universal model for OTFS systems with generalized waveform has been developed.Furthermore,the average bit error probability(ABEP)upper bounds of the optimal maximum likelihood(ML)detector are first derived for OTFS systems with generalized waveforms.Specifically,for OTFS systems with the ideal waveform,we elicit the ABEP bound by recombining the transmitted signal and the received signal.For OTFS systems with practical waveforms,a universal ABEP upper bound expression is derived using moment-generating function(MGF),which is further extended to MIMO-OTFS systems.Numerical results validate that our theoretical ABEP upper bounds are concur with the simulation performance achieved by ML detectors.

Optical frequency comb technology: from ground to space

Optical frequency combs,as powerful tools for precision spectroscopy and research into optical frequency standards,have driven continuous progress and significant breakthroughs in applications such as time-frequency transfer,measurement of fundamental physical constants,and high-precision ranging,achieving a series of milestone results in ground-based environments.With the continuous maturation and evolution of femtosecond lasers and related technologies,optical frequency combs are moving from ground-based applications to astronomical and space-based applications,playing an increasingly important role in atomic clocks,exoplanet observations,gravitational wave measurements,and other areas.This paper,focusing on astronomical and space-based applications,reviews research progress on astronomical frequency combs,optical clock time-frequency networks,gravitational waves,dark matter measurement,dual-comb large-scale absolute ranging,and high-resolution atmospheric spectroscopy.With enhanced performance and their gradual application in the field of space-based research,optical frequency combs will undoubtedly provide more powerful support for astronomical science and cosmic exploration in the future.

The Time-Frequency Energy Attenuation Factor and Its Application on the Basis of Gauss Linear Frequency-Modulated Continuous Wavelet Transform

Based on the Gauss linear frequency modulated wavelet transform, a new characteristic index is presented, namely time frequency energy attenuation factor which can reflect the difference features of waveform in earthquake focus mechanism, wave traveling path and its attenuation characteristics in focal area or near field. In order to test its validity, we select the natural earthquakes and explosion or collapse events whose focus mechanisms vary obviously,and some natural earthquakes located at the same site or in a very small area. The study indicates that the time frequency energy attenuation factors of the natural earthquakes are obviously different with that of explosion or collapse events, and the change of the time frequency energy attenuation factors is relatively stable for the earthquakes under the normal seismicity background. Using the above mentioned method, it is expected to offer a useful criterion for strong earthquake prediction by continuous earthquake observation.

Joint AVO inversion in the time and frequency domain with Bayesian interference

Amplitude variations with offset or incident angle （AVO/AVA） inversion are typically combined with statistical methods, such as Bayesian inference or deterministic inversion. We propose a joint elastic inversion method in the time and frequency domain based on Bayesian inversion theory to improve the resolution of the estimated P- and S-wave velocities and density. We initially construct the objective function using Bayesian inference by combining seismic data in the time and frequency domain. We use Cauchy and Gaussian probability distribution density functions to obtain the prior information for the model parameters and the likelihood function, respectively. We estimate the elastic parameters by solving the initial objective function with added model constraints to improve the inversion robustness. The results of the synthetic data suggest that the frequency spectra of the estimated parameters are wider than those obtained with conventional elastic inversion in the time domain. In addition, the proposed inversion approach offers stronger antinoising compared to the inversion approach in the frequency domain. Furthermore, results from synthetic examples with added Gaussian noise demonstrate the robustness of the proposed approach. From the real data, we infer that more model parameter details can be reproduced with the proposed joint elastic inversion.

Applications of Fractional Lower Order Time-frequency Representation to Machine Bearing Fault Diagnosis

The machinery fault signal is a typical non-Gaussian and non-stationary process. The fault signal can be described by SaS distribution model because of the presence of impulses.Time-frequency distribution is a useful tool to extract helpful information of the machinery fault signal. Various fractional lower order(FLO) time-frequency distribution methods have been proposed based on fractional lower order statistics, which include fractional lower order short time Fourier transform(FLO-STFT), fractional lower order Wigner-Ville distributions(FLO-WVDs), fractional lower order Cohen class time-frequency distributions(FLO-CDs), fractional lower order adaptive kernel time-frequency distributions(FLO-AKDs) and adaptive fractional lower order time-frequency auto-regressive moving average(FLO-TFARMA) model time-frequency representation method.The methods and the exiting methods based on second order statistics in SaS distribution environments are compared, simulation results show that the new methods have better performances than the existing methods. The advantages and disadvantages of the improved time-frequency methods have been summarized.Last, the new methods are applied to analyze the outer race fault signals, the results illustrate their good performances.

Application of time–frequency entropy from wake oscillation to gas–liquid flow pattern identification

Gas–liquid two-phase flow abounds in industrial processes and facilities. Identification of its flow pattern plays an essential role in the field of multiphase flow measurement. A bluff body was introduced in this study to recognize gas–liquid flow patterns by inducing fluid oscillation that enlarged differences between each flow pattern. Experiments with air–water mixtures were carried out in horizontal pipelines at ambient temperature and atmospheric pressure. Differential pressure signals from the bluff-body wake were obtained in bubble, bubble/plug transitional, plug, slug, and annular flows. Utilizing the adaptive ensemble empirical mode decomposition method and the Hilbert transform, the time–frequency entropy S of the differential pressure signals was obtained. By combining S and other flow parameters, such as the volumetric void fraction β, the dryness x, the ratio of density φ and the modified fluid coefficient ψ, a new flow pattern map was constructed which adopted S（1–x）φ and （1–β）ψ as the vertical and horizontal coordinates, respectively. The overall rate of classification of the map was verified to be 92.9% by the experimental data. It provides an effective and simple solution to the gas–liquid flow pattern identification problems.

Precise time frequency synchronization technology for bistatic radar

A complete method of synchronization technology of bistatic radar using global position system （GPS） is presented. The pulse per second signal （1PPS） is elaborately modified to increase the time synchronization precision and keep loop locking. A very high time synchronization precision is achieved. Using the modified 1PPS to discipline the local OCXO, the reference frequency signal achieves both high long term stability （LTS） and short term stability （STS） properties. An algorithm, named phase abrupt change CFAR is presented to restrain the 1PPS phase abrupt change and keep loop locking. The experimental results indicate that this time and frequency synchronization method is effective and the time synchronization precision of the synchronization system can be improved from ±100 ns to ±25 ns. In addition, the phase noise is improved to 20 dB.

Experimental validation of a signal-based approach for structural earthquake damage detection using fractal dimension of time frequency feature

This article extends a signal-based approach formerly proposed by the authors, which utilizes the fractal dimension of time frequency feature （FDTFF） of displacements, for earthquake damage detection of moment resist frame （MRF）, and validates the approach with shaking table tests. The time frequency feature （TFF） of the relative displacement at measured story is defined as the real part of the coefficients of the analytical wavelet transform. The fractal dimension （FD） is to quantify the TFF within the fundamental frequency band using box counting method. It is verified that the FDTFFs at all stories of the linear MRF are identical with the help of static condensation method and modal superposition principle, while the FDTFFs at the stories with localized nonlinearities due to damage will be different from those at the stories without nonlinearities using the reverse-path methodology. By comparing the FDTFFs of displacements at measured stories in a structure, the damage-induced nonlinearity of the structure under strong ground motion can be detected and localized. Finally shaking table experiments on a 1：8 scale sixteen-story three-bay steel MRF with added frictional dampers, which generate local nonlinearities, are conducted to validate the approach.

Design and Analysis of Spatial Modulation Based Orthogonal Time Frequency Space System

In this paper,we design a spatial modulation based orthogonal time frequency space(SMOTFS)system to achieve improved transmission reliability and meet the high transmission rate and highspeed demands of future mobile communications,which fully utilizes the characteristics of spatial modulation(SM)and orthogonal time frequency space(OTFS)transmission.The detailed system design and signal processing of the SM-OTFS system have been presented.The closed-form expressions of the average symbol error rate(ASER)and average bit error rate(ABER)of the SM-OTFS system have been derived over the delay-Doppler channel with the help of the union bounding technique and moment-generating function(MGF).Meanwhile,the system complexity has been evaluated.Numerical results verify the correctness of the theoretical ASER and ABER analysis of the SM-OTFS system in the high signal-to-noise ratio(SNR)regions and also show that the SM-OTFS system outperforms the traditional SM based orthogonal frequency division multiplexing(SM-OFDM)system with limited complexity increase under mobile conditions,especially in high mobility scenarios.

Numerical Prediction Methods for Clock Deviation Based on Two-Way Satellite Time and Frequency Transfer Data

Three functional models, polynomial, spectral analysis, and modified AR model, are studied and compared in fitting and predicting clock deviation based on the data sequence derived from two-way satellite time and frequency transfer. A robust equivalent weight is applied, which controls the significant influence of outlying observations. Some conclusions show that the prediction precision of robust estimation is better than that of LS. The prediction precision calculated from smoothed observations is higher than that calculated from sampling observations. As a count of the obvious period variations in the clock deviation sequence, the predicted values of polynomial model are implausible. The prediction precision of spectral analysis model is very low, but the principal periods can be determined. The prediction RMS of 6-hour extrapolation interval is Ins or so, when modified AR model is used.

Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time （HB-AFT） do- main technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

Adaptive Fourier Decomposition Based Time-Frequency Analysis

The attempt to represent a signal simultaneously in time and frequency domains is full of challenges. The recently proposed adaptive Fourier decomposition （AFD） offers a practical approach to solve this problem. This paper presents the principles of the AFD based time-frequency analysis in three aspects： instantaneous frequency analysis, frequency spectrum analysis, and the spectrogram analysis. An experiment is conducted and compared with the Fourier transform in convergence rate and short-time Fourier transform in time-frequency distribution. The proposed approach performs better than both the Fourier transform and short-time Fourier transform.

Modeling of cascaded high isolation bidirectional amplification in long-distance fiber-optic time and frequency synchronization system

We propose a physical model of estimating noise and asymmetry brought by high isolation Bi-directional erbiumdoped fiber amplifiers(Bi-EDFAs),no spontaneous lasing even with high gain,in longdistance fiber-optic time and frequency(T/F)synchronization system.It is found that the Rayleigh scattering noise can be suppressed due to the high isolation design,but the amplified spontaneous emission(ASE)noise generated by the high isolation Bi-EDFA and the bidirectional asymmetry of the transmission link caused by the high isolation Bi-EDFA will deteriorate the stability of the system.The calculated results show that under the influence of ASE noise,the frequency instability of a 1200 km system composed of 15 high isolation Bi-EDFAs is 1.773×10^(-13)/1 s.And the instability caused by asymmetry is 2.6064×10^(-16)/30000–35000 s if the total asymmetric length of the bidirectional link length is 30 m.The intensity noises originating from the laser and detector,the transfer delay fluctuations caused by the variation in ambient temperature and the jitter in laser output wavelength are also studied.The experiment composed of three high isolation Bi-EDFAs is done to confirm the theoretical analysis.In summary,the paper shows that the short-term instability of the T/F synchronization system composed of high isolation Bi-EDFAs is limited by the accumulation of ASE noise of amplifiers and the laser frequency drift,while the long-term instability is limited by the periodic variation in ambient temperature and the asymmetry of the amplifiers.The research results are useful for pointing out the direction to improve the stability of the fiber-optic T/F synchronization system.

The time and frequency standard system for FAST receivers

This paper reports on the time and frequency standard system for the Five-hundred meter Aperture Spherical radio Telescope(FAST),including the system design,stability measurements and pulsar timing observations.The stability and drift rate of the frequency standard are calculated using 1-year monitoring data.The UTC-NIM Disciplined Oscillator(NIMDO)system improves the system time accuracy and stability to the level of 5 ns.Pulsar timing observations were carried out for several months.The weighted RMS of timing residuals reaches the level of less than 3.0μs.

Prediction study of hydrocarbon reservoir based on time-frequency domain electromagnetic technique taking Ili Basin as an example

The time-frequency domain electromagnetic(TFEM)sounding technique can directly detect oil and gas characteristics through anomalies in resistivity and polarizability.In recent years,it has made some breakthroughs in hydrocarbon detection.TFEM was applied to predict the petroliferous property of the Ili Basin.In accordance with the geological structure characteristics of the study area,a two-dimensional layered medium model was constructed and forward modeling was performed.We used the forward-modeling results to guide fi eld construction and ensure the quality of the fi eld data collection.We used the model inversion results to identify and distinguish the resolution of the geoelectric information and provide a reliable basis for data processing.On the basis of our results,key technologies such as 2D resistivity tomography imaging inversion and polarimetric constrained inversion were developed,and we obtained abundant geological and geophysical information.The characteristics of the TFEM anomalies of the hydrocarbon reservoirs in the Ili Basin were summarized through an analysis of the electrical logging data in the study area.Moreover,the oil-gas properties of the Permian and Triassic layers were predicted,and the next favorable exploration targets were optimized.

Joint transfer of time and frequency signals and multi-point synchronization via fiber network

A system of jointly transferring time signals with a rate of 1 pulse per second （PPS） and frequency signals of 10 MHz via a dense wavelength division multiplex-based （DWDM） fiber is demonstrated in this paper. The noises of the fiber links are suppressed and compensated for by a controlled fiber delay line. A method of calibrating and characterizing time is described. The 1PPS is synchronized by feed-forward calibrating the fiber delays precisely. The system is experimen- tally examined via a 110 km spooled fiber in laboratory. The frequency stabilities of the user end with compensation are 1.8x 10-14 at 1 s and 2.0x 10-17 at 104 s average time. The calculated uncertainty of time synchronization is 13.1 ps, whereas the direct measurement of the uncertainty is 12 ps. Next, the frequency and 1PPS are transferred via a metropoli- tan area optical fiber network from one central site to two remote sites with distances of 14 km and 110 km. The frequency stabilities of 14 km link reach 3.0x 10-14 averaged in 1 s and 1.4x 10-17 in 104 s respectively; and the stabilities of 110 km link are 8.3 x 10-14 and 1.7 x 10-17, respectively. The accuracies of synchronization are estimated to be 12.3 ps for the 14 km link and 13.1 ps for the 110 km link, respectively.